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Finite element analysis of maxillary bone stress caused by Aramany Class IV obturator prostheses
Finite element analysis of maxillary bone stress caused by Aramany Class IV obturator prostheses Elcio Ricardo Miyashita,a Beatriz Silva Câmara Mattos, DDS, PhD,b Pedro Yoshito Noritomi, DS,c and Hamilton Navarro, DDS, PhDd School of Dentistry, University of São Paulo, São Paulo, Brazil; Renato Archer Information Technology Center, Ministry of Science and Technology, Campinas, Brazil Statement of problem. The retention of an Aramany Class IV removable partial dental prosthesis can be compromised by a lack of support. The biomechanics of this obturator prosthesis result in an unusual stress distribution on the residual maxillary bone. Purpose. This study evaluated the biomechanics of an Aramany Class IV obturator prosthesis with finite element analysis and a digital 3-dimensional (3-D) model developed from a computed tomography scan; bone stress was evaluated according to the load placed on the prosthesis. Material and methods. A 3-D model of an Aramany Class IV maxillary resection and prosthesis was constructed. This model was used to develop a finite element mesh. A 120 N load was applied to the occlusal and incisal platforms corresponding to the prosthetic teeth. Qualitative analysis was based on the scale of maximum principal stress; values obtained through quantitative analysis were expressed in MPa. Results. Under posterior load, tensile and compressive stresses were observed; the tensile stress was greater than the compressive stress, regardless of the bone region, and the greatest compressive stress was observed on the anterior palate near the midline. Under an anterior load, tensile stress was observed in all of the evaluated bone regions; the tensile stress was greater than the compressive stress, regardless of the bone region. Conclusions. The Aramany Class IV obturator prosthesis tended to rotate toward the surgical resection when subjected to posterior or anterior loads. The amount of tensile and compressive stress caused by the Aramany Class IV obturator prosthesis did not exceed the physiological limits of the maxillary bone tissue. (J Prosthet Dent 2012;107:336-342)
Clinical Implications
The size and location of the surgical resection and the patient’s dental status determine the prosthetic planning for obturator prostheses. An analysis of the stress distribution of the Aramany Class IV prosthesis on the residual maxilla provided an understanding of the biomechanics of this removable partial dental prosthesis. This understanding is central to prosthetic planning for this obturator prosthesis to rehabilitate the patient and preserve the residual anatomical structures.
Graduate student, Department of Maxillofacial Surgery, Prosthesis and Traumatology, School of Dentistry, University of São Paulo. Associate Professor, Department of Maxillofacial Surgery, Prosthesis and Traumatology, School of Dentistry, University of São Paulo. c Engineer, Researcher, Renato Archer Information Technology Center, Ministry of Science and Technology. d Associate Professor, Department of Prosthesis, School of Dentistry, University of São Paulo. a
b
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May 2012 The surgical treatment of oral cancer results in anatomical and functional sequelae that can lead to functional disorders, psychological disorders, and esthetic issues.1,2 Surgical repairs using rotation flaps, soft tissue grafting, or bone grafting are not entirely effective in patients with extensive maxillary defects.2 Prosthetic rehabilitation can satisfactorily restore the functions of mastication1 and phonetics,2 thereby improving the patient’s quality of life. Extensive maxillary bone loss has a negative impact on the biomechanics of a maxillary obturator. Leverage and fulcrum lines can drastically increase stress on the supporting tissues during mastication,3,4 and the weight of the prosthesis on the supporting tissues can be an aggravating factor.5 Thus, analyses of the configuration and size of the maxillary lesion and of the remaining teeth are central to the success of the prosthesis and to the preservation of the supporting anatomical structures.6 A prosthetic design that is appropriate for the patient’s specific oral conditions is of utmost importance to the improvement of the stability and durability of the obturator prosthesis.4,7-9 Among the obturator prosthesis framework designs, one that warrants particular attention is the Aramany Class IV obturator design. Class IV defects are characterized by the resection of the premaxillae and the posterior maxilla on one side.6,7 This type of extreme defect has a negative impact on the biomechanics of the supporting tissues. Bone remodeling depends on the load level; stresses between 4 MPa and 8 MPa act as stimuli and increase bone density, but a stress of 9 MPa results in resorption and decreases bone density.10 The finite element method is an important research tool in the field of dentistry. This approach has been used for biomechanical analyses and has the advantages of being noninvasive and allowing the visualization of superimposed structures and the definition of the material properties
Miyashita et al
of craniofacial structures.11 In addition, this method can be used to establish the location, magnitude, and direction of an applied force and to locate stress points that can be measured theoretically. Importantly, this method can be repeated as many times as is necessary because it does not affect the physical properties of the analyzed materials.12 Numerous studies have reported that computed tomography (CT) scans, recorded as Digital Imaging Communications in Medicine (DICOM) files, can be used for the development of a 3-dimensional (3-D) model that can be evaluated by using finite element analysis.12-14 The purpose of this study was to evaluate, by using finite element analysis, the stress on the maxilla when an Aramany Class IV obturator prosthesis was subjected to posterior and anterior loads.
MATERIAL AND METHODS After approval was obtained from the Ethics Committee of the University of São Paulo Dental School, an adult man (>25 years of age) with no congenital or acquired defect in the craniofacial region underwent a CT scan (Light Speed 16 Pro; GE Medical Systems, Milwaukee, Wisc). The CT data were recorded as DICOM files and exported to a software package (InVesalius Software, v1.0; Renato Archer Information Technology Center, Campinas, Brazil) for image segmentation and conversion to stereolithography (STL) format. The STL files were transferred to a computer program (Magics X Service Pack 2 software, v1.1.17; Materialise, Leuven, Belgium), which was used to evaluate the files for possible image distortion.12,14 The STL files were then imported with another software package (Rhinoceros 3-D software; Robert McNeel & Associates, Seattle, Wash) and computer processed (Workstation Sun Microsystem ultra 20 M2; Sun Microsystems do Brasil Ltda, São
Paulo, Brazil) to generate a 3-D computer-aided design (CAD) model that simulated an Aramany Class IV maxillary defect.13 The lining mucosa was edited manually. To create a 3-D model of the removable partial dental prosthesis components, the STL model was prototyped with a rapid prototyping machine (ZPrinter 310 Plus; Z Corp, Burlington, Mass). An impression of the prototype was made with silicone putty (Silibor; Artigos Odontológicos Clássico Ltda, São Paulo, Brazil) to manufacture a maxillary cast poured with type IV dental stone (Durone C; Dentsply, Catanduva, Brazil). The cast was sectioned to simulate an Aramany Class IV maxillary defect, defined as a maxillary defect that crosses the midline, with a limited horizontal hard palatal shelf 6 identical to that edited on the CAD model of the maxilla. The experimental model considered a midline resection, and results indicated that stress tended to dissipate on the horizontal shelf; thus, this model is not truly representative of the clinical situation. Subsequently, the retention and stability components of the prosthesis were planned14 with a surveyor (Delineador B2; Bio-Art Equipamentos Odontológicos Ltda, São Carlos, Brazil). The wax pattern of the removable partial dental prosthesis was designed onto this cast to represent the metal framework of the prosthesis. The cast with the wax pattern was digitized with a surface scanner (Modela 3D Plotter MDX-20; Roland DG Corp, Hamamatsu-Shi, Shizuokaken, Japan). The data were transferred to the Rhinoceros 3-D software program, and the information obtained was superimposed onto the CAD model of the maxilla. A 1 mm width was established for the metal components, and the acrylic resin base of the prosthesis was edited manually. Thus, the CAD geometry consisted of the maxillary bone, teeth, mucosa, and obturator prosthesis (Fig. 1).
