Evaluation of Obstructive Sleep Apnea Syndrome by Computational Fluid Dynamics Somsak Sittitavornwong, Peter D. Waite, Alan M. Shih, Roy Koomullil, Yasushi Ito, Gary C. Cheng, and Deli Wang The amelioration of obstructive sleep apnea syndrome (OSAS) by maxillomandibular advancement (MMA) surgery can be predicted by analyzing anatomical airway changes with 3-dimensional (3D) geometrical reconstruction and computational fluid dynamics. Computer Enabling Technology Lab (ETLab) and Computational Simulation Lab (CSLab) can be used to analyze anatomic airway change for previously operated patients with a clinical cure of OSAS. MMA surgery reduces airway resistance and pressure effort (gradient) of OSAS by increasing the dimension of the airway. ETLab has been used to reconstruct the upper airway as a 3D computer model (bone and soft tissue surrounding the pharyngeal airway) from existing helical computed tomography scan format of OSAS patients. ETLab can compare and construct the geometry with numerical meshes of the airway between pre- and postoperative MMA by the use of bioengineering software. This technology uses high-fidelity computation fluid dynamic simulations, developed at the CSLab, for prediction and analysis of the flow field in the airway for pre- and postoperative MMA. It is possible to use the simulation to predict the likely success of future treatment and develop a prognostic factor. The soft- and hard-tissue mesh is used to determine the preand postoperative differences in the facial and pharyngeal tongue base for soft-tissue change associated with hard-tissue movement. This correlation predicts the amount of surgical movement necessary to create an adequate airflow. These results help define the surgical techniques in OSAS for more precise identification of upper airway anatomical features. This process correlates the area and pressure change at the velopharynx, oropharynx, and retroglossal space of the upper airway by the ETLab. Results can compare with polysomnogram and cure rates. 3D computer analysis can be used to test flow dynamics in the human airway for surgical treatment of OSAS. (Semin Orthod 2009;15:105-131.) Published by Elsevier Inc.
bstructive sleep apnea syndrome (OSAS) is one of the most common sleep disorders1 which is an important public health problem.2-7 The syndrome is now recognized as being very prevalent, and current epidemiologic data indicates that sleep apnea syndrome is second only to asthma in the prevalence league table of chronic respiratory disorders.8 Furthermore, there is increasing evidence that sleep apnea syndrome is associated with a considerable number of adverse sequelae, both behavioral and physical. Behavioral consequences include daytime sleepiness, impaired concentration, and neuropsychological dysfunction, whereas physical conse-
O Department of Oral and Maxillofacial Surgery, The University of Alabama at Birmingham, Birmingham, AL (S.S., P.D.W.). Department of Mechanical Engineering, The University of Alabama at Birmingham, Birmingham, AL (A.M.S., R.K., Y.I., G.C.C.). Department of Hematology and Oncology, The University of Alabama at Birmingham, Birmingham, Alabama (D.W.). Address correspondence to Deli Wang, PhD, Hematology and Oncology, The University of Alabama at Birmingham, Birmingham, AL; E-mail: sjade@uab.edu Published by Elsevier Inc. 1073-8746/09/1502-0$30.00/0 doi:10.1053/j.sodo.2009.01.005
Seminars in Orthodontics, Vol 15, No 2 (June), 2009: pp 105-131
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quences include cardiovascular disorders, particularly hypertension. The combination of acute and chronic hemodynamic effects in OSAS have been associated with increased risk of myocardial infarction, cerebrovascular accidents, hypertension, congestive heart failure, and motor vehicle crashes.4,9-16 Population-based studies suggest that 2% of women and 4% of men older than 50 years of age have symptomatic obstructive sleep apnea.17 Approximately 1 in 5 adults has at least mild OSAS and 1 in 15 adults has OSAS of moderate or worse severity.7 The prevalence of OSAS increases with age, with a 2-to 3-fold greater prevalence in older persons (âą–65 years) compared with those in middle age (30 to 64 years).7 It is estimated that 98% of adults with OSAS lack a specific upper airway pathology of an obstructing nature, such as benign or malignant neoplastic lesions originating in pharyngeal structures or inflammatory or metabolic enlargement of pharyngeal soft tissue structures.18 This disorder is associated with significant morbidity and even some mortality.19 Various surgical procedures for OSAS include uvulopalatopharyngoplasty, laser midline glossectomy and lingualplasty, inferior sagittal mandibular osteotomy and genioglossal advancement with hyoid myotomy and suspension, maxillomandibular osteotomy and advancement, and tracheotomy. These surgical procedures for OSAS are aimed at creating more space in the breathing airway. They are not indicated for central apneas or hypopneas because the underlying pathophysiology is more likely to be related to abnormalities of chemoreceptor function and central control mechanisms than to obstruction of the upper airway. Bixler et al20 stated that central sleep apnea (apnea caused by episodic pauses in respiratory effort rather than airway collapse) is found most often in the older age group. In view of this consideration, nocturnal assessment of respiratory and sleep parameters is essential for a proper evaluation of existing sleep-related breathing disorders21 before surgery. Full cardiorespiratory polysomnography (PSG) allows a complete evaluation to determine whether nocturnal respiratory disturbances are associated with upper airway obstruction or are central in nature. Many studies have shown that nasal continuous airway pressure (nCPAP) therapy is highly accepted (35-80% of users).22,23 Unfortunately,
the long-term compliance with nCPAP is reported in the literature to be poor.24 Surgery appears to be an effective and adequate alternative for those patients who do not want to tolerate nCPAP therapy their entire life or for patients for whom nCPAP is not an optimal treatment due to anatomical abnormalities.22,23 In treating OSAS, it is important to detect the severity of the disease and site of occlusion in the airway for each patient. Objective testing can be helpful in confirming the diagnosis and excluding other sleep disorders that might be causing the symptoms. Clinical indications for upper airway imaging are evolving for patients being treated with dental appliances and upper airway surgery. Many studies25-28 have attempted to assess and predict physical pathologies and outcome of treatment for OSAS; however, it is difficult to demonstrate, predict and compare the anatomy of the pharynx in patients with OSAS. This difficulty is a result of the complex 3-dimensional aspect of airway anatomy. Anatomic abnormalities of the pharynx are thought to play a role in the pathogenesis of OSAS. Upper airway imaging modalities to detect anatomic abnormalities include nasopharyngoscopy, cephalometrics, computed tomography (CT), and magnetic resonance imaging (MRI). These imaging modalities have been used to study the effect of respiration, weight loss, dental appliances, and upper airway surgery on elimination or improvement of upper airway obstruction. The MRI and CT allow quantification of the airway and surrounding soft tissue structures in 3 dimensions.27,29-46 Upper airway imaging is a powerful technique for the study of the mechanisms underlying the pathogenesis, biomechanics, and efficacy of treatment options in patients with OSAS. Imaging studies provide significant insight into the static and dynamic structure, function of the upper airway and soft-tissue structure during wakefulness and sleep.37-39,43,44 Unfortunately, it is still difficult to understand and predict pathophysiology of the airway in OSAS; consequently, additional diagnostic tests are to needed to guide treatment recommendations. High-quality diagnostic imaging can be used for a clinical predictor in OSAS.47 The authors of many studies27,28,48-58 have attempted to accurately quantify the dimensions, configurations, sites of obstruction, and collapsibility of upper airways. In recent years, sleeping fiber optic en-
Evaluation of OSAS by Computational Fluid Dynamics
doscopy has been used as an effective method to locate the obstruction site. However, this procedure can be a disturbance to normal sleep and is sometimes refused by examinees. Because most patients prefer radiological examinations rather than invasive ones, radiology could be an ideal way to locate the obstructive site in OSAS.27,33,59 Mueller’s maneuver is a diagnostic technique to detect airway narrowing. It is performed by attempting to inhale against pinched-off nose and closed mouth with a fiberoptic nasopharyngoscope in place. The resulting negative inspiratory pressure will cause the walls of the upper airway to collapse in the narrowed airway. A positive test is suggestive of OSAS. Terris, et al60 explored the reliability of the Mueller’s maneuver and found that the severity of sleep-disordered breathing based on the apnea hypopnea index (AHI) is correlated positively with the Mueller’s maneuver. Hsu et al47 used a computer-assisted quantitative video endoscopic upper airway analysis to compare static and dynamic upper airway morphology between patients with OSAS and normal subjects. With this technology, they were able to predict which patients would have OSAS and confirmed the Mueller test findings.47 The upper airway begins at the nose and ends at the larynx. Therefore, a complete assessment of the upper airway evaluates the entire length of this anatomic region, including the bony framework and soft tissue. Although office assessment of these structures does not necessarily mimic the appearance of behavior of these structures during physiological sleep, the office examination can give important information as to the site of obstruction during sleep that can help direct therapy.61 Li et al52 stated the value of 3D-CT scan in providing the surgeon with anatomic information relevant in planning the upper airway surgery and monitoring its outcome. The geometry and caliber of the upper airway in apneic patients differs from those in nonapneic ones.62 The apneic airway is smaller and is narrowed laterally. Oda et al56 evaluated the pharyngolaryngeal region with 3D-CT in the OSAS and non-OSAS patient. The volume of the upper airway changed mildly between 9.2 cm3 and 11.56 cm3 in the expiration and inspiration phase in a non-OSAS individual while sleeping. It fluctuated moderately between 3.74 cm3 and 9.91 cm3 in a habitual snorer and changed
