Thesis

University of Sydney

A study into the Biomedical Consequences of Orthodontic Loading and Biting Forces on the Mandible.

A dissertation submitted to the school of Aerospace, Mechanical & Mechatronic Engineering in candidacy for the degree of Bachelor of Engineering (Mechatronic) / Bachelor of Arts

Supervisor: Professor M.V. Swain

by Tom Tramby

Sydney, NSW October 2006

Acknowledgements I would like to most of all thank my family and especially my parents for the support that they have given me throughout this study and more importantly for the time before to get me to this stage, this is more yours than mine.

I would like to thank my supervisor, Professor Mike Swain, for his assistance, guidance and support throughout the duration of this thesis.

I would also like to thank Professor Norton Duckmanton for the help and support he gave me and especially for his sense of humour.

This study could not have been completed without the help of the staff at Leap Australia, especially Jindong, who made the task of conducting the finite element analysis a whole lot easier.

I would also like to thank Mark Hubble for his contribution and help throughout the development of the models.

Declaration Declaration To complete this study I have had to complete a number of tasks as detailed below. I have undertaken these through guidance by my thesis supervisor Professor Mike Swain and Professor Norton Duckmanton. I have undertaken and completed the following tasks: •

I have carried out a literature review of pervious work completed with regard to the biomedical consequences of biting forces on the mandible.

•

I modified the original model consisting of a solid cortical and cancellous bone structure and teeth, originally developed by Dr Ionut Ichim and proved

by Claire Field, into the models which have been used throughout the study.

•

I have conducted a finite element analysis on these models.

•

I have compiled, documented and examined the results and discussed their meaning and significance.

•

I have validated the work done in this study through comparisons to previous works completed.

•

I have discussed implications, conclusions and possible future work.

The above represents an accurate summary of the student’s contribution.

Signed……………………………………….(Tom Tramby)

Signed……………………………………….(Norton Duckmanton)

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Abstract Abstract The objective of this study is firstly to establish highly accurate three-dimensional model of the mandible, teeth and surrounding structure. To establish a highly accurate three-dimensional model of a conventional denture and an implant retained overdenture and to perform a finite element analysis that reflects the structural response of the mandible to a variety of forces and consider the variations caused by denture and the differences between the types of denture in order to gain a greater understanding of the biomedical consequences of biting forces on the human mandible. This study then aims to relate the biomedical consequences found in the cortical and cancellous bone structures as a result of loading on the various structures above the bone to Frost’s Mechanostat hypothesis in order to quantify this theory in relation to the human mandible.

The models developed consisted of cancellous and cortical bone structures, PDL, dentin, enamel, (natural dentition model), mucosa, acrylic resin, artificial teeth, (conventional denture and implant-restrained over-denture models) soft denture liner, (conventional denture model) and implants. (implant-restrained over-denture model) The models developed within this study include material properties which have been compensated for in previous studies to accurately represent the oral environment. The finite element models developed within this study provide highly accurate and detailed results as a fine mesh was selected. The selection of this mesh supplemented the high level of accuracy maintained throughout this study. The detail which the models were generated with and the mesh selected allowed the results generated to be legitimised though consultation with previous studies.

The stresses generated by the models in the region local to the loaded tooth had similar tendencies in both the cortical and the cancellous bone structure. The stresses around the canine tooth yielded the least difference between the models while the stresses found local to the molar while being loaded, although there were signs to show that the implant-restrained over-denture model was approaching those stresses, yielded the greatest difference in stress. The stresses experienced globally were similar in their distribution and concentration but there was significant magnitude lacking. This lack was especially prominent to the posterior of the mandible and slightly less so at the centre anterior. Again the canine tooth displayed reasonably good level of stress concentration especially with the implant-restrained over-denture model.

The results found that the threshold stress, MESr, where bone resorption commences is 1.5MPa in the cortical bone and 0.25MPa in the cancellous bone. This position lies, as expected, between the average stresses found in the natural mandible model and the two denture models. The average stresses in the cortical and cancellous bones in the natural mandible were found to be 2MPa and 0.9MPa. The conventional denture model displayed average stresses of 0.45MPa and 2.6*10-3MPa while the implantrestrained over-denture model displayed average stresses of 0.9MPa and 0.18MPa in the cortical and cancellous bone structures.

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Table of Contents Table of Contents Acknowledgements ......................................................................................................ii Declaration.................................................................................................................. iii Abstract........................................................................................................................iv Table of Contents .........................................................................................................v List of Figures........................................................................................................... viii List of Tables ..............................................................................................................xv Chapter 1. Introduction...............................................................................................2 1.1 General Overview ................................................................................................3 1.2 Dental Structures..................................................................................................4 1.3 Introduction to Dentures ......................................................................................6 1.4 Introduction to Implants.......................................................................................8 1.5 Introduction to the Mechanostat Hypothesis .......................................................9 1.6 Introduction to the Finite Element Method........................................................10 Chapter 2. Literature Review ...................................................................................12 2.1 Implants..............................................................................................................13 2.1.1 Background .................................................................................................13 2.1.2 History.........................................................................................................14 2.1.3 Dental Implants...........................................................................................15 2.1.4 Contemporary Issues...................................................................................16 2.1.4.1 Implant Development...........................................................................17 2.1.4.2 Bone Damage and Preservation ...........................................................18 2.1.4.3 Number of Implants .............................................................................20 2.1.4.4 Implant Anchorage Design ..................................................................21 2.1.4.5 Impact of Immediate Loading..............................................................22 2.1.4.6 Maintenance Requirements..................................................................23 2.1.4.7 Patient Satisfaction...............................................................................24 2.2 Biomedical Investigations of Oral Environments Using the Finite Element Method .....................................................................................................................26 2.2.1 Finite Element Method Validation through Convergence Checks .............28 2.2.2 Validated Biomedical Investigations of Oral Environments using the Finite Element Method ..............................................................................30 2.2.2.1 Finite element method simulation of bone resorption beneath a complete denture. Maeda and Wood (1989)......................................31 2.2.2.2 Finite element analysis of crestal bone loss around porous-coated dental implants. Vaillancort et al (2004) ...........................................34 2.2.2.3 Finite element analysis of stress relaxation in soft denture liner.

Sato et al (2000).................................................................................36 2.2.2.4 The dynamic behaviour of a lower complete denture during unilateral loads: Analysis using the finite element method.

Takayama et al (2001) .......................................................................38 2.2.2.5 The influence of occlusal loading on stresses transferred to implant-supported prostheses and supporting bone: A threedimensional finite element study. Eskitascioglu et al (2004) ............40

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Table of Contents 2.2.2.6 Biomedical aspects of marginal bone resorption around osseointegrated implants: Considerations based on a 3D FEA. Kitamura et al (2003).........................................................................42 2.2.3 Summary .....................................................................................................43 Chapter 3. Modelling .................................................................................................45 3.1 Requirements .....................................................................................................46 3.2 Construction.......................................................................................................46 3.2.1 Construction of the Specific Models...........................................................47 3.2.2 Construction of the Natural Dentition Model .............................................48 3.2.3 Construction of the Conventional Denture Model......................................51 3.2.4 Construction of Implant-Supported Over-Denture Model..........................53 3.2.4.1 Implant Construction ...........................................................................55 3.3 Difficulties .........................................................................................................55 Chapter 4. Finite Element Analysis..........................................................................57 4.1 Mesh Selection...................................................................................................58 4.2 Forces.................................................................................................................60 4.2.1 Magnitude ...................................................................................................60 4.2.2 Angle...............................................................................................................62 4.2.3 Location ......................................................................................................62 4.3 Boundary Conditions .........................................................................................63 4.4 Material Properties.............................................................................................64 4.5.1 Specific Material Properties........................................................................65 4.6 Complete Finite Element Model........................................................................66 Chapter 5. Results......................................................................................................69 5.1 Notes on results..................................................................................................70 5.1.1 Technique of Averaging .............................................................................70 5.1.2 Scale of Figures...........................................................................................70 5.1.3 Side Reference ............................................................................................70 5.1.4 Stresses Analysed........................................................................................70 5.1.5 Load Reference. ..........................................................................................71 5.1.6 Local / Global Comparisons .......................................................................71 5.2 Natural Dentition Model ....................................................................................72 5.2.1 Cortical Bone Reaction of Loading on the Molar.......................................72 5.2.2 Cancellous Bone Reactions of Loading on the Molar ................................75 5.2.3 Cortical Bone Reactions of Loading on the Canine....................................78 5.2.4 Cancellous Bone Reactions of Loading on the Canine...............................79 5.2.5 Cortical Bone Reaction of Loading on the Incisor .....................................82 5.2.6 Cancellous Bone Reactions of Loading the Incisor....................................84 5.3 Conventional Denture Model.............................................................................86 5.3.1 Cortical Bone Reactions of Loading on the Molar .....................................86 5.3.2 Cancellous Bone Reactions of Loading on the Molar ................................88 5.3.3 Cortical Bone Reaction of Loading on the Canine .....................................90 5.3.4 Cancellous Bone Reactions of Loading on the Canine...............................92 5.3.5 Cortical Bone Reactions of Loading on the Incisor....................................94

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Table of Contents 5.3.6 Cancellous Bone Reactions of Loading on the Incisor...............................96 5.4 Implant-Restrained Over-Denture Model ..........................................................98 5.4.1 Cortical Bone Reaction of Loading on the Molar.......................................98 5.4.2 Cancellous Bone Reactions of Loading on the Molar ..............................100 5.4.3 Cortical Bone Reactions of Loading on the Canine..................................103 5.4.4. Cancellous Bone Reactions of Loading on the Canine............................104 5.4.5 Cortical Bone Reactions of Loading on the Incisor..................................107 5.4.6 Cancellous Bone Reactions of Loading on the Incisor.............................108 5.5 Summary ..........................................................................................................110 Chapter 6. Discussion. .............................................................................................116 6.1 Validation.........................................................................................................116 6.2 Limitations .......................................................................................................117 6.2.1 Rotational (TMJ) Joint..............................................................................117 6.2.2 Size of Mandible .......................................................................................117 6.2.3 Posterior area of Dentures.........................................................................118 6.2.4 Muscles Modelled.....................................................................................118 6.3 Comparisons. ...................................................................................................118 6.3.1 Local Maximum and Average Stresses around the Loaded Sites.............119 6.3.2 Global Maximums and Average Stresses from Molar Loading. ..............123 6.3.3 Global Maximums and Average stresses from Canine Loading. .............127 6.3.4 Global Maximums and Average stresses from Incisor Loading...............131 6.4 Findings............................................................................................................135 6.5 Implications......................................................................................................136 Chapter 7. Conclusion. ............................................................................................141 Bibliography .............................................................................................................142

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List of Figures List of Figures Figure 1: Depiction of the crown and root.......................................................................4 Figure 2: Tooth structure .................................................................................................4 Figure 3: Internal structure of the mandible ....................................................................5 Figure 4: Frost’s mechanostat..........................................................................................9 Figure 5: Missing front tooth .........................................................................................13 Figure 6: Bridge and Maryland Bridge..........................................................................13 Figure 7: Partial denture and flipper ..............................................................................14 Figure 8: Titanium implant with artificial tooth ............................................................14 Figure 9: False teeth made with porcelain .....................................................................15 Figure 10: Dental implants mimic the role of tooth roots..............................................15 Figure 11: Front tooth with implant...............................................................................15 Figure 12: Dental implants on the lower and upper jaw................................................16 Figure 13: Bar anchorage with five and two implants...................................................20 Figure 14: Bar and ball anchorage system.....................................................................21 Figure 15: Two-dimensional finite element models from Vaillancort et al (2004) Sato et al (2000) and Maeda and Wood (1989) ...........................................27 Figure 16: Two-dimensional finite element models from Takayama et al (2001) Eskitascioglu et al (2004) and Kitamura et al (2003) ..................................27 Figure 17: Simple mesh applied to a section of an ‘object’...........................................29 Figure 18: 2D finite element model of a maxillary cancellous bone and results of Maeda and Wood’s (1989) study.................................................................31 Figure 19: Results from Maeda and Wood’s (1989) study............................................32 Figure 20: Finite element model of implant used by Vaillancort et al (2004)...............34 Figure 21: Results of Vaillancort’s et al (2004) study...................................................35

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List of Figures Figure 22: Model used by Sato el at (2000)...................................................................36 Figure 23: Two example of stress distribution results from Sato’s et al (2000) study.............................................................................................................37 Figure 24: Model used by Takayama et al (2001) .........................................................38 Figure 25: Models with the values and distribution of loads applied in Eskitascioglu’s et al (2004) study ................................................................40 Figure 26: Distribution of stresses within implant and abutment ..................................41 Figure 27: Distribution of stresses within framework ...................................................41 Figure 28: Distribution of stresses within occlusal surface material .............................41 Figure 29: Model used by Kitamura et al (2003)...........................................................42 Figure 30: Depiction of a human mandible ...................................................................46 Figure 31: Original structure of the mandible and teeth ................................................48 Figure 32: Hollowed Cortical Bone...............................................................................48 Figure 33: Enamel..........................................................................................................49 Figure 34: Dentin ...........................................................................................................49 Figure 35: PDL ..............................................................................................................49 Figure 36: Cancellous and cortical bone with sockets...................................................50 Figure 37: Conventional denture model ........................................................................51 Figure 38: Conventional denture model showing mucosa layer....................................51 Figure 39: Conventional denture model showing glue layer .........................................52 Figure 40: Conventional Denture...................................................................................52 Figure 41: Two implant supported over-denture model ................................................53 Figure 42: Ball (left) and bar (right) attachments ..........................................................53 Figure 43: Two implant retained over-denture ..............................................................54

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List of Figures Figure 44: Abutment Selection Flowchart showing the chosen 4mmH, model 61165 O-Ring abutment...............................................................................54 Figure 45: Internal structure of an implant ....................................................................55 Figure 46: Course and fine mesh models.......................................................................59 Figure 47: Results of an FEA on the course and fine mesh models ..............................59 Figure 48: Maximum unilateral bite forces ...................................................................61 Figure 49: Unilateral bite forces at the force level ‘as when chewing’ ........................61 Figure 50: Muscles connected to the human mandible..................................................62 Figure 51: Force location of finite element model.........................................................63 Figure 52: Locations of rotational joint components which where fixed in the X, Y and Z space and allowed to rotate............................................................64 Figure 53: The modelled ‘food’ over the pre-molar ......................................................64 Figure 54: All three final models Complete with boundary conditions and force locations .......................................................................................................67 Figure 55: Natural dentition model with loading on the molar .....................................72 Figure 56: Von Mises stresses on cortical bone structure from molar loading – Natural dentition model ...............................................................................73 Figure 57: First principle stress (left) and strain (right) in cortical bone structure from molar loading – Natural dentition model ............................................73 Figure 58: Von Mises stresses on cancellous bone structure from molar loading – Natural dentition model ...............................................................................75 Figure 59: First principle stresses on cancellous bone structure from molar loading – Natural dentition model ...............................................................75 Figure 60: First principle strains on cancellous bone structure from molar loading – Natural dentition model ............................................................................76 Figure 61: Von Mises stresses on cancellous bone structure from molar loading – Natural dentition model ...............................................................................76 Figure 62: First principle stress (left) and strains (right) on inside of cancellous bone structure from molar loading – Natural dentition model ....................77

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List of Figures

Figure 63: Natural dentition model with loading on the canine ....................................78 Figure 64: Von Mises stresses on cortical bone structure from canine loading – Natural dentition model ...............................................................................78 Figure 65: First principle stress (left) and strain (right) cortical bone structure from canine loading – Natural dentition model ...........................................79 Figure 66: Von Mises stresses on cancellous bone structure from canine loading – Natural dentition model ...............................................................................80 Figure 67: First principle stress (left) and strains (right) on cancellous bone structure from canine loading – Natural dentition model ............................80 Figure 68: Natural dentition model with loading on the central incisor ........................82 Figure 69: Von Mises stresses on cortical bone structure from central incisor loading – Natural dentition model ...............................................................82 Figure 70: First principle stress (left) and strain (right) cortical bone structure from central incisor loading – Natural dentition model...............................83 Figure 71: Von Mises stresses on cancellous bone structure from central incisor loading – Natural dentition model ...............................................................84 Figure 72: First principle stresses (left) and strains (right) on cancellous bone structure from central incisor loading – Natural dentition model................84 Figure 73: Conventional denture model with loading on the molar ..............................86 Figure 74: Von Mises stresses on cortical bone structure from molar loading – Conventional denture model ........................................................................87 Figure 75: First principle stress (left) and strain (right) cortical bone structure from molar loading – Conventional denture model.....................................87 Figure 76: Von Mises stresses on cancellous bone structure from molar loading – Conventional denture model ........................................................................88 Figure 77: First principle stress (left) and strains (right) on cortical bone structure from molar loading – Conventional denture model.....................................89 Figure 78: Conventional denture model with loading on the canine .............................90 Figure 79: Von Mises stresses on cancellous bone structure from canine loading – Conventional denture model ........................................................................90

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List of Figures Figure 80: First principle stress (left) and strains (right) on cancellous bone structure from canine loading – Conventional denture model.....................91 Figure 81: Von Mises stresses on cancellous bone structure from canine loading – Conventional denture model ........................................................................92 Figure 82: First principle stress (left) and strains (right) on cancellous bone structure from canine loading – Conventional denture model.....................93 Figure 83: Conventional denture model with loading on the central incisor.................94 Figure 84: Von Mises stresses on cortical bone structure from canine loading – Conventional denture model ........................................................................94 Figure 85: First principle stress (left) and strains (right) on cortical bone structure from canine loading – Conventional denture model....................................95 Figure 86: Von Mises stresses on cortical bone structure from incisor loading – Conventional denture model ........................................................................96 Figure 87: First Principle stress (left) and strains (right) on cortical bone structure from incisor loading – Conventional denture model ...................................96 Figure 88: Implant-restrained over-denture model with loading on the molar..............98 Figure 89: Von Mises stresses on cortical bone structure from molar loading – Implant-restrained over-denture model........................................................98 Figure 90: First principle stress in cortical bone structure from molar loading – Implant-restrained over-denture model........................................................99 Figure 91: First principle strains in cortical bone structure from molar loading – Implant-restrained over-denture model........................................................99 Figure 92: Von Mises stresses in cancellous bone structure from molar loading – Implant-restrained over-denture model......................................................100 Figure 93: First principle stress in the cancellous bone structure from molar loading – Implant-restrained over-denture model......................................101 Figure 94: First principle strains in the cancellous cortical bone structure from molar loading – Implant-restrained over-denture model ...........................101 Figure 95: Implant-restrained over-denture model with loading on the canine...........103 Figure 96: Von Mises stresses in cortical bone structure from canine loading – Implant-restrained over-denture model......................................................103

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List of Figures Figure 97: First principle stress (left) and strains (right) in cortical bone structure from canine loading – Implant-restrained over-denture model .................104 Figure 98: Von Mises stresses in cancellous bone structure from canine loading – Implant-restrained over-denture model......................................................105 Figure 99: First principle stress (left) and strains (right) in cancellous bone structure from canine loading – Implant-restrained over-denture model ..105 Figure 100: Implant-restrained over-denture model with loading on the incisor ........107 Figure 101: Von Mises stresses in cortical bone structure from incisor loading – Implant-restrained over-denture model......................................................107 Figure 102: First principle stress (left) and strains (right) in cortical bone structure from incisor loading – Implant-restrained over-denture model.................108 Figure 103: Von Mises stresses in cancellous bone structure from incisor loading – Implant-restrained over-denture model...................................................109 Figure 104: First principle stress (left) and strains (right) in cancellous bone structure from incisor loading – Implant-restrained over-denture model ..109 Figure 105: Local Stresses and Strains ........................................................................109 Figure 106: Global Stresses and Strains - Molar Loading...........................................109 Figure 107: Global Stresses and Strains - Canine Loading .........................................109 Figure 108: Global Stresses and Strains - Incisor Loading..........................................109 Figure 109: Local maximum Von Mises stress experienced by the cortical bone structure......................................................................................................119 Figure 110: Local average Von Mises stress experienced by the cortical bone structure......................................................................................................120 Figure 111: Local maximum Von Mises stress experienced by the cancellous bone structure (logarithmic x-axis)............................................................121 Figure 112: Local average Von Mises stress experienced by the cancellous bone structure (logarithmic x-axis).....................................................................122 Figure 113: Global maximum stresses experienced by the cortical bone structure from molar loading (logarithmic x-axis)....................................................123 Figure 114: Global average stresses experienced by the cortical bone structure from molar loading ....................................................................................124

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List of Figures

Figure 115: Global maximum stresses experienced by the cancellous bone structure from molar loading (logarithmic x-axis).....................................125 Figure 116: Global average stresses experienced by the cancellous bone structure from molar loading (logarithmic x-axis)....................................................126 Figure 117: Global maximum stresses experienced by the cortical bone structure from canine loading (logarithmic x-axis) ..................................................127 Figure 118: Global average stresses experienced by the cortical bone structure from canine loading ...................................................................................128 Figure 119: Global maximum stresses experienced by the cancellous bone structure from canine loading (logarithmic x-axis) ...................................129 Figure 120: Global average stresses experienced by the cancellous bone structure from canine loading (logarithmic x-axis) ..................................................130 Figure 121: Global maximum stresses experienced by the cortical bone structure from incisor loading (logarithmic x-axis) ..................................................131 Figure 122: Global average stresses experienced by the cortical bone structure from incisor loading...................................................................................132 Figure 123: Global maximum stresses experienced by the cancellous bone structure from incisor loading (logarithmic x-axis) ...................................133 Figure 124: Global average stresses experienced by the cancellous bone structure from incisor loading (logarithmic x-axis) ..................................................134 Figure 125: Frost’s mechanostat..................................................................................137 Figure 126: Cortical Bone structure values as they relate to Frost’s mechanostat hypothesis ..................................................................................................138 Figure 127: Cancellous Bone structure values as they relate to Frost’s mechanostat hypothesis .............................................................................139

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List of Tables List of Tables Table 1: Element and node numbers for Durkee’s et al (1991) convergence study ......30 Table 2: Material properties used by Maeda and Wood (1989) ....................................31 Table 3: Material properties used by Vaillancort et al (2004) .......................................34 Table 4: Material properties used by Sato el at (2000)..................................................36 Table 5: Material properties used by Takayama et al (2001) ........................................39 Table 6: Material properties used in Eskitascioglu’s et al (2004) study........................40 Table 7: Material properties used by Kitamura et al (2003)..........................................42 Table 8: Mesh details for the course and fine mesh models ..........................................59 Table 9: Mesh details for finite element models............................................................60 Table 10: Forces used in the finite element models.......................................................62 Table 11: Material properties used throughout this study .............................................66 Table 12: Final mesh details for finite element models.................................................67 Table 13: Final forces used in the finite element models ..............................................67 Table 14: Final material properties used throughout this study.....................................67 Table 15: Local maximum Von Mises stress experienced by the cortical bone structure......................................................................................................119 Table 16: Local average Von Mises stress experienced by the cortical bone structure......................................................................................................120 Table 17: Local maximum Von Mises stress experienced by the cancellous bone structure......................................................................................................121 Table 18: Local average Von Mises stress experienced by the cancellous bone structure......................................................................................................121 Table 19: Global maximum stresses experienced by the cortical bone structure from molar loading ....................................................................................123 Table 20: Global average stresses experienced by the cortical bone structure from molar loading .............................................................................................124

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List of Tables Table 21: Global maximum stresses experienced by the cancellous bone structure from molar loading ....................................................................................125 Table 22: Global average stresses experienced by the cancellous bone structure from molar loading ....................................................................................125 Table 23: Global maximum stresses experienced by the cortical bone structure from canine loading ...................................................................................127 Table 24: Global average stresses experienced by the cortical bone structure from canine loading ............................................................................................128 Table 25: Global maximum stresses experienced by the cancellous bone structure from canine loading ...................................................................................129 Table 26: Global average stresses experienced by the cancellous bone structure from canine loading ...................................................................................130 Table 27: Global maximum stresses experienced by the cortical bone structure from incisor loading...................................................................................131 Table 28: Global average stresses experienced by the cortical bone structure from incisor loading............................................................................................132 Table 29: Global maximum stresses experienced by the cancellous bone structure from incisor loading...................................................................................133 Table 30: Global average stresses experienced by the cancellous bone structure from incisor loading...................................................................................134

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V{tÑàxÜ D Introduction

Introduction

Chapter 1

Chapter 1. Introduction This chapter introduces the areas of interest of this study. It will cover the background of the problem, the focus of the study and the methods of investigation. It will detail the motivation behind the study and the expected results to be generated. The first section of this chapter will initially present a general introduction to the problem that this study is investigating. It will outline the objective as well as the motivation behind the study. This will be followed by an introduction to dental structures with particular emphasis on the mandible which is the focus of this study. In the absence of teeth dentures are used which will be briefly described along with their history and development and the current use of conventional dentures and implant-restrained over-dentures. Frost’s Mechanostat Hypothesis (Frost, 2003) will then be explained with relevance to the study before an explanation of the finite element method with will be utilised in order to produce the results that this study is seeking. The history of this methodology will be explored with an in depth analysis of this method conducted in chapter 2.