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1 CAD geometry consisting of maxillary bone, teeth, mucosa, and obturator prosthesis.
2 Finite element mesh.
Table I. Young’s modulus and Poisson’s ratio for anatomical structures and materials Materials
Young’s Modulus (Gpa)
Poisson’s ratio
Cortical bone18
14.7
0.3
Dentin
13.7
0.31
Palatal mucosa
0.68
0.45
Acrylic resin21
2.83
0.45
149
0.35
19 20
Cobalt-chromium alloy
22
Finite element analysis The CAD model generated in the previous steps served as the basis for the creation of the finite element mesh. The data from the CAD model were imported to a software package (Femap with NEi Nastran, NEi Software, Inc, Westminster, Calif ) in 3 different file formats: Step 214 (*.stp);
Acis (*.sat); and Parasolid (*.x_t). This software was used to evaluate the model for possible geometric inconsistencies, such as the absence of surfaces or curves and the formation of spaces between surfaces, and for dimensional inconsistencies, which were standardized in millimeters. The program used quadratic tetrahedral elements to determine vol-
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ume.12,14 The finite element mesh was generated in a controlled manner, which permitted better geometric homogeneity of the elements and better discretization of the model. To generate the mesh, the contact between the surfaces of interest was determined for the root surfaces and the alveolar bone surfaces, the hard palate mucosa and the hard palate bone, the hard palate mucosa and the palatal plate of the prosthesis, and the dental crown surfaces and the retention clasps of the prosthesis. This study considered a fixed interaction between the surfaces; all contacts between surfaces of interest were determined for a glueing with no dislocation between the surfaces. The teeth were considered as a whole, regardless of the differences between the dental pulp, dentin, cementum, and enamel.15 The periodontal ligament was not considered because it contributes little to the results of the finite element analysis.14,16 For the same reason, no distinction was made between cortical bone and cancellous bone, and the cortical bone was considered to be uniform in all regions.14, 17 Unlike the periodontal ligament, the contribution of the oral mucosa to the results of finite element analysis is not generally disregarded; therefore, the hard palate mucosa was considered in the analysis. The geometry of finite elements generated in the present study reached 166,046 elements and 281,928 nodes (Fig. 2). The elastic modulus (Young’s modulus) and Poisson’s ratio were determined for each anatomical structure and material: specifically, cortical bone,18 dentin,19 palatal mucosa,20 acrylic resin,21 and cobalt-chromium alloy22 (Table I). All elements were considered to be bodies with isotropic physical characteristics.12,14,15,18,20,23,24 A force of 120 N was applied to the occlusal (representing the posterior teeth) and to the incisal platforms (representing the anterior teeth) of the obturator prosthesis.25 To process the mesh, it was determined that the model should demonstrate linear
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3 A, Posterior load: stress distribution on palate. B, Posterior load: stress distribution along resection lines. C, Posterior load: stress distribution on alveolar bone adjacent to root surfaces. Maximum principal stress (MPa): compressive stress (blue); tensile stress (red).
4 A, Anterior load: stress distribution on palate. B, Anterior load: stress distribution along resection lines. C, Anterior load: stress distribution on the alveolar bone adjacent to root surfaces. Maximum principal stress (MPa): compressive stress (blue); tensile stress (red). elastic mechanical behavior.12,14,18,26 The results presented are based on a qualitative analysis, corresponding to the scale of maximum principal stress (represented by a color scale) and a quantitative analysis expressed in MPa.
RESULTS Posterior load Stress distribution on the palate was observed for the load applied to the posterior occlusal platform of the obturator prosthesis, causing a compressive stress of 3.25 MPa near the midline; this stress decreased gradually toward the posterior palate. Tensile stress was distributed over the anterior palate and alveolar ridge (3.68 MPa) and over the posterior palatal surface (2.37 MPa) (Fig. 3A). Compressive stress (3.62 MPa) connected to the resection lines was also observed along the midline, extending
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to the anterior resection line. Tensile stress was distributed over the transverse surface of the anterior resection line, reaching an intensity of 6.63 MPa in certain areas (Fig. 3B). Because of the stress distribution on the alveolar bone, predominantly tensile stress was observed in the apical regions of the teeth closest to the resection. The greatest distribution of tensile stress was observed in the region of the first premolar. Significant tensile stress (3.46 MPa) was observed in the area corresponding to the buccal surface of the root apex, and tensile stress of 2.15 MPa was observed in the area corresponding to the palatal surface of the root at the midcervical level. In the area corresponding to the mesial surface of the root, in the cervical region, compressive stress of 1.56 MPa was observed. On the alveolar surface of the second premolar, tensile stress was distributed in the area corresponding to the buccal surface of the root in the apical (1.93 MPa)
and cervical regions (2.37 MPa). No distribution of compressive or tensile stress was observed in the molar region (Fig. 3C). Anterior load Stress distribution on the palate was observed for the load applied to the anterior incisal platform of the obturator prosthesis, causing tensile stress of 2.27 MPa on the posterior palate near the midline. On the palatal surface of the alveolar ridge, the observed tensile stress was 2.72 MPa, but no compressive stress was observed. Minimal compressive stress (0.5 MPa) was observed in the region of the anterior palatal resection (Fig. 4A). Considerable tensile stress (7.27 MPa) was distributed along the resection line in the anterior region of the maxillary resection near the first premolar and along the buccal cortex. Minimal tensile stress (0.5 MPa) was distributed over the palatal region of
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Volume 107 Issue 5 the anterior resection line (Fig. 4B). Greater tensile stress was distributed over the alveolar bone in the cervical regions of the teeth closest to the anterior resection line; this stress gradually decreased toward the posterior teeth. Most of the stress was observed in the first premolar region. In the area corresponding to the mesial surface of the root in the cervical region, considerable tensile stress (up to 6.30 MPa) was observed. In the area corresponding to the palatal surface of the root at the midcervical level, tensile stress of 2.15 MPa was observed. In the area corresponding to the mesial surface of the root in the cervical region, compressive stress of 1.56 MPa was observed. Tensile stress was observed on the alveolar bone of the second premolar in the areas corresponding to the mesial (4.59 MPa) and distal surfaces of the root in the cervical region (4.55 MPa). Isolated points of tensile stress were observed in the first molar region; levels of 4.12 MPa were recorded in the area corresponding to the mesial surface of the root in the cervical region. Tensile stress of 1.36 MPa was observed in the area corresponding to the mesial surface of the root of the second molar in the cervical region (Fig. 4C).
