Static Analysis of Total Knee Joint Replacement

Mechanics, Materials Science & Engineering, July 2017 – ISSN 2412-5954

Static Analysis of Total Knee Joint Replacement 1 Vinay Kumar. P1, 2, S. Nagakalyan2, b 1 – Department of Mechanical & Aerospace Engineering, Indian Institute of Technology Hyderabad, TS, India 2 – Department of Mechanical Engineering, Kommuri Pratap Reddy Institute of Technology, Hyderabad, TS, India DOI 10.2412/mmse.16.23.38 provided by Seo4U.link

Keywords: tibial component, femoral component, tibial insert, contact stresses, wear.

ABSTRACT. Knee joint is important joint in human. This joint is also called as weight bearing joint and stabilizes the body movements. The disease caused to knee joint due to Rheumatoid arthritis, Osteo-arthritis and Traumatic arthritis is called Knee joint failure. The failure knee joint is replaced by artificial components either partially or totally. 3Dimensional assembly in different orientations of knee joint components are modelled in SolidWorks V6. Analysis in different orientations is performed using Ansys14 software. The early failure (wear and tear) of knee joint implant components is found out by evaluating contact stresses between the Femoral component and UHMWPE. The metallic implant material used in this project is TNTZ (titanium β alloy) and compared with CoCr, Ti6Al4V. It is observed, the contact stresses are less in UHMWPE with TNTZ material is used as compared to other materials.

Introduction. The contact stresses of knee prosthetic depend on the amount of load applied and the contact area between the femoral and tibial components [1]. It also depends on the angle of flexion and extension. If the load on the knee prosthetic increases, the life of the knee prosthetic decreases.

The meniscus in the knee joint is multifunctional component; it plays a major role in load transmission, shock absorption and lubrication [2]. The failure of meniscus is the meniscal tear, it causes severe pain in the knee joint. The contact stresses are high in the articular cartilage after meniscectomy as compared to that of a knee joint. Failure knee joint is replaced by metallic implants [3]. After knee surgery, the stress shielding increases at the knee joint leading to gradual bone loss and knee joint failure. FEA analysis is done to obtain the stresses at the knee joint between the femoral bone and the implant. In the hybrid implant the stresses produced are less when compared to commercial implant, providing better stress shielding as compared to the conventional implant. Total knee replacement failure is due to loosening of femoral component, tibial-femoral instability, and fatigue failure of tibial tray [4]. These are due to over weight of the body and mal-alignment of the knee joint. The dynamic and finite element models of fixed and mobile implants are developed and demonstrated the performance of knee joint and contact pressure distribution in the tibio-femoral contact surfaces at different orientations. Ma-alignment indicate severe stress shielding in the knee joint leads to bone resorption. This will result in more chance to failure of knee joint, induces more pain to the patient. Surgical repair of patella-femoral joint is known as Patella-femoral arthroplasty where the patella and femoral parts are replaced by artificial components [5]. The implant designs are Richards type II patello-femoral prosthesis, Physiological model of knee, Journey patello-femoral joint prosthesis, Genesis II total knee prosthesis and Journey patello-femoral joint prosthesis. The von misses stresses are evaluated during 1200 flexion of knee joint and the effect of stress shielding is found. The FEA results are compared with the experimental results. From the results it indicates that during flexion, the Richards II patello-femoral prosthesis has higher stress compared with the other patella-femoral prosthesis, and in Genisis II total knee prosthesis the stress shielding is high compared to physiological model of knee joint. The materials used in knee replacement surgery must be biocompatible, light weight and should have high strength to weight ratio [6]. Most commonly used materials in knee replacement surgery are titanium alloys, cobolt chromium alloys, steel alloy, etc. © 2017 The Authors. Published by Magnolithe GmbH. This is an open access article under the CC BY-NC-ND license http://creativecommons.org/licenses/by-nc-nd/4.0/

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Mechanics, Materials Science & Engineering, July 2017 – ISSN 2412-5954