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Introduction

Chapter 1

1.1 General Overview Wolff’s law formulates a long known fact that ‘if you don’t use it you lose it’. This law, developed by the German anatomist and surgeon Julius Wolff, in the 19th century, which states that a bone in a healthy person or animal will adapt to the loads under which it is placed under. That is, if the loading on a bone increases, the bone will remodel itself over time to become stronger and resist that sort of loading. The converse is true as well, if the loading on a bone decreases, the bone will be adapted and become weaker. This law has been developed further and will be explored later in an analysis of Frost’s Mechanostat principle. This relationship is evident among edentulous patients who all experience bone resorption within the maxilla and mandible. The rate of bone resorption varies between patients and is also affected by the type of dentures worn. This correlation has been an ongoing area of investigation within the dental research community but is still not adequately understood.

Establishing a solid knowledge base of the affects that a variety of dentures have on the rate of bone resorption of edentulous patients is of significance importance and will be the foundation knowledge to designing better dentures and the improvement of the bone resorption rate. The ability to research this field through the use of accurate stress analysis software can assist the investigation of forces and resultant stresses and ultimately reduce the research periods which experimentation procedures pose.

To gain a good understanding of the resultant stresses induced within the mandible and surrounding structures this study will employ computer modelling and Finite Element Analysis (FEA). This project presents unique difficulties in both modelling and the FEA due to the complexity and sophistication of the free form surfaces involved in dental structures. A high level of intricacy is required within the models due to irregularities in geometry and non-homogenous material features. A method to achieve an accurate stress analysis with models of such a complex nature is to perform a finite element analysis. This method enables an accurate result to be achieved using a mesh of variable detail. This method allows results to be of clinical veracity without using destructive clinical investigative methods. This computer generated mathematical technique assists in developing numerical solutions that predict the resultant physical response to the loading of the mandible. The Finite element analysis within this study utilises an accurate model of dental and denture structures, realistic boundary conditions and realistic structural and biological tissue characterization.

The objective of this study is firstly to establish highly accurate three-dimensional model of the mandible, teeth and surrounding structures. To establish a highly accurate three-dimensional model of a conventional denture and an implant retained over-denture. To perform a Finite Element Analysis that reflects both the structural response of the mandible to a variety of forces and considers the variations caused by denture and the differences between the types of denture. This study then aims to relate the biomedical consequences found in the cortical and cancellous bone structures as a result of loading on the various structures above the bone to Frost’s Mechanostat hypothesis in order to quantify this theory in relation to the human mandible.

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Introduction

Chapter 1

1.2 Dental Structures The tooth, which is embedded within the bones of the jaw primarily perform the function of mastication. Teeth are rigid, calcified structures which are made up of several components, divided into two major sections, the root, which is the portion embedded within the mandible, and the crown which is the section protruding out from the gum. (Fig. 1)

Figure 1: Depiction of the crown and root

Surrounding the bottom of the tooth (Fig. 2) is a segment of the gum called the periodontal ligament (PDL) which serves the function of supporting and cushioning the tooth inside its rigid socket. The core of the tooth consists of the pulp chamber which contains the connective tissue, blood vessels and nerves, this tissue extends to the root apex. Surrounding the pulp is the dentin, which is a hard substance making up the bulk of the tooth. Surrounding the dentin in the root area is a layer of cementum whereas the enamel encompasses the crown region.

Figure 2: Tooth structure

The enamel surrounds and protects the dentin of the crown section. It is the hardest tissue within the human body and protects the tooth from the dangers which exist within the oral environment. (Spiller M. 2000) The enamel is produced by ameloblast

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Introduction

Chapter 1

cells which create a hard, thin, calcified substance resistant to mechanical and chemical attack. It is made up of enamel rods which are parallel to each other and project perpendicularly from the surface of the underlying dentin. (Spiller M. 2000) The bulk of the tooth is made up of the dentin. The dentin, which surrounds the pulp, has similar material prosperities to that of bone. The structure of dentin is highly organised, consisting of an array of tubules, or parallel pores, that extend from the pulp cavity to the enamel junction.

The Periodontal Ligament (PDL_ is the segment of gum which exists between the tooth and the bone socket and acts as an anchorage for the tooth. This consists of fibrous connective tissue (fibroblasts) that progress perpendicularly from the tooth surface to the bone socket. In the event of tooth malfunction the periodontal ligament becomes narrow and connective fibrous tissues are disarrayed.

The mandible consists of two parts, (Fig.3) cancellous and the cortical bone. The core of the mandible consists of the cortical bone which is a compact bone, it has a slow turnover rate and has a high resistance to bending and torsion. This bone provides strength where bending is undesirable and provides support for the tooth structure and functional loading.

Figure 3: Internal structure of the mandible

The cancellous bone directly surrounds the cortical bone. It is a compact bone which supports and protects the tooth and is dependent on the functional forces implemented by a tooth to maintain its structure.

The condition of the mandible is of considerable importance when considering bone resorption. This study will focus on the structural response to loads within the cortical and cancellous bone as well as the gum and denture materials as a result from orthodontic loading. This will be done by analysing accurate three-dimensional finite element models.

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1.3 Introduction to Dentures Dentures, or dental plates, are artificial teeth which are used when patients have lost teeth on their mandibular arch, maxillary arch, or both. The reasons a patient looses their teeth and becomes edentulous are varied ranging from severe malnutrition, lack of oral hygiene, trauma or genetic defects such as Dentinogenesis Imperfecta. An edentulous patient can improve their mastication ability though the use of dentures as well as enhance the aesthetic appeal of their mouth and allow them more self esteem and a greater quality of life.

If a patient is missing only one or some of their teeth on particular arch removable partial dentures may be worn. Fixed partial dentures, also known as crowns or bridges, can also be worn by patients missing one or some of their teeth but these are more expensive than removable partial dentures and are not always appropriate.

Complete dentures are used when a patient has lost all their teeth in either or both arches.

Dentures have been found dating from the 15th century and have probably been used earlier. These early dentures were carved from bone or ivory or constructed with teeth from a dead, or living, donor. (Bellis, 2005) These dentures were uncomfortable and would rot with extended use. Porcelain dentures came into existence around 1770 through Alexis Duchâteau. His former assistant, Nicholas Dubois De Chemant received the first British patient in1791 for “a composition for the purpose of making of artificial teeth either single double or in rows or in complete sets and also springs for fastening or affixing the same in a more easy and effectual manner than any hitherto discovered which said teeth may be made of any shade or colour, which they will retain for any length of time and will consequently more perfectly resemble the natural teeth.” (Bellis, 2005) He began selling his products in 1792. Single porcelain teeth were made in 1808, manufactures then turned to vulcanite and then in the 20th century, acrylic resin.

One of the most ‘natural’ problems to occur with dentures is that patients are not used to having something in their mouth that is not food. The brain senses the object as ‘food’ and consequentially the salivary glands are made to produce more saliva and to secrete it at a higher rate. Dentures also create sore spots as they rub and press on the mucosa. This can be aided through readjustments. Some patients also experience gagging. This may be caused by the denture having a too loose fitting, being too thick or not extended far enough posteriorly onto the soft palate. Gagging can also be attributed to psychological denial of the denture. This cause is the most difficult to combat as it is out of the dentists control. In these cases an implant supported palateless denture may have to be constructed or a hypnotist may need to be consulted. Another major problem regarding conventional dentures is keeping them in place. Support, stability and retention are the three things which need to be considered regarding the existence of removable oral products.

Support refers to how effective the underlying mucosa, the oral tissue including gums and the vestibules, keeps the conventional denture from movement in the vertical

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plane towards the relative arch, and thus being excessively depressed and moving deeper into the arch. For the mandibular arch, the arch that this study is concentrating on, this function is provided by the gingiva and the buccal vestibule. The larger the denture flanges (part of the denture that extends into the vestibule), the better the support.

Implants have played a major role in recent time as they increasing the stability of dentures. When pressure is applied to a mandible bereft of teeth the mandible reacts to the lack of stress by resorption. After a number of years the level of resorption can be quite significant. With implants integrated into the treatment, the mandible can sustain greater levels of stress to assist and combat the occurrence of resorption.

Stability refers to how efficiently the denture is stabilised on the horizontal plane, or prevented from sliding either from side to side or front to back. The stability is increased by improving the denture base to remain smooth and have continuous contact with the edentulous ridge. Patients with a higher and wider ridge will have better stability however this, barring surgical intervention, is not something that can be controlled or improved.

Retention refers to how well a denture is prevented from movement away from the direction of insertion in the vertical plane. Retention is improved by a having a good mimic of the interior, intaglio surface of the denture to the underlying surface of the mucosa.

The installation of a complete set of dentures is a challenge for a number of reasons.

Even experienced dentists may face problems as a successful installation requires the consideration of many factors, a negative outcome of any one of them can result in a failure of the entire denture. After the instillation of a denture most patients will need at least two readjustments in order to remove sore spots and correct the dentures fit.

One of the most critical aspects in denture instillation is the making of the denture.

The denture must be made perfectly to models the patients edentulous gum. Border moulding must be used to ensure the dentures edges do not aggressively contact the edges of the mouth. If the denture is not made properly a patient may face endless problems. The mandible is generally harder to design a denture for than the maxillary because there is no suction to hold it in place. Because of this mandibular dentures are more commonly supported by implants.

Most dentures will experience some problems regarding their support, stability, retention or a combination of these. This is because the act of mastication incorporates numerous variables the most simple of which is the lever action caused when biting.

Force on the rear of the denture will cause the front to be pulled away and vice versa.

Although ideally a denture will be perfectly fitted this situation is rarely met and thus fits which are imperfect are very common. Denture adhesive is utilised to compensate the imperfect fit and the denture pulling away from the gum but is only an imprecise solution.

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1.4 Introduction to Implants Dental implants are used to artificially replace the root of a tooth. There are several types of implants but the most commonly used is the osseointegrated implant, which is based upon the discovery by Professor Per-Ingvar BrĂĽnemark that titanium could be successfully incorporated into bone when osteoblasts grow on and into the rough surface of the implanted titanium. This is the basis of the structural strength of the implant. Implants typically consist of a titanium screw with a roughened surface. This surface can be treated via a number of methods, namely plasma spraying, etching or sandblasting to increase the integration potential of the implant.

To install an implant, a pilot hole is first bored into the recipient bone while taking care to avoid vital structures such as the inferior dental nerve. This hole is then expanded by re-drilling with progressively wider drill bits. A saline spray is used to keep the temperature of the hole to below 47ÂşC as overheating the area can damage the osteoblast cells. Once the hole is of sufficient size, the implant, which can be selftapping, is screwed into place, again taking care not to place too much load onto the surrounding bone. Once this is in place a cover screw is placed and the site is allowed to heal. Immediate loading is a relative new practice but with good success rate is becoming very acceptable.

The success of an implant depends on many factors such as the dentist’s skill, quality and quantity of the bone available at the site, and also the patient's oral hygiene. Over five years the success rate of dental implants is around 75-95% with smokers experiencing a significantly poorer success rate.

A dental implant is generally regarded as a failure if it is lost, mobile or shows periimplant bone loss of greater than 1mm in the first year after implanting and greater than 0.2mm a year after that. An implant may also fail because of poor positioning, or as a consequence of an initial overloading causing failure to integrate, but these scenarios are less common. Dental implants are not susceptible to dental caries but they can develop a periodontal condition called peri-implantitis where correct oral hygiene routines have not been followed.

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1.5 Introduction to the Mechanostat Hypothesis The mechanostat hypothesis for bones refers to load bearing bones (LBB) which include the tibias, femurs, humorous, vertebrae, radii, mandible, maxillae, wrists, hips etc. It describes how these load bearing bones react to the load that they are placed under. That is, if a bone is placed under excess stress it will, over time, grow stronger to resist such loads and conversely, if a bone is placed under reduced stress it will resorb and become weaker. The relationship between a bone’s load and its remodelling rate can be seen in Figure 4.

Figure 4: Frost’s mechanostat

Figure 4 shows the combined modelling and remodelling effects on the strength of load bearing bones (LBB). (Frost, H. 2003) The horizontal axis represents the area where the bone does not experience any net gain or loss. The dotted line represents how the bone acts either side of this equilibrium axis. The horizontal line at the bottom of the graph represents the typical peak strains, starting at zero on the far left hand side, to MESr, MESm, MESp and eventually the fracture strain, Fx. MES (r, m & p) represent the bone’s genetically determined threshold strains for the various conditions. ‘r’ being the resorption level where a bone is acting as if disused, below which the maximal disuse-mode activity occurs and above which it begins to decline or turn off. ‘m’ being the modelling threshold, below which, assuring it stays above MESr, a bone retain its strength and in and above which modelling usually turns into strengthening a bone. ‘p’ being the pathological threshold above which unrepaired microscopic fatigue damage can begin to accumulate.

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The lower dotted line, existing in the disuse window (DW) reaching into the MESr area, suggests how disuse-mode remodelling would remove bone next to the marrow if the strains stray below the MESr range but otherwise the bone would retain its strength if it is operating the in adapted window. (AD) The upper dashed line, in the mild overload window (MOW) suggests how a bone would increase its strength through modelling drifts when strains exist in or above the MESm threshold. This is the common area of existence for healthy growing mammals. Beyond the MESp, in the pathological overload window (POW) threshold lamellar bone formation usually replaced by woven bone drifts resulting ultimately in fracture if the bone reaches the Fx threshold.

1.6 Introduction to the Finite Element Method Finite Element Analysis (FEA) is a computerised technique used to create simulations for engineering analysis. It utilises a numerical technique called the finite element method (FEM). This technique has been developed from the work of Richard Courant in 1943 who utilised the Ritz method of numerical analysis and minimisation of variational calculus to obtain approximate solutions to vibration systems.

The FEA method represents an object by a geometrically similar model consisting of a number of linked, simplified representations of discrete regions, or finite elements.

Each element is then subjected to equations of equilibrium and physical considerations such as compatibility and constitutive relations and a representation of simultaneous equations are generated. While this is an approximating method the results can be bettered by refining the mesh applied by adding elements and nodes.

The finite element method can be applied to a number of situations including mechanical objects, heat transfer, fluid dynamics and electromagnetism.

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V{tÑàxÜ E Literature Review

Literature Review

Chapter 2

Chapter 2. Literature Review This chapter reviews the verified literature published pertaining to the instillation of dental implants and their analysis using the finite element method. This chapter is split into two sections. The first section covers the literature published regarding the installation of dental implants. It covers the procedure of instillation, the problems faced during this and the contemporary issues surrounding their use. The Second section covers the biomedical investigations of oral environments using the finite element method. This section will cover the published literature which has considered the oral environment with the aid of a finite element analysis. It will consider both early studies which developed two-dimensional models and more recent studies which have developed three-dimensional models.

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2.1 Implants This section of the literature review looks at articles pertaining to dental implants placed in the mandible. It covers the background and history of dentures and also the current issues surrounding the installation of implant-retained over-dentures.

2.1.1 Background Dentures perform the role of replacing missing (Fig. 5) or irreversibly damaged teeth that have to be removed. Dentures can be either removable or fixed by a variety of methods. When a tooth is missing it must be replaced to prevent the teeth either side of the gap from gradually tilting toward the gap and the teeth in the opposite jaw moving toward the space.

Figure 5: Missing front tooth

Dentures can be implemented in a variety of forms. Full dentures are used to restore both the teeth and the underlying bone when all the teeth are missing in an arch. If a patient is not missing all their teeth and still has generally healthy teeth adjacent to a gap, fixed partial dentures, or a fixed bridge can be used. (Fig.6, Fig.7) Fixed partial dentures are anchored to the surrounding teeth by attachment to crowns, or caps, that are affixed to the healthy teeth. Removable partial dentures are used when there are insufficient natural teeth to support a fixed bridge. These rest on the soft tissue of the jaw and are held in place with metal clasps. The newest method of fixing dentures is to use implants. Dental implants allow prosthetic teeth to be implanted directly in the bones of the jaw.

Figure 6: Bridge and Maryland Bridge

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Figure 7: Partial denture and flipper

2.1.2 History The practice of replacing missing teeth is not a new one. The methods and materials used have changed a lot over time. The earliest methods included using animal teeth and pieces of bone in place of the missing teeth. Two such false teeth were found wrapped in gold wire in the ancient Egyptian tomb of El Gigel. (Bellis, 2005)Over the last few centuries false teeth have been made from a variety of materials including ivory, porcelain platinum and in the case of George Washington, wood. (Bellis, 2005) These early attempts at replacing missing teeth were usually carved by hand in order to mimic the appearance and function of natural teeth.

Figure 8: Titanium implant with artificial tooth

The origins of dental implants date back to 1952 when Professor Per-Ingvar Br책nemark stumbled upon the tendency for titanium to bond irreversibly to living bone tissue. He found this tendency when he was unable to remove any of his boneanchored titanium microscopes which he was using in his research in the university town of Lund, Sweden. He coined this discovery osseointegration. (Bellis, 2005) With further research Dr. Br책nemark showed that titanium could be permanently integrated into living bone with a very high degree of predictability and without long term soft tissue inflammation or ultimate fixture rejection.

Contemporary dentures are far more sophisticated in their design and materials.

Thanks to modern technology and advancements in material manipulation synthetic plastic resins and lightweight metal alloys are now used to create stronger and less

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conspicuous false teeth. (Fig. 8) Teeth made from acrylic resins last around five to eight years as this material is relatively wear-resistant. Porcelain is also used as it mimics the look of natural teeth very well. (Fig. 9) It is usually used for the upper front teeth as these are the most visible however the forces present when biting or chewing with porcelain teeth can damage natural teeth so this material should not be used in partial dentures as these will contact natural teeth. These advancements and enhanced techniques of affixation have improved the comfort and effectiveness of the dentures.

Figure 9: False teeth made with porcelain

2.1.3 Dental Implants Implants are currently the best option for missing tooth replacement for they act like the roots of teeth. (Fig. 10, Fig. 11) Once they have been inserted and healed in place, dentures or crowns may be attached. Dentures, when held in place by implants (Fig. 12) will not slip around and if crowns are used then these will act like normal teeth.

Figure 10: Dental implants mimic the role of tooth roots

Figure 11: Front tooth with implant

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Implants however can only be used if there is enough bone in the jaw to secure them.

Patients who have had teeth missing for a long period of time may find this a problem as the bone around missing teeth gradually disappears. However in some cases it is possible to grow bone around the area in preparation for an implant. The implants themselves are a small titanium fixture. This fixture, which serves as a replacement root is placed in the bone of the upper or lower jaw and allowed to bond with the existing bone.

Figure 12: Dental implants on the lower and upper jaw

To complete the dental implant procedure a patient needs around four to nine months and in some cases longer. This time allows the replacement teeth to be made and for the jawbone to grow around the implants. It usually takes several months for the bone cells to grow around the implants. Once this is complete a small incision in the gum tissue is made to connect a healing post to the implants. Once the gum tissue has healed around the post the replacement teeth can be inserted.

2.1.4 Contemporary Issues The technique of inserting implants has been widely accepted and used, however longitudinal studies have been limited and only commenced around 1987. Since then there have been a number of studies concentrating on several aspects of dental implants. The first of which is the development of the procedure. This considers various methods and techniques and the success rates of each. These reports have been integral to the development of implant dentures as, arguably, the most important factor to do with implant dentures, or any project, is the success rate. Then there are articles dealing with bone damage and preservation which look at the subsequent health of the bone within the jaw and around the implant. This issue is pertinent to dentures in general as one important role that dentures play is to prevent the continued loss of bone which comes about with missing teeth. Dentures play a part in reducing this occurrence and even to reverse this trend in some cases. Implant dentures and, to a lesser degree, other forms of replacement teeth can, however, be harmful for the remaining bone material through excess forces produced by the foreign attachments.

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When considering the design of the dentures there are two major factors which need to be considered. These are the number of implants to be used and the design of the anchorage system. As a general consideration it is assumed that less is better as it creates less strain and alteration for the jaw. However, one must ensure that the number of implants are sufficient to hold the false teeth in place and to be able to withstand the required forces. Anchorage design is also important for similar reasons to the implant numbers. The most prevalent designs are those of ball clip and of a bar.

Again it is best to reduce the foreign impact on the jaw meaning that the size of bar attachments is not as preferred as ball clips, however, the strength of the anchorage design must be considered.

Once an implant has been installed into a patient’s mouth there are three considerations which must be addressed and which have been the subject of many studies. Post surgery maintenance and patient satisfaction are important factors for dental implants. Like any service aimed at providing assistance to people, one must ensure that the resulting situation is not worse than the situation the procedure was trying to fix. The practice of immediate loading is another aspect which ties in with patient satisfaction. Any patient undergoing this procedure obviously wants their mouth to resume common functionality as soon as possible. Using original techniques would not allow immediate loading of the replacement teeth, however, with advancements in methods and materials the practice of immediate loading has become a possibility and, as shown in many cases, with a high degree of success.

2.1.4.1 Implant Development Although the notion of implants was first conceived in 1952, the development placing the implant into the mandible was not achieved for a number of years. This technique, when developed, displayed very positive results. The placement of implants into the mandible was in part originally proposed by Van Steenberghe et al (1987) who proposed the use of only two implants in edentulous mandibles.

The placement of implants in the mandible was a technique developed to improve upon the existing technique of placing implants in the maxilla. The maxilla cannot stabilise and support implants as well as the mandible as it consists of a looser arrangement of trabecular bone. (Jaffin et al 1991) The anatomic structure of the maxilla and bone morphology can affect the number, size and type of implant, especially when dealing with atrophied edentulous jaws. Maxilla implants also require more maintenance than mandible implants and are more likely to fail. (Hutton et al, 1995) Raghoebar (2005) compared full implants placed in the maxilla and the mandible in edentulous patients. While all patients with successful implants reported a high degree of satisfaction the implants placed in the mandible reported a higher success rate of 96% compared to 86% success rate of implants placed in the maxilla.

However placing implants into the mandible is often accompanied by a significant loss in depth and width of basal bone due to the reduction of residual ridge.

Van Steenberghe’s (1987) technique of only using two implants in edentulous mandibles boasted a 98% success rate of a period up to 52 months. A 97% success

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rate using 2 implants, splinted or solitary and irrespective of keratinizined tissue or duration of edentulism was reported by Mericske-Stern et al (1994). Over-dentures supported by two implants were reported by Jemt et al (1996) to have a success rate of 100%. Over this study of five years the marginal bone loss averaged 0.5mm mean and another report, compiled by Naert et al (1999), found that all over-denture anchorage systems had a success rate of 100% after five years. Although these reports and others all point to implant supported dentures having significant success rates, there exists controversy regarding the treatment and indications. (Batenberg et al 1998, Burns, 2000) However regardless of the controversy, implant supported dentures have displayed great rates of success and look to continue to be the most effective form of tooth replacement available.

Weng (2003) in a study looking at the success rates of 492 patients concluded that the success or failure of a tooth restoration depends not greatly on factors like anchorage system or installation method but found that the biggest single factor affecting success rate was the size of the implant. He concluded that implants, where possible, should be greater than ten millimetres in length.

2.1.4.2 Bone Damage and Preservation Bone preservation plays a very large role in the analysis of the effectiveness of tooth replacements. Without replacement teeth, bones within the mouth will deteriorate possibly to the extent where implant dentures are no longer an option. However in some cases this lost bone can be grown back. The practice of replacing teeth has the obvious intention to restore the functionality of the mouth and to restore the aesthetics but also to maintain jaw health and bone preservation.