DISCUSSION The process of finite element analysis began with the creation of a CAD model developed from the CT scans of selected biological structures.12,14 CT imaging yields highly complex images because of the morphology of biological structures. The bone density values provided by the CT scan were only considered during image segmentation in the original model. Density values were used to distinguish among the DICOM data provided for soft tissues, bone, and dental tissues; this method is the only way to reconstruct a CAD model of the maxilla. Adapting this complexity to the capacity of computing systems is essential to improving this process. Thus, the initial model was adjusted
to stabilize the CAD model that was subsequently exported to create the finite element geometry.12,14 The degree of complexity in finite element analysis is determined by the number and type of finite elements and by the physical and mechanical behaviors being considered. Numerous dental studies using finite element analysis have considered biological tissues to be materials with isotropic properties.12,14,15,18,20,23,24 The majority of these analyses have treated the materials as having linear elastic properties, in which the structural deformation is directly proportional to the applied forces.12,14,15,26 The same considerations were applied in the present study. In this study, a force of 120 N was applied to the prosthesis, a value previously established in a report that investigated occlusal force in partially edentulous patients with maxillary lesions.25 Most patients with residual support in premolar and/or molar regions tend to apply loads to their residual teeth, selecting this area as the best location for mastication.1 The maximal occlusal force measured at the best masticatory location varies according to gender, age, state of dentition, and anterior versus posterior regions.25 The mean maximal occlusal force at the best masticatory location for patients with remaining natural teeth and an obturator prosthesis has been reported to be 120 N.25 To the authors’ knowledge, no report identifying the maximal occlusal force values for artificial teeth located in a defect area is available, with the exception of a 52 N for complete denture wearers; thus, the experimental load used in the current study was 120 N.25 The analysis reported here, based on the finite element method, has limitations that should be considered when results are considered. The generation of the CAD geometry imposed some simplifications on the model, including a disregard for the periodontal ligament16,18,19 and lack of distinction between cortical and cancellous bone.16 The reported results
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only estimate locations and values for stress distribution within this study design. Principal stress represents the maximum value in only 1 dimension. Maximum principal stress analysis, which is associated with displacement analysis, may also be used to illustrate movement tendencies. Rotation is a large-scale movement that is directly related to dynamic analysis. In this sense, the static analysis conducted in this work is only able to indicate trends in movement. Because the model is static, maximum principal stress information can be used to indicate a rotation trend. This trend permits an assessment of whether greater tensile or compressive stress has occurred and in which direction it occurred. The experimental model considered a midline resection, and its results only indicate the tendency for stress to dissipate on the horizontal palatal shelf; thus, these results are not representative of the clinical situation. The obturator prosthesis exhibited a tendency to undergo vertical dislodgement under posterior and anterior loads and this tendency of the prosthesis to rotate may be expressed in the digital model by using the location and intensity of the tensile and compressive stresses. Thus, the great tensile stress at the limits of the maxillary resection and at the posterior palatal area (Figs. 3B and 4B, red), as well as the compressive stress at the anterior palate (Figs. 3A and 4A, blue), suggest the direction of prosthesis displacement under the applied load. The authors must emphasize that this study used static displacement; because movement is a dynamic condition and this analysis was limited by a static field, results may be interpreted only as displacements. Nevertheless, these results demonstrated the necessity of using the maximum number of direct and indirect retainers for prosthetic stability and warrant further studies to investigate different prosthetic designs.4,5,7-9 The prosthesis displayed a tendency to rotate under posterior load;
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May 2012 the axis of rotation was located near the resection line at the midline of the maxilla. Compressive stress was observed on the surface of the palate, distributed to the alveolar ridge, and on the resection line. However, the intensity of this stress was not sufficient to cause bone resorption according to a study on bone behavior under mechanical stimuli that resulted from critical stress values for mandibular bone at a initial composite (cancellous plus cortical) density of 1.0 g·cm-3.10 Edentulous mandibles and maxillae from fresh cadavers with a mean age of 83.25 years have been reported to have averaged composite densities of 1.18 g·cm3 and 0.67 g·cm3, respectively.17 Age-related decreases in bone density are well known, and this change is more evident in the posterior maxillary region; the cortical bone surfaces remain relatively hard.17 A fully mineralized solid matrix of bone, such as cortical bone, is considered to be quite uniform and its density can be measured.17 The present study considered the cortical densities of 3 different areas of the maxilla. Palatal shelves contain little bone marrow, and their composite densities are different from those of the buccal and alveolar cortical regions. Thus, only cortical density was considered in the current study. A value for the overall maxillary cortical density was not available for comparison with the present results; therefore, the results were compared to findings from a study that also used finite element analysis with tetrahedral elements with isotropic and linear elastic physical bone properties.10 To establish a parameter for bone physiology with remodeling under a load, it was assumed that 1.0 g·cm-3 was an appropriate density value in the present study.10 The compressive stress observed on the surface of the palate might be related to the location of the prosthetic retainers on the teeth. A study using a photoelastic model reported that retention clasps located on the buccal surfaces of the teeth caused stress distribution near the resection line and on the central portion of the