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acutely between 2.73 cm3 and 16.01 cm3 in an OSAS patient. As anatomic abnormalities of the pharynx are thought to play a role in the pathogenesis of OSAS, Li et al52 stated that the retropalatal space is the most relevant upper airway 3D-CT scan parameter identified in sleep disordered breathing patients and the decreased lateral dimension of the retropalatal space is significantly associated with a compromised airway in sleep-disordered breathing subjects. After surgery the increased lateral dimension of the retropalatal space is thought to be one of the reasons for the decrease in AHI found during postoperative polysomnographic studies. Schwab et al62 used MRI to study the upper airway and surrounding soft-tissue structures in 21 normal subjects, 21 snorer/mild apneic subjects, and 26 patients with OSAS. They reported that at minimum airway area, thickness of the lateral pharyngeal muscular walls, rather than enlargement of the parapharyngeal fat pads, was the predominant anatomic factor causing airway narrowing in apneic subjects. The fat pad size at the level of the minimum airway was not greater in apneic than normal subjects. Shintani et al58 suggested dynamic MRI is useful to detect the level of occlusion during sleep and the severity of OSAS and that this detection can assist in treatment. In addition, they found the severity of AHI and oxygen saturation (SpO2) are significantly correlated with the width of the airway space at the base of the tongue and hypopharynx. By using statistic pressure-area relationships, Isono et al38 found that the passive pharynx is more narrow and collapsible in sleep-apneic patients than in matched controls. This is consistent with the other studies.58,63 The retropositioned mandible will allow the tongue to impinge on the pharyngeal airway and decrease the air flow during sleep. Shintani et al58 reported the severity of AHI and SpO2 are significantly correlated with the width of the airway space at the base of the tongue and hypopharynx. Therefore, AHI and SpO2 can predict and interpret the outcomes of pre- and postoperative OSAS.
Engineering Background After several decades of computer development, computer-aided engineering (CAE) has become a matured technology that plays an important role in the engineering community for design,
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analyses, and performance predictions.64,65 The development is especially significant during the past 2 decades when computer hardware performance-cost ratio has increased constantly. This provides the computational engineers with computing resources that was unimaginable just a decade ago. The enabling technologies associated with CAE involve the scientific disciplines of numerical geometry modeling, numerical mesh generation, scientific visualization, virtual environment technology, and high-performance parallel computing. They enable the use of simulation disciplines such as computational fluid dynamics (CFD) and computational structure mechanics (CSM), which use numerical methods to solve the governing equations that provide high-fidelity computational simulations of fluid flow transport phenomena and structure behaviors.66 Such computational technologies can benefit the medical communities in understanding hemodynamics and mechanics of human biological systems as well.65,67 To enable these computational technologies, however, the first step is to generate high-quality numerical meshes while maintaining geometry fidelity. There have been many numerical geometry algorithms presented during the past few decades, such as the cubic spline, Hermit spline, Bezier spline, and B-spline.68 Among them, the non-uniform rational B-spline (NURBS) has gained great popularity in the CAE community and is the de facto industry standard for the representation and design of a geometry.69 There are major benefits of representing geometry in NURBS. First, NURBS retains the strong geometrical properties, such as the convex hulls, local control, and affine maps (invariant under regular geometrical transformation, such as scaling, rotating, and translating). NURBS provides a unified mathematical basis and can represent many analytic geometries accurately. NURBS formulations for curves and surfaces can be found in many publications. However, most of the applications associated with mesh-based computational technologies are mainly 3D volumetric applications. Therefore, we not only describe NURBS formulations in curves and surfaces, but also demonstrate applications using NURBS volumetric formulations.70 Mesh generation is a step preceeding computational simulations. It is important to have meshes of high quality while maintaining high
geometry fidelity so the numerical simulation process can be steady, robust, and accurate. Based on the numerical algorithms, the mesh generation techniques generally can be classified into either structured, unstructured, hybrid, or generalized meshes.71-73 For these types of meshes, major algorithms, such as elliptic, hyperbolic and algebraic methods for structured meshes, Delaunay, and advancing front methods for unstructured meshes, have been published extensively. Delaunay triangulation is a mathematical and geometrical technique used to model 3D structures. The mesh generation process for a complex configuration, however, is still time-consuming and challenging. Particularly, the quality of meshes plays an essential role in the computational simulations as it affects the efficiency in convergence and accuracy. Lowquality elements induce numerical errors.71 For a complex configuration, it might take substantial effort and time to create high-quality meshes. This is especially true when applying structured mesh topology for complex geometry. The flexibility of unstructured meshes is essential for 3D complex geometry to shorten turnaround time in a design or analysis process. Therefore, unstructured meshes in this study because the geometry of the upper airway is inherently complex. The enabling and computational technologies have proven track records in sophisticated engineering applications to demonstrate their benefits in revealing the physical phenomena without trial and error and expensive experiments.74-78 The Computer Enabling Technology Lab (ETLab) and CFD79 enable all capabilities to enhance the innate abilities in both physical and mental realms to participate in certain activities. In physiology and medicine, some researchers80-82 tried to simulate the airflow in the human respiratory system and found significant medical implications and applications. The CAE has enabled surgeons to characterize the static and dynamic morphology of the subjects’ upper airway and to derive reliable indicators to predict OSAS.55,83 In view of these considerations, the OSAS study model and airway simulation could be performed by the collaboration of the ETLab and CSLab. These study applications can greatly help the medical community to understand the dynamics and behaviors of a human body as well as
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design a medical treatment. This technique uses CFD to predict the presence, severity, and outcomes of OSAS by the use of CT scans and PSG data of adult OSAS patients who underwent maxillomandibular advancement (MMA).
Preliminary Studies Our previous studies30,36,84-87 have reviewed the pathophysiologic nature of OSAS and its current management. By standard treatment and our reviews, the examination should begin with calculation of the body mass index (BMI) and measurement of the neck size. A neck circumference greater than 17 inches is highly correlated with apnea.88 It has been shown that patients with OSAS have a shorter cranial base and a smaller cranial base flexure angle. Sleep apneics frequently have a cranial base length of 76.5 mm (normal, 83.3 mm) and a cranial base flexure angle of 122 degrees (normal, 129 degrees).36,89 These measurements may cause airway impingement and obstruction. Clinicians should carefully examine all aspects of the nose and evaluate any septal deviation, turbinate hypertrophy, masses, polyps, or collapse of the nasal valve.90 The oral examination should document tongue and palate size. Normally, the uvula should be visible with phonation. A long palate is one that descends below the base of the tongue and cannot be directly seen. Such a palate may be relative in macroglossia and further compromise the airway. The nasal pharynx, oral pharynx, and hypopharynx can best be evaluated by endoscopic pharyngoscopy. The goals of upper airway examination are directed at identification of traditional sites and causes of obstruction—tonsils, ectopic thyroids, radiation fibrosis, vocal chord paralysis, and lymphoma.90 One should also try to predict the site of obstruction during sleep, such as retrognathia, which allows the tongue to fall backward during supine sleep and obstruct the airway. Another important goal is to identify areas in which surgery might reduce resistance, increase size, or decrease collapsibility of the airway. Rational surgical treatment should be directed at eliminating the obstruction without creating functional impairment. Because nasopharyngoscopy is important in the evaluation of the upper airway, the Mueller maneuver should be performed.
