三級異常咬合的特徵之一是下顎過度生長，但目前對於此種異常咬合的下顎局部結構的形態變異仍待釐清。下顎前突伴隨上顎正常的三級異常咬合經常使用頦帽裝置來進行矯正治療。而對於上顎後縮並伴隨下顎前突的三級異常咬合則使用上顎前方牽引整合頦帽裝置(OMA)加以治療。雖然三級異常咬合之下顎骨整形治療效果已廣泛地利用傳統測顱術進行分析。然而，這些分析卻無法提供下顎骨形態變化的詳細確切位置。

本論文主要的研究目的有兩項，第一項是利用幾何形態測量學來探討整形治療對下顎形態的變化，其方法包括普氏疊合分析、形態統計分析、薄板仿樣分析與應變張量分析。第二項則是使用有限元素分析法來探討整形力的大小與方向對下顎的生物力學影響。並利用此二項結果進一步的探討瞭解整形力對下顎的生物力學效應(應力與應變分佈)與下顎形態變化的相互影響關係。

結果顯示應變張量分析能有效地表示出下顎的形態差異。其中，下巴附近、門齒齒槽骨區域與下顎支上方部位是主要的尺寸與形狀變化的最顯著局部區域。整形治療後的下顎生長方向明顯地被改變，方向改朝為垂直下顎平面伸張生長。此種下顎生長趨勢改變在頦帽裝置與上顎前方牽引整合頦帽裝置治療者都有發現。此外，利用下顎矯正結果的形態扣除三級下顎自然的生長因素，以分析模擬單純由整形力所造成的下顎形態影響，也獲得初步的下顎形態變化結果。至於三維下顎有限元素分析方面，研究發現整形力的施力方向比施力大小來得重要，主要是彎矩效應在此下顎結構的施力方向，此彎矩對於應力與應變分佈的角色扮演著重要的影響。透過應變張量分析與有限元素分析的比對，初步無法直接獲得應力和應變分佈與下顎形態變化之相互關係。推測可能的原因為下顎有限元素分析中的模擬條件過於簡化，或是兩者不同分析方法(尤其在維度的差異)本來就無法進行比對探討。

Overdeveloped mandible is one of the features in Class III malocclusion, but the significance of morphological variations in regional configuration of the mandible remains unclear. For Class III malocclusion with or without maxillary retraction, the orthopedic technique with chin cup appliance is frequently required to correct the mandibular prognathism. Class III subjects with a retrognathic maxilla and prognathic mandible could be improved intermaxillary skeletal disharmony by occipito-mental anchorage (OMA) appliance of maxillary protraction combined with chin cup for orthopedic treatment. The effects of orthopedic therapy on the mandible in Class III malocclusion have been investigated extensively through cephalometric analyses. However, the actual sites of skeletal change in the mandible are not detectable with conventional cephalometric analysis.

The aims of this study were two folds. First, to investigate the mandibular morphological changes under orthopedic force by the integration of new geometric morphometric analyses, including: Procrustes superimposition, biostatistical estimation, thin-plate spline interpolation, and strain tensor analysis. Second, to analyze the biomechanical responses of orthopedic mandibular treatment under varied force magnitudes and directions with finite element (FE) analysis. Furthermore, the results of the morphological changes are linked with the biomechanical responses from FE analysis to establish the relationship between morphological change and stresses distribution under corrective forces.

The results show that the strain tensor analysis effectively demonstrated the morphological differences of the mandible under orthopedic forces. The significant local deformations of size and shape changes were revealed at the region of chin, incisor alveolus as well as the upper portion of the ascending ramus. The growth directions (principal strain vector) of the Class III mandible was significantly redirected to the direction perpendicular to the long axis of general mandibular morphology after orthopedic therapy. The patterns of growth vectors on the Class III mandible were almost the same in both the chin cup and the OMA appliance therapies. Furthermore, the pretreatment effects (without Class III growth) in morphological changes were detected, using the after treatment shape to eliminate the natural growth of Class III mandible. From the finite element analysis of the three-dimensional mandible structure, it revealed that the direction of orthopedic force applied is more important than the magnitude of force. The key factor is the bending effect of the orthopedic force. The relationship between morphological change and stresses and strains distribution could not be identified in this study. The reason might be the simplistic assumptions of this FE pilot study in representing the mandibular biomechanical response to the orthopedic force. Moreover, it may be insufficient to obtain the correlation base on these two different methods especially when their dimensions are mismatch.