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remaining palate, and that retention clasps located on the lingual surfaces of the teeth caused less compressive stress.9 The metal framework design used in this study was proposed by Aramany and consists of buccal retainers on the premolars and palatal retainers on the molars.7 The reciprocating arms remain completely above the height of teeth contour to stabilize the dental prosthesis during insertion and removal. The present study used static analysis, and the reciprocating arms of the Aramany Class IV framework design were not considered in the digital model because they were not expected to affect the results. Based on this framework design, the results demonstrate that under a posterior load, more stress is distributed to the osseous tissue in the premolar region, less stress is distributed in the molar region, and more stress dissipation occurs in the premolar area and at the anterior resection, all of which is consistent with previous observations.9 The distribution of tensile stress on the alveolar bone, which was more intense in the apical regions and less intense in the cervical regions of the teeth and was limited to the areas of the first and second premolars, has previously been described.8 In the present study, no stress was observed on the alveolar bone in the molar region; this result is not in agreement with those of a previous study that used an experimental model not based on tooth anatomy or clinical prosthetic design.4 Under an anterior load, minimal compressive stress was observed on the surface of the palate, indicating that the prosthesis caused no significant distribution of compressive stress on the maxillary bone. The tensile stress observed in the posterior region of the palate might be clinically interpreted as a tendency of the prosthesis to be dislodged toward the midline. The increased distribution of tensile stress on the anterior resection line along the buccal cortex and near the first premolar also suggested a tendency of the prosthesis to be dis-
lodged; the rotation axis was located near the anterior resection line. The intensity of the applied stress was not sufficient to cause bone resorption because increased bone density has been observed under constant loading stresses of 4, 6, and 8 MPa.10 Periodontal and orthodontic studies based on finite element analysis have suggested that only stresses greater than 5 MPa can trigger the process of bone resorption.23,24 However, this value should only be considered as a reference for the physiological limits of bone tissue because the present experimental model did not consider the biomechanical behaviors of the periodontal ligament and cancellous bone. The stress distribution did not exceed the physiological limits of the bone tissue. The locations and intensities of the tensile and compressive stresses observed in the digital model merely suggest tendencies of the prosthesis to be dislodged. Therefore, the framework design used in this study was considered to be optimal. The 3-D maxillary model was based on a CT scan of an individual without periodontal disease; the locations and the intensities of the stress distributions observed under the experimental conditions might inform and guide prosthetic planning in clinical situations in which periodontal disease is present and the Aramany Class IV obturator prosthesis is required.
CONCLUSIONS Under the experimental conditions used in the present study, there was evidence that the Aramany Class IV obturator prosthesis may dislodge, tending to rotate toward the resection area when loads are applied to the posterior and anterior regions. Under a force of 120 N applied to the occlusal and incisal platforms, the tensile and compressive stress caused by the Aramany Class IV obturator prosthesis did not exceed the physiological limits of the maxillary cortical bone tissue.
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Volume 107 Issue 5 REFERENCES 1. Matsuyama M, Tsukiyama Y, Tomioka M. Clinical assessment of chewing function of obturator prosthesis wearers by objective measure of masticatory performance and maximum occlusal force. Int J Prosthodont 2006;19:253-7. 2. Eckardt A, Teltzrow T, Schulze A, Hoppe M, Kuettner C. Nasalance in patients with maxillary defects - reconstruction versus obturation. J Craniomaxillofac Surg 2007;35:241-5. 3. Desjardins RP. Obturator prostheses design for acquired maxillary defects. J Prosthet Dent 1978;39:424-35. 4. Firtell DN, Grisius RJ. Retention of obturator-removable partial dentures: a comparasion of buccal and lingual retention. J Prosthet Dent 1980;43:212-7. 5. Schwartzman B, Caputo A, Beumer J. Gravity-induced stresses by an obturator prostheses. J Prosthet Dent 1990;64:466-8. 6. Aramany MA. Basic principles of obturator design for partially edentulous patient. Part I: classification. J Prosthet Dent 1978;40:554-7. 7. Aramany MA. Basic principles of obturator design for partially edentulous patient. Part II: design principles. J Prosthet Dent 1978;40:656-62. 8. Schwartzman B, Caputo A, Beumer J. Occlusal force transfer by removable apartial denture designs for a radical maxillectomy. J Prosthet Dent 1985;54:397-403. 9. Myers RE, Mitchell DL. A photoelastic study of stress induced by framework design in a maxillary resection. J Prosthet Dent. 1989;61:590-4. 10.Li J, Li H, Shi L, Fok AS, Ucer C, Devlin H, et al. A mathematical model for simulating the bone remodeling process under mechanical stimulus. Dent Mater 2007;23:1073-8.
11.Sun J, Jiao T, Tie Y, Wang DM. Threedimensional finite element analysis of the application of attachment for obturator framework in unilateral maxillary defect. J Oral Rehabil 2008; 35:695-9. 12.Gao J, Xu W, Ding Z. 3D finite element mesh generation of complicated tooth model based on CT slices. Comput Meth Programs Biomed 2006;82:97-105. 13.Ramos A, Simões JA. Tetrahedral versus hexahedral finite elements in numerical modelling of the proximal femur. Med Eng Phys 2006;28:916-24. 14.Zhao L, Herman E, Patel PK. The structural implications of a unilateral facial skeletal cleft: a three-dimensional finite element model approach. Cleft Palate Craniofac J 2008;45:121-30. 15.Rubin C, Krishnamurthy N, Capilouto E. Stress analysis of human tooth using a three-dimensional finite element model. J Dent Res 1982;62:82-6. 16.Reina JM, Garcia-Aznar JM, Dominguez J, Doblare M. Numerical estimation of bone density and elastic constants distribution in a human mandible. J Biomech 2007;40:828-36. 17.Seong WJ, Kim UK, Swift JQ, Heo YC, Hodges JS, Ko CC. Elastic properties and apparent density of human edentulous maxilla and mandible. Int J Oral Maxillofac Surg 2009;38:1088-93. 18.Moroi HM, Okimoto K, Moroi R, Terada Y. Numeric approach to the biomechanical analysis of thermal effects in coated implants. Int J Prosthodont 1993;6:564-72. 19. Sano H, Ciucchi B, Mathews WG, Pashley DH. Tensile properties of mineralized and demineralized human and bovine dentin. J Dent Res 1994;73:1205-11. 20.Ress JS, Huggett R, Harrison A. Finite element analysis of the stress-concentrating effect of fraenal notches in complete dentures. Int J Prosthodont 1990;3:238-40.