There have been many studies looking at this aspect of replacement teeth, Atwood et al (1971) and Tallgren (1972) showed that the cancellous ridge displayed a height reduction of around 0.4mm per year in the edentulous anterior mandible resulting from physiological changes. (Sadowsky, 2001) Timo et al (2000) also found a reduction in the width of the ridge of between 0.4mm to 0.6mm in patients wearing implant retained mandibular over-dentures. However, Jemt et al, (1996) Quirynen et al (1992) and Naert et al (1998) have shown the edentulous anterior mandible may resorb only by 0.5mm over the first five years and that resorption can remain as low as 0.1mm annually over the long term. Adell et al (1981) found similar results for implant supported complete dentures. Kordatzis (2003) looked at factors affecting such resorption and found that while initial height of the mandible, years of being edentulous and number of dentures failed to show an association with the resorption rate, sex showed as a great dependency factor with females being at greater risk of resorption.

Baron et al (2005) looked at bone loss in relation to the distance between existing teeth and the implant. He found that as the tooth-implant distance increased, the area of atrophy became rapidly larger then decreased gradually. He reported that distances of 8mm to 14mm between the tooth and the first implant and of 17mm to 21mm

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between the tooth and the second implant were associated with a more pronounced bone loss and should be avoided.

Positive bone remodelling in the anterior mandible has been observed in relation to the loading of the implants. This reaction, due to the increased function on the implants seems to be regardless of the method of attachment. The type of denture may however play a part in this. Jacobs et al (1992) found that using an over-denture design the annual rate of posterior mandibular resorption increased by two to three times. This however was limited to those patients who were edentulous for less than 10 years. However, Davis et al (1999a) found that complete dentures supported by implants may not only preserve bone but also regenerate posterior bone. (Sadowsky, 2001) Davis (1999) also found that in edentulous patients implants placed in the posterior portion of the mandible conserve and in some cases enhance the bone of the mandible.

There have been problems reported by Lechner et al (1996), Jacobs et al (1993) Maxson et al (1990) and Barber et al (1990) when using various designs of implant supported mandibular over-dentures to support maxillary complete dentures. In these cases there is often a significant transfer of occlusal forces onto the anterior maxilla which causes cancellous bone resorption and soft tissue inflammation. (Sadowsky, 2001) This increase of forces can also, according to Haraldson et al, (1988) generate more midline fractures of the opposing denture. The maxillary dentures also experienced a loss of fit and a need for realignment in 25% to 33% of patients over a five year period according to Payne et al (2000a) and Watson et al. (1996) These findings however may not be caused by the combination of the two opposing dentures. Narhi et al (2000) found, while evaluating a trans-mandibular prosthesis, single-bar over-denture, and complete denture (Sadowsky, 2001) over a six year period, a continuous maxillary ridge with reduction independent of prosthesis type Rigid or non-rigid connection of dentures to implants seems to make no significance difference to the rate of bone loss according to Block (2002) nor does the presence of cantilever extensions. (Wennstrom, 2004) One factor that does make significant difference is the amount of crestal bone maintained at implants. (Cooper, 2002a) In order to preserve the maxillary bone Thiel et al (1996), Lang et al (1992), Wismeijer et al (1995a) and Denissen et al (1993) have considered the occlusal concept an important one and recommended that there should be no anterior contact during excursive mandibular movements (Sadowsky, 2001) Thiel et al (1996) also recommends that regular recalls be conducted to evaluate the over-denture on extension base fit and the maximal extension. He has also emphasised considering the appropriate plane of occlusion to decrease the need to have the maxillary denture relined.

Patients with extremely resorbed mandibles pose a difficulty for placing implants.

While there have been many techniques developed to enlarge the denture-bearing area of the mandible most have improved the retention and stability of the dentures only temporarily. Stellingsma (1998) reported a 100% success rate of 10 patients over 31 months by using sandwich osteotomy, which is to surgically divide the bone, with an

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autogenous bone graft followed by placement of four implants in the interforaminal region.

Implant supported over-dentures in patients with extremely resorbed mandibles do, regardless of the increased difficulty of installation, provide the patient with a great increase in masticatory function regardless of treatment protocol. (Stellingsma, 2005) Hanson (2004) also found that implants placed in patients with extremely resorbed mandibles last a long time reporting a 100% success rate and no reports of discomfort or pain in 38 patients after average of eight years. 1 Bone preservation is obviously an important factor given the tendency to lose bone before replacement teeth are used. This occurrence however cannot be predicted with any form of accuracy as yet as most literature on the topic is reflective.

2.1.4.3 Number of Implants One variable that is always considered when installing dental implants is the number of implants. (Fig.13) This is an important factor as the number of implants impacts on virtually all other factors of implant dentures. A finite element analysis was carried out to compare 2 and 4 implants placed in the interforaminal region of the mandible.

This was conducted by Meijer et al (1994) who found that neither model demonstrated a reduction in the principle stresses providing that the load was uniformly distributed.

Figure 13: Bar anchorage with five and two implants

Batenburg et al (1998a) and Mericske-Stern (1990) have also conducted experiments which result in similar findings. Batenburg et al (1998a) looked at 60 patients with mandibular over-dentures, these people were divided into two groups, one with two implants and one with four implants. There were no findings of significant difference in peri-implant health. Mericske-Stern (1990) looked at 67 patients split into three groups. The first, 29 people with 2 implants connected with a bar, the second, 27 with 2 solitary ball anchors and the third group of 11 people with three or four implants splinted with a bar. She found no significance difference in the retention, stability or occlusal equilibration with a change in the number of implants.

1

14 patients had implants for over ten years, 12 had implants between five and ten years, and 12 had implants for less than five years.

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Fontijn-Tekamp et al (1998) looked at the masticatory forces between a four implant transmandibular design and two anteriorly placed endosseous implants. Again no significance difference was found between these mainly implant-borne and mucosaimplant–borne treatments (Sadowsky, 2001) Geertman et al (1999) also considered the masticatory forces and found similar results. However in this study all patients wore opposing complete dentures which may have been a limiting factor (Glantz, 1985) Batenburg et al (1998a) and Mericske-Stern (2000) have recommended that in light of these studies that only two implants should be used to support a mandibular overdenture unless the patient has a dentate maxilla with implants being less than eight millimetres in length and less than three and a half millimetres in width, has a sensitive mucosa, high muscle attachments, sharp projections, large V-shaped ridges or patients with high retention needs. Batenburg (1998) supports this, arguing that only two implants should be used unless the situation involves a edentulous maxilla, narrow mandibular arch, extreme resorption of the mandible or mandibular pain.

Hobkirk and Havthoulas (1997) however argue that with a smaller number of implants there are associated more localized patterns of force which create the possibility of excessive force around the implants. Whereas the use of a larger number of implants resulted in pronounced leverage effects on what?.

2.1.4.4 Implant Anchorage Design Anchorage design for fixing dentures to patients mandibles (Fig. 14) impacts virtually every aspect of implant dentures. There are a number of anchor designs available however due to contradictory results of studies looking at two implants, either interconnected or independent implants, it is difficult to determine a superior anchorage design.

Figure 14: Bar and ball anchorage system

Menicucci et al (1995, 1998a) conducted in vitro and in vivo studies comparing the stresses on the bone around the two implants using both a barclip or ball attachments for over-dentures. The results of this study were consistent with a photoelastic analysis (Kenney et al, 1998) which found greater stresses on the peri-implant bone with a barclip attachment. Contradicting this study however Gotfredsen (2000) found

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that rigid bars contributed to load sharing in an in vivo study on force transmission onto implants supporting over-dentures.

The two different anchorage systems for retaining an over-denture, when mounted on two implants, showed no difference in implant survival rate, health of peri-implant tissue or marginal bone loss. These conclusions were drawn from the results of a number of longitudinal studies by Gotfredsen and Holm (2000), Naert et al (1998) and Bergendal and Engquiest. (1998) Chao et al (1998) maintains that the type of connection is not a significant factor in the stress concentration and that more influence comes from occlusal forces.

Mericske-Stern (1998) backs this up arguing that the loading of implants is more significantly affected by factors including the superstructure fit and occlusion and that the anchorage system plays a minor, if any, part at all. Fontijn-Tekamp et al (1998) also argues that the type of support for dentures does not affect the maximum bite force of the wearer, rather this was affected by the sex of the patient and the type of denture.

Engquist et al, (1988) Wright (1998) and Naert et al (1997a) have proposed a method of using two implants with an interconnecter parallel to the hinge axis and a resilient over-denture on an ovoid or round bar. This technique aims to enhance free rotation during dorsal loading with twist-free load transmission to the implants. The use of a rigid versus moveable retention mechanism remains controversial however because Burns (2000) stipulates in a review of mandibular over-denture treatment concepts proposes that these concepts were based on empirical data.

Bars may have been shown to be more retentive (Naert et al, 1994) but ball attachments cost less, are less technique sensitive (Naert et al, 1991), easier to clean (Cune et al, 1994) and their potential for mucosal hyperplasia is easier to reduce (Krennmair, 2001). A cantilever bar, a non-cantilevered bar, and solitary attachments were tested by Sadowsky and Caputo (2000) in a photoelastic analysis to investigate the stress transfer of different anchorage designs on four implants in the parasymphyseal region supporting an over-denture. This investigation showed that there is little difference in stress transfer with intimate extension base contact.

2.1.4.5 Impact of Immediate Loading Immediate loading of implant dentures is the newest facet of this procedure which has been investigated. Immediate loading impacts greatly on patient satisfaction however it must be done in a manner which doesn’t affect the success rate of the implants. The cost of such a procedure is not an issue as Attard (2006) has shown that the associated clinical costs using an immediate protocol is in fact slightly less than the cost of treating patients with a conventional protocol.

A 96% implant success rate was achieved by Gatti et al (2000) who completed a prospective study where 21 patients were restored immediately after implant placement in the anterior mandible, and a U-shaped bar connecting 4 implants was

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loaded with an implant-retained over-denture. Cooper et al (1999) achieved a 95.6% success rate by using a single stage surgical placement of 2 micro-threaded screw implants to immediately support a relieved mandibular over-denture, followed by ball attachments 3 months later.

100% implant success rate was achieved by Roynesdal et al (2001) who used two titanium-sprayed solid screw implants in the interforaminal region and connecting the over-denture prosthesis to the ball attachment after three weeks. Although this perspective study had a small sample size and short observation period, it is a promising treatment concept due largely to the high satisfaction rate.

Stricker (2004) also reported a 100% success rate after two years in his study of ten edentulous patients between 48 and 74 years old. His study suggested that the immediate loading of two dental implants can be successful and recommends that further support be given to the use of a rough implant surface in residual bone. 100% success rates were also recorded by Nikellis et al (2004) and Cooper (2002b) in their respective studies analyzing immediate loading.

Immediate loading seems to be a practice which can be used to great success.

However it must be done with great care and in controlled conditions so that the procedure is not undermined by an increased failure rate.

2.1.4.6 Maintenance Requirements Replacement teeth primarily aim at increasing a patients quality of life. While dentures can do this greatly they can be undermined if a patient perceives the consequential maintenance requirements to be too great. Studies investigating maintenance look at both regular maintenance but also the rate of complications which occur and consequently result in a degree of unscheduled maintenance. There have been many studies, both prospective and retrospective, of post-insertion complications with two implants, splinted and un-splinted, retaining a mandibular over-denture. 2 Most of these studies have found that the maintenance requirements are greatest during the first year after insertion of the implants 3 and that these requirements are generally related to the alteration on contour and repair of the matrix or patrix. (Payne, 2000b) After many studies however it is still difficult to determine which of the ball or bar designs require more maintenance. (Naert 1999, Gotfredson, 2000, Bergendal, 1998) Schmitt (1998) and Behr (67) argue that gold alloy bars seem to wear more and fracture more frequently than ball attachments.

O-rings generally have to be replaced in every one out of two patients within the first year. Clip adjustments are required in up to 62% of patients while fractures generally occur in up to 33% of patients. The chance of clip loosening in the acrylic resin is 2

Authors include Naert et al, (1999) Watson et al, (1996, 1997) Payne et al, (2000) Gotfredsen and Holm, (2000) Bergendal and Engquist, (1998) Hemmings et al, (1994) Johns et al, (1992) Walton et al, (1994) den Dunnen et al, (1997) and Davis et al (1996) 3 Authors include Naert et al, (1999) Watson et al, (1997) Hemmings et al, (1994) Johns et al, (1992) Walton et al, (1994) den Dunnen et al, (1997) and Davis et al (1996)

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increased with the shortening of the bar segment however it is debatable how important the use of a metal reinforcement in the mandibular over-denture prosthesis is. Low fracture rates with high-impact resin have raised a few questions (Payne, 2000b) especially when considered with the additional expenditures and increased implant loading with metal frameworks. (Davis, 1999b) Naert’s (1999) study showed that people with bar systems revealed more mucositis and gingival hyperplasia then unsplinted groups.

Palmer (2005) showed that, on average, within three years around 10% of cases experience loosening of screws, 40% will require re-cementation if only temporary cement is originally used and 40% will display fractures or chips to composite components of bridges. Payne (2000a) showed by comparing the burden of prosthodontic maintenance with that of implant supported mandibular over-dentures with more than two implants there exists no statistical difference and all the designs appeared to function as hinging over-dentures after 5 years. Of all the studies on maintenance there has been however, few studies which have looked into the frequency of relines between splinted and unsplinted attachments or among two, three or four implants. (Payne, 2000a) 2.1.4.7 Patient Satisfaction Patient satisfaction is in some respects the most important aspect of the success of dentures and dental implants. While other factors directly impact on patient satisfaction and the success rate technically determines how useful a product is, patient satisfaction ultimately determines how successful a product will be. Many authors 4 have looked at patient satisfaction. Maijer et al (1999) found a higher rate of satisfaction in those patients with mandibular over-dentures retained by two implants over 5 years. These findings were collaborated by Raghoebar et al (2000) who also considered complete denture patients who had undergone pre-prosthetic surgery.

Feine et al (1994) compared the satisfaction of patients with fixed implant prostheses to that of those with long-bar, removable, implant-supported prosthesis. Feine found that half the patients chose the removable style for ease of cleaning and aesthetics.

These were generally chosen by patients over 50 years old while younger patients generally chose the fixed design for stability and ability to chew.

Grandmont et al (1994) found that although fixed implant complete dentures are significantly better for chewing harder foods there was no difference in overall satisfaction. This study was of psychometric and functional measurements of 15 edentulous patients who wore both fixed implant prosthesis and a long-bar overdenture. 110 edentulous patients who were either fitted with implants with ball attachments, two implants with an interconnecting bar, or four interconnected implants, most of which were at least ten millimetres long, were studied by Wismeijer 4

Naert et al, (1999) Krennmair and Ulm, (2001) Raghoebar et al, (2000) Burns et al, (1995) Feine et al, (1994) de Grandmont et al, (1994) Boerrigter et al, (1995) Humphries et al, (1995) Wismeijer et al, (1992) Meijer et al, (1999) Harle and Anderson, (1993) Wismeijer et al, (1997)

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et al (1997). From this study no significant differences were found in patient satisfaction.

Fontijn-Tekamp et al (2001) however found a higher satisfaction rate, due to pain and discomfort experienced during biting and chewing, in those patients fitted with dentures fixed with mandibular retained implants. He also found that complete denture wearers experienced the most pain especially in the mandible rather than the maxilla.

Raghoebar (2003) looked at the satisfaction of treatment methods for people with lower denture complaints. He looked at three treatments, meticulous construction of a new set of dentures, construction of a new set of dentures following pre-prosthetic surgery to enlarge the denture-bearing area and construction of an implant-retained mandibular over-denture. Raghoebar (2003) found no difference in the success or the satisfaction of recipients between the differing methods. Ohkubo (2006) found that for people with unstable mandibular implants, restrained dentures transitional implants can immediately improve the comfort for the wearer and that this method had a 100% satisfaction rate.

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2.2 Biomedical Investigations of Oral Environments Using the Finite Element Method Although bone resorption among denture wearers is clinically well known and predictable, quantifying the stresses involved and adapting Frost’s mechanostat hypnotises with more relevance than simply a theoretical explanation still proves difficult. There have been a number of techniques employed to further understand this trend, initially focusing on the measurement of bone resorption, Naert et al. (2002) conducted a radiographic evaluation to determine marginal bone levels around implant-supported restorations, while Kordatzis et al (2003) made measurements on rotational tomograms. However measurements of the internal strains and stresses are far more conducive to a greater understanding of the mechanisms involved. These can be measures clinically through the use of strain gauges however this clinical method can be quite invasive and hence in not preferable. FEA investigations were initiated in the early 1970’s (Choi A, et al. 2005) has revolutionised dental biomedical research.

Vollmer et al. used strain gauges to correlate FEA results and found that the FEA results were accurate and much less invasive. (Vollmer D, et al. 2000) FEA is now the preferred method for analysing stresses as it is non-invasive and non-destructive.

Finite element analysis (FEA) is an accurate and sophisticated method for investigating the stresses involved in dental structure simulations. The application of this technique can assist in the biomedical investigations of all the oral environments including the cancellous and cortical bone, mucosa, PDL, dentin and enamel as well as the denture materials such as the soft denture liner, acrylic resin, artificial teeth and the titanium and gold components of the implants. Finite element analysis allows detailed results of multiple simulated dental scenarios to be evaluated with a high level of accuracy and resolution. Initial FEA models were two-dimensional and provided a limited scope of results. (Williams et al. 1986) These models were produced with varying degrees of detail, examples of two-dimensional finite element models from Vaillancort et al (2004) Sato et al (2000) and Maeda and Wood (1989) can be seen in figure 15

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Figure 15: Two-dimensional finite element models from Vaillancort et al (2004) Sato et al (2000) and Maeda and Wood (1989)

More recent studies by, for example, from Takayama et al (2001) Eskitascioglu et al (2004) and Kitamura et al (2003) (Fig. 16) have developed three-dimensional models of mandibles with dentures in order to analyse the crestal bone loss around implants beneath the dentures.

Figure 16: Two-dimensional finite element models from Takayama et al (2001) Eskitascioglu et al (2004) and Kitamura et al (2003)

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These studies have considered various aspects and dental simulations and their results and recommendations have considered facets of dental loading including the impacts of occlusal adjustments to move load point palatally (Maeda and Wood, 1989) and other adjustments in order to reduce the rate of bone resorption (Kitamura et al, 2003) 2.2.1 Finite Element Method Validation through Convergence Checks The method of analysing finite elements to evaluate stress is a highly accurate and precise method utilising computational methods made possible through highly sophisticated software. It calculates a series of differential equations to calculate the reactive stresses, strains and displacements on a model with physical properties set by the relative material data. The model is represented in the software by a set of mathematical relationships, or a numerical model. The FEM is particularly useful when analysing the dental environment due to the ability of the computational method to handle the complex geometry and scenarios presented by the oral structure.

The FEM divides a model into a number of finite areas, or elements. (Fig. 17) These elements makeup the basic structure used for finite element analysis. These elements are joined through nodes, (Fig. 17) which are mathematical relationships used to describe the relationship between two elements. Once an entire model has been divided up into elements it is referred to as a ‘mesh’ (Fig. 17) for it takes the shape of a mesh covering the model. A mesh can be defined as coarse or fine depending on the number and size of the elements. The more elements used, and consequently the smaller the elements are, the finer the mesh is. A finer mesh will result in more accurate predictions. Once a mesh has been applied the other major requirement of FEA is that material properties be assigned. This is usually in the form of Young’s Modulus and Poisson’s Ratio. Young’s Modulus is the constant of proportionality between stress and strain where Poisson’s Ratio is the ratio of lateral strain to longitudinal strain. FEA is concerned in establishing compatibility with each element and equilibrium as the modes. The FEM attempts to minimise the total potential energy of the structure in regards to a set displacement field. (Farah et al, 1973) FEM simulates a comparable mathematical representation of a certain physical model and predicts relative results regarding stresses, strains and displacements.

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Figure 17: Simple mesh applied to a section of an ‘object’

The FEM calculates the stresses, strains and displacements by calculating these factors for each element and then using the relationships that the nodes represent and combine the individual results to produce a global result. Due to the nature of this method, the greater the number of nodes, and the finer the mesh, the more accurate the result will be.

Although FEM is only a prediction it is currently the most accurate method available for calculating the results it obtains. Other methods such as mathematical techniques, photo-elastic systems and laser holographic interferometry produce results which are not as accurate for they only examine the surface stresses and differ significantly from clinical research results. (Jones et al 2001) The FEM has the ability to consider the interior stresses of a model and is more suited to produce quantitative results.

Because the FEM is only a prediction, regardless of its power and accuracy, all of its calculations involve some degree of error and this occurrence, if not monitored, can cause significant difference in the results due to each FEA usually having a significantly high number of calculations. This error can be considered and monitored using convergence checks and mesh refinements. These processes involves comparing the results of meshes to finer meshes and checking to see if there has been any significant gain in the result accuracy in relation to the extra computational time and resource usage as each subsequent analysis which has more elements will require a longer solution generation time and additional computational expense. Durkee et al (1991) argues that while it is important to have accurate results they should not be obtained through excessive mesh generation.

Differences in mesh refinement can greatly vary the resultant predictions. This was analysed by Durkee et al (1991) where the importance of mesh refinement was highlighted in his study where he developed four mesh types for a 2-D dental model.

(Table 2.2.1) The first mesh he developed consisted of 164 elements and 183 nodes.

Each mesh developed had progressively more elements and nodes and the results become progressively more accurate. (Table 1) This study shows a significant

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increase in the results achieved through the first and second mesh where the change between the final two meshes yielded small changes. The difference in stress dropped from an 80% change between meshes one and two to <1% change between meshes three and four. (Table 2.2.1) Similar drops in percentage change are evident in all aspects of the results. This illustrates the importance of mesh refinement as the initial mesh can yield quite different results from clinically obtained results. This procedure should be performed routinely when conducting FEAâ&#x20AC;&#x2122;s in order to produce the most accurate results possible.

Model Element Number Node Number 1st Mesh 164 183 2nd Mesh 460 493 3rd Mesh 806 853 4th Mesh 1118 1177 Table 1: Element and node numbers for Durkeeâ&#x20AC;&#x2122;s et al (1991) convergence study

2.2.2 Validated Biomedical Investigations of Oral Environments using the Finite Element Method Bone resorption under dentures, implant-restrained and conventional, has been documented and studied a number of times in varying detail. It is inherently difficult to reproduce the complex nature that is the oral environment in sufficient detail to produce results which are clinically valid. The studies covered in this section have attempted to represent their dental structures with a complexity and sophistication sufficient to match the results of clinical investigation using the FEM with various degrees of intricacy.

The dental environment is quite a complicated model to replicate, especially when dentures are included. The mandible alone consists of two types of bone structure plus the mucosa layer and the denture consists of various layers of resin, liner and when implants are included gold and aluminium components. Early studies utilising the FEM considered two-dimensional models of the structure but the validation systems in place for these models provided a limited scope of results to be achieved. (Williams et al. 1986) Three-dimensional studies have become predominate due to their ability to produce results of a greater accuracy and especially their ability to analyse tissue strain. (Jones et al 2001)

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2.2.2.1 Finite element method simulation of bone resorption beneath a complete denture. Maeda and Wood (1989) Maeda and Wood (1989) developed a two-dimensional model of the maxillary denture base, occlusal table, cancellous mucosa, cortical bone and cancellous bone (Fig. 18) for a plane-stress finite-element simulation. The nodal data and material data can be seen in table 2 They applied a vertical load of 100N at the facial edge of the occlusal table, above the crest of the cancellous ridge and at the palatal edge, they also applied a lateral load of 20N at the palatal edge. Maeda and Wood (1989) were investigating bone resorption beneath a maxillary conventional denture, for they argued that while Epker and Frost (1965) have postulated that it is the physical property of bone which causes remodelling, bone resorption appears to be associated with tensile strains under some conditions, while under other conditions it appears to be associated with compressive strains.

Figure 18: 2D finite element model of a maxillary cancellous bone and results of Maeda and Woodâ&#x20AC;&#x2122;s (1989) study

Material Prosperities Material Type Young's Modulus (MPa) Poisson's Ratio Cancellous Bone 1500 0.3 Cortical Bone 10,000 0.3 Mucosa 10 0.4 Acrylic Resin 2000 0.3 Table 2: Material properties used by Maeda and Wood (1989)

The results in figure 18 show the simulation after five calculations, ie. time segments.