[1] Enlow DH, Hans MG. Essentials of facial growth. W. B. Saunders, Philadelphia Pennsylvania, 1986.

[2] Lavelle CLB. A preliminary study of mandibular shape. J Craniofac Genet Dev Biol 1985; 5:159-165.

[3] Angle EH. Classification of malocclusion. Dental Cosmos 1899; 41:248-264.

[4] Ackerman JL, Profitt WR. Diagnosis and planning treatment in orthodontics. In: Graber TM, Swain, BF (Eds). Current Orthodontic Concepts and Techniques. WB Saunders Co., Philadelphia, pp. 1-110, 1975.

[5] Rakosi T, Schilli W. Class III anomalies: a coordinated approach to skeletal dental, and soft tissue problems. J Oral Surg 1981; 39:860-870.

[6] Allright WC, Burndred WH. A survey of handicapping dentofacial anomalies among Chinese in Hong-Kong, Int J Dent 1964; 14:505-519.

[7] Kitai N, Takada K, Yasada Y, Adachi S, Sakuda M. School health database and its application. J Japan Orthod Soc 1989; 24:33-38.

[8] Chang HP. Components of Class III malocclusion in Taiwanese. Kaohsiung J Med Sci 1985; 1:144-155.

[9] Graber LW. Chin cup therapy for mandibular prognathism. Am J Orthod 1977; 72:23-41.

[10] Jacobson A, Evans WG, Preston CB, Sadwsky PL. Mandibular prognathism, Am J Orthod 1974; 66:140-71.

[11] Kameda A. The Begg technique in Japan. Am J Orthod 1982; 81:209-227.

[12] Yang WS. The study on the orthodontic patients who visited department of orthodontics, Seoul National University Hospital. J Korean Dent Assoc 1990; 28:811-821.

[13] Susami R, Asai Y, Hirose K, Hosoi T, Hayashi I. The prevalence of malocclusion in Japanese school children. J Jpn Orthod Soc 1972; 31:319-324.

[14] Sanborn RT. Differences between the facial skeletal patterns of Class III malocclusion and normal occlusion. Angle Orthod 1955; 25:208-222.

[15] Dietrich UC. Morphological variability of skeletal Class III relationships as revealed by cephalometric analysis. Trans Eur Orthodo Soc 1970; 46:77-88.

[16] Ellis EE, McNamara JA Jr. Components of adults Class III malocclusion. J Oral Maxillofac Surg 1984; 42:295-305.

[17] Cohlmia JT, Ghosh J, Sinha PK, Nanda RS, Currier GF. Tomographic assessment of temporomandibular joints in patients with malocclusion. Angle Orthod 1996; 66:27-35.

[18] Kerr WJ, Ten Have TR. Mandibular position in Class III malocclusion. Br J Orthod 1988; 15:241-245.

[19] McNamara JA Jr. A method of cephalometric evaluation. Am J Orthod 1984; 86:449-469.

[20] Nanda RS, Merrill RM. Cephalometric assessment of sagittal relationship between maxilla and mandible. Am J Orthod Dentofac Orthop 1994; 105: 328-344.

[21] Ahlgren J. Form and function of Angle Class III malocclusion. A cephalometric and electromyographic study. Trans Eur Orthod Soc 1970; 77-88.

[22] Björk A. Some biological aspects of prognathism and occlusion of the teeth. Acta Odont Scand 1950; 9:1-4.

[23] Stephen HY. A roentgenographic cephalometric study of prognathism in Chinese males and female, Am J Orthod 1968; 38:305-320.