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To reiterate a positive Mueller’s maneuver is lateral collapse of the airway when the patient attempts to inhale with the nose obstructed.91 Endoscopy can easily evaluate the shape of the airway at various locations. Retroposition of the mandible and tongue will produce a transverse airway that is diminished in the anterior posterior dimension.92 Nasal obstruction by itself is seldom the cause of OSAS, but it can increase negative pharyngeal pressure, leading to obstruction and collapse.93 Assessment of the upper airway can be performed by physical examination, endoscopy, manometry, computed tomography, magnetic resonance imaging, acoustic reflection, and somnofluoroscopy, but cephalometric evaluation provides a simple, inexpensive, readily accessible, and valuable method of screening. The benefits of cephalometry are its allowance of longitudinal comparison over time and treatment and its allowance of the comparison of populations.94 It is also useful for measuring airway changes in a patient before and after treatment. Waite et al84,87 performed comparative preoperative and postoperative cephalometric radiographs after MMA surgery, and clinicians can easily see a dramatic increase in the size of the posterior airway space (Fig 1). Changes in the posterior airway space are thought to increase the pharyngeal volume and decrease the airway resistance. However, cephalometric radiographs are not the best method for evaluating the pharyngeal air space. There are patients with severe apnea who appear to have a normal cephalometric analysis and adequate posterior airway spaces. The limitations of cephalometry are that it is only 2-dimensional and not dynamic. It is not yet possible to calculate the amount of MMA needed to create the necessary change in the posterior airway space. There are examples in our study87,95,96 of an increase in normal airway space because of advancement surgery and the elimination of apnea. Because surgery is a major modality in the treatment of OSAS and because MMA has been shown to be one of the most effective surgical options, we have continued and observed the responses of our treatment in OSAS patients. In our previous study of OSAS in 20 consecutive subjects undergoing MMA, we used the CT scans for pre- and postoperative evaluation. We analyzed preoperative and postoperative scans by
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Figure 3. Change in anteroposterior airway dimensions starting at the level of the hard palate (level 1) and then caudally every 10 mm until the level of the hyoid bone (level 8). There are significant enlargements at all levels except level 4.
Figure 1. Superimposed cephalometric tracing shows skeletal advancement of maxilla and mandible with increase in size of posterior airway. Reprinted with permission from Waite PD, Shetter SM: Maxillomandibular advancement surgery: A cure for obstructive sleep apnea syndrome. In: Waite PD, ed. Oral and Maxillofacial Treatment of Obstructive Sleep Apnea. Maxillofac Surg Clin North Am 7:327-336, 1995.
measuring the anteroposterior and lateral airway dimensions (Fig 2) starting at the level of the hard palate (level 1) and then caudally every 10-mm until the level of the hyoid bone (levels 8). There are significant enlargements in anteroposterior and lateral dimension (Figs 3 and 4) at all levels except level 4 in anteroposterior dimension and level 8 in lateral dimension (P � 0.05). During MMA surgery, muscles, ligaments and tendons attached to the jaw are not detached but equally advanced and straightened with the advancement of their bony origins. This results in a modification of pharyngeal and palatal muscles, as well as the lingual and suprahyoid muscles. Within the pharynx, skeletal expansion and enlargement of the pharyngeal soft-tissue tube is achieved. The effectiveness of MMA is most likely a combination of a change in tension in
Figure 2. Method for measurements of the (A) anteroposterior and (B) lateral of the airway.
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Table 2. Results of MMA for OSAS96
Figure 4. Change in lateral airway dimensions starting at the level of the hard palate (level 1) and then caudally every 10 mm until the level of the hyoid bone (level 8). There are significant enlargements at all levels except level 8.
the suprahyoid and velopharyngeal muscles, even if the mechanical enlargement of the posterior airway space contributes to that effect. Advancement of the maxilla pulls the soft tissue of the palate forward and upward. It also pulls the palatoglossal muscles forward and increases tongue support. Waite et al87,95,96 found that MMA enlarges the entire velopharynx by elevating the tissues attached to the maxilla, mandible, and hyoid and results in increased tension on suprahyoid and velopharyngeal musculature. These studies shows airway enhancement in the anteroposterior and lateral dimensions as anticipated by forward advancement of the facial skeleton.87,95,96 This confirms that MMA is very effective because it increases the upper airway at multiple levels. This mechanism, as proposed by others,57,97,98 is consistent with our finding that the geometry of the airway changes remarkably after MMA. Subsequently, investigations have begun to evaluate the changes in the posterior airway
Results
AHI
Desaturation
Number of Patients
Percent of Total (%)
Excellent Good Satisfactory Poor
ⱕ 10 ⱕ 10 ⱕ 20 ⬎ 20
⫽0 ⱕ 20 ⬎ 20 ⬎ 20
20 26 15 10
28.2 36.6 21.1 14.1
AHI, apnea hypopnea index; Desaturation, number of oxygen desaturations below 90%, n ⫽ 71. Reprinted with permission from. Reprinted with permission from Waite PD, Shetter SM: Maxillomandibular advancement surgery: A cure for obstructive sleep apnea syndrome. In: Waite PD, ed. Oral and Maxillofacial Treatment of Obstructive Sleep Apnea. Maxillofac Surg Clin North Am 7:327-336, 1995.
space by 3D MRI.62 Again, it appears that advancement of the tongue and widening of the lateral pillars occurs with mandibular advancement. Waite et al96 found significant correlation of the results, such as AHI, arousal index, desaturation events ⬍90%, longest event, low oxygen, and total obstructive hyponea between pre- and postoperative MMA for 16 OSAS patients at 5 to 39 months after surgery (Table 1). All these results support MMA treatment and can be used for indirect interpretation of the outcome. MMA is successful because it enlarges the posterior airway space at multiple levels which are generally involved in cases of apnea. Maxillary advancement will flare the alar base, open the nasal valve, and advance and support the palate. Mandibular advancement will increase the tongue space, support the tongue and pull it forward, and prevent tongue impingement on the posterior airway space.96 Waite and Shettar96 published a report of 71 OSAS patients who underwent MMA and received
Table 1. Long-Term Mean Results for MMA with OSAS at 5 to 39 Months96 Parameters Measured
Preoperative
Postoperative
⌬
P Value
Mx. advance Md. advance PAS BMI kg AHI Arousal index Desaturation events ⬍ 90% Longest event Low oxygen Total obstructive hypopnea
102.1 mm 118.8 mm 8.6 mm 32.5 96.6 44.3 31.3 114 50 s 72% 120
110.4 mm 129.2 mm 16.4 mm 31.9 95.0 9.5 5.5 15 26 s 88% 35
8.3 mm 10.3 mm 7.8 mm 0.6 1.6 34.8 25.8 99 24 s 24% 85
⬍ 0.001 ⬍ 0.001 ⬍ 0.004 NS NS ⬍ 0.001 ⬍ 0.001 ⬍ 0.002 ⬍ 0.001 ⬍ 0.01 ⬍ 0.01
⌬, change; Mx., maxilla; Md., mandible; PAS, posterior airway space; AHI, apnea hypopnea index; Desaturation, number of oxygen desaturations ⬍ 90%. Reprinted with permission from Waite PD, Shetter SM: Maxillomandibular advancement surgery: A cure for obstructive sleep apnea syndrome. In: Waite PD, ed. Oral and Maxillofacial Treatment of Obstructive Sleep Apnea. Maxillofac Surg Clin North Am 7:327-336, 1995.