The space between the original cortical bone surface and the displaced surface is regarded as the Resorbed area which expanded palatally and posteriorly from the facial surface with each calculation. Figure 18 shows the resorption differences due to different loading conditions. The resorbed area became smaller and more evenly distributed over the cancellous ridge as the load point moved from the facial edge of the occlusal table to the palatal edge. Figure 18 shows the results of a rebased denture after the third calculation with the load point initially above the crest of the cancellous

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ridge and then moved to the palatal edge at the time of rebasing. Figure 18 shows a comparison between load points after a rebase had been done on the third calculation.

The first keeps the load point at the facial edge of the occlusal table where as the comparative results looks at the load point being moved from the facial edge of the occlusal table to the palatal edge at the time or rebase. We see that when the load point was kept at the facial edge of the occlusal table there was more bone resorption than if no rebase had occurred. When the load was moved to the palatal edge at the time of rebase the degree of bone resorption was similar to the response before rebasing, although the topography of the alveolus bone was undesirable. Figure 19 shows a comparison of five calculations with and without rebase with the load point maintained at the palatal edge. In this instance there is no difference in the degree of resorption and its distribution between the rebased and the un-rebased condition.

Figure 19: Results from Maeda and Woodâ&#x20AC;&#x2122;s (1989) study

This study made a number of assumptions, the most significant being the selection of 05.MPa stress as the threshold stress. This figure was arbitrary and as such the selection of a higher threshold would have produced a smaller change and conversely

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the selection of a lower threshold would produce a higher change. This selection produced an observable change at 100N however the actual threshold is not known.

These results suggest that the rebasing of a denture could result in a greater instance of resorption than an ill-fitting denture. This may arise because a loose denture could move without producing the same concentration of stress on the facial aspect of the cancellous ridge. Although rebasing a denture can improve stability and retention it could also increase bone resorption.

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2.2.2.2 Finite element analysis of crestal bone loss around porous-coated dental implants. Vaillancort et al (2004) Vaillancort et al (2004) considered bone resorption around dental implants using a two-dimensional finite element models. The implants used in this study are shown in figure 20, and correspond to the bucco-lingual and mesio-distal sections of canine mandibles. The Mechanical prosperities of this model are shown in table 3.

Figure 20: Finite element model of implant used by Vaillancort et al (2004) Material Properties Material Type E (GPa) v Ti6A14V 110 0.33 Midas Gold alloy (bridge) 83 0.3 Cortical bone 7.5 0.4 Cancellous bone 0.5 0.3 Porous coating-ingrown bone zone 5.5 0.3 Table 3: Material properties used by Vaillancort et al (2004)

G (GPa) 41.4 31.8 2.7 0.2 2.1

These results (Fig. 21) indicate that at most implant surfaces (buccal, lingual, mesial, and distal), the equivalent stresses in crestal bone adjacent to the coronal and nonporous-coated zone of the partially porous-coated implants were lower than around the most coronal region of the fully porous-coated implants. It is suggested that crestal bone loss in this case was related to bone disuse atrophy due to the region of lower stress around the partially porous-coated implants corresponded to observed areas of crestal bone loss in animal studies. This study determined that a stress equal to

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1.6MPa was sufficient to avoid bone loss due to disuse atrophy in the canine mandibular premolar region.

Figure 21: Results of Vaillancortâ&#x20AC;&#x2122;s et al (2004) study

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2.2.2.3 Finite element analysis of stress relaxation in soft denture liner. Sato et al (2000) Soft denture liners have been used as a cushion between the acrylic resin of the denture and the denture bearing tissue with sore or atrophied mucosa. Elasticity and resiliency of the liner assists the load distribution produced by the denture to be evenly distributed over the denture-bearing area and avoiding local concentration of stress which can lead to bone resorption. The purpose of Satoâ&#x20AC;&#x2122;s et al (2000) study was to evaluate the effect of the properties of soft denture liners in terms of the resultant stress distribution and to obtain fundamental knowledge to assist in the customisation of the soft denture liners for individual patients. Sato et al (2000) developed a two dimensional finite element model of a denture, with the liner, and the cortical bone with the mucosa. (Fig. 22) A number of various material properties were used in order to analyse the resultant stresses with various liners. (Table 4)

Figure 22: Model used by Sato el at (2000)

Material Type Denture Base Resin Soft Denture Liner Mucosa Cortical Bone

Material Properties Young's Modulus (MPa) 2650 1.25, 2.5, 5.0, 10.0, 30.0, 2650 1.25, 2.5, 5.0 24115 Table 4: Material properties used by Sato el at (2000)

Poisson's Ratio 0.3 0.3 0.4 0.15

Two examples of the resultant stresses are shown in figure 23. The results found that to obtain the optimum cushioning effect, the most elastic soft denture liner is not always the right choice and that thickness of the soft denture liner had almost no effect on stress ratio in this study and excessively thick soft denture liners are not only unnecessary but also harmful because increasing the thickness of the soft denture liner

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weakens the denture base. Also results found that the stress ratio decreased proportionally with the Young’s modulus of the soft denture liner with a thin mucosa.

However if the liner has a lower Young’s modulus than the mucosa the stress concentration is adversely affected.

Figure 23: Two example of stress distribution results from Sato’s et al (2000) study

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2.2.2.4 The dynamic behaviour of a lower complete denture during unilateral loads: Analysis using the finite element method. Takayama et al (2001) This study examined the correlation between the location and direction of unilateral loads and the dynamic behaviour of a complete denture. Takayama et al (2001) utilised a three dimensional finite element model (Fig. 24) consisting of the body of the mandible, cancellous mucosa and a complete denture. The material properties used throughout this study can be seen in table 5

Figure 24: Model used by Takayama et al (2001)

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Material Type Artificial Teeth Acrylic Resin Mucosa Compact Bone Cancellous Bone

Chapter 2

Material Properties Young's Modulus (kgf mm-2) Poisson's Ratio 300 0.3 200 0.3 0.1 0.3 2000 0.3 150 0.3 Table 5: Material properties used by Takayama et al (2001)

This study highlighted the potential problem with modelling the interface between the denture base and the mucosa as a â&#x20AC;&#x2DC;stuckâ&#x20AC;&#x2122; or bonded condition. There is little problem when the displacement is very small but as the load condition becomes large the results are compromised because separating or sliding at the interface is curbed.

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2.2.2.5 The influence of occlusal loading on stresses transferred to implantsupported prostheses and supporting bone: A three-dimensional finite element study. Eskitascioglu et al (2004) The study by Eskitascioglu et al (2004) used a three-dimensional finite element model of a mandibular section of bone (Fig. 25) with a missing second premolar and its superstructure and upon the occlusal surface of the tooth loads were placed in three locations. The material prosperities used in this study can be seen in table 6.

Figure 25: Models with the values and distribution of loads applied in Eskitasciogluâ&#x20AC;&#x2122;s et al (2004) study

Material Properties Material Type Elastic Modulus (E) (GPa) Poisson's Ratio (u) Titanium (abutment, implant) 110 0.35 Spongy Bone 1.37 0.3 Cortical Bone 13.7 0.3 Co-Cr alloy (framework) 218 0.33 Feldspathic porcelain (occlusal material) 82.8 0.35 Table 6: Material properties used in Eskitasciogluâ&#x20AC;&#x2122;s et al (2004) study

This study addressed the limited knowledge about the influence of occlusal loading on the stress distribution in an implant-supported fixed partial denture and supporting bone tissue. The resultsâ&#x20AC;&#x2122; clinical implications are important for it could predict the decrease of von Mises stress within the mandible. The results however need to be verified by long-term clinical trials. Figure 26 and figure 27 show results within the implant and abutment and also within the framework respectively while figure 28 shows results on the occlusal surfaces.

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Figure 26: Distribution of stresses within implant and abutment

Figure 27: Distribution of stresses within framework

Figure 28: Distribution of stresses within occlusal surface material

The results found that loading at one location induced higher von Mises stress values in the bone than loading at two or three locations while the stresses induced on the occlusal surface in the framework were reduced with multiple load points. The study also found that excessive loading may decreases bone density around the neck of implants and lead to crater-like defects. Vertical loading at one location produced stresses on the cortical bone and implant while multiple load points produced lower stresses distributed to the framework and occlusal surfaces.

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2.2.2.6 Biomedical aspects of marginal bone resorption around osseointegrated implants: Considerations based on a 3D FEA. Kitamura et al (2003) Kitamura et al (2003) explored the hypothesis that although bone loss around implants is reported as a complication when it progresses uncontrolled, resorption does not always lead to implant loss, but it may be the result of biomedical adaptation to stress.

This was done by investigating the influence of marginal bone resorption amount and shape on stress in the bone and implant. Nine finite element models (Fig. 29) were developed, a non-resorption base model and eight variations all with respective implants. The material properties used in this study can be seen in table 7

Figure 29: Model used by Kitamura et al (2003)

Material Type Cortical Bone Cancellous Bone Titanium Gold Alloy

Material Properties Young's Modulus (GPa) Poisson Ratio 14 0.3 3 0.3 110 0.35 100 0.3 Table 7: Material properties used by Kitamura et al (2003)

This study found that regardless of load direction, bone stresses were higher in the pure vertical resorption models than in the base model and increased with resorption depth. The stresses in the cortical bone however were found to be much lower in the conical resorption models that in both the base and the pure vertical resorption models of the same resorption depth. The cancellous bone displayed a tendency converse to this under buccolingual load. This load resulted in the highest stress in the implant increasing linearly with the resorption depth for each model and the location of this maximum stress approached the void existing below the abutment screw.

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2.2.3 Summary All of the studies to date which have investigated the biomedical consequences of biting forces and orthodontic loading on the mandible do not develop models which are completely accurate of the oral environment being investigated. These studies proved a good estimation of the reactions taking place however cannot produce results which are completely accurate. This study aims to produce a high definition model which will not merely provide estimations of the reactions but production a replication of the system and consequently a replication.

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V{tÑàxÜ F Modelling

Modelling

Chapter 3

Chapter 3. Modelling Accurate modelling of the oral environment being considered is paramount to this study for the validity of the FEA results depend heavily on the model produced. Three separate models were produced for this study, a natural mandible, an edentulous mandible with a conventional denture and an edentulous mandible with an implantsupported over denture supported with two implants. This chapter will discuss the processes involved in the design of these models, their foundation, construction and finally their material properties and limitation and difficulties involved with the modelling. This chapter will first consider the requirements of the models are in order to achieve the desired outcomes.

The construction of the various models investigated focusing first on the natural dentition model. This section will discuss the alterations made to the original model, which was developed through the utilisation of CT scans, to produce the natural mandible model used to analyse the natural state stresses experienced by the mandible. The conventional denture model will then be considered with an outline of the changes made in the mandible from the natural mandible model. This section and will also illustrate the differences required between the two models as well as the construction of the conventional denture. Finally the implant-restrained over-denture model will be discussed focusing on the choices made in the selection of the denture used as well as outline the differences required and modelled in this model from the previous two. This section will consider the construction of the mandible and denture but will not look into the construction of the implants themselves. The implants will be considered in the following section. This section will discuss the choice of implants, materials used as well as the assumptions made and the reasons why they have been made. The final section in this chapter will cover the difficulties experienced and ultimately the limitation of the models developed.

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Chapter 3

3.1 Requirements CAD software is designed primarily for engineering purposes and as such is extremely good at modelling objects with flat or smooth surfaces. Engineering models may in themselves be extremely complicated however the individual parts of an engineering model are generally fairly simple containing generally flat or smooth surfaces. Modelling natural shapes, or free form modelling, presents a high degree of difficulty as the surfaces involved are very complicated and hence are very difficult to model. Representing these shapes can be done by making models which approximate the shapes however developing a replica of these shapes can be extremely difficult due to the intricacies in geometry. For this study to be accurate it is imperative that the models are developed as accurately as possible. In order to develop realistic threedimensional models specific data is required within the reconstruction phase. Only a high fidelity, comprehensive, detailed model with appropriate material properties and accurate geometry will be able to produce results which are clinically accurate. A complete, detailed, accurate model will be an effective tool in performing computational based research into the biomedical consequences to biting forces. The models will be developed from a foundation model using information generated through CT scans. This method ensures highly accurate, precise geometrical relationships within the accuracy of the CT images.

3.2 Construction The mandible used was based upon a human mandible, as seen in figure 30. This structure contains the trabecular, alveolar, or cancellous bone, cortical bone and dentin. These are the fundamental structures from which the other components will be developed.

Figure 30: Depiction of a human mandible

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Chapter 3

In order to replicate the dental models such as those shown in figure 30, computerised reconstruction technology needs to be used. The exact shapes of the cancellous bone, cortical bone and teeth need to be recreated to generate the foundation of the models.

CT scans were used to obtain the recreated models of these complicated surfaces. CT scans were used because this method can create accurate cross-sectional geometries, this method is a non-destructive method meaning that the reference mandible is not damaged and the clarity of the digital images created are of an extremely high standard.

To generate CT images for the model X-rays were needed to be directed at an adult human mandible. The image is generated through accumulating the areas of like intensities of the X-ray beams as they pass through the mandible. Areas with a high intensity x-ray beam, that is it is still bright after passing through the mandible, define areas of the model which are denser than areas where the X-ray beam is less intense.

3.2.1 Construction of the Specific Models The mandible structure, comprising of the cancellous bone, cortical bone and the teeth were generated by Dr Ionut Ichim, The University of Otago, New Zealand, this model is the basis of the models generated in this study. This model was developed from a adult human mandible through the use of Computer Tomography (CT) imaging which was essential in realising the generation of these accurate three-dimensional models.

The 3D model was reconstructed from a stack 117 CT slices of a dentate human mandible taken at 1mm intervals with 0.5mm interpolation. (Ichim et al 2006) The images obtained through CT imaging were loaded into a CAD program, Rhinoceros 3D, and the models were further developed using this program. The dentin, PDL and enamel were all created through relational modelling, i.e. modifying the existing structures, where as the mucosa, soft denture liner and dentures were created using the existing mandible structure as a foundation.

The final dental models consist of a natural mandible, a mandible with a conventional denture and a mandible with a implant retained over-denture. These replications consist of, for the natural mandible denture model, the cancellous bone, cortical bone, PDL, dentin and enamel. The natural implant model, the cancellous bone, cortical bone, mucosa, soft denture liner and denture consisting of acrylic resin and artificial teeth, and the implant retained over-denture consisting of the cancellous bone, cortical bone, mucosa and denture consisting of acrylic resin and artificial teeth as well as the implants. These models will form the basis of the finite element analysis. These models replicate situations used in clinical treatment. The FEA results obtained in this study are accurate and reliable due to the precision and accuracy of the models developed.

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Modelling

Chapter 3

3.2.2 Construction of the Natural Dentition Model The original structure, consisting of the cancellous bone, cortical bone and teeth were created by Dr. Ionut Ichim, University of Otago, New Zealand. (Fig. 31) The first stage in the development of the model was to extract the cancellous bone from the cortical bone. The Cortical bone was initially solid and this was done to make it hollow so that it would accurately reflect a real mandible. (Fig. 32)

Figure 31: Original structure of the mandible and teeth

Figure 32: Hollowed Cortical Bone

To create the PDL and enamel the teeth were first duplicated. These duplications were then offset to create a shell for the dentin. (Fig. 33) These offset shells were then split with respect to the cortical bone line, the area above the bone line, which comprises

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Modelling

Chapter 3

the crown area of the tooth is the enamel (Fig. 34) while the area below the bone line, comprising of the root area is the PDL. (Fig. 35) The thickness of the PDL was set to 0.3 millimetres. (Wheeler et al. 2003)

Figure 33: Enamel

Figure 34: Dentin

Figure 35: PDL

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Modelling

Chapter 3

The sockets for the teeth inside the bones were then generated. (Fig. 36) These were created using a simple boolean cut operation to remove portion of the cancellous and cortical bone which is taken up by the PDL. The model was than created by combining the cancellous bone, the hollowed cortical bone, the PDL, dentin and enamel. No mucosa layer was developed in this model as teeth, when loaded, act directly onto the mandible bone and the mucosa layer, surrounding the teeth, does not affect the stresses experienced.

Figure 36: Cancellous and cortical bone with sockets

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Modelling

Chapter 3

3.2.3 Construction of the Conventional Denture Model The conventional denture model of the mandible bone was initially developed with the same method as the natural mandible. Again the first stage in the development of the model was to extract the cancellous bone from the cortical bone so that the cortical bone would accurately reflect a human mandible. This model (Fig. 37) did not require sockets as there are no teeth present.

Figure 37: Conventional denture model

A mucosa layer was then developed, this was done by offsetting the top surface of the mandible. (Fig. 38) The mucosa layer did not extend all the way down the sides of the mandible for although this is not anatomically correct for the purpose of this study it was still accurate as the loads being considered act from on top of the denture and not from the side of the mandible.

Figure 38: Conventional denture model showing mucosa layer

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Modelling

Chapter 3

The adhesive layer was then generated in the same manner as the mucosa layer by use of offsetting. (Fig. 39) The denture was developed in two sections, firstly the acrylic resin portion and secondly the artificial teeth. Dentures are made by moulding a resin around the mucosa so that the denture fits comfortably for the wearer. The model was developed in roughly the same manner by offsetting the surface of the mandible to reflect it and fit comfortably. The teeth are then duplicated and set into this surface.

(Fig. 40)

Figure 39: Conventional denture model showing glue layer

Figure 40: Conventional Denture

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3.2.4 Construction of Implant-Supported Over-Denture Model The cancellous bone and the cortical bone and mucosa layers were initially taken from the conventional denture model. No adhesive layer was required in this model as the implants were used to retain the denture. The denture in this model was based upon the conventional denture. It was modified to fit the new mucosa surface as this model does not have the adhesive layer. (Fig. 41) It was then modified to contain implants.

Figure 41: Two implant supported over-denture model

In the design of the implants there were a number of issues which needed to be considered. Firstly, and most significantly, is what type of implant system to model.

Implant retained over-dentures can be retained via a number of methods. Firstly an implant system can have any number of implants most typically from two to six. The denture then can be retained by various superstructures, typically via ball or bar attachment. (Fig. 42)

Figure 42: Ball (left) and bar (right) attachments

I chose to limit the scope of this study to consider a two implant O-Ring abutment retained over-denture. (Fig. 43) I chose this one as the scope of this study only allows one design to be considered and this design and for the price that a patient can have

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Modelling

Chapter 3

these installed they receive the most benefit. It would be a possibility for the scope of other studies to consider other configurations however the scope of this study will only consider the most typical configuration. The O-Ring abutment chosen was a 4mmH, model 61165. (Replace, 2001) This was chosen because it is the most typical abutment used. (Fig. 43)

Figure 43: Two implant retained over-denture

Figure 44: Abutment Selection Flowchart showing the chosen 4mmH, model 61165 O-Ring abutment

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Chapter 3

3.2.4.1 Implant Construction The internal structure of implants is also of concern. The abutment screw does not always reach the bottom of the cavity in which it is screwed and as such there is often a gap of varying size between the abutment screw and the implant. This becomes a problem when the mandible resorbs past the end point of the screw and the denture becomes retained by a hollow support. This can, and does lead to the implant breaking. Kunavisarut C, et al. (2002) (Fig. 45) conducted a study in which he considered various screw / implant gaps and their resulting breaking probabilities. The scope of this study does not consider the implant breaking and is only considering an â&#x20AC;&#x2DC;idealâ&#x20AC;&#x2122; situation where the screw fits the implant perfectly leaving no gap.

Figure 45: Internal structure of an implant

3.3 Difficulties There were a number of difficulties faced in reconstructing the dental models, most importantly ensuring that the models generated were sufficiently sophisticated and accurate. The complex geometries made the models difficult to manipulate through all stages of the study. The teeth posed a number of difficulties, firstly in regard to their initial geometry. The teeth that were received overlapped through their adjoining teeth a little and this had to be rectified. There were two methods which could have been used to rectify this, firstly the teeth could have been realigned so that they were not overlapping and secondly they could be trimmed at the areas that they were overlapping. The later method was chosen as this was determined to be the method which posed the least change to the overall model and this would result in a lesser impact on the final model.

The teeth also caused a problem when applying a mesh. The teeth, when divided into the PDL, dentin and enamel are significantly complicated and hence are the limiting factor in applying the mesh. To overcome this there are two methods that may be employed, firstly regarding the model and secondly the method. Firstly the model could have been simplified to allow the mesh to fit it, or secondly the detail of the mesh could be reduced as a coarser mesh is more robust and can take to models with a higher degree of complexity. I decided to use the later option as this poses the least impact on the overall study.

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V{tÑàxÜ G Finite Element Analysis

Finite Element Analysis

Chapter 4

Chapter 4. Finite Element Analysis The primary objective of this study is to conduct a finite element analysis on a highly accurate three-dimensional model of the mandible and various natural tooth and denture configurations. Finite element analysis is a mathematical technique for analysing stress, which breaks down a physical structure into substructures called â&#x20AC;&#x2DC;finite elementsâ&#x20AC;&#x2122;. The finite elements and their interrelationships are converted into equation form and solved mathematically. The finite element analysis will be completed using ANSYS 10.0 SP1. This chapter will look at the methods involved in conducting this study upon the models developed.

Issues considered in this chapter are as follows: Mesh Selection, this section will consider the mesh generation and mesh selection for the model in order to obtain a highly accurate and reliable results; the forces applied to each model and discuss the rationality behind applying each force; The boundary conditions and the rationality behind these; the force angles of the forces applied; the material properties for each part of the model and denture structures and the source of each property; and to give a summary of this chapter the final finite element model will consider the complete models summarising their respective properties and the conditions which have been placed on them.

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Finite Element Analysis

Chapter 4

4.1 Mesh Selection In order to complete a finite element analysis a mesh, either shell or solid, must be first developed. This mesh is used to accurately reflect the behaviour of the model when placed under certain loads. The better the mesh selection is the better the results and prediction will be. A mesh divides the model into many pieces, after fixation points and loads are applied each piece is analysed and the localised results of each piece are combined to produce a global result. A good selection of the individual pieces is essential in yielding results that accurately mirror the biological responses evident as a consequence of loading the various dentures. For this study I have used a solid mesh to produce results that accurately reflect the internal reactions within the dental structure as a shell mesh is not sufficient for the detail required within the results. The accuracy of the analysis is directly dependent on the specific elements chosen to create the mesh. The three-dimensional finite element model containing a high order of tetrahedral elements is capable of reciprocating in vivo biological reactions. Another aspect that requires attention when creating a finite element mesh is the number of elements that will constitute the complete model. With a larger number of elements comes a higher degree of accuracy within the results. A mesh which is produced with a high resolution and a large number of elements will decrease the errors evident within the results when it replaces the modelled dental structure. However the size of the mesh determines the complexity of the mathematical problem to be solved. A very fine mesh can produce accurate results but is also resource and time consuming. With all finite element analyses a compromise needs to be made between accuracy obtained and time consumed. Many tools are available to help with this compromise such as fast finite element (FFE) solvers and the use of more powerful machines but ultimately the compromise must always be made.

The mesh used within this study is a solid mesh so that the results obtained will be accurate throughout the entire 3D model. The mesh will incorporate parabolic tetrahedral components to more accurately replicate the biological response of the dental structure to loading. A parabolic tetrahedral mesh is more effective than a linear tetrahedral mesh as a parabolic tetrahedral mesh in providing accurate results as it utilises more nodes. Where a linear tetrahedral mesh utilises four nodes, a parabolic tetrahedral mesh utilises ten nodes. These consist of four corner nodes, six mid-side nodes and six edges. (Chandrupatla et al, 2002) This method greatly enhances the finite element analysis especially when representing curved surfaces and edges.

In generating the finite element analysis model used within this study I had to consider the number and size of elements. As seen in figure 46, figure 47 and table 8 the number and size of elements can produce vastly different results. The most startling difference in the results obtained is around the area where least stress is experienced. In looking at the results in figure 47 you can see the stress patterns around the load site are relatively similar as there are large changes in stress levels and all three models detect this adequately. However as we look to the anterior of the mandible, where the least stress is experienced the model with the higher number of elements displays a range of difference not displayed by the other models. In many

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studies areas of less stress are generally not as important as high stress areas, however in this study the areas of least stress is exactly what is being looked at, and this lack of detail around the areas of least stress indicates results that are not as accurate.