These materials are having high strength but more weight. Stress shielding causes bone resorption and leads to failure of total knee replacement surgery. The patient experiences more pain than before surgery. The implant young’s modulus and bone young’s modulus is different which increases effect of stress shielding [7]. To reduce the stress shielding between the bone and the implant, alternate materials are introduced which are having low young’s modulus and high strength. Titanium-β alloy is a suitable bio-compatible material with low young’s modulus. The strength of the alloy is increased, maintaining low young’s modulus by different strengthening mechanism such as strain hardening, grain modification, etc. Wear of TKR is due to more contact area and high contact stresses in the knee joint [8]. Wear analysis is performed experimentally and numerically and compared the results. The results show very near values. Author predicted that it taken 2 months to conduct experiment and 2 hours to find computational wear. The contact stresses are depend on the sagittal radius of knee joint and lower contact stresses are seen in polyethylene chopped fiber composite artificial joint compared to polyethylene [9]. Jasper Harris [10] studied the mechanical properties of UHMWP in order gain a better understanding of wear. Depending upon material treating, the strength of the material can vary in different directions. 3 Dimensional CAD model of knee joint implants can be done by tomographic data and MIMICS software [11]. Brandi C Kar et al. [12] studied various knee implants, materials, wear analysis of knee joint implants and its biomechanics.

3D CAD Model of Knee Joint Implant. Three-dimensional CAD model is developed in SolidWorks V6 software according to ISO standards ISO 7207 - 1: 2007. The generated CAD models are imported to Ansys 14.0 for static analysis of the knee joint implants to evaluate the contact stresses between the femoral and tibial insert components at the different flexion angles such as 150, 450 and 600. The geometrical 3D model of femoral component, tibial component and UHMWPE is shown in the Fig. 1.

(a) Femoral Component

(b) Tibial Component

(c) Tibial Insert

Fig. 1. Knee joint components.

During the knee motion, the knee flexion’s and extends from 00 to 900 shown in the Fig. 2. At this instant, loads are acted at the contact regions of femur bone, meniscus normal to the thigh- bone.

a)

0-degrees

b)

30-degrees

c)

60-degrees

Fig. 2. Knee motion from 00 to 900.

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d)

90-degrees

Mechanics, Materials Science & Engineering, July 2017 – ISSN 2412-5954

The assembly of knee joint implant comprises of femoral component (fixed to femur bone), tibial insert (UHMWPE in between femur & shin bone) and tibial baseplate (fixed to shin bone).

Considering the knee joint kinematics, various geometric orientations of the knee joint implant are modelled shown in the Fig. 3.

(a) 150 Flexion Angle

(b) 450 Flexion Angle

(c) 600 Flexion Angle Fig. 3. Knee joint implant at different flexion angles.

FE Analysis Assumptions in the model: The following assumptions are made in solving the problem numerically 1.

The knee implant is made of linear, elastic, isotropic, homogeneous material;

2.

The contact surfaces are perfectly bonded together;

3.

The load applied on femoral component is equal for magnitude and direction;

4.

The tibial tray is fixed and constrained in all degrees of freedom;

5.

In the fixed implants, polyethylene insert is fixed to the tibial tray, and there is no movement with the femoral component.

Materials and their properties: Materials. The materials which are used in knee joint replacement surgery must have certain properties as per ISO standards. 

Anti-allergic;



Biocompatible;



Non-corrosive; MMSE Journal. Open Access www.mmse.xyz

Mechanics, Materials Science & Engineering, July 2017 – ISSN 2412-5954



Non-toxic.

The following are some materials which used in knee joint implants: 1.

Cobalt chromium alloy (CoCrMo);

2.

Stainless steel 316L;

3.

Titanium alloy’s;

4.

Ti-6Al-4V;

5.

Ti-29Nb-13Ta-4.6Zr also known as TNTZ etc.;

6.

Porous Tantalum;

7.

Ultra High Molecular Weight Polyethylene (UHMWPE).

Properties.

Table 1. Mechanical properties of materials.

Material

Density Young’s (Kg/m3) modulus (GPa)

Poisson’s ratio

Tensile yield strength (MPa)

Ultimate tensile strength (MPa)

CoCr

7990

200

0.3

560

1000

Ti6Al4V

4430

113.8

0.36

880

950

TNTZ

6075

35

0.36

800

820

SS 316L

7990

193

0.3

290

558

UHMWPE

926

0.69

0.45

21

48

Porous Tantalum

2490

3.5

0.34

51

110

Model validation with Experimental results. The failure of knee joint implant replacement is because of wear between Femoral component, PE insert and Tibial Tray. The early detection of contact stresses in the contact areas of implant components prevents wear and increases the life of knee joint implant replacement. Tomaso et al. [1] conducted experiments on knee joint component to find the contact stresses at different stages of gait cycle between Femoral component, Tibial Tray and PE insert. The femoral component (implant to femur bone) and tibial tray (implant to shin bone) is made of Cobalt chromium and tibial insert(bearing component) is prepared of UHMWPE (Ultra High Molecular Weight Polyethylene). The CAD model of knee joint components is validated by the experimental results. Vertical load is applied on the model at various flexion angles from 15 0 – 600 as follows.