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Table 3. Mean Posterior Airway Changes After MMA for 42 Patients With OSAS Measured by Cephalometry Mean Mean Mean Mean Mean Mean Mean Mean
mandibular advancement maxillary advancement preoperative length postoperative length preoperative volume postoperative volume preoperative resistance postoperative resistance
8.69 mm 7.49 mm 8.88 mm* 8.70 mm* 9.69 mL 16.93 mL 28.72 10.47
n ⫽ 42. *No significant difference. Reprinted with permission from Waite PD, Shetter SM: Maxillomandibular advancement surgery: A cure for obstructive sleep apnea syndrome. In: Waite PD, ed. Oral and Maxillofacial Treatment of Obstructive Sleep Apnea. Maxillofac Surg Clin North Am 7:327-336, 1995.
postsurgical polysomnography. On the basis of a success criterion of an AHI less than 10, the cure rate was 65%. If an AHI less than 20 is considered a success, the cure rate for MMA is 86%. Table 2 shows the response of OSAS patients who underwent MMA and also shows that if success is described as a AHI of less than 10 then 64.8% achieved at least a good-to-excellent result. Successful treatment of OSAS by MMA has been reported by many centers throughout the world. Waite and Shettar reported on a study96 of 42 patients with OSAS. All patients were evaluated for the purpose of correlating surgical advancement with change in posterior airway space area, volume, and resistance (Table 3). With the previously stated limitations in mind, cephalometrics were obtained preoperatively, immediately postoperatively, and at least 1 month after the procedure. The length of the airway space was defined from the lowest point of the pterygoid fissure and basion to a line through C4 and the hyoid bone. The area of the space was calculated by serial diameter measurements every 5 mm. The volume of the airway is calculated by (area) ⫻ (length). Resistance was calculated by (length) ⫻ (K constant) divided by radius.4 The radius is one-half the mean of the total diameter measurements. In all 42 cases, the airway area (cm2) and volume (cm3) enlarged whereas the resistance significantly decreased. The mean resistance changed from 28.72 preoperatively to 10.47 postoperatively. It appears that MMA increases the upper airway and decreases the resistance. Changes in air flow are inversely proportional to the resistance, and resistance is inversely proportional to the radius raised to
the fourth power. Therefore, a small change in airway diameter produces a significant increase in air flow. There is much evidence that supports MMA treatment for OSAS. Li et al99 reviewed long-term clinical results of OSAS and demonstrated that MMA achieves long-term cure in most patients. This was supported by the study of Nimkarn and Waite30 (Table 4). The relatively large maxillary advancements observed in these subjects (approximately 7.5 mm) seem to be relatively stable over the long term. In the mandible, the average advancement was approximately 10 mm, with the chin segment being advanced an additional 4 mm. Again, this seemed to be relatively stable with a negligible amount of postsurgical instability occurring. The long-term postsurgical position was not statistically significantly different from the immediate postsurgical position for any variable (t test). Only gonion vertical demonstrated a significant correlation between the amounts of surgical advancement. The results of this study are of interest because they indicate that large surgical advancement of the maxilla and mandible in OSAS patients are relatively stable over the long term. The findings of this study were supported by Conradt et al.29 They reported postoperative success which has been proven to be stable over a long period (2-year). In conclusion, MMA is safe and effective and it should be presented as an alternative option to CPAP. When prolonged CPAP maintenance and follow-up over a lifetime are considered, surgical therapy is also found to be cost effective. However, the correlation of hard with softtissue changes and the airflow in the airway space has not been reported because apnea is not a simple problem of tubular physics.
Scientific Methodology for CFD Study of the Airway in OSAS (Editor’s note: The mathematical and engineering principles in the following are included in an effort to completely present the rationale for this technology. It is understood that it is of limited application for the clinical orthodontist.) In an effort to develop and test the application of computer ETLab in the analysis of the anatomic airway, the authors created 2 planning steps.
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Table 4. Surgical Movements and Postsurgical Instability of Skeletal Landmarks30 Landmark
Mean Surgical Movement (mm)
Post-Surgical Instability (mm)
T Test
Correlation
PNS horizontal ANS horizontal A point horizontal UIA horizontal LIA horizontal B Point Horizontal Pg horizontal Me horizontal Gonion horizontal PNS vertical ANS vertical Mx 1 vertical Md 1 vertical Pg vertical Me vertical Gonion vertical
7.3 ⫾ 2.3 7.4 ⫾ 2.0 7.5 ⫾ 2.2 9.0 ⫾ 2.9 10.0 ⫾ 2.8 9.6 ⫾ 2.8 13.8 ⫾ 5.2 11.4 ⫾ 5.0 5.8 ⫾ 3.8 1.1 ⫾ 1.4 0.5 ⫾ 2.9 0.7 ⫾ 2.1 2.4 ⫾ 3.5 0.3 ⫾ 4.5 4.0 ⫾ 2.5 ⫺1.7 ⫾ 3.9
0.4 ⫾ 1.8 0.7 ⫾ 2.2 0.43 ⫾ 1.6 1.1 ⫾ 2.0 ⫺0.1 ⫾ 2.1 ⫺0.7 ⫾ 2.9 ⫺0.1 ⫾ 3.9 0.3 ⫾ 3.8 ⫺0.7 ⫾ 3.8 0.3 ⫾ 1.1 0.0 ⫾ 2.2 0.7 ⫾ 1.6 0.8 ⫾ 2.2 0.3 ⫾ 3.6 1.0 ⫾ 2.0 2.1 ⫾ 3.6
0.53 0.25 0.52 0.25 0.95 0.54 0.96 0.87 0.58 0.56 1.00 0.35 0.49 0.85 0.25 0.07
⫺0.52 ⫺0.57 ⫺0.60 ⫺0.46 ⫺0.36 ⫺0.08 ⫺0.49 ⫺0.12 ⫺0.50 ⫺0.19 ⫺0.55 ⫺0.25 ⫺0.37 ⫺0.45 ⫺0.20 ⫺0.71*
*Significant correlation (⬎0.7 or ⬍ ⫺0.7) for the mean surgical movements and postsurgical instability, a negative value represents posterior or superior movement and a positive value represents anterior or inferior movement. Reprinted with permission from Nimkarn Y, Miles PG, Waite PD: Maxillomandibular advancement surgery in obstructive sleep apnea syndrome patients: Long-term surgical stability. J Oral Maxillofac Surg 53:1414-1418, 1995; discussion:1418-1419.
1) Reconstruction of Facial Geometry and Mesh (Preprocessor for Geometry Reconstruction and Mesh Generation) Reconstruction of facial geometry from 3D-CT data. All 3D-CT scans of the cases, including preand postoperative MMA, are transformed to surface geometry of the face and airway for the stereoscopic models. The anatomical references and landmarks are reidentified on these models. As a result, it is possible to compare the data of these stereoscopic models between pre- and postoperative MMA. The changing of facial soft-tissue profile. This step helps the clinician determine and predict the correlation of changing surgical bone and soft tissue after MMA (horizontal advancement of maxilla and mandible). With these numbers of percent changes between bone and soft tissue, one can compare the numbers of polysomnogram (AHI, SpO2, BMI) and interpret for the outcome of correlation. The changing of upper airway region. With static stereoscopic displays of pre- and postoperative MMA, the alteration of airway dimension (selecting area, volume) of the airway are recorded, compared, and correlated with the polysomnograms. On the basis of our previous study, many of the cases had an AHI greater than 40, which is classified as severe OSAS.36,96 Consequently, severe cases are then selected for the CFD simulation study. Models for dynamic stereoscopic displays of
pre- and postoperative MMA are used for the study of the airflow simulation. The tidal volume in adults which is normally 5 to 7 mL/kg100 is used for the volume of simulating airflow. The usual I:E ratio100 (inspiration time/expiration time) of 1:2 will be a number for setting stimulation. Peak pressure at the end of inspiration (Ppeak) at ⫾ 15 cm H2O is monitored.63 The dimension (diameter, area, and volume in different levels) of pre-/postoperative airway are recorded and compared using the technology developed by ETLab. The CFD simulations are conducted to obtain velocity and impedance of the airflow through various pre-/postoperative geometries of upper airway. Impedance in the airway can be visualized as the opposition to airflow in a sinusoidal wave fashion. The correlation of the number between PSG, dimension of airway, and airflow properties are analyzed with the use of statistics.
2) Visualization of Geometrical Mesh and Airflow Simulation The variable numbers of fluid dynamics are the pressure gradient (⌬p), airflow resistance, flow rate, volume and diameter of airway at the region of the affected airway level, such as retropalatal and retroligual areas. These numbers are compared with the number of polysomnogram (AHI, SpO2, BMI) and interpreted for the corre-
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Cephalometric Landmarks102 Cephalometric landmarks are used in junction with imaging obtained during CT scanning.