Figure 46: Course and fine mesh models

Figure 47: Results of an FEA on the course and fine mesh models

Mesh Course Fine Element Size (mm) 6 1.5 Number of Elements 19749 88919 Number of Nodes 37533 151632 Table 8: Mesh details for the course and fine mesh models

Usually mesh creation is limited by the accuracy of the results obtained. The method for selecting a mesh is to do convergence checks. This is to firstly apply a mesh of respective detail and calculate the results. The mesh is then halved in size, or doubled with respect to the number of elements, and then analysed again. The results are recorded and this process is repeated a number of times. Each time the results are recorded they are analysed with respect to all the previous results. For the initial stages you expect relatively large differences in the results. The process is stopped when the differences in results with each halving of the mesh size is negligible. The reasoning behind this is that it is pointless generating a finer mesh as the difference in results is minimal.

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Finite Element Analysis

Chapter 4

In this study, due to the complexity of the model used, the mesh selection process was somewhat different. Computational time and resource usage was not an issue as I was using the computers at Leap Australia and my simulations were run overnight. The limiting factor in the mesh selection was simply which mesh would work. Due to the complexity of the models extremely fine meshes simply could not be applied. I had to keep increasing the element size until the mesh was successfully applied. The models involving dentures were not as complicated as the natural mandible model and hence a finer mesh could be applied to these. However for consistency, since the results I was striving for were comparative, I applied the same mesh to each model. The final mesh details can be seen in table 9. A mesh of this size is capable of producing results that accurately mimic the biological response of the mandible to the loads applied.

Mesh Details Model Nodes Elements

Natural Dentitions Conventional Denture Implant-Restrained Over-Denture 152781 111809 207432 88838 62461 121904 Table 9: Mesh details for finite element models

4.2 Forces The primary objective of this study is to generate a greater understanding of the reduced stress experienced within the mandible due to the cushioning effect of the denture. The reduced stress experienced inside the mandible not only is due to the cushioning effect of the denture but also because the patient cannot bite as hard. This factor has been taken into account in this study.

4.2.1 Magnitude The bite forces of seven groups of people were analysed in a study by FontijnTekamp et al (2000). These groups consisted of female subjects in two over-denture groups, two full-denture groups and three groups with natural dentitions. All edentulous subjects had a full maxillary denture and, in the mandible either an implant-retained over-denture on two permucosal, cylindrical IMZ implants or a transmandibular implant (implant group); an over-denture on at least 2 functional, natural bare roots in the mandible (root-overlay group); a conventional, full denture with a mandibular symphyseal bone height between 9 and 15mm (full denture grouplow mandible); or a conventional, full denture with a mandibular symphyseal bone height above 16mm (full denture group-high mandible). Subjects in the naturaldentition groups had either: a shortened dental arch with all anterior teeth present and three or four occluding pairs of premolars (shortened-arch group); a complete-natural dentition and ages comparable with those of the groups described previously (complete arch- group-old); or a complete-natural dentition group composed of dental students (complete-arch group-young) Figures 48 and 49 show the results of the study by Fontijn-Tekamp et al (2000).

Figure 48 shows the maximum bite force possible by each group while figure 49 shows the average ‘when chewing’ bite force of each group. As the ‘when chewing’

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state is the most common for a mandible to exist in this study has considered these figures for analysis. The groups or interest are complete arch (old), implant and full dentures (high). The older group was chosen to eliminate any discrepancy in the results caused by a simulated difference in age of the models and the high arch was chosen for the models, for reasons described in chapter three, have a high arch. The final values for the forces used can be seen in table 10

Figure 48: Maximum unilateral bite forces

Figure 49: Unilateral bite forces at the force level â&#x20AC;&#x2DC;as when chewingâ&#x20AC;&#x2122;

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Finite Element Analysis

Tooth Pre Molar Canine Central Incisor

Natural Mandible 125 80

Chapter 4

Bite Forces (N) Implant-restrained overdenture 70 50

Conventional Denture 37 20

60 40 Table 10: Forces used in the finite element models

16

4.2.2 Angle The angle of the forces acting on the teeth, although pertinent to the stresses experienced in the mandible, are considered but not modelled in this study. This is because due to the nature of the model and in particular the rotation joint the biting forces are naturally added into the analysis.

4.2.3 Location The biting force of a human mandible is generated predominantly by the masseter which â&#x20AC;&#x2DC;pullsâ&#x20AC;&#x2122; the mandible from the bottom posterior of this bone. In order to produce results which are clinically valid this condition must be modelled accurately.

Figure 50: Muscles connected to the human mandible

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To reproduce the condition found in clinical situations the forces have been applied at the same location that the masseter acts. (Fig. 50) This allows the models to ‘act’ like a real mandible and also creates a situation where the results generated are replications of the results that would be found in a clinical study.

Figure 51: Force location of finite element model

4.3 Boundary Conditions Boundary conditions are essential for a FEA to produce consistent and accurate results. Boundary conditions ensure that the dental model does not translate or rotate in an undesirable manner whilst undergoing loading. The boundary conditions set for this study can be seen in figure 51.

A rotational point has been set at the upper back of the mandible. Although this joint in clinical situations is a sliding joint, the rotational joint modelled (Fig. 52) reflects the clinical situation accurately enough to be valid. The other aspect of the boundary conditions is the model of the food. (Fig. 52, Fig. 53)) This is an object placed upon the selected tooth in order to provide resistance, or act as ‘food’. It was set with the material properties of 5 MPa for Young’s modulus and 0.3 for Possion’s ratio which estimates a soft rubber like substance as food would be. Although denture wearers cannot chew food which is as hard as food chewable by people with natural dentitions the food modelled for each of the finite element models is the same so that the differences in stress experienced in the mandible is not cause by a difference in the

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Finite Element Analysis

Chapter 4

food but rather the cushioning effect of the denture and the decreased chewing ability.

Due to the soft nature of the food block it does experience deformation during the simulations, which does accurately simulate a clinical situation. The food block doesnâ&#x20AC;&#x2122;t move though as the top surface is rigidly fixed while the rest of it is allowed to move which allows for the compression.

Figure 52: Locations of rotational joint components which where fixed in the X, Y and Z space and allowed to rotate

Figure 53: The modelled â&#x20AC;&#x2DC;foodâ&#x20AC;&#x2122; over the pre-molar

4.4 Material Properties In order for the finite element analysis results to be accurate the components within the models must act realistically. To achieve this, material properties must be assigned to the various components. The components include, in the mandible, the cancellous bone and the cortical bone, in the tooth region, the PDL, pulp, dentin, enamel and mucosa, of the dentures, the acrylic resin, which make up the body of the denture, the adhesive which sits between the mucosa and the denture and the artificial teeth, and the implants.

To obtain the material properties biomaterial testing was conducted upon human dental structures. From these tests the major mechanical properties attained were

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Finite Element Analysis

Chapter 4

Young’s Modulus and Poisson’s Ratio. These are the properties essential for obtaining a structural response within the dental structures. Young’s Modulus is the constant of proportionality between stress and strain. Units of this quantity are the same as stress, ie. force per unit area and Poisson’s ratio is the ratio of lateral strain to longitudinal strain. The material properties in this study were taken from a variety of published sources. The enamel, dentin, PDL, cancellous bone and cortical bone were taken from Three-dimensional finite element stress analysis of the dentate human mandible, (Korioth et al, 1992) the Mucosa layer, denture liner, acrylic resin and titanium prosperities from Finite element analysis of stress relaxation in soft denture liner. (Sato Y, et al. 2000) The final finite element model used in this study will incorporate orthodontic loading conditions, boundary conditions and set material properties in order to accurately simulate biomedical consequences of masticatory forces.

4.5.1 Specific Material Properties The components that were considered in terms of Young’s modulus and Poisson’s ratio in this study were, in the mandible, the cancellous bone and the cortical bone, surrounding the tooth structure, the PDL, pulp, dentin, enamel and mucosa, making up the denture structure the acrylic resin, which makes up the bulk of the denture, the adhesive, which acts as a glue and also to better the fit of the denture and the artificial teeth and also the components of the implants including the titanium, the gold screw, gold alloy, type III and the Co-Cr alloy which makes up the framework.

The PDL properties used within this study will be a standardised value lying inbetween that of an adult and of an adolescent. This is because results obtained from previous PDL property determination tests have shown them to be comparable.

(Tanne et al. 1998) Both the adult and the adolescent PDL respond to orthodontic loads in a normal manner in a clinical environment however adult orthodontic treatment requires a greater treatment period. (Tanne et al. 1998) Therefore we will use a standardised value between the adult and adolescent PDL mechanical prosperities in this study of 1.18 MPa for Young’s modulus and 0.3 for Possions ratio.

Based upon numerous studies and the consensus of a majority of similar finiteelement analyses, it is generally considered that the cortical and cancellous bones are isotropic, homogeneous and linearly elastic. The values of these structures were also taken from a consensus of published texts and are assumed to be, for the cancellous bone, 490 MPa for Young’s Modulus and 0.3 for Possions Ratio, and for the cortical bone 14700 MPa for Young’s Modulus and 0.3 for Possions Ratio.

The implants chosen for modelling in this study are cylindrical implants with a 3.75mm diameter. The apex of which were modelled to be in contact with the lower cortical layer, this is a comparable situation to which would be found in a clinical situation. The implants were installed in the region of the former canines, again correlating to a clinical installation. The implant system was assumed to be made of titanium with a Young’s modulus of 110 GPa and a Possion’s Ratio of 0.35. A fixed bond between the implant and the bone was applied along the entire interface. This

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means that any relative motion between the bone and the implant will not occur under any loading. The material prosperities for the components comprising the tooth and the denture were determined through a survey of literature of similar finite-element studies. All of the materials used within this study constitute a linear static analysis and are all of a homogeneous, isotropic nature. They have been obtained using an ultrasonic method and are summarised in Table 11. The ‘food’ object material properties were determined by studying the material properties of various foods and estimating an average soft food substance. The material properties settled on were 5 MPa for Young’s Modulus and 0.3 for Possions ratio. These simulate a soft rubbery object much like that of a soft food substance.

Structure

Young’s Modulus

Possions Ratio

Mandible

Cancellous Bone Cortical Bone

490 14700

0.30 0.30

Teeth

PDL Pulp Dentin Enamel Mucosa

1.18 2.03 14700 84100 2.5

0.45 0.45 0.31 0.33 0.40

Denture

Acrylic Resin Glue Artificial Teeth

2650 10 82.8

0.30 0.30 0.35

Implants

Titanium Gold Screw Type III gold alloy

110 112 99.3

0.35 0.35 0.35

Co-Cr allow (framework)

218

0.30

Food

Food block 5 Table 11: Material properties used throughout this study

0.30

4.6 Complete Finite Element Model.

The three-dimensional models completed for finite element analysis in this study will enable a highly accurate study of the biological responses to biting forces for people with natural dentitions, conventional dentures and implant-restrained over-dentures.

The natural dentitions model consists of 152,781 nodes and 88, 838 elements, the conventional denture model consists of 111, 809 nodes and 62, 461 elements and the implant-restrained over-denture consists of 207,432 nodes and 121,904 elements.

(Table 12) The mesh which comprises these nodes and elements has a size of 1.5mm for all models. (Fig. 46) The boundary conditions set in all the models fix the upper rear of the mandible in X, Y and Z space but allow for rotation. (Fig. 54) The forces applied are relative to the tooth being compressed. (Table 13) The material properties set accurately reflect the material properties found in clinical condition. (Table 14) The complete finite element models can be seen in figure 54 which shows the three models complete with their boundary conditions and force locations.

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Finite Element Analysis

Model Nodes Elements

Tooth Pre Molar Canine Central Incisor

Chapter 4

Mesh Details Natural Dentitions Conventional Denture Implant-Restrained Over-Denture 152781 111809 207432 88838 62461 121904 Table 12: Final mesh details for finite element models

Natural Mandible 125 80

Bite Forces (N) Implant-restrained over-denture 70 50

Conventional Denture 37 20

60

40

16

Table 13: Final forces used in the finite element models

Structure

Youngâ&#x20AC;&#x2122;s Modulus

Possions Ratio

Mandible

Cancellous Bone Cortical Bone

490 14700

0.30 0.30

Teeth

PDL Pulp Dentin Enamel Mucosa

1.18 2.03 14700 84100 2.5

0.45 0.45 0.31 0.33 0.40

Denture

Acrylic Resin Glue Artificial Teeth

2650 10 82.8

0.30 0.30 0.35

Implants

Titanium Gold Screw Type III gold alloy

110 112 99.3

0.35 0.35 0.35

Co-Cr allow (framework)

218

0.33

5

0.3

Food

Food object

Table 14: Final material properties used throughout this study

Figure 54: All three final models Complete with boundary conditions and force locations

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V{tÑàxÜ H Results

Results

Chapter 5

Chapter 5. Results This chapter documents the results found from the completion of the finite element analysis upon the three-dimensional models of the natural dentition, the conventional denture and the implant-restrained over-denture. The biological consequences from all models will be focused upon in term of Von Mises stress, first principle stress and strain. Discussion of the results will not be provided in this chapter. This chapter will merely document the results found, a discussion including comparisons will be conducted in the next chapter. The highly detailed nature of the models created is a major factor in insuring that the results generated by the finite element analysis achieve clinical validity. The results provided by this study support and supplement previous research conducted into the biomedical consequences of biting forces on the mandible. The first section of this chapter will cover aspects of the results which are relevant to their validity and which must be considered with viewing the results. This chapter will then consider the models and will look at the biomedical consequences of biting forces on each. The final section will summarise the results in a tabulated format for ease of reference.

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5.1 Notes on results This section will cover aspects of the results that need to be considered when reading the results. These include how the average stresses and strains were calculated, the scales relevant when viewing the figures and the language used to describe the results.

5.1.1 Technique of Averaging To compare two different models, or sets of results, one method is to look at a number of points and compare these points to the corresponding points on the other models.

This study has approximated this method by looking at certain points on each model and averaging them to compare the averages. Each model was divided into three parts, the anterior part being in-between the canine teeth and the side parts being inbetween the canine and the second molar. The stresses experienced in these three sections are then averaged. This method makes it easier to see the differences between the models. The maximums in each region are also taken into consideration for a better understanding of the biological response experienced.

5.1.2 Scale of Figures The figures shown in this chapter are at differing scales. This is to allow a greater understanding of the stress and strain distribution of each of the models. The graphs are also of differing scales. Some scales are logarithmic to display the results clearer while others are linear.

5.1.3 Side Reference The results make numerous references to the stresses and strains on the sides of the mandible. These references are in the form of working and non-working side. The working side is side which is being loaded by the food object.

5.1.4 Stresses Analysed There are three types of stresses and strains considered in this study. These are the Von Mises stress, first principle stress and first principle strain. The first principle stresses and strains consider the directional aspects involved while the Von Mises stress considers only the magnitude of the stress. The three aspects are considered in the results section to provide a comprehensive overview of the biomedical reactions to the biting forces. The discussion and analysis considers only the Von Mises stress as this only considers the magnitude aspect of the stresses involved and is directly related to the resorption of the mandible.

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5.1.5 Load Reference.

Throughout the results a load on the various models is referred to. This load is an effective load created by the relative food object and the force acting up on the bottom of the mandible.

5.1.6 Local / Global Comparisons This study makes reference to numerous local and global results. The local results refer to the stresses found around the area which is being virtually loaded by the food object. This area extends half way down the mandible side and anteriorly to the midpoint of the tooth in-front of the loaded tooth and posteriorly to the mid-point of the tooth behind the loaded tooth.

The global reactions refer to the stresses experienced by the entire mandible when a tooth is being loaded. The global analysisâ&#x20AC;&#x2122;s consider stresses experienced in the three sections referred to in section 5.1.1 as a result of each specific tooth being loaded.

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5.2 Natural Dentition Model This section will cover the biological reactions taking place in the natural dentitions model in the cortical and cancellous bone for loads being placed on the molar, (Fig.55) the canine and the incisor. These results will consider the Von Mises stress, first principle stress and strain for both the local area around each of the loads and the global reaction caused by the loads.

5.2.1 Cortical Bone Reaction of Loading on the Molar

Figure 55: Natural dentition model with loading on the molar

The cortical bone was analysed using the finite element method for Von Mises stresses, principle stresses and principle strains. These stresses and strains directly influence the remodelling of the bone, both the cortical and cancellous. These stresses and strains endured in the cortical bone structure are substantial as they provide an indication of the localised characteristics and the degree of resorption experienced in the cortical bone. The degree of which is directly dependent on the magnitude of the stresses and strains induced.

In the cortical bone we see (Fig.56) a high concentration of stress located around the base the molar which is being loaded. This is a desirable result as it is expected that the tooth will act directly on the bone structure resulting in high stress concentrations.

The maximum Von Mises stress within the cortical bone structure is 17MPa. This stress reduces around half way down the cortical bone where the stresses range from 1MPa to 3MPa and then increases slightly at the bottom of the cortical bone, averaging around 3.5 MPa which is due to the masseter acting up on the mandible.

This stress is located around the base of the pre-molar tooth and dissipates with distance away from the loaded molar.

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Figure 56: Von Mises stresses on cortical bone structure from molar loading â&#x20AC;&#x201C; Natural dentition model

The first principle stresses within the cortical bone show the specific stress mechanisms of compression and tension present in the structure. In the cortical bone structure there exists levels of both tensile and compression stresses. The cortical experiences mainly compression forces locally around the base of the loaded molar reaching around 0.6MPa and averaging 0.4MPa. The strains experienced within the cortical bone structure reflect the stresses present within the structure. The strains experienced by the cortical bone structure directly affect the occurrence of the resorption, or in this case particularly the maintaining of the bones integrity. The strains experienced by the cortical bone locally around the loaded molar reach 2.4*10-4m/m close to the apex of the bone and average 2.0 *104 m/m for the local area.

Figure 57: First principle stress (left) and strain (right) in cortical bone structure from molar loading â&#x20AC;&#x201C; Natural dentition model

The Von Mises stresses experienced by the cortical bone are significant to the analysis of the resorption process. The magnitude of the Von Mises stress experienced locally around the loaded molar is not maintained globally however a relatively high level of Von Mises stress is found throughout the cortical bone. The lowest level of

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stress concentration is found forward of the loaded molar around a third of the way down the mandible side. Here the value of the Von Mises stress reaches around 0.3MPa. This level of stress is not reflected around the rest of the cortical bone structure however, the anterior of the mandible averages 2.7MPa and reaches up to 6.2MPa in isolated locations. non-working side also maintains a high level of Von Mises stress. With a maximum of 7.3MPa it averages around 3.2MPa. The First Principle stress maintains reflects the trend of the Von Misses stress globally. (Fig. 57) There exists a region of low tensile stress concentration in anterior of the loaded molar towards the bottom of the mandible which reaches up to 0.0073MPa in tensile stress. The majority of the mandible experiences compression stress. Above the region of tensile stress on the working side of the mandible the cortical bone experiences an average of 1.7MPa in compression stress. The anterior of the mandible experiences both compression and low tensile stress. Ranging from an average of 0.0032MPa, but reaching up to 0.0092MPa in tension to an average of 2.0MPa and reaching up to 2.7MPa in compression.

Considering stresses globally the highest stress concentration away from the loading point is found on the non-working side. The stresses around the base of the molars in the cortical bone reach 9.0 MPa, however this is relatively localised, the region around this maxima averages around 5.0 MPa while on the non-working side of the mandible the stress concentration in the cortical bone structure averages around 1.8MPa in compression with a small region reaching as low as .037MPa The strain concentration globally is also reflective of the global stress concentrations.

(Fig. 57) These strains are a consequence of the loading conditions placed upon the system. Areas of high stress are reflected by areas of high strain. Areas of high strain are present where there are areas of high tensile and compressive strains. The region of low stress concentration of the lower section of the working side of the mandible is present with the stress in this area approaching 1.0*10-5m/m. The higher strain region on working side of the mandible reaches 2.14*10-4m/m while it averages around 1.8*10-4 m/m. The anterior section of the cortical bone structure experiences stresses as high as 2.05*10-4 m/m but averages around 1.5*10-4 m/m. The stress concentration in the non-working side of the cortical bone structure reaches 4.4*10-4 m/m and averages 1.5*10-4 m/m throughout the mandible.

On first inspection these stresses experienced by the cancellous bone appear to be lower than those experienced by the cortical bone structure. This difference is present due to the different material properties of the cancellous and cortical bone structures and is reflective of results gained by clinical inspection.

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5.2.2 Cancellous Bone Reactions of Loading on the Molar The Von Mises stress is concentrated around the loaded molar is the cancellous bone reflecting the stress pattern found in the cortical bone structure. (Fig. 58) The highest Von Mises stress found in the local area being 0.44MPa which is lower than the stress experienced by the cortical bone structure. The average Von Mises stress found in the local region is 0.22 MPa.

Figure 58: Von Mises stresses on cancellous bone structure from molar loading â&#x20AC;&#x201C; Natural dentition model

The first principle stress found in the local region consists of both tensile and compressive stress. Behind the loaded molar there is an area of tensile stress caused by the loading being effectively placed at a forward angle due to the rotational joint, (Fig. 59) the peak tensile stress being 0.044MPa. The majority of the stress however is compression stress, reaching 0.24MPa inside the tooth cavity but averaging only 0.041MPa for the area surrounding the tooth.

Figure 59: First principle stresses on cancellous bone structure from molar loading â&#x20AC;&#x201C; Natural dentition model

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Figure 60: First principle strains on cancellous bone structure from molar loading â&#x20AC;&#x201C; Natural dentition model

The strain pattern show a high concentration of strain inside the tooth socket. (Fig.60) This reaches 6.4*10-4m/m. The average for this area though is 1.2*10-4m/m.

Considering the Von Mises stress pattern globally there is a relatively high amount of stress throughout the cancellous bone structure. (Fig. 61) Surprisingly we find the maximum point at the anterior of the mandible where it reaches 1.6MPa. The average for this area is only 0.11MPa so this is a very localised high spot. On the working side of the mandible we see a large area of high stress concentration. The maximum in this region is only 0.44MPa but this is fairly well distributed averaging 0.15MPa for the region. The non-working side of the mandible peaks at 0.18MPa and averages 0.71MPa.

Figure 61: Von Mises stresses on cancellous bone structure from molar loading â&#x20AC;&#x201C; Natural dentition model

The maximum first principle stress also occurs at the anterior of the mandible in the cancellous bone structure. (Fig.62) This maximum is 1.3MPa, and is fairly well distributed throughout the anterior section averaging 0.9MPa. The working side,

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which is being loaded at the molar has a high stress point toward the bottom of the cancellous bone structure of 0.16MPa, and averages 0.085MPa. The non-working side peaks at a relative high 0.16MPa and this stress is well distributed throughout the side averaging 0.078MPa.

Figure 62: First principle stress (left) and strains (right) on inside of cancellous bone structure from molar loading â&#x20AC;&#x201C; Natural dentition model

The strain distribution also shows a maximum concentration at the anterior of the mandible. The strain here reaches 2.6*10-3m/m, the average strain for the anterior section of the mandible is 1.3*10-4m/m. This strain is relatively well distributed throughout the cancellous bone structure, the sides reach a maximum strain value of 3.3*10-4m/m and 6.8*104m/m for the non-working and working sides respectively and average 8.2*10-5m/m and 9.8*10-4m/m.

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5.2.3 Cortical Bone Reactions of Loading on the Canine

Figure 63: Natural dentition model with loading on the canine

With the virtual load being placed in the canine (Fig.63) the highest level of Von Mises stress is found locally at the base of the loaded canine tooth where it reaches 5.3 MPa. (Fig. 64) The stress concentration drops off quickly though averaging 1.5 MPa for the local area.

Figure 64: Von Mises stresses on cortical bone structure from canine loading â&#x20AC;&#x201C; Natural dentition model

Locally the first principle stress reaches 1.1MPa in compression however this maxima is an isolated high as the average first principle stress around the loaded canine is 0.12MPa. (Fig. 65) in compression which is closely neighboured by low tensile stresses due to the localised nature of the force acting downwards on the canine tooth causing a small bending moment between itself and the simulated masseter muscle acting up on the posterior of the mandible causing a small degree of tensile stress.