Table 2. Loads at various flexion angles.

Flexion angle (0)

Load applied (N)

15

2200

45

3200

60

2800

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Mechanics, Materials Science & Engineering, July 2017 – ISSN 2412-5954

The maximum pressure is calculated at the contact regions between Femoral component, PE insert, and Tibial Tray tabulated in Table 3.

Table 3. Validation of results: Superior surface.

Flexion angle (Deg)

Load applied (N)

Experiment[1] (MPa)

FEM[1]

15

2200

14.5

15

15.61

45

3200

25

27.7

27.86

60

2800

22

24.6

24.89

FEM (MPa)

(MPa)

Fig. 4 shows model validation for maximum pressures at the contact regions of knee implant between Experimental results and FEM simulations.

From the model validation results, the FEM simulations are conducted on the knee joint implant using different materials on designed knee joint implant.

CoCr

15.616

15

14.5

22

24.6

25

24.89

27.86

Experiment Results 27.7

Author FEM

15 DEG

45 DEG

60 DEG

Fig. 4. Validation results.

Results and Discussion. The total knee joint implant components are designed in SolidWorks V6 and Finite Element Analysis is performed at various flexion angles (150, 450, 600 ), to determine the contact stresses between Femoral component & PE insert.

Case 1: Titanium alloy (Ti-6Al-4V) is used.

Case 2: Titanium β-alloy (TNTZ) is used.

The contact stresses between Femur component and Polyethylene insert for above two cases are obtained at different flexion angles and are compared with the experimental results [1] and tabulated in Table 4. From the results it is found that, the contact stresses are less with TNTZ material compared with Ti-6Al-4V, Co-Cr and to the experimental results. This proves that the knee joint model is best suitable and increases life of the knee joint implant replacement.

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Mechanics, Materials Science & Engineering, July 2017 – ISSN 2412-5954

Table 4. Contact stresses between FC and PE insert for case 1 & 2 respectively Flexion Load angle (Deg) applied (N)

Experiment[1] FEM[1] (MPa) (MPa)

FEM Case 1 FEM Case 2 (MPa) (MPa)

15

2200

14.5

15

18.38

10.6

45

3200

25

27.7

30.79

21.7

60

2800

22

24.6

34.65

20.2

15 DEG

60 DEG

22

20.212

24.6

21.719

25

TNTZ

10.616

14.5

15 45 DEG

Experiment Results 27.7

Author FEM

28.651

24.6

Ti6Al4V

22

30.795

16.386

15

14.5

27.7

Experiment Results

25

Author FEM

15 DEG

(a) Ti6Al4V

45 DEG

60 DEG

(b) TNTZ

Fig. 5. Comparison of contact stresses between FE and TB insert.

The contact stresses on PE insert for different materials at various flexion angles and at different loading conditions are shown in the Fig. 6 to Fig. 8.

The following figures are the stresses in the UHMWPE components at flexion angle 150 with Co-Cr, Ti-6Al-4V and TNTZ alloys.

(a)

Co-Cr alloy

(b)

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Ti-6Al-4V alloy

Mechanics, Materials Science & Engineering, July 2017 – ISSN 2412-5954

(c) TNTZ

20 15

Co-Cr

TNTZ

10

Ti-6Al-4V

5

Ti-6Al-4V TNTZ

Co-Cr

0 15 Deg Flexion Angle at 2200 N Load

(d) Comparison of contact stresses between FE and TB insert with Co-Cr, Ti-6Al-4V & TNTZ Fig. 6. 150 Flexion Angle – UHMWPE @ 2200N Load.

The following figures are the stresses in the UHMWPE component at flexion angle 450 with Co-Cr, Ti-6Al-4V and TNTZ alloys respectively.

(a) Co-Cr Material

(b) Ti-6Al-4V alloy

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Mechanics, Materials Science & Engineering, July 2017 – ISSN 2412-5954

(c) TNTZ alloy

35 30 25

Co-Cr

20 15

TNTZ

10

Ti-6Al-4V

Ti-6Al-4V TNTZ

5 Co-Cr

0 45 Deg Flexion Angle at 3200 N Load

(d) Comparison of contact stresses between FE and TB insert with Co-Cr, Ti-6Al-4V & TNTZ alloy’s respectively.

Fig. 7. 450 Flexion Angle – UHMWPE @ 3200N Load.

The following figures are the stresses in the UHMWPE component at flexion angle 600 with Co-Cr, Ti-6Al-4V and TNTZ alloys respectively.