Hard tissue part (Fig 5)
Figure 5. Facial landmarks of hard tissue.
lation outcomes. The postprocessor for the flowfield visualization, feature extraction are detailed. To obtain retrospective data. our study charts are reviewed for OSAS patients who received MMA surgery. The inclusion criteria were as follows: (1) completion of a polysomnographic study before and a minimum of 6 months after surgery; (2) a standardized helical CT scan with the patient’s trago-canthal line perpendicular to the ground while the end of expiration taken in 1-month preoperative and 6-month postoperative MMA; and (3) a preoperative AHI greater than 25 events per hour on attended PSG. PSG is performed with the use of 2-channel electroencephalography (EEG; C3-A2, O2-A1), left and right electroencephalogram (EO6), submental electromyogram, body position, electrocardiogram, oronasal airflow (nasal pressure of thermista) with respiratory events defined by the American Academy of Sleep Medicine.101 The references of points and lines on facial and neck areas are defined and are used for measurement and statistical correlations.
Selection of Anatomic Landmarks The facial and neck landmarks of the airway are selected and defined mathematically, acknowledged and defined.
S (sella): the point of sella tursica Na (nasion): the point of frontonasal suture Co (condylion): the highest and most posterior point of the mandibular condyle Po (porion): the central point on upper border of external auditory meatus Or (orbitale): the lowest point of the orbit A (subspinale): the most concave point between the anterior nasal spine (ANS) and maxillary alveolar process B (submentale): the most concave point of mandibular alveolar process Go (gonion): the lowest and furthermost of mandibular angle—the half-divided angle of ramus and mandibular plane ANS: the most anterior of maxilla on the palatal plane PNS (posterior nasal spine): the most posterior of maxilla on the palatal plane Pog (pogonion): the most anterior of the chin convexity Me (menton): the lowest point of the mandibular symphysis Gn (gnathion): the lowest and most anterior point of the chin—the half-divided angle of Na-Pg plane and Go-Me plane Angulations and distance Hard tissue part (Fig 5) FH-SN: the angle between the Frankfort horizontal and SN planes Co-Gn: the distance from the Co-to Gn-points Co-A: the distance from the Co-to A-points SN-MP: the angle between the SN and Go-Me planes Soft-tissue part (Fig 6) A (glabella): the most prominence of midsagittal plane of the forehead B (eye): the point between the AC plane and perpendicular line of the orbit C (subnasale): the junction of nasal alar base and upper lip
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UFH (upper facial height): the distance from the eye to the C-point (subnasale), on the AC plane LFH: the distance from the C-point (subnasale) to the H-point (soft-tissue menton) on the CG plane ULL (upper lip length): the distance from the C-to E-points on the CG plane LLL (lower lip length): the distance from the E-to H-points on the CG plane TL (throat length): the distance from the I (throat point) to H points (soft-tissue menton) LCTA (lip chin throat angle): the angle between the HI and FG planes Modified Cephalometric Landmarks54 In addition to conventional cephalometric landmarks, modified landmarks are obtained to enhance the data quality. Reference landmarks (Fig 7A) Figure 6. Facial landmarks of soft tissue.
D (upper vermillion border): the midpoint of vermillion border of the upper lip E (stomion): the junction of upper and lower lips F (lower vermillion border): the midpoint of vermillion border of the lower lip G (soft-tissue pogonion): the junction of the perpendicular line from Pog to N-Pog plane H (soft-tissue menton): the junction of the halfdivided angle of N-Pog and Go-Me plane I (throat point): the junction of the chin and neck lines (UFH) upper facial plane: the plane from the A-point (glabella) to C-point (subnasale) Lower facial plane (lower facial height [LFH]): the plane form the C-point (subnasale) to G-point (soft pogonion) FH: Frankfort horizontal plane SN: Sella-nasion plane MP: Mandibular plane Soft-tissue part (Fig 6) NLA (nasolabial angle): the angle between the nasal alar base and upper lip at C-point (subnasale) FCA (facial contour angle): the angle between the AC and GC planes
AH: the most anterior and superior point on the body of the hyoid bone, representing the inferior part of the tongue Ba (basion): the most postero-inferior point on the clivus pm: Pterygomaxillare: the intersection between the nasal floor and the posterior contour of the maxilla GE: the genial tubercle, representing the most posterior point of the mandibular symphysis and the anteroinferior part of the tongue V: vallecula, the intersection of epiglottis and the base of the tongue T: the tip of the tongue H: the most superior point of the tongue in relation to the line from V to T LPW: lower pharyngeal wall, intersection of a perpendicular line from V with the posterior pharyngeal wall MPW: middle pharyngeal wall, intersection of a perpendicular line from U with the posterior pharyngeal wall U: tip of the uvula, the most posteroinferior point of the uvula UPW: upper pharyngeal wall, intersection of the pterygomaxillare-basion (pm-Ba) line and the posterior pharyngeal wall
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Linear measurements (Fig 7B) V-T: the distance from V to T, tongue length H-VT: the perpendicular distance from H to the line connecting V and T, tongue height pm-UPW: the distance from pm to UPW, nasopharyngeal airway space U-MPW: the distance from U to MPW, oropharyngeal airway space V-LPW: the distance from V to LPW hypopharyngeal airway space PASmin: the minimal distance between the base of the tongue and the posterior pharyngeal wall, posterior airway space pm-U: the distance from pm to U, length of the soft palate SPT: the maximal thickness of the soft palate measured perpendicular to the pm-U-line CL: contact length between the dorsal contour of the tongue and the soft palate V-FH: the perpendicular distance from V to FH, the vertical position of vallecula V-cc: the distance from V to the cervical columna, measured parallel to FH, the horizontal position of Vallecula
Angular measurements NL/pm-U the inclination of the length axis of the soft palate relative to the nl line V-T/FH the inclination of the length axis of the tongue relative to the FH line Volume measurements
Figure 7. (A) Landmarks of pharyngeal airway. (B) Linear measurements of the pharyngeal airway. Reprinted with permission from Wolford L, Hilliard F, Dugan D: Surgical Treatment analysis in patients with obstructive sleep apnoea syndrome. II. Soft tissue morphology. J Laryngol Otol 103:293-297, 1989.
FH: Frankfort horizontal, the line between the porion (Po) and orbitale (Or) pm-U: the line between the pm and uvula (U) NL: nasal line, the line between the ANS and pm
TV: volume of tongue—the lower part of the tongue is reduced to a geometrical polygon where the boundaries are defined by line segments connecting the following points, V, AH, GE, and T. The upper part of the tongue area is defined as the dorsal and superior contour of the tongue from V through H to T SPV: volume of soft palate—measures along the anterior and posterior contour of the soft palate. The superior outline is a line through pm perpendicular to the pm-u-line OV: oral volume—includes tongue volume and extends superiorly to the outline of the soft and hard palate OPV: oropharyngeal volume—includes OV and the area defined by the point pm, UPW,
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LPW and V along the posterior pharyngeal wall and the dorsal outline of the tongue, including the soft palate volume, SPV
Ratios TV/OV ⫽ Relationship between the tongue and oral volume TV/OPV ⫽ Relationship between tongue and the oropharyngeal volume SPV/OV ⫽ Relationship between the soft palate and oral volume SPV/OPV ⫽ Relationship between soft palate and the oropharyngeal volume The pre-/postoperative 3D-CT scans are then transformed to 3D geometry reconstruction and mesh generation in the next step. The geometry reconstruction and mesh generation is a scientific visualization for high-performance parallel computing. The patient’s trago-canthal line is kept perpendicular to the ground at expiration. Therefore some landmarks of the nonsurgical bones, such as skull base and upper-facial third areas are used for referencing and superimposing. The surgical-affected areas, including bone and soft tissue, are quantified and compared between pre- and postoperative MMA. 1) Reconstruction of Facial Geometry and Mesh (Preprocessor for Geometry Reconstruction and Mesh Generation) This preprocessing step in numerical simulations is a critical step, because the geometrical fidelity and mesh quality can greatly affect both the convergence of numerical calculations and, more importantly, the accuracy of the result.