The strain experienced locally is relatively low reaching only 1.2*10-4m/m towards the junction of the cortical bone and the canine tooth, the local area maintains the stress averaging 7.8*10-5m/m.

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Figure 65: First principle stress (left) and strain (right) cortical bone structure from canine loading â&#x20AC;&#x201C; Natural dentition model

Globally the Von Misses concentration in the cortical bone when the canine is loaded is relatively low. There is high stress concentration to the posterior of the mandible on the working side where it reaches 4.3MPa, the average of this side however is 1.5MPa. On the non-working side, the side has a lower stress concentration averaging 1.2MPa and reaching only 1.62MPa. The anterior area of the mandible understandably experiences higher levels of stress concentration as this is the area in which the loading is located. The stress at the anterior of the mandible reaches 5.3MPa and averages 2.1MPa. Globally the majority of the stress experienced is acting in compression. (Fig. 65) The posterior of the mandible on non-working side to the loading experiences a high concentration of first principle stress. This is due to the high stiffness of the cortical bone resisting the bending moment created and being compressed due to the force at the bottom of the mandible due to the masseter muscle, here the stress reaches 4.6MPa. The average first principle stress for this region however is only 1.2MPa in compression and no tensile stress occurs in this region. There is a small amount a tensile stress to the posterior of the region however the scope of this study is only concerned with the area under the teeth and dentures. The first principle strain is high in comparison to its maximum in that there is not much differentiation between its maximum and the average. On the working side of the mandible the strain reaches 1.2*10-4m/m and averages 6.7*10-5m/m. At the anterior of the mandible strains of 1.2*10-4m/m is also experienced but averages slightly lower with 4.9*10-5m/m. The non-working side of the mandible reaches strains up to 2.4*10-4m/m. However this is quickly dissipated as this side averages 1.0*10-4m/m.

5.2.4 Cancellous Bone Reactions of Loading on the Canine The local Von Mises stress concentrated around the loaded canine in the cancellous bone reaches 0.29MPa and averages 0.075MPa. (Fig. 66) The first principle stress reaches 0.071MPa at the canine which is being loaded and the local area stress reaches 0.018 ?Pa. The strain around the canine tooth reaches 6.5*10-4m/m and but this stress is very localised inside the tooth socket and drops very quickly locally for the average strain for the local area is 6.9*10-4m/m. (Fig. 67)

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Figure 66: Von Mises stresses on cancellous bone structure from canine loading â&#x20AC;&#x201C; Natural dentition model

Figure 67: First principle stress (left) and strains (right) on cancellous bone structure from canine loading â&#x20AC;&#x201C; Natural dentition model

The concentration of Von Mises stress is a maximum at the anterior of the mandible where it reaches 0.68MPa however this is fairly localised, the average of the anterior of the mandible reaching 0.061MPa. There is a high level of stress concentration on the non-working side of the mandible to the posterior, where although the maximum only reaches 0.086MPa the average is relatively high at 0.071MPa. The working side of the mandible has lower stresses, reaching 0.12MPa but averaging only 0.036MPa. The first principle stress is well distributed throughout the cancellous bone structure.

There is a large area of high stress concentration to the posterior of the non-working (loaded or unloaded?)side of the structure where it reached 0.1MPa, this side only averages 0.04MPa though. The maximum first principle stress is experienced at the anterior of the mandible at 0.3MPa, this is not well distributed though as the average is 0.043MPa. The working side reaches 0.14MPa and averages 0.019MPa. The first principle strain is also heavily concentrated to the working side of the mandible. The maximum strain on this side is 2.1*10-4m/m, and this is fairly well

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distributed throughout the cancellous bone structure, averaging 9.3*10-5m/m. The anterior section of the mandible is where the strain concentration is the highest, reaching 6.5*10-5m/m, and averaging 8.3*10-5m/m. The working side of the mandible reaches 1.2*10-4m/m but only averages 3.8*10-5m/m.

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5.2.5 Cortical Bone Reaction of Loading on the Incisor

Figure 68: Natural dentition model with loading on the central incisor

When the loading is placed on the incisor (Fig. 68) there are high Von Mises stress concentrations visible in the incisor tooth which is being loaded however these stresses are not transferred to the cortical bone. (Fig. 69) This can be for a number a reasons including differences in material properties but most likely the bulk of the stress is being transferred to the cancellous bone. While we can see stresses up to 9.5MPa being experienced by the base of the tooth the maximum stress encountered in the cortical bone locally around the loaded incisor is 3.5MPa. Locally this is transferred well into the cortical bone with the local area around the loaded incisor averaging a stress concentration level of 2.3MPa.

Figure 69: Von Mises stresses on cortical bone structure from central incisor loading â&#x20AC;&#x201C; Natural dentition model

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Figure 70 shows a high instance of tensile stress located at the forward base of the incisor (0.8 MPa). This maximum is present due to the angle of the central incisor as it would pivot around the intersection of the tooth and the cortical bone and the root of the tooth would create tension with the anterior part of the cortical bone. This instance of stress is however very small and localised as the majority of the stress occurrence in the region local to the loaded incisor is in compression again due to the angle of the central incisor, which faces forward, pushing down on the anterior part of the cortical bone. The local compressive stress reaches 1.2MPa but only averages 0.1MPa. The strain experienced locally is relatively low but consistent. The maximum strain experienced locally is only 0.02*10-4m/m but this is transferred well into the cortical bone with the local average around the loaded central incisor being 0.7*10-5m/m

Figure 70: First principle stress (left) and strain (right) cortical bone structure from central incisor loading â&#x20AC;&#x201C; Natural dentition model

The Von Mises stress caused by the loading of the central incisor is transferred well into the cortical bone structure. At the anterior of the mandible the cortical bone experiences the highest level of stress concentration reaching 3.5 MPa however the average stress concentration drops to 0.85 MPa. The sides of the mandible maintain a higher average stress level, the non-working side average Von Mises stress is 1.2 MPa and reaches 1.5 MPa while the working side has an average of 1.1 MPa and reaches 1.4 MPa. The anterior section of the mandible experiences the lowest average of first principle stress, it reaches 1.2MPa in compression but averages only 0.15MPa in compression.

The non-working side and working side average, in compression, 0.4MPa and 0.38MPa respectively. Both sides have a high stress concentration point toward the posterior of the mandible behind the molar where the stresses reach, in compression, 3.0MPa and 2.8MPa respectively. The global instance of first principle strain is consistent throughout the mandible. At the anterior of the mandible the strain reaches 2.0*10-5m/m and averages 4.0*10-5m/m. The sides of the mandible retain a relatively high level of strain, averaging for the non-working side and working side respectively 5.0*10-5m/m and 4.0*10-5m/m with maximums of 1.7*10-4m/m and 1.75*10-4m/m.

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5.2.6 Cancellous Bone Reactions of Loading the Incisor The Von Mises stress concentration is at its highest at the site of the loaded incisor.

Here the stress reaches 0.47MPa, the local average Von Mises stress is 0.045MPa. (Fig. 71) The maximum first principle stress is also found at the base of the loaded incisor. Here the maximum stress is 0.53MPa but only averages 0.012MPa. (Fig. 72) The maximum strain point is also found at the base of the incisor which is being loaded. Here it reaches 8.6*10-4m/m but the local area only averages 3.8*10-4m/m.

Figure 71: Von Mises stresses on cancellous bone structure from central incisor loading â&#x20AC;&#x201C; Natural dentition model

Figure 72: First principle stresses (left) and strains (right) on cancellous bone structure from central incisor loading â&#x20AC;&#x201C; Natural dentition model

The maximum concentration of Von Mises stress is found at the anterior of the mandible. Here the stress reaches 0.47 MPa, this stress is not transferred relatively

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well as the average stress for the anterior section is only 0.031MPa. The sides also experience relatively low levels of stress, reaching 0.055MPa and 0.066MPa for the non-working and working side respectively and averaging 0.033MPa and 0.029MPa. The maximum principle stress distribution is focused towards the posterior of the mandible. The non-working side peaks at 0.081 MPa while the working side peaks at 0.075 MPa. The averages for these sides are 0.018 MPa and 0.017 MPa respectively.

The maximum first principle stress is experienced at the anterior of the cancellous bone structure. here the maximum stress is 0.53 MPa but only averages 0.012MPa Under the loaded central incisor the first principle stress reaches 0.53 MPa but this dissipates rapidly with distance as the average is only 0.011 MPa. The strain concentration reflects the stress concentration found in the cancellous bone structure. There are high strain concentrations found at the posterior of both sides of the mandible but the maximum point is located at the anterior underneath the loaded central incisor. Here the strain reaches 8.6*10-4m/m and averages at 3.1*10-4m/m. The sides reach 1.3*10-4m/m and 1.4*10-4m/m for the non-working and working sides respectively average at 4.9*10-5m/m and 3.0*10-5m/m.

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5.3 Conventional Denture Model This section will cover the biological reactions taking place in the conventional denture model in the cortical and cancellous bone for loads being placed on the molar, the canine and the incisor. These results will consider the Von Mises stress, first principle stress and strain for both the local area around each of the loads and the global reaction caused by the loads. The first part of this section will consider the biological reactions due to virtual loading on the second molar. (Fig. 73) 5.3.1 Cortical Bone Reactions of Loading on the Molar

Figure 73: Conventional denture model with loading on the molar

The cortical bone experiences its highest level of stress concentration slightly to the posterior of the molar which is being loaded. (Fig.74) This is possible due to the manner in which the mandible rotates upwards causing a greater force to come from the posterior of the tooth. The stress in this region reaches 2.7 MPa. The local region does not experience the same level of stress concentration. The immediate area under the denture quickly drops to an average of 1.2 MPa while the stresses about a quarter of the way down the mandible average about 0.7 MPa.

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Figure 74: Von Mises stresses on cortical bone structure from molar loading â&#x20AC;&#x201C; Conventional denture model

An analysis of the first principle strain of the cortical bone structure shows an interesting result in regard to the location of compressive and tensile stresses. There exists a relative high concentration, up to 0.05MPa, of tensile stress around a location which by inspection should be undergoing compression. This however is due to the nature of the denture. The relative force acting downwards on the denture is distributed forward along the denture and consequently down upon the anterior section of the mandible. This results in tensile stress being experienced towards the posterior of the mandible. (Fig.75) There is compression stress also present in the local region of the loaded molar of up to 1.35 MPa The mandible experiences its highest magnitude of first principle strain locally to the load area. The strain reaches 0.17*10-4m/m this however dissipates quickly averaging 5*10-5m/m locally around the load site.

Figure 75: First principle stress (left) and strain (right) cortical bone structure from molar loading â&#x20AC;&#x201C; Conventional denture model

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The Von Mises stress concentration is highest at the base of the loading, however it is also significantly (2.3 MPa) at the posterior of the denture on the non-working side.

There is a region of extremely low stress concentration dropping to values as low as 0.15MPa forward of the loading point, half way down the what? side of the mandible.

On the loaded side the average stress concentration experienced by the cortical bone is 0.67MPa. This increases slightly to the anterior of the mandible averaging around 1.0MPa but drops again, only slightly on the non-working side to an average of 0.9MPa. The region of tensile stress on top of the cortical bone expectantly causes a relative high level of compression stress towards the anterior of the mandible. This strain reaches up to 1.2MPa in compression but at the anterior still only averages 0.28 MPa in compression. The working side experiences an average stress of 0.4MPa in compression while the non-working side, although experiencing 2.6MPa in compression averages globally 0.4MPa. There are relative high levels of strain experienced below the denture to the posterior of the mandible. These reach 0.17*104 m/m on both sides. Strains of this magnitude are not however repeated throughout the mandible with the sides averaging 2.0*10-5m/m and 3.5*10-5m/m for the working and non-working side respectively. The anterior of the mandible experiences a stress of 8.9*10-5m/m and averages 2.5*10-5m/m.

5.3.2 Cancellous Bone Reactions of Loading on the Molar The Von Mises stress underneath the loaded molar is relatively low reaching only 0.0025MPa. (Fig.76) The average for this area is also very low due to the cushioning effect of the denture, the average Von Mises stress is 0.0014MPa. The stress under the load site is relatively low due to the dampening effect of the denture. Under the loaded molar the stress reaches 0.00059MPa, the average first principle stress in the local area being 0.00083MPa. There are relative low strain concentrations below the load site. (Fig. 77) The local maximum strain being only 1.5*10-4m/m and averaging 1.1*10-4m/m.

Figure 76: Von Mises stresses on cancellous bone structure from molar loading â&#x20AC;&#x201C; Conventional denture model

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Figure 77: First principle stress (left) and strains (right) on cortical bone structure from molar loading â&#x20AC;&#x201C; Conventional denture model

The point of highest Von Mises stress concentration is found towards the anterior of the mandible. This is due to the denture redistributing the force forward. The stress found here reaches 0.0029 MPa, the average Von Mises stress on the anterior of the cancellous bone structure is 0.0018MPa. The working side reaches 0.0025MPa under the load site, but the average stress on the working side is only 0.0011MPa. The stress on the non-working side is minimal reaching only 0.0017MPa and averaging just 0.00096MPa. The first principle stress peaks at the anterior of the mandible at 0.0035MPa, the average for this region being 0.0011MPa. The sides of the mandible have low first principle stress concentrations, peaking at 0.0028MPa and 0.00082MPa for the working and non-working sides respectively and averaging 0.0013MPa and 0.00012MPa. The maximum strain concentrations are located at the anterior of the cancellous bone structure. Here the strain reaches 5.8*10-4m/m, the average for this area is 2.8*10-4m/m. The working side has a relative high maximum at 5.6*10-4m/m but the average stress is still low at 2.3*10-4m/m. The non-working side only reaches 1.8*10-4m/m and averages 9.8*10-5m/m.

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5.3.3 Cortical Bone Reaction of Loading on the Canine

Figure 78: Conventional denture model with loading on the canine

With loading on the canine (Fig. 78) the local Von Mises stress around the loaded canine tooth is relatively high but is not the highest stress concentration in the system.

The stress under the denture local to the loading reaches 0.58MPa however this stress is quickly dissipated with the average local stress being only 0.41MPa. (Fig. 79) This is due to the denture not being able to penetrate the mandible and place stresses further down into the bone structure. The first principle stress locally around the load site is relatively low. It reaches 0.37MPa and is dissipated quickly averaging 0.16MPa. (Fig. 80) The strain pattern reflects the stress pattern in that it is dissipated quickly. Under the denture at the load site the maximum stress reached is 3.2*105 m/m. This drops quickly as you move further away from the top of the mandible, due to the conventional dentures inability to place stress into the bone structure, and averages 1.8*10-4m/m for the localised strain around the load site.

Figure 79: Von Mises stresses on cancellous bone structure from canine loading â&#x20AC;&#x201C; Conventional denture model

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Figure 80: First principle stress (left) and strains (right) on cancellous bone structure from canine loading â&#x20AC;&#x201C; Conventional denture model

The highest instance of Von Mises stress occurs to the posterior of the mandible, due to the bending moment, on the non-working side of the bone structure. The maximum here reaches 0.81MPa and the stress from this bending moment is reasonably well transferred through the cortical bone structure averaging 0.49MPa throughout the non-working side of the mandible. The working side experiences similar stress pattern although not to the same magnitude due to the loading point being closer to the bending moment. A Von Mises stress of 0.56MPa is experienced at the posterior region of the denture, due to the bending moment and this is also transferred to the working side averaging 0.23MPa. The anterior section of the mandible experiences the lowest levels of stress and geometry of the mandible and somewhat nullifies the effect of the bending moment. The maximum for this area is 0.59MPa which is caused by the loading however this is quickly dissipated and the average Von Mises stress of the anterior section of the cortical bone structure is only 0.23MPa. The maximum occurrence of first principle stress occurs to the posterior of the mandible on the non-working side. Here stresses of 0.83MPa are experienced. This stress is primarily due to the bending moment created by the loading condition. This stress drops quickly but is still transmitted well through the non-working side of the cortical bone structure averaging 0.31MPa. The working side has a similar stress distribution pattern but with a lower magnitude. The posterior of the working side reaches 0.56MPa but the average of this side is only 0.15Pa. This is still higher than the stresses experienced at the anterior of the mandible. The maximum first principle stress is 0.56MPa but the average for this region is only 0.12MPa. The global strain pattern reflects the stress pattern found. There is a maximum strain point towards the posterior of the non-working side of the mandible which is caused by the resultant bending moment from the loading conditions. This maximum, of 5.5*10-5m/m, is dissipated quickly but a relatively high level of stress is maintained throughout the side of the mandible averaging 1.9*10-5m/m. The working side reflects this at a lesser magnitude. The maximum point, which is found roughly at the same

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location is 3.8*10-5m/m while the average for the side is 1.1*10-5m/m. Although the loading is towards the anterior of the mandible this region experiences the least amount of strain. The maximum strain location for this region is located under the load point, which is the canine tooth on the denture, and is 3.2*10-5m/m. Because of the dentures inability to produce strain further down the bone structure this strain is quickly dissipated and the average strain for the anterior region is 8.9*10-6m/m.

5.3.4 Cancellous Bone Reactions of Loading on the Canine The maximum Von Mises stress point is found under the loading site. Here the stress reaches 0.00095MPa. This stress is fairly well distributed, averaging 0.00067MPa in the local area underneath the loaded canine. (Fig. 81) The first principle stress underneath the loaded canine reaches a stress point of only 0.0014MPa, the average stress for the local area is 0.00098MPa. The strain under the loaded incisor is relatively high peaking at 2.2*10-4m/m, the local average strain being 1.6*10-4m/m.

(Fig. 82)

Figure 81: Von Mises stresses on cancellous bone structure from canine loading â&#x20AC;&#x201C; Conventional denture model

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Figure 82: First principle stress (left) and strains (right) on cancellous bone structure from canine loading â&#x20AC;&#x201C; Conventional denture model

The Von Mises stress concentration reaches its maximum below the load point reaching 0.00095MPa. The average for the anterior section is 680Pa. The nonworking side has a relative high concentration of stress reaching 750Pa and averaging 430Pa. The working side, although reaching 764 Pa has a low average Von Mises stress of 340Pa. There is a small area on the non-working side of the mandible which undergoes tensile stress but the majority of the mandible undergoes compressive stress. At the anterior this stress reaches 1390Pa but only averages 780Pa. The sides of the mandible undergo much less stress reaching 170Pa and 810Pa for the nonworking and working sides respectively and averaging 80Pa. and 160Pa. The strain distribution is concentrated at the anterior of the mandible. The peak strain at the anterior reaches 2.2*10-4m/m and averages at 1.6*10-4m/m however these strains are localised to the anterior with the sides peaking at 4.4*10-5m/m and 1.6*10-4m/m and only averaging 3.1*10-5m/m and 4.8*10-5m/m for the non-working and working sides respectively.

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5.3.5 Cortical Bone Reactions of Loading on the Incisor

Figure 83: Conventional denture model with loading on the central incisor

With a virtual load placed on the incisor (Fig. 83) the stress transmitted from the incisor tooth of the mandible places stress on top of the cortical bone however this does not resonate into the bone structure in any significant way. On top of the cortical bone the stress reaches 0.42MPa. (Fig. 84) This however is only on the top surface of the cortical bone. Looking at the local area around the load point a significant area of low stress is evident directly below this local maximum. The average stress for local area is 0.36 MPa. There is very low first principle stress concentration locally around the site of the loaded incisor. (0.22MPa) with a local average also remaining low (90000Pa). The local strain concentration around the site of the load is very low.

Because the denture doesnâ&#x20AC;&#x2122;t act directly on top of the mandible the strain concentrations are very low and dissipate very quickly. The maximum strain value local to the load site is 2.1*10-5m/m and the average for this area is 1.1*10-5m/m.

(Fig. 85)

Figure 84: Von Mises stresses on cortical bone structure from canine loading â&#x20AC;&#x201C; Conventional denture model

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Figure 85: First principle stress (left) and strains (right) on cortical bone structure from canine loading â&#x20AC;&#x201C; Conventional denture model

The maximum occurrence of Von Mises stress is caused by the bending moment, which arises from the loading conditions of the mandible. The stress caused by the virtual load acting down in anterior of the denture does not produce stress of any significance. The maximum stress concentration is 0.63MPa and is found to the posterior of the non-working side of the mandible. This stress is transferred through the side of the mandible averaging 0.19MPa. The other side of the mandible mirrors this stress pattern. The stress on the working side only reaches 0.52MPa and the average for this side is 0.18MPa. This is still higher than the anterior region of the mandible which does experience a high level of stress on the top surface of the cortical bone of 0.42MPa however this stress does not maintain through the cortical due to the dentures having no presence inside the bone structure and the average for this region drops to 0.13MPa. Reflecting the Von Mises stress pattern the highest instance of first principle stress occurs to the posterior of the non-working side of the mandible, underneath the posterior of the denture. This again is due to the bending moment created and not the force acting down on the denture. This maximum is 0.63MPa, and is resounded through the non-working side of the denture averaging 0.19MPa throughout the cortical bone structure. Again the working side mirrors the stress pattern to a lesser degree. The maximum here is 0.52MPa and average is 0.18MPa. The lowest concentration of stress is found in the anterior of the mandible. The maximum here reaches 0.22MPa and averages 3400Pa. The strain concentration is also concentrated around the posterior of the mandible due to the bending moment created. The strain concentration is lowest at the anterior of the mandible reaching only 2.1*10-5m/m and averaging 6.3*10-6m/m. On the sides the strain concentration is highest, especially on the non-working side of the mandible. The maximum on the non-working side is 4.1*10-5m/m whereas the maximum on the working side, which is located in relatively the same location, is 3.4*10-5m/m. The average for both are 1.3*10-5m/m and 1.8*10-5m/m respectively.

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5.3.6 Cancellous Bone Reactions of Loading on the Incisor The Von Mises stress under the loaded incisor reaches 650Pa but dissipates quickly, averaging 340Pa in the area local to the load. (Fig. 86) The local first principle stress under the central incisor reaches 890 Pa and is fairly well distributed through the local area averaging 510Pa. (Fig. 87) The local strain pattern reflects the local stress pattern. The maximum stress reached under the loaded incisor is 1.4*10-4m/m, and the local area average strain is 1.1*10-4m/m.

Figure 86: Von Mises stresses on cortical bone structure from incisor loading â&#x20AC;&#x201C; Conventional denture model

Figure 87: First Principle stress (left) and strains (right) on cortical bone structure from incisor loading â&#x20AC;&#x201C; Conventional denture model

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The distribution of Von Misses stress is centred under the central incisor which is being loaded. Here the stress reaches 650Pa, the average for the anterior section of the cancellous bone is 410Pa. The stresses reduce greatly along the sides, the nonworking side reaching 420Pa and averaging 80Pa while the working side only reaches 340Pa and averages 160Pa. The first principle stress is also uniformly low, the anterior section having a maximum stress of 893Pa but only averaging 420Pa, the sides have very low maximums and averages of 83Pa and 78Pa for the maximums of the non-working and working side respectively and their averages being just 30Pa and 48Pa. The strain pattern reflects the stress pattern in the cancellous bone. The maximum strain is found on the non-working side of the mandible, peaking at 3.3*105 m/m, this side averages 1.6*10-5m/m. The working side does not quite experience the same level of strain, it undergoes a maximum of 2.8*10-5m/m but still averages at 1.4*10-5m/m. The anterior section of the mandible experiences a maximum strain of 2.8*10-5m/m and averages 1.4*10-5m/m.

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5.4 Implant-Restrained Over-Denture Model This section will cover the biological reactions taking place in the implant-restrained over-denture model in the cortical and cancellous bone for loads being placed on the molar, the canine and the incisor. These results will consider the Von Mises stress, first principle stress and strain for both the local area around each of the loads and the global reaction caused by the loads. The first part of this section will consider the biological reactions due to the virtual loading on the second molar. (Fig.88) 5.4.1 Cortical Bone Reaction of Loading on the Molar

Figure 88: Implant-restrained over-denture model with loading on the molar

The existence of implants doesnâ&#x20AC;&#x2122;t increase the stress in the area local to the load by any significant degree. The highest level of stress experienced below the site being loaded is 2.5MPa. (Fig. 89) This stress is relatively well uniform through the local area and creates a stress field with an average Von Mises stress of 1.8MPa.