[24] Chan KH. Class III malocclusion in Chinese (Cantonese): Etiology and treatment. Am J Orthod Dentofac Orthop 1974; 65:152-157.

[25] Jacobson A, Evans MS, Preston CB, Sadowsky PL. Mandibular prognathism. Am J Orhtod 1974; 66:141-171.

[26] Joffe BM. Cephalometric analysis of mandibular prognathism. Master’s thesis, University of the Witwatersrand, Johannesburg, 1964.

[27] Bjork A, Skieller V. Facial development and tooth eruption. Am J Orthod 1972; 62:339-383.

[28] Moss ML, Salentijn L. The logarithmic growth of the human mandible. Acta Anat 1970; 77:341-360.

[29] Enlow DH. Role of the TMJ in facial growth and development, conference on examination, diagnosis, and management of temporomandibular disorders. Chicago: American Dental Association, 1983.

[30] Hans MG, Enlow DH, Noachtar R. Aged-related differences in mandibular ramus growth: a histologic study. Angle Orthod 1995; 65:335-340.

[31] Weinberger BW. Orthodontics: An historical review of its origin and evolution. CV Mosby, St. Louis, 1926.

[32] Deguchi T, McNamara JA Jr. Craniofacial adaptations induced by chincup therapy in Class III patients. Am J Orthod Dentofac Orthop 1999; 115: 175-182.

[33] Vego L. Early orthopedic treatment for Class III skeletal patterns. Am J Orthod 1976; 70:59-69.

[34] Allen RA, Connolly IH, Richardson A. Early treatment of Class III incisor relationship using the chincap appliance. Eur J Orhtodont 1993; 15:371-376.

[35] Janzen EK, Bluher JA. The cephalometric, anatomic and histologic changes in Macaca mulatta after application of a continuous-acting retraction force on the mandible. Am J Orthod 1965; 51:823-855

[36] Joho JP. The effects of extraoral low-pull traction to the mandibular detition of Macaca Mulatta. Am J Orthod 1973; 64:555-577.

[37] Asano T. The effects of mandibular retractive force on the growing rat mandible. Am J Orthod Dentofac Orthop 1986; 90:464-474.

[38] Irie M, Nakamura S. Orthopedic approach to severe skeletal Class III malocclusion. Am J Orthod 1975; 67:377-392.

[39] Suzuki N. A cephalometric observation on the effect of the chin cap. J Jpn Orthod Soc 1972; 31:64-74.

[40] Sugawara J, Asano T, Endo N, Mitani H. Long-term effects of the chincap therapy on skeletal profile in mandibular prognathism. Am J Orthod Dentofac Orthop 1990; 98:127-133.

[41] Abu Alhaija ESJ, Richardson A, long-term effect of the chincap on hard and sort tissues. Eur J Orhtodont 1999; 21:291-298.

[42] Üçüncü N, Üçem TT, Yüksel S, A comparison of chincap and maxillary protraction appliances in the treatment of skeletal Class III malocclusion. Eur J Orhtodont 2000; 22:43-51.

[43] Pearson LE, Treatment of a severe openbite excessive vertical pattern with an electric non-surgical approach. Angle Orthod 1991; 61:71-76.

[44] Hata S, Ito T, Nakagawa M, Kamogashira K, Ichikawa K, Matsumoto M, Chaconas SJ, Biomechanical effects of maxillary protraction on the craniofacial complex. Am J Orthod Dentofac Orthop 1987; 91:305-311.

[45] Canut JA, Dalmases F, Gandia JL, Salvador R. Effects of maxillary protraction determined by laser metrology. Eur J Orthodont 1990; 12:340-345.

[46] Graber TM, Chung DDB, Aoba TJ. Dentofacial orthopedics versus orthodontics. J Am Dent Assoc 1967; 75:1145-1160.

[47] Thilander B. Chin-cap treatment for Angle Class III malocclusion: a longitudinal study. Trans Eur Orthod Sco 1965; 67:311-327.

[48] Armstrong CJ. A clinical evaluation of the chin cup. Aust Dent J 1961; 6:338-346.