and other unneeded information. It has been discovered that using a 3D median convolution filter followed by light 3D Gaussian blur filter removes most undesirable noise while still maintaining a high fidelity to the original. To extract the desired geometry of the airway, the 3D image data must then be segmented. Surfaces defined by a radical shift in the scalar values in the image volume are relatively simple to segment. Examples of these types of surfaces include bone boundaries in CT data and the boundary between flesh and air in CT or MRI data. However, this process requires the research team members from both medical and engineering schools to work closely to ensure that proper surface information are extracted. The National Library of Medicine Insight Segmentation and Registration Toolkit (ITK; http:// www.itk.org)105 provides many advanced noise reduction and segmentation algorithms which are leveraged with for this work. Demonstrated in Fig 8A and B is the preliminary result to extract the boundary surfaces for the geometry of interest. This example indicates the appropriate approaches as suggested; however, more time and effort are needed to enhance the algorithms to extract the geometry more accurately. For a NURBS curve of order k, as shown in Fig 8s, it can be expressed as follows:
n
C (u) ⫽
wipiNik(u) 兺 i⫽0 n
兺
i⫽0
Reconstruction of Facial Geometry From 3D-CT Scan When an image dataset is acquired, there can be many factors103,104 that affect its quality other than the resolution. The noise in the dataset is one of the issues that must be addressed. This issue can be mitigated through the use of mathematical algorithms on the raw data provided by the imaging systems. To use the image data for segmentation and surface extraction, noise can be selectively removed through the careful application of selected 3D imaging filters. It is important to keep the use of such filtering to an absolute minimum so the resulting image is as coherent to the original as possible while attempting to remove only noise
(1)
wiNik(u)
Where pi (i ⫽ 0, . . . , n) denotes the deBoor control polygon and the wi are the weights associated with each control point. The Nik共u兲 Nik共u兲 is the normalized B-Spline basis function of order k and is defined recursively over a knot vector T ⫽ Ti (i ⫽ 0 . . . n ⫹ k) by the recurrence relations as shown in the following equation.
Nik(u) ⫽
(u ⫺ Ti)Nik⫺1(u) ⫹
Ti⫹k⫺1 ⫺ Ti k⫺1 (u) (Ti⫹k ⫺ u)Ni⫹1 Ti⫹k ⫺ Ti⫹1
(2)
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Ni1(u) ⫽
再
1, if 0,
Ti ⱕ u ⬍ Ti⫹1
otherwise
T ⫽ Ti i ⫽ 0, 1, . . . , n ⫹ k For the knot vector T, it contains the nondecreasing knot values with the multiplicity k for the knot value 0 and 1 on both ends of the knot vector so the NURBS curve can be used to interpolate the first and last control points
p0 and pn. For example, a knot vector T can be listed as following: T ⫽ 兵0, 0, . . . 0, Tk, . . . , Tn, 1, 1, . . . , 1其 and Ti ⱕ Ti⫹1. A NURBS surface (Fig 8B) is actually the tensor product of the NURBS curve definition as shown in Eq. (1). It can assume the form as below:
Figure 8. Facial landmark location. 1 & 7, right and left lateralciliary points located above most lateral aspect of eyebrows; 2 & 6, right and left superciliary points located above most superior aspect of eyebrows; 3 & 5, right and left interciliary points located above medial aspect of eyebrows; 4, midnose point located on midline of nasal bridge in line with medial canthi; 9 & 10, right and left infraorbital points located on infraorbital notches; 8 & 11, right and left zygomatic points located on outer orbital region, equidistant below the lateral canthi as 1 and 7 are above; 12 & 16, right and left maxillary points located on cheek one quarter distance between right and left ala and right and left temporomandibular joint, respectively; 13 & 15, right and left lateral alar points located on lateral alar rims; 14, nasal tip point located on nasal tip; 17 & 18, right and left nasolabial points located on nasolabial fold, midway between right and left ala and commissures, respectively; 19 & 26, right and left cheek points located on cheek one-quarter distance between right and left commissures and temporomandibular joints, respectively; 21 and 24 right, and left commissure points located on commissures; 20 & 25, right and left mid-cheek points located 2 cm between points 19 through 21 and 24 through 26, respectively; 22 & 23, right and left upper lip points located on peaks of Cupid’s bow; 28, mid-lower lip point; 27 & 29, right and left lower lip points located on middle of lower lip vermillion halfway between points 21 through 28 and 24 through 28, respectively; 32, mid-chin point located 2 cm below point 28; 31 & 33, right and left chin points located 2 cm lateral to point 32 and 2 cm below points 27 and 29, respectively; 30 & 34, right and left lateral chin points located 2 cm lateral to points 31 and 33 and 2 cm below points 27 and 29, respectively. Reprinted with permission from Nooreyazdan M, Trotman CA, Faraway JJ: Modeling facial movement. II. A dynamic analysis of differences caused by orthognathic surgery. J Oral Maxillofac Surg 62:13801386, 2004.106 (Color version of figure is available online.)
Evaluation of OSAS by Computational Fluid Dynamics
m
n
兺 兺 wijpijNik (u)Njk (v) i⫽0 j⫽0 1
S (u, v) ⫽
m
n
兺 兺 wijNi
i⫽0 j⫽0
k1
2
(3)
k2
(u)Nj (v)
Where pij is a 3D NURBS control point net, and i ⫽ 0 . . . m, j ⫽ 0 . . . n, wij are the weights associated with each control point. The Nik1共u兲 and Njk2共v兲 denote the normalized basis functions of order k1 and k2 over 2 kt vectors T1 ⫽ Ti, I ⫽ 0 . . . m and T2 ⫽ Tj, j ⫽ 0 . . . n. The basis functions are defined recursively in the same way as in the curve. NURBS surface formulation thus provides a strong mathematical foundation to correspond the facial landmarks with the control points, which allows the to interpolation of the displacement of cervicocraniofacial skeletal reference points. Mapping a dense NURBS surface control point net on the patient’s pre- and postoperative face is used to calculate the transformation matrices between these 2 sets of control points to identify the deformation. Such deformation data are stored in a database as supplemental information to predict the postoperative geometry change based on preoperative 3D scanned images and statistical values from literature. The transformation matrices are then applied to move control Points pij in each region. Once pij are obtained, the facial surface covered by this NURBS surface patch are interpolated using Eq. (3), and blended with rest of the static facial surface region to regain the entire facial soft-tissue surface. The geometry reconstruction approach to extract the facial surface is used as well as skeletal structure for pre- and postoperative patient datasets to determine the change of facial landmark points with respect to the skeletal change due to the MMA procedure. To calculate the transformation matrices more precisely for these landmark points, a NURBS surface patch is placed over the facial region that covers these landmark points. Comparisons of the pre- and postoperative NURBS surface are conducted to calculate the offset of each control point. The landmark points are projected onto these NURBS surfaces to interpolate the offset of these landmark points. As shown in Figs 9 and 10, the NURBS surface can be used properly for this purpose as a result of the many important properties of a NURBS surface, including local control (ie, the
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change of a control point will only affect the geometry nearby, not propagating through the entire surface). With these processes, all 3D-CT scans of OSAS cases, including pre- and postoperative MMA, are transformed to surface geometrical mesh of the face and airway for the stereoscopic models. The anatomical references and landmarks are identified on these models. Therefore, it is possible to compare the data of these static models between pre- and postoperative MMA. At this point, attention is focused on 2 areas: the changing of facial soft-tissue profile and the changing of the upper airway region. The changing of facial soft-tissue profile. The land marks of facial and neck areas are defined and represented on the 3D geometrical modeling of pre- and postoperative MMA. Preoperative and 6-month postoperative MMA in 3D geometrical modeling are analyzed and compared in facial/ neck soft-tissue dimensional change and preand postoperative pharyngeal airway volume, to assess whether there is a correlation between the increase in pharyngeal airway space and decrease in AHI. The average facial/neck soft-tissue change is expressed as percentage of dento-osseous movement by superimposing of the pre- and postoperative images (Fig 11). These numbers accurately predict the postoperative facial appearance of the patient who undergoes MMA. Wolford et al102 reported the facial soft-tissue changes and expressed as percentage of dentoosseous movement for advancement of maxilla and mandible by using cephalogram (Fig 12). This step helps the clinician determine and predict the correlation of changing surgical bone and soft tissue after MMA (horizontal advancement of maxilla and mandible). With these numbers of percent changes between bone and soft tissue, it is possible to compare the numbers of polysomnogram (AHI, SpO2, BMI) and interpret for the co-relation outcomes. The changing of the upper airway region. With the geometry extracted, it is possible to calculate the volume of airspace and area of any given cross sections. Such information is very useful for quantitative comparison. Polyhedron volume calculation can be achieved by the summing of signed volumes of tetrahedra defined by correctly oriented triangles and an arbitrary point,107 which will allow the development of a new algorithm that allows the researcher to calculate the vol-
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zi). The signed volume of the signed volume of the tetrahedra is Volume共Vo V1 V2 V3 兲 1
冤
1
1
1
1
xo x1 x2 x3
⫽ det yo y1 y2 y3 6 zo z1 z2 z3
冥
(4)
The volume of a closed triangulated mesh M can be computed as the sum of the signed volumes of tetrahedra, each of which is defined by one of the triangular faces Fi ⫽ VFi0VFi1VFi2 and an arbitrary point V. The triangular faces are assumed to be counterclockwise oriented as viewed from the outside of the closed mesh. The volume of the closed mesh is Volume共M兲 Figure 9. A NURBS surface patch is mapped onto a hypothetical human face, and the control point new location can be calculated based on the surface perturbation. (Color version of figure is available online.)