(a) Co-Cr alloy

(b) Ti-6Al-4V alloy

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Mechanics, Materials Science & Engineering, July 2017 – ISSN 2412-5954

(c) TNTZ alloy

30 25 20

Co-Cr

15 TNTZ

10

Ti-6Al-4V

5

Ti-6Al-4V TNTZ

Co-Cr

0 60 Deg Flexion Angle at 2800 N Load

(d) Comparison of contact stresses between FE and TB insert with Co-Cr, Ti-6Al-4V & TNTZ alloy’s respectively Fig. 8. 600 Flexion Angle – UHMWPE @ 2800N Load.

Summary. From the comparison of FEA results with experimental results Fig. 4, it was observed that the contact stresses are more in the Ti-6Al-4V material knee joint implant compared to the CoCr material. This increase in the contact stresses results in increase in wear between the Femoral component and PE insert and increases the life of the knee joint implant.

From the comparison of FEA results with experimental Fig. 5, it was observed that the contact stresses are 33% less in the TNTZ material knee joint implant compared to the CoCr material. This reduction in the contact stresses proves reduction in wear between the Femoral component and PE insert and increases the life of the knee joint implant.

By using TNTZ material for knee joint implant, the overall weight of the knee joint implant is reduced by 23.96 % compared to the implant used by Tomaso et al [1].

Acknowledge. Authors express deep sense of gratitude to IIT Hyderabad & special thanks to KPRIT. References [1] Tomaso Villa, Francesco Migliavacca, Dario Gastaldi, Maurizio Colombo, Riccardo Pietrabissa.

Contact stresses and fatigue life in a knee prosthesis: Comparison between in vitro measurements and MMSE Journal. Open Access www.mmse.xyz

Mechanics, Materials Science & Engineering, July 2017 – ISSN 2412-5954

computational simulations. J. of Biomechanics. 2004 37, 45-53. DOI 10.1016/S00219290(03)00255-0 [2] E. Pena, B. Calvo, M.A. Martinez, D. Palanca, M.Doblare. Finite element analysis of the effect of meniscal tears and meniscectomies on human knee biomechanics. Clinical Biomechanics. 2005, 20, 498-507. DOI 10.1016/ j.clinbio mech.2005.01.009 [3] Habiba B, Ziauddin M, Milan M, Md. Youssef. Finite element investigation of hybrid and conventional knee implants. International J. of Engineering 2009, 3. 257-264.

[4] M. Sivasankar, V. Mugendiran, S. Venkatesan, A. Velu. Failure analysis of knee prosthesis.

Recent Research in Science and Technology. 2010, 2(6), 100-106.

[5] Bernardo I, Hans-Peter W. van J, Luc L and Nico V. Periprosthetic stress shielding in patellafemoral arthroplasty: A numerical analysis. SIMULIA Customer Conference. 2011, 1-12.

[6] Y.Kalyana, Suneel. D and Lingaraju. D. Alternate materials for modeling and analysis of prosthetic knee joint. International Journal of Science and Advanced Technology. 2011, 1(5). 262266.

[7] M. Niinomi and M. Nakai. Titanium-based biomaterials for preventing stress shielding between implant devices and bone. International Journal of Biomaterials. 2011, 10.1155, 1-10. DOI 10.1155/2011/836587 [8] Lucy A. Knight, Saikat P, John C. Coleman, Fred B, Hani H, Danny L. Levine, Mark T, and Paul J. R. Comparison of long-term numerical and experimental total knee replacement wear during simulated gait loading. Journal of Biomechanics. 2007, 40, 1550-1558. DOI 10.1016/j.jbio mech.2006.07.027 [9] C. Shashishekar, C.S. Ramesh. Finite element analysis of prosthetic knee joint using ansys. WIT press. 2007, 12, 1-8. DOI 10.2495/BIO070071 [10] Jasper H. A study of the mechanical properties of Ultra High Molecular Weight Polyethylene.

University of PitsBurgh. Available at http://www.phyast.pitt.edu/~reupfom/Jasper.pdf [11] Piotr Borkowski, Tomasz Sowinski, Krzysztof Kwiatkowski, Konstanty Skalski, Magdalena Zabicka, Mark Polczynski. Geometric Modeling of knee Joint including Anatomical Properties.

Biomechanica, Vol. 9, 2006.

[12] Brandi C. Carr, Tarun G. Knee Implants, Review of models and Bio-mechanics. Elsevier, Materials and Design. 2009, 30. 398–413. DOI 10.1016/j.matdes.2008.03.032

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