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21.Peyton FA, Craig RG. Current evaluation of plastics in crown and bridge prosthesis. J Prosthet Dent 1963;13:745-53. 22.Morris HF. Properties of cobalt-chromium metal ceramic alloys after heat treatment. J Prosthet Dent 1990;63:426-33. 23.Poppe M, Bourauel C, Jäger A. Determination of the elasticity parameters of the human periodontal ligament and the location of the center of resistance of single-rooted teeth a study of autopsy specimens and their conversion into finite element models. J Orofac Orthop 2002;16:358-70. 24.Kojima Y, Fukui H. A numerical simulation of tooth movement by wire bending. Am J Orthod Dentofacial Orthop 2006;130:452-9. 25.Wedel A, Yontchev E, Carlsson GE, Ow R. Masticatory function in patients with congenital and acquired maxillofacial defects. J Prosthet Dent 1994;72:303-8. 26.Sandu L, Faur N, Bortun C. Finite element stress analysis and fatigue behavior of cast circumferential clasps. J Prosthet Dent 2007;97:39-44. Corresponding author: Dr Beatriz Silva Câmara Mattos School of Dentistry University of São Paulo Av. Lineu Prestes, 2227 05508-000 Cidade Universitária São Paulo, SP BRAZIL Fax: +5511-30917887 E-mail: [email protected] Copyright © 2012 by the Editorial Council for The Journal of Prosthetic Dentistry.
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Clinical Implications
The size and location of the surgical resection and the patient’s dental status determine the prosthetic planning for obturator prostheses. An analysis of the stress distribution of the Aramany Class IV prosthesis on the residual maxilla provided an understanding of the biomechanics of this removable partial dental prosthesis. This understanding is central to prosthetic planning for this obturator prosthesis to rehabilitate the patient and preserve the residual anatomical structures.
Graduate student, Department of Maxillofacial Surgery, Prosthesis and Traumatology, School of Dentistry, University of São Paulo. Associate Professor, Department of Maxillofacial Surgery, Prosthesis and Traumatology, School of Dentistry, University of São Paulo. c Engineer, Researcher, Renato Archer Information Technology Center, Ministry of Science and Technology. d Associate Professor, Department of Prosthesis, School of Dentistry, University of São Paulo. a
b
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May 2012 The surgical treatment of oral cancer results in anatomical and functional sequelae that can lead to functional disorders, psychological disorders, and esthetic issues.1,2 Surgical repairs using rotation flaps, soft tissue grafting, or bone grafting are not entirely effective in patients with extensive maxillary defects.2 Prosthetic rehabilitation can satisfactorily restore the functions of mastication1 and phonetics,2 thereby improving the patient’s quality of life. Extensive maxillary bone loss has a negative impact on the biomechanics of a maxillary obturator. Leverage and fulcrum lines can drastically increase stress on the supporting tissues during mastication,3,4 and the weight of the prosthesis on the supporting tissues can be an aggravating factor.5 Thus, analyses of the configuration and size of the maxillary lesion and of the remaining teeth are central to the success of the prosthesis and to the preservation of the supporting anatomical structures.6 A prosthetic design that is appropriate for the patient’s specific oral conditions is of utmost importance to the improvement of the stability and durability of the obturator prosthesis.4,7-9 Among the obturator prosthesis framework designs, one that warrants particular attention is the Aramany Class IV obturator design. Class IV defects are characterized by the resection of the premaxillae and the posterior maxilla on one side.6,7 This type of extreme defect has a negative impact on the biomechanics of the supporting tissues. Bone remodeling depends on the load level; stresses between 4 MPa and 8 MPa act as stimuli and increase bone density, but a stress of 9 MPa results in resorption and decreases bone density.10 The finite element method is an important research tool in the field of dentistry. This approach has been used for biomechanical analyses and has the advantages of being noninvasive and allowing the visualization of superimposed structures and the definition of the material properties
Miyashita et al
of craniofacial structures.11 In addition, this method can be used to establish the location, magnitude, and direction of an applied force and to locate stress points that can be measured theoretically. Importantly, this method can be repeated as many times as is necessary because it does not affect the physical properties of the analyzed materials.12 Numerous studies have reported that computed tomography (CT) scans, recorded as Digital Imaging Communications in Medicine (DICOM) files, can be used for the development of a 3-dimensional (3-D) model that can be evaluated by using finite element analysis.12-14 The purpose of this study was to evaluate, by using finite element analysis, the stress on the maxilla when an Aramany Class IV obturator prosthesis was subjected to posterior and anterior loads.
MATERIAL AND METHODS After approval was obtained from the Ethics Committee of the University of São Paulo Dental School, an adult man (>25 years of age) with no congenital or acquired defect in the craniofacial region underwent a CT scan (Light Speed 16 Pro; GE Medical Systems, Milwaukee, Wisc). The CT data were recorded as DICOM files and exported to a software package (InVesalius Software, v1.0; Renato Archer Information Technology Center, Campinas, Brazil) for image segmentation and conversion to stereolithography (STL) format. The STL files were transferred to a computer program (Magics X Service Pack 2 software, v1.1.17; Materialise, Leuven, Belgium), which was used to evaluate the files for possible image distortion.12,14 The STL files were then imported with another software package (Rhinoceros 3-D software; Robert McNeel & Associates, Seattle, Wash) and computer processed (Workstation Sun Microsystem ultra 20 M2; Sun Microsystems do Brasil Ltda, São
Paulo, Brazil) to generate a 3-D computer-aided design (CAD) model that simulated an Aramany Class IV maxillary defect.13 The lining mucosa was edited manually. To create a 3-D model of the removable partial dental prosthesis components, the STL model was prototyped with a rapid prototyping machine (ZPrinter 310 Plus; Z Corp, Burlington, Mass). An impression of the prototype was made with silicone putty (Silibor; Artigos Odontológicos Clássico Ltda, São Paulo, Brazil) to manufacture a maxillary cast poured with type IV dental stone (Durone C; Dentsply, Catanduva, Brazil). The cast was sectioned to simulate an Aramany Class IV maxillary defect, defined as a maxillary defect that crosses the midline, with a limited horizontal hard palatal shelf 6 identical to that edited on the CAD model of the maxilla. The experimental model considered a midline resection, and results indicated that stress tended to dissipate on the horizontal shelf; thus, this model is not truly representative of the clinical situation. Subsequently, the retention and stability components of the prosthesis were planned14 with a surveyor (Delineador B2; Bio-Art Equipamentos Odontológicos Ltda, São Carlos, Brazil). The wax pattern of the removable partial dental prosthesis was designed onto this cast to represent the metal framework of the prosthesis. The cast with the wax pattern was digitized with a surface scanner (Modela 3D Plotter MDX-20; Roland DG Corp, Hamamatsu-Shi, Shizuokaken, Japan). The data were transferred to the Rhinoceros 3-D software program, and the information obtained was superimposed onto the CAD model of the maxilla. A 1 mm width was established for the metal components, and the acrylic resin base of the prosthesis was edited manually. Thus, the CAD geometry consisted of the maxillary bone, teeth, mucosa, and obturator prosthesis (Fig. 1).