ume of the airway between two selected planes within the region of interest. The volume of the airway can be obtained by the volume of a closed triangulated mesh as following formulation108: Consider a tetrahedron V0V1V2V3, where Vi (i ⫽ 0, 1, 2, 3) denotes each vertex, Vi ⫽ (xi, yi,
⫽
兺
triangle Fi
Volume共V VFi0 VFi1 VFi2 兲 (5)
To avoid computational error, V is chosen to be the center of M. Figure 13A and B shows the focusing area of the airway that we are interested in that will be applied as with the volume of a closed triangulated mesh as above. With this step explanation, the changing area and volume of the airway geometry can be determined. Figures 14 and 15 show the pre- and postoperative MMA of the same patient in anteroposterior and lateral direction subsequently.
Figure 10. NURBS control points and the associated geometry for A-curve, B surface.
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Selecting Cases for Computational Fluid Dynamics (CFD) CFD-Based Flow Solver Once the geometry of the object of interest is extracted and the associated mesh is generated, CFD-based numerical simulations can be performed to analyze the transport phenomena of flow through the airway. The CFD-based numerical simulation is conducted by solving the governing equations that describe the transport phenomena of continuum fluid flows, such as air. The governing equation consists of a set of coupled nonlinear equations, such as continuity and Navier-Stokes equations.66 The geometry of interest is very complex, deriving an analytic (ie, exact) solution of the governing equation is impractical. Hence, numerous numerical methods have been developed to solve for the set of coupled nonlinear governing equations. There are 2 major approaches used to solve the governing equations: pressure-based and density-based Figure 11. Superimposition of pre- and post-operative 3D-CT scan of MMA will be measured and expressed as percentage of dentoalveolar movement.
After airway geometry reconstruction from 3D-CT scans, it is possible to see the remarkable changes in the static stereoscopic displays. With the static stereoscopic displays of pre- and postoperative MMA, the changing of dimensions (area, volume) of the airway are recorded, compared, and elicited with the PSG data correlation. Generation of Numerical Mesh Model Once the geometry of interest is extracted, numerical meshes must be generated before CFD simulations can take place. This requires the numerical mesh generation algorithms to be robust for complex biological geometry so that high quality meshes can be produced. Demonstrated in Fig 16 are the high-quality surface and volume meshes generated using direct 3D advancing front method.109 This is the algorithm that is used for mesh generation as it provides robust and high quality meshes. Such mesh generation is used for next step simulations of flowfields using sophisticated computational fluid dynamics software developed at CSLab.
Figure 12. Wolford et al102 stated the facial soft tissue change expressed as percentage of dentoosseous movement for advancement of maxilla and mandible individually.
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Figure 13. Preliminary result of (A) volume rendering and (B) extracting surfaces for geometry of interest. (Color version of figure is available online.)
methods. The pressure-based method, which solves pressure as one of the dependent variables and obtains density from the equation of state, is widely used to solve the low-to-medium speed incompressible and compressible flow, es-
pecially for the internal flow. In contrast, the density-based method, which solves density as one of the dependent variables and obtains pressure from the equation of state, is most often used to solve the compressible high-speed flow,
Figure 14. (A) Pre- and (B) postoperative MMA images of the OSAS patient with subtraction 3D-CT scan demonstrate lateral enhancement of the airway.
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Figure 15. (A) Pre- and (B) postoperative MMA images of the OSAS patient with subtraction 3D-CT scan demonstrate anteroposterior enhancement of the airway.
especially for the external flow. Each method has its strengths and weaknesses. In grid topology, there are 2 major approaches used in CFD solvers: structured grid and unstructured grid solvers. The structured grid flow solvers use either quadrilateral (for 2D) or hexahedral (for 3D) mesh to discretize (that is, to convert a continuous space into an equivalent discrete space for easier calculation) the flow domain of
interest such that indexes of the mesh are in order. The unstructured grid flow solvers use quadrilateral and triangular (for 2D) or tetrahedral, hexahedral, prism, and pyramid (for 3D) mesh to represent the computational domain such that the mesh indexes are not in order (or not in a structured manner). The structured grid flow solver has good numerical accuracy in resolving the viscous boundary layer but is inef-
Figure 16. High quality surface and volume meshes for a femoral artery. (Color version of figure is available online.)
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ficient in modeling complex geometries. The unstructured grid flow solver in contrast has a numerical dissipation problem in the viscous layer if the triangular or tetrahedral mesh is used but is very efficient in handling complex geometry problems. Researchers have developed a hybrid grid or generalized grid technology to combine the strength of both grid topologies. In the present study, we used 2 in-house CFD flow solvers, UNIC and HYB3D, to simulate flow through pre- and postoperative upper airway and explore their suitability. The UNIC code is an unstructured grid pressure based Navier-Stokes flow solver, developed by Dr Y.S. Chen of Engineering Sciences, Inc.110,111 The UNIC code has been well vali-
dated and used to simulate a great variety of engineering problems ranging from internal to external flows and incompressible to compressible flow. One of the examples is the numerical simulation of flood flow through a femoral artery, as shown in the Fig 17. Numerous submodels were incorporated in the code to model various physics and transport phenomena. These submodels include (1) finite-rate and equilibrium chemistry for combustion, (2) conjugate heat transfer for coupling heat convection and conduction, (3) 2-equation eddy viscosity models for turbulence effects, (4) both the heterogeneous spray model with Eulerian/Lagrangian approach and the homogeneous spray model with the Eulerian/Eulerian approach and real-fluid property
Figure 17. Study of hemodynamics in the femoral artery using UNIC code. (A) Geometry and mesh of the femoral artery, (B) shear stress of the artery surface, and (C) pressure of the artery surface and vectors at inlet and exit planes. (Color version of figure is available online.)