Figure 89: Von Mises stresses on cortical bone structure from molar loading â&#x20AC;&#x201C; Implantrestrained over-denture model

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The first principle stress is relatively low around the site of the loaded molar due to the stress in a large part is being transferred to the site of the implant. (Fig. 90)The local maxima around the load site is 0.2MPa in compression while locally there is a mixture of compressive and tensile stresses averaging 0.12MPa compressive on the top surface of the mandible and down the side directly beneath the load site and 0.4MPa in tensile strain behind this compressive stress area. The local strain around the load site is relative low, tensile strain. It reaches 7.2*10-5m/m but only averages 4*10-5m/m. (Fig. 91)

Figure 90: First principle stress in cortical bone structure from molar loading â&#x20AC;&#x201C; Implantrestrained over-denture model

Figure 91: First principle strains in cortical bone structure from molar loading â&#x20AC;&#x201C; Implantrestrained over-denture model

The implants change the makeup of the stress pattern experienced by the cortical bone. The maximum stress encountered is at the connection between the cortical bone and the implant, this maximum is 82.6MPa. This stress dissipates somewhat but a relatively high level of stress is maintained throughout the anterior region of the

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cortical bone averaging 1.7MPa. The stresses experienced on the non-working side of the mandible average 1.2MPa, reaching 3.4MPa and on the working side average 0.2MPa and reaches 0.9MPa. The majority of the mandible is undergoing tensile stress, this is due to the force being transferred to the anterior of the mandible via the denture and in turn creating a bending moment towards the posterior of the denture and thus placing it under tensile stress. There are areas of compressive stress particularly directly under the load site and around the implants. This is a desirable result as it shows that force is being transferred through the implants. The highest compressive and tensile stresses are at the site of the implants. Here we see stresses of 3.8MPa in compression and 32MPa in tensile stress. The majority of the anterior section is under tensile stress averaging 4.2MPa. The non-working side of the mandible is also under tensile stress, peaking at 3.9MPa and averaging 4.1MPa. The working side, which experiences the loading, undergoes compressive stress of 0.2 MPa and averages 0.1MPa but generally is undergoing an average tensile stress of 0.38MPa. The global strain pattern is heavily concentrated toward the posterior of the non-working side of the mandible on top and underneath the working side however the maximum strain point of 3.2*10-5m/m is at the site of the left implant. This strain is transferred to some degree casing an area of relatively high strain below the implants, averaging 6.9*10-5m/m. The non-working side of the mandible peak strain is 2.3*10-5m/m and has a relatively high average of 8.7*10-5m/m while the working side reaches1.6*10-5m/m on the bottom side of the cortical bone but averages only 2*10-5m/m.

5.4.2 Cancellous Bone Reactions of Loading on the Molar The Von Mises stress transferred to the cancellous bone is relatively low local to the loaded molar on the implant-restrained over-denture. The maximum local stress is 0.14MPa and the local area averages 0.1MPa. (Fig. 92)

Figure 92: Von Mises stresses in cancellous bone structure from molar loading â&#x20AC;&#x201C; Implantrestrained over-denture model

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The cancellous bone experiences both compression and tensile stresses. (Fig. 93) Under the denture at the site of the loaded molar the cancellous bone experiences compressive stresses of up to 50000Pa. The area local to the loaded molar experiences mostly compressive stresses averaging 24000Pa. The strain experienced by the cancellous bone under the loaded molar is very low. (Fig. 94) The local maximum is only 1.2*10-4m/m while the local average is 1*10-4m/m.

Figure 93: First principle stress in the cancellous bone structure from molar loading â&#x20AC;&#x201C; Implantrestrained over-denture model

Figure 94: First principle strains in the cancellous cortical bone structure from molar loading â&#x20AC;&#x201C; Implant-restrained over-denture model

The effect of the implants is very evident in the analysis of the global distribution of Von Mises stress in the cancellous bone. The maximum stress point is located at the implant and around the implant site is a large area of high stress concentration. At the implant site the Von Mises stress reaches 2.4MPa and the average for this area is 0.11MPa. There are minimal stresses present in the sides of the mandible however.

The non-working and working sides of the mandible reach only 0.46MPa and 0.91MPa respectively and average 54026Pa and 41568Pa. Globally the cancellous bone experiences mostly tensile stresses with obvious areas of compressive stress. The implant creates both compressive and tensile stress as a consequence of it being loaded at an angle it pushes on one side of the cavity and pulls on the other. Around the implant we find the highest levels of compressive and

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tensile stresses reaching 2.3MPa in tensile stress and 0.33MPa in compression. The average stress for this area is 65000Pa. In the posterior region of the non-working side there is a high concentration of tensile stress reaching 0.11MPa. The average for this side is 29000Pa however. The working side yields much lower stress, reaching only 65000Pa and averaging 20000 Pa. The maximum strain experienced within the cancellous bone is found at the implant site, here the strain reaches 4.5*10-3m/m. The overall stress is low though with the anterior section averaging 6*10-4m/m and the non-working and working sides averaging 8.2*10-5m/m and 7.7*10-5m/m with maximums of 1.8*10-4m/m and 1.7*10-4m/m respectively.

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5.4.3 Cortical Bone Reactions of Loading on the Canine

Figure 95: Implant-restrained over-denture model with loading on the canine

When the load is acting on the canine (Fig. 95) there is an extremely high level of local stress under the loaded canine. Here the stress reaches 249MPa. (Fig. 96) This extremely high level of stress is present because the load is directly placed on top of the implant. The extremely high nature of this stress could be a result of the thread being over the edge of the top of the cortical bone structure thus creating a situation where there is significant force on a very small area. This high level of stress is not maintained throughout the local area though as it averages 1.1Mpa. There is also a high level first principle stress directly under the implant, here the stress reaches 65MPa, however this again is extremely localised being diffused quickly and the local area averaging 0.13MPa.

Figure 96: Von Mises stresses in cortical bone structure from canine loading â&#x20AC;&#x201C; Implantrestrained over-denture model

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Figure 97: First principle stress (left) and strains (right) in cortical bone structure from canine loading â&#x20AC;&#x201C; Implant-restrained over-denture model

The strain also reaches a maximum under the implant. This maximum however is not as drastically different with respect to the averages as the stresses are. (Fig. 97) The strain under the implant reaches 7.3*10-3m/m while the local area average 1.6*105 m/m. While there is an extremely high maximum at the site of the implant the averages and other maximums are more evenly distributed. The maximum point is 249MPa at the site of the implant however the average for the anterior section is only 0.53MPa. The sides have similar averages of 0.5MPa and 0.68MPa for the nonworking and working sides respectively, the maximums for these sides are a reasonably large 2.3MPa and 1.3MPa. While the maximum first principle strain is not as drastically high as the maximum Von Mises stress it is still relatively very high at 65MPa. The average for the anterior section however the lowest average of the three sections at 0.13MPa. The averages for the sides are 1MPa and 0.32MPa for the non-working and working sides respectively and they reach 2.3MPa and 1.5MPa. The strain distribution is more evenly spread throughout the mandible. The maximum strain experienced under the implant is 7.9*10-3m/m. This is higher than the maximums experienced on the sides which are 1.6*10-4m/m and 9.9*10-5m/m for the non-working and working sides respectively.

The average strain at the anterior of the mandible is 2.1*10-5m/m and the averages for the non-working and working sides respectively are 6.9*10-5m/m and 2.4*10-5m/m.

5.4.4. Cancellous Bone Reactions of Loading on the Canine The maximum stress experienced under the cancellous bone is not as drastically high as the stress experienced in the cortical bone structure. The maximum stress experienced here is 14.9MPa and the average stress for the area local to this load is

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40000Pa. (Fig. 98) The maximum first principle stress reached is under the loaded canine is 13.5MPa, the average for this local area is 0.13MPa. (Fig. 99)

Figure 98: Von Mises stresses in cancellous bone structure from canine loading â&#x20AC;&#x201C; Implantrestrained over-denture model

Figure 99: First principle stress (left) and strains (right) in cancellous bone structure from canine loading â&#x20AC;&#x201C; Implant-restrained over-denture model

The maximum strain is also reached under the loaded canine, the maximum strain experienced in the cancellous bone structure is 7.7*10-2m/m while the local area averages 2.3*10-4m/m. The stress reached at the anterior of the mandible is the maximum global stress at 14.9MPa, the average for the anterior section is 40000Pa. The maximum stresses found on the sides are relatively high reaching 0.39MPa and

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0.53MPa for the non-working and working sides respectively and averaging 48000Pa and 32000Pa. The maximum global first principle stress is experienced at the anterior of the mandible, here it reaches 13.5MPa, and averages 26000Pa. The sides reach relatively high stresses, reaching 0.11MPa and 0.31MPa for the non-working and working side respectively and this stress is better distributed through the non-working side as the both average 16000Pa. The strain achieved at the anterior of the mandible is the global maximum of 7.7*10-2m/m but this strain is not distributed well through the anterior section for it averages only 5.8*10-6m/m. The sides average higher strains, averaging 3.3*10-4m/m and 3.1*10-5m/m for the non-working and working sides respectively as they reach 5.4*10-4m/m and 8.4*10-4m/m.

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5.4.5 Cortical Bone Reactions of Loading on the Incisor

Figure 100: Implant-restrained over-denture model with loading on the incisor

When the incisor is loaded (Fig.100) the maximum Von Mises stress reached local to the load point is very high due to the impact of the implants. The maximum stress reached is 186MPa which is very high in comparison to the rest of the mandible.

(Fig.101) The local average in the anterior section of the mandible is 0.39MPa. The first principle strain also reaches a very high maximum stress at the site of the implant. (Fig.102) The anterior section of the mandible reaches a maximum first principle stress of 47.9MPa but only averages 0.19MPa. The local strain pattern also reaches its maximum at the site of the implant, here the strain reaches 5.8*10-3m/m and averages 1.7*10-5m/m.

Figure 101: Von Mises stresses in cortical bone structure from incisor loading â&#x20AC;&#x201C; Implantrestrained over-denture model

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Figure 102: First principle stress (left) and strains (right) in cortical bone structure from incisor loading â&#x20AC;&#x201C; Implant-restrained over-denture model

The Von Mises stress is most concentrated at the anterior of the mandible as here it reaches 186MPa. This however is very localised as the average for this section is only 0.19MPa. The sides reach reasonable highs of 1.7MPa and 1.3MPa for the nonworking and working side respectively, these sides average 0.71MPa and 0.72MPa. The first principle stress reaches a high at the site of the implant reaching 47.9MPa, this anterior section has an average first principle stress of 2600Pa. The first principle stresses also reach reasonably high first principle stresses of 1.7MPa and 1.3MPa for the non-working and working sides respectively as they average 0.33MPa and 0.52MPa. The strain pattern reflects the stress patterns in the cortical bone structures.

The maximum is at the site of the implant at 5.8*10-3m/m, the average for this area is 3.3*10-6m/m. The sides reach 1.2*10-4m/m and 9.0*10-5m/m for the non-working and working sides respectively and average 2.8*10-5m/m and 3.2*10-5m/m.

5.4.6 Cancellous Bone Reactions of Loading on the Incisor The maximum Von Mises stress reached under the loaded incisor in the cancellous bone structure is 11.1MPa. (Fig.103) This is a relative high stress concentration and it is distributed well through the local area which average 2.1MPa. The first principle stress maximum is also experienced at the site of the implant. (Fig.104) This is also a relative high maximum stress concentration of 10MPa but is localised much more than the Von Mises stress is as the local average is only 0.11MPa. The strain concentration also reaches its maximum at the implant of 2.0*10-2m/m. The local strain average is 2.4*10-4m/m.

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Figure 103: Von Mises stresses in cancellous bone structure from incisor loading â&#x20AC;&#x201C; Implantrestrained over-denture model

Figure 104: First principle stress (left) and strains (right) in cancellous bone structure from incisor loading â&#x20AC;&#x201C; Implant-restrained over-denture model

The maximum global Von Mises stress found in the cancellous bone structure is found at the site of the implant where it reaches 11.1MPa. This however dissipates quickly as the anterior section averages just 26000Pa. The sides reach relatively high maximums of 0.42MPa and 0.41MPa for the non-working and working sides respectively however these also dissipate quickly as they average just 31000Pa and 32000Pa. The maximum first principle stress at the site of the implant is also very high reaching 10MPa. This, like the Von Mises stress dissipates quickly as the anterior section only averages 22000Pa. The sides again reach relatively high stresses of 0.39MPa and 0.28MPa but only average 11000Pa and 16000Pa. The strain pattern reflects the stress pattern experienced in the cancellous bone structure. The maximum

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strain is reached at the site of the implant at 2.0*10-2 where the anterior section averages 4.1*10-5m/m. The non-working and working sides reach 6.2*10-4m/m and 6.1*10-4m/m which is better distributed on the working side as they reach an average of 3.2*10-5m/m and 3.1*10-5m/m respectively.

5.5 Summary This section summarises the results generated by the finite element analysis in a tabulated form. The results are categorised and tabulated for ease of reference. The tables are considerable in size and thus it is hard to gather meaning from them. These tables, figures 105, 106, 107 and 108 are designed to simply summarise the complete set of data found, simpler tables and explanations are provided in the next chapter.

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Figure 105: Local Stresses and Strains

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Figure 106: Global Stresses and Strains - Molar Loading Biomedical Consequences of Orthodontic Loading and Biting Forces on the Mandible.

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Figure 107: Global Stresses and Strains - Canine Loading

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Figure 108: Global Stresses and Strains - Incisor Loading

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Chapter 6

Chapter 6. Discussion.

This section considers the results which have been obtained and the manner in which they were generated. It provides an interpretation of the results as well as possible implications that they hold. This section will initially provide a validation of the study by comparing the material, method and results generated to previous studies. This chapter will then look at the limitations and how these impact on the results. Once these have been discussed comparisons of the results will be made. This section will make comparison of the results in a number of categorises between the three models.

Then the finding from these comparisons will be examined and finally the implications from these findings will be discussed.

6.1 Validation The models in this study have been developed with a high level of accuracy and detail. Previous models which have been developed in consideration to bone resorption have been of reasonable accuracy and varied detail. In previous studies various aspects of the system have been omitted. These have included the mucosa (Kitamura et al., 2003), PDL, (Vaillancort et al., 2004), artificial teeth (Sato et al., 2000), cancellous bone (Maeda and Wood, 1989) (Sato et al., 2000) and the soft denture liner (Maeda and Wood, 1989) (Takayama et al., 2001). The natural dentition model consisted of the cancellous bone, cortical bone, PDL, dentin and enamel. It possessed the entire range of teeth and the complete mandibular bone structure. The conventional denture model consisted of the cancellous bone, the cortical bone, mucosa, soft denture liner, acrylic resin and artificial teeth. The implant-restrained over-denture model consisted of the cancellous bone, cortical bone, mucosa, acrylic resin, artificial teeth and implants. These models are accurate as they were developed from CT scans and manipulated in Rhinoceros 3D, v. 3 SR 2. The models had relevant material properties assigned so that they would completely reflect the clinical situation. The models have been developed with minimal inconsistencies and realistic dental structures.

The results obtained through FEA within this study, due to the accuracy of the models and the mesh generation, are considered highly reliable and detailed. This study employed a parabolic tetrahedral mesh as opposed to a linear tetrahedral mesh for parabolic tetrahedral meshes are superior in their capacity to produce accurate results.

This method was used by Cattineo et al (2005) for its superior accuracy especially with complicated geometry. The accuracy of the results is heavily dependent on the generation of the mesh. The mesh generated for this study supersedes previous mesh generations. Two dimensional studies have produced models with an extremely low number of elements and nodes. Sato et alâ&#x20AC;&#x2122;s (2000) model consisted of 220 elements and 134 nodes while Meade and Wood (1989) used 576 elements and 325 nodes for their model. Three dimensional models are inherently more complicated and thus require a finer mesh. Eskitascioglu et al (2004) developed a model with 180884 elements and 320083 nodes and Kitamura et al (2003) produced a number of models for his study ranging from 2022 to 5296 elements and from 180956 to 24558 nodes.

For my study I have used Ansys V10 SP1 for itâ&#x20AC;&#x2122;s accuracy and have developed three

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finite element models with 152781, 111809, 207432 nodes and 88838, 62461, 121904 elements for the natural dentitions, conventional denture and implant-restrained overdenture models. Thus a highly accurate and detailed finite element analysis was performed and the results reflect the biomedical consequences to biting forces.

The results achieved in this study reflect results and patterns found in previous finite element analysis studies and clinical observations into the stress patterns found in the human mandible. The overall stress patterns found within the cortical and cancellous bone structures display a high level of stress towards the posterior sections of the mandible which are caused by the creation of a bending moment created from the force being applied particularly towards the anterior of the mandible. This pattern is reflected in stress distribution patterns generated by the study of Choi et al. (2004) where similar stress concentrations were found. Throughout the results there emerged a band where it is hypothesised that the threshold stress lies for the discontinuance or commence of bone resorption. This band, 1 â&#x20AC;&#x201C; 1.5MPa, is slightly higher that the value proposed by Maeda and Wood (1989) (0.5MPa) however my proposal may be a little high as a threshold value of 0.5MPa would still correspond to the results generated in this study however I have chosen to propose a value higher than Maeda and Wood (1989) based upon the strength of my results and the non-commitment that Maeda and Wood (1989) display to their value.

6.2 Limitations There are several factors which need to be considered when viewing these results.

These do not detract from the results in any significant way but must be mentioned.

These limitations are in regard to the tempromandibular (TMJ) or rotational joint at the back of the mandible, the size of the mandibles and the posterior area of the dentures.

6.2.1 Rotational (TMJ) Joint The tempromandibular joint at the back of the mandible has been modelled as a rotational joint. This is not strictly anatomically correct as this joint has a sliding component however a rotational joint is a good approximation and does not adversely affect the results.

6.2.2 Size of Mandible A patient who wears dentures, conventional or otherwise, will have a resorbed mandible prior to the denture being installed. This is because the mandible will have already experienced a loss in loading hence will have experienced resorption. The mandibles used in the conventional denture and the implant restrained over-denture are the same size as the mandible used in the natural mandible. For this reason there is a validity issue as a mandible requiring a denture would never be the size as is modelled. I have modelled the mandibles this size as this study is looking into the changes in stress resulting from just the dentures themselves and not any decrease in

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mandible size. A mandible of smaller size would experience a higher level of stress and would artificially change the results obtained in this study.

6.2.3 Posterior area of Dentures Both dentures designed extend back further than a denture realistically would.

Dentures are normally trimmed around this area so as to create a more comfortable fit for the wearer. Although this might not be a great difference in terms of the volumetric difference between the real dentures and the models it would be a significant difference in terms of the comfort for the wearer. This difference however does not impact of the results and the difference this area makes to the stresses realised is considered to be small.

6.2.4 Muscles Modelled The forces modelled in the finite element model simulate the masseter muscle, the buccinators muscle however has not been modelled. This, in comparison, is a smaller muscle and does not provide a relatively significant amount of force for chewing.

Thus this lack of detail is not considered to adversely affect the results.

6.3 Comparisons.

This section compares the results found for each of the models. This section concerns itself only with the Von Mises stresses found as these are more relevant when considering bone regeneration as the first principle stresses and strain relate more to bone fracture. This section will first consider the local stresses, that is the area directly surrounding the loaded tooth and then will consider the global stresses, as explained in section 5.1.6, experienced when loading each of the teeth.

There are several extremely high maximums experienced by the implant-restrained over-denture model. These are caused by the thread overlapping the top of the bone structure and thus crating a situation where the load is being focused on a very small area. In clinical situations the bone would quickly remould itself away from this an distribute the load more evenly. Because of the existence of these extreme highs this study has not only looked at the maximum strains experienced but also the averages.

Analysing the average stresses nullifies the effect of these outlying maximums and provides a platform for a better understanding of the stresses involved.

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6.3.1 Local Maximum and Average Stresses around the Loaded Sites.

The section will consider the stresses experienced local to the load site on each of the models. The local area does not comprise of the entire side or anterior section but rather only to the mid point of the neighbouring teeth and half way down the mandible side. Table 19 and figure 109 display the local maximums found in the cortical bone at each of the load sites of the incisor, canine and molar.

Cortical Local Stress (MPa) Maximums Loading Site Incisor Canine Molar Model Natural Dentitions 3.5 5.3 17 Conventional Dentures 0.42 0.58 2.7 Implant-Restrained Over-Dentures 186 249 2.5 Table 15: Local maximum Von Mises stress experienced by the cortical bone structure

Cortical Local Maximums Load Site Incisor

Canine

Molar

1000

Force (MPa)

100

10

1

0.1

Natural Dentitions

Conventional Dentures

Implant-Restrained Over-Dentures

Figure 109: Local maximum Von Mises stress experienced by the cortical bone structure

This data shows that when the incisor or canine is loaded the implant-restrained overdenture provides a significantly higher stress concentration than either the conventional denture or even the natural dentitions. Due to an extremely high maximum stress concentration at the site of the implants this data has been weighted towards the implant-restrained over-denture and is consequently hard to read. The extremely high readings of stress are caused by the thread of the implants overlapping the top surface of the cortical bone and thus creating a situation where there is a relatively high force acting on an extremely small area. It is because of these extremely high readings, especially due to the denture that average readings for the local area have also been taken (Table 20 and Figure 110) and these provide better understanding of the forces involved.

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Cortical Local Stress (MPa) Averages Incisor Canine Molar Model Natural Dentitions 2.3 1.5 3.5 Conventional Dentures 0.36 0.41 1.2 Implant-Restrained Over-Dentures 1.2 1.1 1.8 Table 16: Local average Von Mises stress experienced by the cortical bone structure Cortical Local Averages

4

3.5

Force (MPa)

3

2.5

2

1.5

1

0.5

0 Incisor

Canine

Molar

Load Site Natural Dentitions

Conventional Dentures

Implant-Restrained Over-Dentures

Figure 110: Local average Von Mises stress experienced by the cortical bone structure

Considering the average local forces experienced by the cortical bone structure. Here we see the conventional denture exerts the most stress when biting using the molar.

This however is probably largely due to the increased biting capacity at the molar.

The maximum bite force that the conventional denture exerts is around 1MPa. The implant denture surprisingly has a relative low stress concentration around the canine and the incisor however this may be due to the stress being concentrated in the cancellous bone. We see the natural dentition model the average stress exceeds 1.5MPa at all three sites and peaks at 3.5MPa when loaded at the molar.

Considering the maximum forces exerted onto the cancellous (Table 21 and Fig. 111) bone structure we see the same extreme stress concentration exerted by the implantrestrained over-denture at the canine and the incisor. This again is due to the thread of the implant creating a very small surface on which the force is exerted. An interesting point to take away from this data set however is that the stresses experienced by cancellous bone structure of the natural dentitions model. The stresses here are much lower, while the cortical cone structure experienced averages all over 1.5MPa, the cancellous bone does not experience a maximum over 0.47MPa.

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Cancellous Local Stress (MPa) Maximums Loading Site Incisor Canine Molar Model Natural Dentitions 0.47 0.29 0.44 Conventional Dentures 0.00065 0.00095 0.0025 Implant-Restrained Over-Dentures 11.1 14.9 0.14 Table 17: Local maximum Von Mises stress experienced by the cancellous bone structure

Cancellous Local Maximums Load Site Incisor

Canine

Molar

100

Force (MPa)

10

1

0.1

0.01

0.001

0.0001

Natural Dentitions

Conventional Dentures

Implant-Restrained Over-Dentures

Figure 111: Local maximum Von Mises stress experienced by the cancellous bone structure (logarithmic x-axis)

The reduction in stress concentration can be accounted for by a number of reasons.

The material prosperities probably play a big part, not just in their ability to endure stress but also in the fact the harder outer layer, the cortical bone structure, probably restrains the teeth from exerting their full force into the cancellous bone.

Cancellous Local Stress (MPa) Averages Incisor Canine Molar Model Natural Dentitions 0.045 0.075 0.22 Conventional Dentures 0.00034 0.00067 0.0014 Implant-Restrained Over-Dentures 0.021 0.04 0.1 Table 18: Local average Von Mises stress experienced by the cancellous bone structure

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Cancellous Local Averages

1 Incisor

Canine

Molar

Force (MPa)

0.1

0.01

0.001

0.0001

Load Site

Natural Dentitions

Conventional Dentures

Implant-Restrained Over-Dentures

Figure 112: Local average Von Mises stress experienced by the cancellous bone structure (logarithmic x-axis)

The average stresses found locally in the cancellous bone are as expected. (Table 22 and Fig. 112)We see the largest stresses found in the natural dentitions, the lowest in the conventional denture and the implant-restrained over-denture lying in the middle.