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1 CAD geometry consisting of maxillary bone, teeth, mucosa, and obturator prosthesis.
2 Finite element mesh.
Table I. Young’s modulus and Poisson’s ratio for anatomical structures and materials Materials
Young’s Modulus (Gpa)
Poisson’s ratio
Cortical bone18
14.7
0.3
Dentin
13.7
0.31
Palatal mucosa
0.68
0.45
Acrylic resin21
2.83
0.45
149
0.35
19 20
Cobalt-chromium alloy
22
Finite element analysis The CAD model generated in the previous steps served as the basis for the creation of the finite element mesh. The data from the CAD model were imported to a software package (Femap with NEi Nastran, NEi Software, Inc, Westminster, Calif ) in 3 different file formats: Step 214 (*.stp);
Acis (*.sat); and Parasolid (*.x_t). This software was used to evaluate the model for possible geometric inconsistencies, such as the absence of surfaces or curves and the formation of spaces between surfaces, and for dimensional inconsistencies, which were standardized in millimeters. The program used quadratic tetrahedral elements to determine vol-
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ume.12,14 The finite element mesh was generated in a controlled manner, which permitted better geometric homogeneity of the elements and better discretization of the model. To generate the mesh, the contact between the surfaces of interest was determined for the root surfaces and the alveolar bone surfaces, the hard palate mucosa and the hard palate bone, the hard palate mucosa and the palatal plate of the prosthesis, and the dental crown surfaces and the retention clasps of the prosthesis. This study considered a fixed interaction between the surfaces; all contacts between surfaces of interest were determined for a glueing with no dislocation between the surfaces. The teeth were considered as a whole, regardless of the differences between the dental pulp, dentin, cementum, and enamel.15 The periodontal ligament was not considered because it contributes little to the results of the finite element analysis.14,16 For the same reason, no distinction was made between cortical bone and cancellous bone, and the cortical bone was considered to be uniform in all regions.14, 17 Unlike the periodontal ligament, the contribution of the oral mucosa to the results of finite element analysis is not generally disregarded; therefore, the hard palate mucosa was considered in the analysis. The geometry of finite elements generated in the present study reached 166,046 elements and 281,928 nodes (Fig. 2). The elastic modulus (Young’s modulus) and Poisson’s ratio were determined for each anatomical structure and material: specifically, cortical bone,18 dentin,19 palatal mucosa,20 acrylic resin,21 and cobalt-chromium alloy22 (Table I). All elements were considered to be bodies with isotropic physical characteristics.12,14,15,18,20,23,24 A force of 120 N was applied to the occlusal (representing the posterior teeth) and to the incisal platforms (representing the anterior teeth) of the obturator prosthesis.25 To process the mesh, it was determined that the model should demonstrate linear
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3 A, Posterior load: stress distribution on palate. B, Posterior load: stress distribution along resection lines. C, Posterior load: stress distribution on alveolar bone adjacent to root surfaces. Maximum principal stress (MPa): compressive stress (blue); tensile stress (red).
4 A, Anterior load: stress distribution on palate. B, Anterior load: stress distribution along resection lines. C, Anterior load: stress distribution on the alveolar bone adjacent to root surfaces. Maximum principal stress (MPa): compressive stress (blue); tensile stress (red). elastic mechanical behavior.12,14,18,26 The results presented are based on a qualitative analysis, corresponding to the scale of maximum principal stress (represented by a color scale) and a quantitative analysis expressed in MPa.
RESULTS Posterior load Stress distribution on the palate was observed for the load applied to the posterior occlusal platform of the obturator prosthesis, causing a compressive stress of 3.25 MPa near the midline; this stress decreased gradually toward the posterior palate. Tensile stress was distributed over the anterior palate and alveolar ridge (3.68 MPa) and over the posterior palatal surface (2.37 MPa) (Fig. 3A). Compressive stress (3.62 MPa) connected to the resection lines was also observed along the midline, extending
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to the anterior resection line. Tensile stress was distributed over the transverse surface of the anterior resection line, reaching an intensity of 6.63 MPa in certain areas (Fig. 3B). Because of the stress distribution on the alveolar bone, predominantly tensile stress was observed in the apical regions of the teeth closest to the resection. The greatest distribution of tensile stress was observed in the region of the first premolar. Significant tensile stress (3.46 MPa) was observed in the area corresponding to the buccal surface of the root apex, and tensile stress of 2.15 MPa was observed in the area corresponding to the palatal surface of the root at the midcervical level. In the area corresponding to the mesial surface of the root, in the cervical region, compressive stress of 1.56 MPa was observed. On the alveolar surface of the second premolar, tensile stress was distributed in the area corresponding to the buccal surface of the root in the apical (1.93 MPa)
and cervical regions (2.37 MPa). No distribution of compressive or tensile stress was observed in the molar region (Fig. 3C). Anterior load Stress distribution on the palate was observed for the load applied to the anterior incisal platform of the obturator prosthesis, causing tensile stress of 2.27 MPa on the posterior palate near the midline. On the palatal surface of the alveolar ridge, the observed tensile stress was 2.72 MPa, but no compressive stress was observed. Minimal compressive stress (0.5 MPa) was observed in the region of the anterior palatal resection (Fig. 4A). Considerable tensile stress (7.27 MPa) was distributed along the resection line in the anterior region of the maxillary resection near the first premolar and along the buccal cortex. Minimal tensile stress (0.5 MPa) was distributed over the palatal region of
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Volume 107 Issue 5 the anterior resection line (Fig. 4B). Greater tensile stress was distributed over the alveolar bone in the cervical regions of the teeth closest to the anterior resection line; this stress gradually decreased toward the posterior teeth. Most of the stress was observed in the first premolar region. In the area corresponding to the mesial surface of the root in the cervical region, considerable tensile stress (up to 6.30 MPa) was observed. In the area corresponding to the palatal surface of the root at the midcervical level, tensile stress of 2.15 MPa was observed. In the area corresponding to the mesial surface of the root in the cervical region, compressive stress of 1.56 MPa was observed. Tensile stress was observed on the alveolar bone of the second premolar in the areas corresponding to the mesial (4.59 MPa) and distal surfaces of the root in the cervical region (4.55 MPa). Isolated points of tensile stress were observed in the first molar region; levels of 4.12 MPa were recorded in the area corresponding to the mesial surface of the root in the cervical region. Tensile stress of 1.36 MPa was observed in the area corresponding to the mesial surface of the root of the second molar in the cervical region (Fig. 4C).