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models for liquid spray flow, (5) the finite volume method for solving radiation transport equation (RTE), (6) solving translational and vibrational energy equations for thermal nonequilibrium effect, and (7) porosity model for flow through a porous media, etc. In addition, the UNIC code uses parallel computing with PVM112 or MPI113 domain decomposition with Metis114 and flexible mesh adaptation to enhance its computational efficiency. We believe the UNIC code is as computationally efficient as any CFD codes and has equipped appropriate models to resolve the underlying physics of flow through airway. The density-based flow solver HYB3D, developed by Koomullil,115,116 is designed for a generalized grid framework and is used to simulate complex geometry problems with ease. Finitevolume schemes for solving an integral form of the Navier-Stokes equations are well suited for generalized grids because a typical generalized grid is an agglomeration of polygons with a different number of sides. Hence, HYB3D uses a cell-centered, finite volume scheme in which cell-averaged flow variables are stored at the cell center. The inviscid numerical flux passing through the cell faces is calculated with Ro’s approximate Riemann solver117 as an exact solution for a linearized Riemann problem. Higherorder accuracy in the spatial discretization is obtained with a linear reconstruction of the primitive variables by use of the values of those in the
neighboring cells. With use of the Taylor’s series expansion, the flow variables are extrapolated to the cell-faces from either side of the face and those values are used to solve the Riemann problem. To avoid spurious values near the regions where there is a sharp jump in the flow variables, a limiter function is used. The limiter function is constructed to satisfy the monotonicity principle and basically ensures that the extrapolated values lie between the maximum and minimum values of the variable in the surrounding cells and the cell under consideration. The temporal integration of the governing equations is achieved by an implicit scheme in which the numerical flux crossing the cell face is a function of the primitive variables at the next time level. The numerical accuracy of the unsteady simulations has been improved with the use of Newton iterations.118 The matrix system resulting from the aforementioned equation is solved with the symmetric Gauss Seidel method. To handle larger grids, a parallel simulation strategy is developed. In this approach, the grid is decomposed into different blocks with the public domain program METIS. The graph of the grid is used in the grid decomposition process. The information across the grid interfaces is passed between different blocks using a message-passing interface, MPI. Hence, we believe the UNIC code is an efficient and appropriate flow model for simulating flow through airway. On the basis of our previous study (Table 5), most cases (17 of 20) have an AHI greater than 40,
Table 5. Demographic and Raw Data Describing the Patient Population Case
Age
Sex
Pre-BMI (kg/m2)
Post-BMI (kg/m2)
Pre-AHI
Pre-SpO2 (%)
Post-AHI
Post-SpO2 (%)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
56 54 46 56 30 57 55 45 56 48 57 60 38 38 52 29 48 32 56 38
M F M M M M M F F M M M M M M F F M F F
28 45 26 33 38 29 33 54 16 42 26 27 32 32 28 42 41 41 30 34
29 44 29 35 39 27 33 55 16 45 27 27 31 31 27 43 48 40 31 36
47.4 99.6 27.2 43.3 107.9 41 28 134 47 60 100 56 51 55 43 122.2 63 130 102 26.8
83 56 81 94 86 84 88 88 87 55 87 88 68 80 75 75 75 84 87 88
7 11 38.2 6.6 28.8 38.3 5.8 15 5 16 47 27 35 55 1.6 5.9 6.5 7 5.7 9
92 91 88 95 88 88 85 83 89 79 78 87 83 85 82 86 96 96 87 98
AHI, apnea hypopnea index.
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Figure 18. (A) Anteroposterior view, and (B) lateral view of pre-operative MMA images of the same OSAS patient demonstrate the airway and direction of simulation airflow. (Color version of figure is available online.)
which are classified as severe OSAS cases. We decided to select only severe cases for CFD simulation. Each case was selected at the same probability. The tidal volume in adults which is normally 5 to 7 mL/kg100 is used for the volume of simulating airflow. The usual I:E ratio100 (inspiration time/ expiration time) of 1:2 is the number for setting stimulation. Peak pressure at the end of inspiration (Ppeak) at ⍞ 15 cm H2O is monitored.63 The dimension (diameter, area, and volume in different levels) of pre-/postoperative airway are recorded and compared with the technology developed by ETLab. The CFD simulations are conducted to obtain velocity and impedance of the airflow through various pre-/postoperative geometries of upper airway (Fig 18). The correlation of the number between PSG, dimension of airway and airflow properties is analyzed with statistics. 2) Visualization of Geometrical Mesh and
Airflow Simulation (Postprocessor for the Flow-Field Visualization and Feature Extraction) To facilitate the CFD simulations of airway, preand postoperative airway geometries must be constructed based on the CT data, followed by numer-
ical mesh generation to represent the discretized geometry. The CFD-based flow solvers and center of numerical simulations need to equip the capability of solving the low-speed compressible flow accurately and efficiently handling problems with complex geometries. Stereoscopic visualization provides researchers rich visual cues to better understand the complex geometry and flow field associated with the upper airway. The variable numbers of fluid dynamics are the pressure gradient (âŒŹp), airflow resistance, flow rate, volume and diameter of airway at the interesting level, such as retropalatal and retrolingual areas. These numbers are compared with the number of polysomnogram (AHI, SpO2, BMI) and interpreted for the correlation outcomes. The postprocessor for the flow-field visualization, feature extraction are detailed next. Postprocessing Algorithms Scientific visualization algorithms, such as isosurfaces and streamlines, can provide the researchers better understanding and exploration of simulated results. These techniques have been developed and are relative mature technologies. The in-house developed visualization soft-
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ware at ETLab, Goggle,119 uses the popular opensource visualization library Visualization Toolkit (VTK)120 to provide these powerful and advanced visualization functionalities. We also provide the new algorithm to Goggle so that mean pressure at a user-defined location within the domain of interest can be obtained by inserting a cutting plane into the domain, extracting the pressure distribution on this cutting plane, and obtaining its mean pressure. Goggle can be tailored for this study to understand the important features of medical significance. This software also can be operate on the stereoscopic display system available at ETLab so that medical and engineering collaborators can analyze the results in real time with the benefit of rich visual cues to better understand the complex geometry and flow field associated with the upper airway. The key aspect of this step is to bring together high-fidelity models, user interaction, and 3D visualization into the same virtual space creating a model that acts like it is real. The goal of this work is to create a physically driven model that is more than a static visualization of data (virtual cardboard). That is, the goal is to create a virtual model of a real furnace that responds in the same way as a real furnace. This will enable the user to interact with the virtual plant in the same manner as the real plant. To achieve this long-term goal, a number of steps must be implemented. In the first steps presented here, the visualization, data, and user interaction all need to be integrated into the virtual model. This model then provides a platform for future inclusion of real time, physicsdriven interaction permitting user query and testing of designs.
Statistical Analysis Descriptive statistics (including mean, range, and standard deviation) are used to describe all measurements acquired from 3D-CT scan data from 20 cases in our previous study. These measurements include dimensional changes of facial soft-tissue profiles, dento-osseous movements, area and volume of the upper airway in pre- and postoperative MMA conditions. The location with the minimum area of the upper airway in pre- and postoperative MMA for each OSAS case is identified through de-
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scriptive analysis. Distribution of each variable is also evaluated. On the basis of 3D-CT scan data for measurements, a paired t test or Wilcoxon signed-rank test is used to compare the individual changes between pre- and postoperative MMA, including dimensions of the facial soft tissue profile, percentage of the dento-osseous movement at each landmark, area at each selected location of the upper airway, and volume of whole upper airway. A summary statistic also is used to compare the changes between pre- and postoperative MMA for anteroposterior and lateral dimensions measured at the different levels of the airway. The significant level for statistical tests is adjusted by multiple comparisons using the Bonfferoni correction method. The overall significant level for statistical inference is controlled to be 0.05. According to our previous study, the majority (17 of 20) of OSAS cases are classified as severe cases (AHI before MMA is greater than 40). In the future, clinicians will have this technology to evaluate the effect of MMA treatment for OSAS by using CFD simulation. For simulated CFD data, it is possible to compare the numbers of fluid dynamics—pressure gradient (âŒŹp), airflow resistance, and flow rate between pre- and postoperative MMA at the area of interest. To address the hypothesis that the cure of OSAS by MMA surgery can be predicted by analyzing anatomical airway changes with the use of 3D geometrical reconstruction and computational fluid dynamics, the variable correlations of OSAS clinical studies (such as AHI, SpO2 and BMI) and geometrical dimensional measurements of the facial soft tissue profiles, area, and volume of the upper airway from 3D CT scan data were evaluated with the Pearson correlation coefficient or Spearman correlation coefficient. The correlations and significant changes of OSAS clinical studies (AHI, SpO2, and BMI) and MMA are useful for the prediction of clinical outcomes in OSAS, including surgical succession, facial soft-tissue profiles, dimensions, and volume of the upper airway. In summary, OSAS is a complex disease process. The most significant forms involve disruption of normal breathing through an abnormal airway. The airway is a 3D structure with com-
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plex anatomy and airflow. This new technology brings complex engineering and mathematical technology together to better understand the complexity of disrupted airflow. The advances gained from this novel application of these technologies offers hope in an attempt to improve the lives of individuals suffering from obstructive sleep apnea syndrome.
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