[49] Mitani H, Sakamoto T. Chin cap force to a growing mandible: long-term clinical reports. Angle Orthod 1984; 54:93-122.

[50] Deguchi T, Kuroda T, Minoshima Y, Graber TM. Craniofacial features of patients with Class III abnormalities: Growth-related changes and effects of short-term and long-term chincup therapy. Am J Orthod Dentofac Orthop 2002; 121: 84-92.

[51] Kettle M A, Burnapp DR. occipito-mental anchorage in orthodontic treatment of dental deformities due to cleft lip and palate. British Dent J 1955; 99:11-14.

[52] Kiyomura H, Niwa K, Hibino T. Two cases of mandibular protrusion treated with occipito-mental anchorage. J Japanese Orthod Soci 1969; 28:134-145.

[53] Kiyomura H. A cephalometric appraisal of mandibular protrusion treated with occipito-mental anchorage. J Japanese Ortho Soci 1970; 29:197-205.

[54] Kinoshita Z, Yamamoto J, Shimozuma K, Kubo S, Kagawa M, Murao S, Yamawaki H. Treatment effects of occipito-mental anchorage appliance and orthopedic mask. J Kinki-Tokai Orthod Soci 1977; 12: 71-81.

[55] Moyers RE, Bookstein FL. The inappropriateness of conventional cephalometrics. Am J Orthod 1979; 75:599-617.

[56] Bookstein FL. On the cephalometrics of skeletal change. Am J Orthod 1982; 82:177-198.

[57] Yaroch LA. Shape analysis using the thin-plate spline: Neanderthal cranial shape as an example. Yearbook Phys Anthro 1996; 39:43-89.

[58] Bookstein FL. Thin-plate splines and the atlas problem for biomedical images. Lecture Notes in Compu Sci 1991; 511:326-342.

[59] Terzopoulos D. Multilevel computational processes for visual surface reconstruction. Computer, Graphics, and Image Processing 1983; 24:52-96.

[60] Bookstein FL. Principal warps: Thin-plate splines and the decomposition of deformations. IEEE Trans Pattern Anal Mach Intell 1989; 11:567-585.

[61] Zelditch ML, Bookstein FL, Lundrigan BL. Ontogeny of integrated skull growth in the cotton rat sigmodon fulviventer. Evolution 1992; 46:1164-1180.

[62] Thompson DW. On growth and form. Cambridge University Press, Cambridge, UK, 1917.

[63] Moyers RE, Bookstein FL, Guire KE. The concept of pattern in craniofacial growth. Am J Orthod 1979; 76:136-148.

[64] Bookstein FL. Looking at mandibular growth: some new geometric methods. In: Carlson, D.S. (Ed.), Craniofacial biology, Monograph No. 10, Craniofacial Growth Series. Center for Human Growth and Development, University of Michigan, Ann Arbor, Michigan, 83-103, 1981.

[65] Bookstein FL. Describing a craniofacial anomaly: finite elements and the biometrics of landmarks location. Am J Phys Anthrop 1987; 74:495-509.

[66] Bookstein FL. The geometry of craniofacial growth invariants. Am J Orthod 1983a; 83:221-234.

[67] Bookstein FL. Measuring treatment effects on craniofacial growth. In: McNamara, J.A., Ribbens, R., Howe, R.P. (Eds.), Clinical alternation of growing face, Monograph No. 14, Craniofacial Growth Series. Center for Human Growth and Development, University of Michigan, Ann Arbor, Michigan, 65-80, 1983b.

[68] Bookstein FL. Tensor biometrics for changes in cranial shape. Ann Hum Biol 1984; 11:413-437.

[69] Moss ML. The application of the finite element method to the analysis of craniofacial growth and form. Acta Morphol Neerl Scand 1985; 23:337-356.

[70] Moss ML, Skalak R, Patel H, Sen K, Moss-Salentijn L, Shinozuka M, Vilmann H. Finite element method modeling of craniofacial growth. Am J Orthod 1985; 87:453-472.