An obvious trend is that the disparity between the models grows as the load point move towards the posterior. This can be accounted for by a number of reasons primarily because of the more dramatically increased chewing ability of posterior natural teeth but also, especially in the implant-restrained over-dentures case, the dentures ability to distribute load over the mandible. Again the stresses experienced by the cancellous bone are far less than those experienced by the cortical bone and apart from the spike by the implant-restrained over-denture model the results are as expected.

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6.3.2 Global Maximums and Average Stresses from Molar Loading.

The section will consider the stresses experienced by the cortical bone and the cancellous bone globally when a load is place upon the molar.

Considering the natural dentition model we see a maximum on the working side of the mandible. (Fig. 113) This is expected as this is the location of the load, the anterior section and the non-working side also have relatively high maximums (>6MPa), the non-working side experiencing a greater level of stress due to the bending moment which is created by the load. The incisor has a significantly high maximum at the anterior which is generated by the implants. Although this is a significant stress as the average distribution shows it is not reflected in the entire anterior section. (Table 23) Cortical Global Stress (MPa) Maximums (molar loading) NonWorking Anterior working Model Natural Dentitions 17 6.2 7.3 Conventional Dentures 2.3 1.9 1.2 Implant-Restrained Over-Dentures 0.9 82.6 3.4 Table 19: Global maximum stresses experienced by the cortical bone structure from molar loading

Cortical Global Maximums (Molar Loading) Load Site Working

Anterior

Non-working

100

Force (MPa)

10

1

0.1

Natural Dentitions

Conventional Dentures

Implant-Restrained Over-Dentures

Figure 113: Global maximum stresses experienced by the cortical bone structure from molar loading (logarithmic x-axis)

The average stress concentration shows a much more balanced and expected result.

The stress peak generated by the implant-restrained over-denture model at the anterior of the mandible does not persist through the bone structure to a significant degree.

The anterior section still has the highest level of stress concentration, due to the implants, which reach 1.7MPa. However the implants do little to restore the stress

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concentrations on the sides of the mandible. An interesting point is that the stress concentration for the two denture models is greater on the non-working side than they are on the working side (the working side is being loaded at the molar) This is because the denture dissipates considerable force over the mandible and consequently the largest cause of stress, not considering the implants, is the bending moment creating on the non-working side.

Cortical Global Stress (MPa) Averages (molar loading) NonWorking Anterior working Model Natural Dentitions 3.5 2.7 3.2 Conventional Dentures 0.665 1 0.9 Implant-Restrained Over-Dentures 0.2 1.7 1.2 Table 20: Global average stresses experienced by the cortical bone structure from molar loading

Cortical Global Averages (Molar Loading)

4

3.5

Force (MPa)

3

2.5

2

1.5

1

0.5

0 Left

Centre

Right

Load Site Natural Dentitions

Conventional Dentures

Implant-Restrained Over-Dentures

Figure 114: Global average stresses experienced by the cortical bone structure from molar loading

When considering the cancellous bone again we see a peak at the anterior of the molar by the implant-restrained over-denture model. Surprisingly the implant-restrained over-denture model exerts more stress on the non-working side of the cancellous bone than the natural dentitions. This is because however, the dentures spread the load out toward the non-working side while the load experienced by the natural dentitions model remains localised on the working side.

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Cancellous Global Stress (MPa) Maximums (molar loading) NonWorking Anterior working Model Natural Dentitions 0.44 1.6 0.18 Conventional Dentures 0.0025 0.0029 0.0017 Implant-Restrained Over-Dentures 0.091 2.4 0.46 Table 21: Global maximum stresses experienced by the cancellous bone structure from molar loading

Cancellous Global Maximums (Molar Loading) Load Site Working

Anterior

Non-working

10

Force (MPa)

1

0.1

0.01

0.001

Natural Dentitions

Conventional Dentures

Implant-Restrained Over-Dentures

Figure 115: Global maximum stresses experienced by the cancellous bone structure from molar loading (logarithmic x-axis)

On average, the maximum stress concentration exerted by the natural dentitions lies on the non-working side of the mandible. The maximum stress produced by the implant-restrained over-denture at the anterior of the mandible is significant however this level of stress, which is created by the implants, is not reflected throughout the mandible as the sides have very low levels of stress concentration.

Cancellous Global Stress (MPa) Averages (molar loading) NonWorking Anterior working Model Natural Dentitions 0.15 0.11 0.71 Conventional Dentures 0.0011 0.0018 0.00096 Implant-Restrained Over-Dentures 0.042 0.11 0.054 Table 22: Global average stresses experienced by the cancellous bone structure from molar loading

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Cancellous Global Averages (Molar Loading) Load Site Working

Anterior

Non-working

1

Force (MPa)

0.1

0.01

0.001

0.0001

Natural Dentitions

Conventional Dentures

Implant-Restrained Over-Dentures

Figure 116: Global average stresses experienced by the cancellous bone structure from molar loading (logarithmic x-axis)

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6.3.3 Global Maximums and Average stresses from Canine Loading.

The implant-restrained over-denture model exerts a significant maximum stress on the cortical bone structure when being loaded at the molar. This again is due to the thread on the implants creating a situation where a relatively high amount of force is being placed on a small area. One significant point to note is that the stresses generated by the natural dentition throughout the cortical bone structure are again all over 1.5MPa.

Cortical Global Stress (MPa) Maximums (canine loading) Nonworking Working Anterior Model Natural Dentitions 4.3 5.3 1.62 Conventional Dentures 0.56 0.59 0.81 Implant-Restrained Over-Dentures 1.3 249 2.3 Table 23: Global maximum stresses experienced by the cortical bone structure from canine loading

Cortical Global Maximums (Canine Loading) Load Site Working

Anterior

Non-working

1000

Force (MPa)

100

10

1

0.1

Natural Dentitions

Conventional Dentures

Implant-Restrained Over-Dentures

Figure 117: Global maximum stresses experienced by the cortical bone structure from canine loading (logarithmic x-axis)

The averages paint a much more understandable picture of the stresses involved. The stresses experienced in the natural dentitions model peak at the anterior where the load is being placed. The sides still experience relatively high level of stress of 1.5MPa and 1.2MPa. The implant-restrained over-denture model expectantly experiences its greatest levels of stress at the anterior of the mandible while the conventional denture experiences its highest level of stress on the non-working side to the bending moment created.

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Cortical Global Stress (MPa) Averages (canine loading) NonWorking Anterior working Model Natural Dentitions 1.5 2.1 1.2 Conventional Dentures 0.23 0.23 0.49 Implant-Restrained Over-Dentures 0.65 1.1 0.5 Table 24: Global average stresses experienced by the cortical bone structure from canine loading

Cortical Global Averages (Canine Loading)

2.5

Force (MPa)

2

1.5

1

0.5

0 Left

Centre

Right

Load Site Natural Dentitions

Conventional Dentures

Implant-Restrained Over-Dentures

Figure 118: Global average stresses experienced by the cortical bone structure from canine loading

Considering the maximum stresses in the cancellous bone structure from loading at the canine tooth we find the implant-restrained over-denture model again display extremely high stresses at the anterior of the mandible. This again is due to the thread of the implants and makes the graphical representation of the data somewhat hard to decipher. An important factor in the data to note though is that all the stress values found in the cancellous bone structure again are lower than the stresses experienced by the cortical bone.

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Cancellous Global Stress (MPa) Maximums (canine loading) NonWorking Anterior working Model Natural Dentitions 0.12 0.68 0.086 Conventional Dentures 0.000764 0.00095 0.00075 Implant-Restrained Over-Dentures 0.53 14.9 0.39 Table 25: Global maximum stresses experienced by the cancellous bone structure from canine loading

Cancellous Global Maximums (Canine Loading) Load Site Working

Anterior

Non-working

100

10

Force (MPa)

1

0.1

0.01

0.001

0.0001

Natural Dentitions

Conventional Dentures

Implant-Restrained Over-Dentures

Figure 119: Global maximum stresses experienced by the cancellous bone structure from canine loading (logarithmic x-axis)

When considering the average stress values of the cancellous bone structure upon being loaded at the canine one surprising aspect is prominent. Both the natural dentitions model and the implant-restrained over-denture model experience greater stress on the non-working side of the mandible then they do at the anterior. This suggests that the bending moments created by loading the forward teeth is more influential on the stresses experienced in the cancellous bone structure than what the direct forces generated from chewing is.

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Cancellous Global Stress (MPa) Averages (canine loading) NonWorking Anterior working Model Natural Dentitions 0.036 0.061 0.071 Conventional Dentures 0.00034 0.00068 0.00043 Implant-Restrained Over-Dentures 0.032 0.04 0.048 Table 26: Global average stresses experienced by the cancellous bone structure from canine loading

Cancellous Global Averages (Canine Loading) Load Site Working

Anterior

Non-working

1

Force (MPa)

0.1

0.01

0.001

0.0001

Natural Dentitions

Conventional Dentures

Implant-Restrained Over-Dentures

Figure 120: Global average stresses experienced by the cancellous bone structure from canine loading (logarithmic x-axis)

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6.3.4 Global Maximums and Average stresses from Incisor Loading.

Again there is an extreme high level of stress at the centre of the mandible caused by the implant-restrained over-denture model which is caused by the threaded implants.

While this makes it hard to extract meaning from the graphical representation of the data the table show that the stresses generated by the implant-restrained over denture model, besides the centre stress, are comparable to the natural dentition model. This is because the side stresses in the natural dentition model are caused solely by the bending moment created while the implant-restrained over-denture combines the stresses caused by the bending moment with the stress generated through the implants which results in a relatively comparable stress level in the sides of the cortical bone structure.

Cortical Global Stress (MPa) Maximums (incisor loading) NonWorking Anterior working Model Natural Dentitions 1.4 3.5 1.5 Conventional Dentures 0.52 0.42 0.63 Implant-Restrained Over-Dentures 1.3 186 1.7 Table 27: Global maximum stresses experienced by the cortical bone structure from incisor loading

Cortical Global Maximums (Incisor Loading) Load Site Working

Anterior

Non-working

1000

Force (MPa)

100

10

1

0.1

Natural Dentitions

Conventional Dentures

Implant-Restrained Over-Dentures

Figure 121: Global maximum stresses experienced by the cortical bone structure from incisor loading (logarithmic x-axis)

It is easier to extract a meaningful interpretation of the data when viewing the average stresses as this removes the anomalies created by the implants. Surprisingly on all the models we see a lower stress concentration at the anterior of the mandible than on the sides. While this is a small difference in the conventional denture model the

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difference in the other two models is significant. This reinforces the role that the bending moment generated by the force plays in producing stress throughout the bone structure. While these stresses are purely caused by the bending moment in the natural dentition model they are combined with the stresses generated by the implants in the implant-restrained over-denture model. Again the implant-restrained over-denture model produces stresses comparable to those generated in the natural dentition model.

Cortical Global Stress (MPa) Averages (incisor loading) NonWorking Anterior working Model Natural Dentitions 1.1 0.85 1.2 Conventional Dentures 0.18 0.13 0.19 Implant-Restrained Over-Dentures 0.72 0.19 0.71 Table 28: Global average stresses experienced by the cortical bone structure from incisor loading

Cortical Global Averages (Incisor Loading)

1.4

1.2

Force (MPa)

1

0.8

0.6

0.4

0.2

0 Left

Centre

Right

Load Site Natural Dentitions

Conventional Dentures

Implant-Restrained Over-Dentures

Figure 122: Global average stresses experienced by the cortical bone structure from incisor loading

The maximum stresses experienced in the cancellous bone structure, generated by the implant-retained over-denture, again is a result of the threaded implant. With this commonality we also see that the cancellous bone again experiences stress level less than those experienced in the cortical bone structure.

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Cancellous Global Stress (MPa) Maximums (incisor loading) NonWorking Anterior working Model Natural Dentitions 0.066 0.47 0.055 Conventional Dentures 0.00034 0.00065 0.00042 Implant-Restrained Over-Dentures 0.41 11.1 0.42 Table 29: Global maximum stresses experienced by the cancellous bone structure from incisor loading

Cancellous Global Maximums (Incisor Loading) Load Site Working

Anterior

Non-working

100

10

Force (MPa)

1

0.1

0.01

0.001

0.0001

Natural Dentitions

Conventional Dentures

Implant-Restrained Over-Dentures

Figure 123: Global maximum stresses experienced by the cancellous bone structure from incisor loading (logarithmic x-axis)

The average stress distribution shows a greater representation of the stresses experienced throughout the mandible. We see that the stresses generated by the implant-restrained over-denture on the sides of the mandible are comparable to those generated by the natural dentitions. Interestingly the stress experienced by the natural dentition model on the non-working side is greater than the stress experienced on the working side. This would be expected to be the same as the load point is close to the centre at the anterior. This result is verifiable however due to the load point being slightly to the left of centre which would create a slightly larger bending moment in the non-working side of the mandible resulting in a greater stress concentration and the observation that the difference between the stresses is relatively small.

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Cancellous Global Stress (MPa) Averages (incisor loading) NonWorking Anterior working Model Natural Dentitions 0.029 0.031 0.033 Conventional Dentures 0.00016 0.00041 0.0008 Implant-Restrained Over-Dentures 0.032 0.026 0.031 Table 30: Global average stresses experienced by the cancellous bone structure from incisor loading

Cancellous Global Averages (Incisor Loading) Load Site Working

Anterior

Non-working

1

Force (MPa)

0.1

0.01

0.001

0.0001

Natural Dentitions

Conventional Dentures

Implant-Restrained Over-Dentures

Figure 124: Global average stresses experienced by the cancellous bone structure from incisor loading (logarithmic x-axis)

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6.4 Findings Analysing the comparisons there are a number of trends which stand out. These are summarised in dot point below for ease of reading: â&#x20AC;˘

Threshold Stress. While it is impossible to determine the exact values of threshold stresses within the scope of this study, the results tended to indicate a threshold value of around 1 - 1.5MPa at which cortical bone resorption either commenced or concluded. This was determined through an observation of the stresses experienced. The conventional denture did not really approach these values. The implant-restrained over-denture approached it but, disregarding the isolated instances of extreme maximums, did not exceed it while the natural dentition model stayed over 1.5MPa the majority of the time.

â&#x20AC;˘

Local Stress. The stresses local to the loaded tooth had a similar pattern in both the cortical and the cancellous bone structure. The greatest difference in local stress experience was found at the molar. This is probably due to a greater difference in chewing ability at the molar than the other teeth. There was a large amount of stress present local to the loaded incisor in the cortical bone structure of the natural dentition model. The denture models did not reflect this increase of stress at the anterior for they lack the influence that the angled tooth makes in generating stress. The implants augmented the stress found in the anterior of the mandible when the incisor was loaded but there is still a significant gap between the stress generated by the implants and the stress generated by a natural incisor. The differences in the local stress experienced at the canine tooth were relatively small.

â&#x20AC;˘

Global Stress. The stress generated through the creation of a bending moment posterior of the mandible is very influential to the global stress pattern. This is created solely through the force acting down on the mandible and is not a product of natural teeth or implants and as such unless a denture wearer is able to chew with the same force as a person with natural dentitions this stress is unattainable.

When the molar is loaded we see a pattern in both bone structures of the natural dentition model for there to be peak stresses on both sides of the mandible and global low at the anterior. This pattern is reversed when using dentures. The implant-restrained over-denture transfers the load to the implants thus creating a stress high point at the anterior of the denture. The conventional denture stress pattern is much more even, generating only a slightly higher stress concentration at the anterior then at the sides of the mandible.

When the canine in loaded the natural dentitions model displays a stress high point at the anterior of the mandible. With canine loading the stress pattern displayed by the natural dentitions model is reflected by the implant-restrained over-denture model but to a lesser degree. The stresses reached in the natural

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dentition model are in excess of 2MPa where as the implant-retained over denture model are just over 1MPa. When the incisor is loaded there is a drop in the stresses at the anterior of the mandible in the natural dentition model. The anterior section of the mandible actually displays the lowest average while the sides reach the maximum stress concentrations. This is because of a lesser force being placed on the tooth which results in a lower stress concentration due to the direct loading. The sides are boosted in stress concentration though the generation of the bending moments. The implant-restrained over-denture reflects this pattern but again to a lesser degree, reaching around 0.7MPa while the stresses in the natural dentitions model reach over 1.2MPa. Although this is a lesser stress than my hypothesis of 1.5MPa for the threshold stress it is to be noted that this case is only for the incisor loading. The anterior section averages over 1.5MPa when the canine and molar teeth are loaded, which on average, is a greater percentage of time.

6.5 Implications While the stresses experienced when using the conventional denture do not approach those generated by natural teeth, the implant-restrained over-denture does start to approximate them. The stresses generated around the incisor using the implantrestrained over-denture come closest to the stresses experienced in the natural dentition model. However the stresses experienced at the molar and the anterior of the mandible, although they approximate the stress pattern of the natural mandible, are significantly reduced in magnitude. To increase the stress concentration in the posterior of the mandible greater biting forces are required at the anterior of the mandible which will generate a larger bending moment at the posterior. The stresses at the anterior of the mandible can be assisted by the instillation of an increased number of implants as currently shown, with two implants, much of the direct vertical force on the incisor is being re-directed to the canine area.

The greatest difference in stresses observed was found in the anterior section and secondly in the posterior section. The area around the canine tooth, especially with the implant-retained over-denture model produced relatively good stress levels compared to those experienced in the natural mandible. This means than in dentures wearers the anterior section would be the area most affected by bone resorption and consequently is the area most in need for modification to reduce this. Steps can be taken in this direction with the use of a higher number of implants. This study focused on implantretained over-dentures with only two dentures. The use of a greater number of implants in the anterior section would increase the stresses experienced in this section and consequently reduce bone resorption here. To reduce the resorption found in the posterior section the biting force allowable with denture wearers need to be considered. This is because a large part of the stress found in the posterior section of a natural mandible is contributed by the bending moment created when biting with the front teeth. This bending moment is greatly reduced in the dentures as the biting force achievable by denture wearers is greatly reduced.

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Discussion

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One of the major aims of this study was to relate the biomedical consequences found in the cortical and cancellous bone structures as a result of loading on the various structures above the bone to Frostâ&#x20AC;&#x2122;s Mechanostat hypothesis. (Fig. 125) A edentulous human mandible will resorb due to the lack of stresses experienced. This processes is slowed by the use of conventional dentures and implant-restrained over-dentures.

These aids do not stop the process, they mealy slow it. Therefore the stresses experienced in the cortical and cancellous bone structures must lie within the disuse window (DW) and below the threshold strain, MESr, where, below, the bone acts as if disused and resorbs, and above where this resorption begins to decline or turn off.

Figure 125: Frostâ&#x20AC;&#x2122;s mechanostat

The stresses induced when using a conventional denture generally lie below 0.5MPa. These stresses are slightly higher when the person bites with their molar but still only reach around 1.8MPa. These stresses are not reflected in the average values however with the conventional denture generating an average stress in the cortical bone of only 0.45MPa and 2.6*10-3Mpa in the cancellous bone.

The implant-retained over-denture reordered some extremely high values of maximum stress around the implants however these stresses are not realistic as the bone experiencing this stress would quickly remodel itself so as to distribute the stress more evenly. The implant-restrained over-denture generates higher stresses in the mandible structure than the conventional denture. In the cortical bone the implantrestrained over-denture generates an average of 0.9 MPa and 0.18Mpa in the cancellous bone structure.

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Discussion

Chapter 6

These stresses are all lower than the benchmark stresses generated by the natural dentitions. In a natural mandible the average stress found throughout the cortical bone structure is a little over 2MPa and in the cancellous bone structure it is 0.5Mpa. Going from these results it is difficult to extract an exact value for the threshold strain MESr however it is possible to say that for the cortical bone structure this strain is around 1.5MPa (Fig. 126) and in the cancellous bone structure it sits around 0.25MPa. (Fig.127)

Figure 126: Cortical Bone structure values as they relate to Frostâ&#x20AC;&#x2122;s mechanostat hypothesis

Figure 126 shows the values of the stresses experienced by the cortical bone structure and how they relate to Frostâ&#x20AC;&#x2122;s mechanostat hypothesis. 1 represents the conventional denture, 2 the implant-restrained over-denture and 3 the natural dentitions model. The threshold stress, MESr, where bone resorption commences is 1.5MPa. The average stress experienced in the cortical bone structure in natural mandibles is higher than this at 2MPa. The average stresses experienced in the cortical bone structure by both the conventional denture and the implant-restrained over-denture is lower than this threshold strain. The conventional denture only produces an average stress of 0.45MPa in the cortical bone structure while the implant-restrained over-denture produces an average stress level closer to the threshold stress at 0.9MPa.

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Discussion

Chapter 6

Figure 127: Cancellous Bone structure values as they relate to Frostâ&#x20AC;&#x2122;s mechanostat hypothesis

Figure 127 shows the values of the stresses experienced by the cancellous bone structure and how they relate to Frostâ&#x20AC;&#x2122;s mechanostat hypothesis. 1 represents the conventional denture, 2 the implant-restrained over-denture and 3 the natural dentitions model. The threshold stress, MESr, where bone resorption commences is 0.25MPa. The average stress experienced in the cancellous bone structure in natural mandibles is higher than this at 0.5MPa. The average stresses experienced in the cancellous bone structure by both the conventional denture and the implant-restrained over-denture is lower than this threshold strain. The conventional denture only produces an average stress of 2.6*10-3MPa in the cancellous bone structure while the implant-restrained over-denture produces an average stress level closer to the threshold stress at 0.18MPa. The reduced stresses found in the mandible of the conventional denture and implantrestrained over-denture models is not solely due to the distribution and cushioning effect of the dentures. The reduced bite forces allowable in these models plays a large part in the reduction of the stresses experienced and it is the combination of these two factors which result in the stresses observed.

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V{tÑàxÜ J Conclusion

Conclusion

Chapter 7

Chapter 7. Conclusion.

This study aimed to develop highly accurate three dimensional models of the human mandible in its natural state, with a conventional denture and an implant-restrained over-denture and to conduct a finite element analysis on these to investigate biomedical consequences of biting forces. Models developed consisted of cancellous and cortical bone structures, PDL, dentin, enamel, (natural dentition model), mucosa, acrylic resin, artificial teeth, (conventional denture and implant-restrained overdenture models) soft denture liner, (conventional denture model) and implants (implant-restrained over-denture model). The models developed within this study include material properties which have been sourced from previous studies to accurately represent the oral environment. The finite element models developed within this study provide highly accurate and detailed results as a fine mesh was selected. The selection of this mesh supplemented the high level of accuracy maintained throughout this study. The detail which the models were generated with and the mesh selected allowed the results generated to be legitimised through consultation with previous studies.

The stresses generated by the models in the region local to the loaded tooth had similar tendencies in both the cortical and the cancellous bone structure. The stresses around the canine tooth yielded the least difference between the models while the stresses found local to the molar while being loaded were greatest. Although there were signs to show that the implant-restrained over-denture model was approaching those stresses, the latter yielded the greatest difference in stress.

The stresses experienced globally were similar in their distribution and concentration but there was significant difference in the magnitude of the stresses. This difference was especially prominent to the posterior of the mandible and slightly less so at the centre anterior. Again the canine tooth displayed reasonably good level of stress concentration especially with the implant-restrained over-denture model.

This study has produced a highly accurate three-dimensional model of three oral environments which were created to investigate the biomedical consequences of biting forces. The finite element analysis conducted produced results which are fundamental to predicting these consequences. These models are a progressive step towards better understanding the implications of Wolffâ&#x20AC;&#x2122;s Law and particularly Frostâ&#x20AC;&#x2122;s Mechanostat hypothesis and how these relate to the oral environment. There is an abundance of avenues further studies may take. These include; considering different numbers of implants to different sizes of mandibles and evaluating several instances of bone resorption. This study has shown that the finite element method is a valuable and highly accurate tool when considering the oral environment for its ability to conduct analysis on highly detailed and complicated models in a non-destructive manner.

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