DISCUSSION The process of finite element analysis began with the creation of a CAD model developed from the CT scans of selected biological structures.12,14 CT imaging yields highly complex images because of the morphology of biological structures. The bone density values provided by the CT scan were only considered during image segmentation in the original model. Density values were used to distinguish among the DICOM data provided for soft tissues, bone, and dental tissues; this method is the only way to reconstruct a CAD model of the maxilla. Adapting this complexity to the capacity of computing systems is essential to improving this process. Thus, the initial model was adjusted
to stabilize the CAD model that was subsequently exported to create the finite element geometry.12,14 The degree of complexity in finite element analysis is determined by the number and type of finite elements and by the physical and mechanical behaviors being considered. Numerous dental studies using finite element analysis have considered biological tissues to be materials with isotropic properties.12,14,15,18,20,23,24 The majority of these analyses have treated the materials as having linear elastic properties, in which the structural deformation is directly proportional to the applied forces.12,14,15,26 The same considerations were applied in the present study. In this study, a force of 120 N was applied to the prosthesis, a value previously established in a report that investigated occlusal force in partially edentulous patients with maxillary lesions.25 Most patients with residual support in premolar and/or molar regions tend to apply loads to their residual teeth, selecting this area as the best location for mastication.1 The maximal occlusal force measured at the best masticatory location varies according to gender, age, state of dentition, and anterior versus posterior regions.25 The mean maximal occlusal force at the best masticatory location for patients with remaining natural teeth and an obturator prosthesis has been reported to be 120 N.25 To the authors’ knowledge, no report identifying the maximal occlusal force values for artificial teeth located in a defect area is available, with the exception of a 52 N for complete denture wearers; thus, the experimental load used in the current study was 120 N.25 The analysis reported here, based on the finite element method, has limitations that should be considered when results are considered. The generation of the CAD geometry imposed some simplifications on the model, including a disregard for the periodontal ligament16,18,19 and lack of distinction between cortical and cancellous bone.16 The reported results
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only estimate locations and values for stress distribution within this study design. Principal stress represents the maximum value in only 1 dimension. Maximum principal stress analysis, which is associated with displacement analysis, may also be used to illustrate movement tendencies. Rotation is a large-scale movement that is directly related to dynamic analysis. In this sense, the static analysis conducted in this work is only able to indicate trends in movement. Because the model is static, maximum principal stress information can be used to indicate a rotation trend. This trend permits an assessment of whether greater tensile or compressive stress has occurred and in which direction it occurred. The experimental model considered a midline resection, and its results only indicate the tendency for stress to dissipate on the horizontal palatal shelf; thus, these results are not representative of the clinical situation. The obturator prosthesis exhibited a tendency to undergo vertical dislodgement under posterior and anterior loads and this tendency of the prosthesis to rotate may be expressed in the digital model by using the location and intensity of the tensile and compressive stresses. Thus, the great tensile stress at the limits of the maxillary resection and at the posterior palatal area (Figs. 3B and 4B, red), as well as the compressive stress at the anterior palate (Figs. 3A and 4A, blue), suggest the direction of prosthesis displacement under the applied load. The authors must emphasize that this study used static displacement; because movement is a dynamic condition and this analysis was limited by a static field, results may be interpreted only as displacements. Nevertheless, these results demonstrated the necessity of using the maximum number of direct and indirect retainers for prosthetic stability and warrant further studies to investigate different prosthetic designs.4,5,7-9 The prosthesis displayed a tendency to rotate under posterior load;
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May 2012 the axis of rotation was located near the resection line at the midline of the maxilla. Compressive stress was observed on the surface of the palate, distributed to the alveolar ridge, and on the resection line. However, the intensity of this stress was not sufficient to cause bone resorption according to a study on bone behavior under mechanical stimuli that resulted from critical stress values for mandibular bone at a initial composite (cancellous plus cortical) density of 1.0 g·cm-3.10 Edentulous mandibles and maxillae from fresh cadavers with a mean age of 83.25 years have been reported to have averaged composite densities of 1.18 g·cm3 and 0.67 g·cm3, respectively.17 Age-related decreases in bone density are well known, and this change is more evident in the posterior maxillary region; the cortical bone surfaces remain relatively hard.17 A fully mineralized solid matrix of bone, such as cortical bone, is considered to be quite uniform and its density can be measured.17 The present study considered the cortical densities of 3 different areas of the maxilla. Palatal shelves contain little bone marrow, and their composite densities are different from those of the buccal and alveolar cortical regions. Thus, only cortical density was considered in the current study. A value for the overall maxillary cortical density was not available for comparison with the present results; therefore, the results were compared to findings from a study that also used finite element analysis with tetrahedral elements with isotropic and linear elastic physical bone properties.10 To establish a parameter for bone physiology with remodeling under a load, it was assumed that 1.0 g·cm-3 was an appropriate density value in the present study.10 The compressive stress observed on the surface of the palate might be related to the location of the prosthetic retainers on the teeth. A study using a photoelastic model reported that retention clasps located on the buccal surfaces of the teeth caused stress distribution near the resection line and on the central portion of the
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remaining palate, and that retention clasps located on the lingual surfaces of the teeth caused less compressive stress.9 The metal framework design used in this study was proposed by Aramany and consists of buccal retainers on the premolars and palatal retainers on the molars.7 The reciprocating arms remain completely above the height of teeth contour to stabilize the dental prosthesis during insertion and removal. The present study used static analysis, and the reciprocating arms of the Aramany Class IV framework design were not considered in the digital model because they were not expected to affect the results. Based on this framework design, the results demonstrate that under a posterior load, more stress is distributed to the osseous tissue in the premolar region, less stress is distributed in the molar region, and more stress dissipation occurs in the premolar area and at the anterior resection, all of which is consistent with previous observations.9 The distribution of tensile stress on the alveolar bone, which was more intense in the apical regions and less intense in the cervical regions of the teeth and was limited to the areas of the first and second premolars, has previously been described.8 In the present study, no stress was observed on the alveolar bone in the molar region; this result is not in agreement with those of a previous study that used an experimental model not based on tooth anatomy or clinical prosthetic design.4 Under an anterior load, minimal compressive stress was observed on the surface of the palate, indicating that the prosthesis caused no significant distribution of compressive stress on the maxillary bone. The tensile stress observed in the posterior region of the palate might be clinically interpreted as a tendency of the prosthesis to be dislodged toward the midline. The increased distribution of tensile stress on the anterior resection line along the buccal cortex and near the first premolar also suggested a tendency of the prosthesis to be dis-
lodged; the rotation axis was located near the anterior resection line. The intensity of the applied stress was not sufficient to cause bone resorption because increased bone density has been observed under constant loading stresses of 4, 6, and 8 MPa.10 Periodontal and orthodontic studies based on finite element analysis have suggested that only stresses greater than 5 MPa can trigger the process of bone resorption.23,24 However, this value should only be considered as a reference for the physiological limits of bone tissue because the present experimental model did not consider the biomechanical behaviors of the periodontal ligament and cancellous bone. The stress distribution did not exceed the physiological limits of the bone tissue. The locations and intensities of the tensile and compressive stresses observed in the digital model merely suggest tendencies of the prosthesis to be dislodged. Therefore, the framework design used in this study was considered to be optimal. The 3-D maxillary model was based on a CT scan of an individual without periodontal disease; the locations and the intensities of the stress distributions observed under the experimental conditions might inform and guide prosthetic planning in clinical situations in which periodontal disease is present and the Aramany Class IV obturator prosthesis is required.
CONCLUSIONS Under the experimental conditions used in the present study, there was evidence that the Aramany Class IV obturator prosthesis may dislodge, tending to rotate toward the resection area when loads are applied to the posterior and anterior regions. Under a force of 120 N applied to the occlusal and incisal platforms, the tensile and compressive stress caused by the Aramany Class IV obturator prosthesis did not exceed the physiological limits of the maxillary cortical bone tissue.
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Volume 107 Issue 5 REFERENCES 1. Matsuyama M, Tsukiyama Y, Tomioka M. Clinical assessment of chewing function of obturator prosthesis wearers by objective measure of masticatory performance and maximum occlusal force. Int J Prosthodont 2006;19:253-7. 2. Eckardt A, Teltzrow T, Schulze A, Hoppe M, Kuettner C. Nasalance in patients with maxillary defects - reconstruction versus obturation. J Craniomaxillofac Surg 2007;35:241-5. 3. Desjardins RP. Obturator prostheses design for acquired maxillary defects. J Prosthet Dent 1978;39:424-35. 4. Firtell DN, Grisius RJ. Retention of obturator-removable partial dentures: a comparasion of buccal and lingual retention. J Prosthet Dent 1980;43:212-7. 5. Schwartzman B, Caputo A, Beumer J. Gravity-induced stresses by an obturator prostheses. J Prosthet Dent 1990;64:466-8. 6. Aramany MA. Basic principles of obturator design for partially edentulous patient. Part I: classification. J Prosthet Dent 1978;40:554-7. 7. Aramany MA. Basic principles of obturator design for partially edentulous patient. Part II: design principles. J Prosthet Dent 1978;40:656-62. 8. Schwartzman B, Caputo A, Beumer J. Occlusal force transfer by removable apartial denture designs for a radical maxillectomy. J Prosthet Dent 1985;54:397-403. 9. Myers RE, Mitchell DL. A photoelastic study of stress induced by framework design in a maxillary resection. J Prosthet Dent. 1989;61:590-4. 10.Li J, Li H, Shi L, Fok AS, Ucer C, Devlin H, et al. A mathematical model for simulating the bone remodeling process under mechanical stimulus. Dent Mater 2007;23:1073-8.
11.Sun J, Jiao T, Tie Y, Wang DM. Threedimensional finite element analysis of the application of attachment for obturator framework in unilateral maxillary defect. J Oral Rehabil 2008; 35:695-9. 12.Gao J, Xu W, Ding Z. 3D finite element mesh generation of complicated tooth model based on CT slices. Comput Meth Programs Biomed 2006;82:97-105. 13.Ramos A, Simões JA. Tetrahedral versus hexahedral finite elements in numerical modelling of the proximal femur. Med Eng Phys 2006;28:916-24. 14.Zhao L, Herman E, Patel PK. The structural implications of a unilateral facial skeletal cleft: a three-dimensional finite element model approach. Cleft Palate Craniofac J 2008;45:121-30. 15.Rubin C, Krishnamurthy N, Capilouto E. Stress analysis of human tooth using a three-dimensional finite element model. J Dent Res 1982;62:82-6. 16.Reina JM, Garcia-Aznar JM, Dominguez J, Doblare M. Numerical estimation of bone density and elastic constants distribution in a human mandible. J Biomech 2007;40:828-36. 17.Seong WJ, Kim UK, Swift JQ, Heo YC, Hodges JS, Ko CC. Elastic properties and apparent density of human edentulous maxilla and mandible. Int J Oral Maxillofac Surg 2009;38:1088-93. 18.Moroi HM, Okimoto K, Moroi R, Terada Y. Numeric approach to the biomechanical analysis of thermal effects in coated implants. Int J Prosthodont 1993;6:564-72. 19. Sano H, Ciucchi B, Mathews WG, Pashley DH. Tensile properties of mineralized and demineralized human and bovine dentin. J Dent Res 1994;73:1205-11. 20.Ress JS, Huggett R, Harrison A. Finite element analysis of the stress-concentrating effect of fraenal notches in complete dentures. Int J Prosthodont 1990;3:238-40.
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21.Peyton FA, Craig RG. Current evaluation of plastics in crown and bridge prosthesis. J Prosthet Dent 1963;13:745-53. 22.Morris HF. Properties of cobalt-chromium metal ceramic alloys after heat treatment. J Prosthet Dent 1990;63:426-33. 23.Poppe M, Bourauel C, Jäger A. Determination of the elasticity parameters of the human periodontal ligament and the location of the center of resistance of single-rooted teeth a study of autopsy specimens and their conversion into finite element models. J Orofac Orthop 2002;16:358-70. 24.Kojima Y, Fukui H. A numerical simulation of tooth movement by wire bending. Am J Orthod Dentofacial Orthop 2006;130:452-9. 25.Wedel A, Yontchev E, Carlsson GE, Ow R. Masticatory function in patients with congenital and acquired maxillofacial defects. J Prosthet Dent 1994;72:303-8. 26.Sandu L, Faur N, Bortun C. Finite element stress analysis and fatigue behavior of cast circumferential clasps. J Prosthet Dent 2007;97:39-44. Corresponding author: Dr Beatriz Silva Câmara Mattos School of Dentistry University of São Paulo Av. Lineu Prestes, 2227 05508-000 Cidade Universitária São Paulo, SP BRAZIL Fax: +5511-30917887 E-mail: [email protected] Copyright © 2012 by the Editorial Council for The Journal of Prosthetic Dentistry.
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