[71] Moss ML, Moss-Salentijn L, Skalak R. Finite element method modeling of craniofacial growth and development. In: Graber, L.W. (Ed.), OrthodonticsState of the art; essence of the science. CV Mosby Co, St. Louis, 143-168, 1986.

[72] Cheverud JM, Lews J, Bachrach W, Lew W. The measurement of form and variation in form: an application of three-dimensional quantitative morphology by finite element methods. Am J Phys Anthropol 1983; 62:151-165.

[73] Cheverud JM, Richtsmeier JT. Finite element scaling applied to sexual dimorphism in Rhesus Macaque (Macaca Mulatta) facial growth. Syst Zool 1986; 35:381-399.

[74] Richtsmeier JT, Cheverud JM. Finite element scaling analysis of human craniofacial growth. J Craniofac Genet Devel Biol 1986; 6:289-323.

[75] Battagel JM. Tensor analysis of facial growth in males. Eur J Orthodont 1995; 17:215-229.

[76] Sameshima GT, Melnick M. Finite element-based cephalometric analysis. Angle Orthod 1994; 64:343-350.

[77] Singh GD, McNamara JA Jr, Lozanoff S. Morphometry of the cranial base in subjects with Class III malocclusion. J Dent Res 1997; 76:694-703.

[78] Singh GD, McNamara JA Jr, Lozanoff S. Localization of deformations of the midfacial complex in subjects with Class III malocclusions employing thin-plate spline analysis. J Anat 1997; 191:595-602.

[79] Singh GD, McNamara JA Jr, Lozanoff S. Mandibular morphology in subjects with Angle’s Class III malocclusion: finite element morphometry. Angle orthod 1998; 68:409-418.

[80] Singh GD, McNamara JA Jr, Lozanoff S. Spline analysis of the mandible in human subjects with Class III malocclusion. Archs Oral Biol 1997; 42:345-353.

[81] Franchi L, Baccetti T, McNamara JA Jr. Thin-plate spline analysis of mandibular growth. Angle Orthod 2001; 71:83-89.

[82] Churches AE, Howlett CR, Waldron KJ, Ward GW. The response of living bone to controlled time-varying loading: method and prelimary results. J Biomech 1979; 12:35-45.

[83] Tanne K. Association between mechanical stress and bone remodeling. J Osaka Uni Dent Sch 1990; 30:64-71.

[84] Tanne K, Hlirage J, Kakiuchi K, Yamagata Y, Sakuda M. Biomechanical effect of anteriorly directed extraoral forces on the craniofacial complex: a study using finite element method. Am J Orhtod Dentofac Orthop 1989; 95:200-207.

[85] Tanne K, Sakuda M. Biomechanical and clinical changes of the craniofacial complex from orthopedic maxillary protraction. Angle Orhtod; 1991; 61:145-152.

[86] Tanne K, Lu YC-L, Tanaka E, Sakuda M. Biomechanical changes of the mandible from orthopedic chin cup force studied in a three-dimensional finite element method. Eur J Orthod 1993; 5:527-533.

[87] Tanne K, Tanaka E, Sakuda M. Stress distribution in the temporomandibular joint produced by orthopedic chin forces applied in varying directions: A three-dimensional analytic approach with the finite element method. Am J Orhtod Dentofac Orthop 1996; 110:502-507.

[88] Tanne K, Matsubara S. Association between the direction of orthopedic headgear force and sutural responses in the nasomaxillary complex. Angle Orthod 1996; 66:125-130.

[89] Tanne K, Miyasaka J, Yamagata Y, Sachdeva R, Tsutsumi S, Sakuda M. Three-dimensional model of the human craniofacial skeleton: method and preliminary results using finite element analysis. J Biomed Eng 1988; 10:246-252.

[90] Tanne K, Hiraga J, Sakuda M. Effects of directions of maxillary protraction forces on biomechanical changes in craniofacial complex. Eur J orhtod 1989; 11:382-391.

[91] Tanne K, Matsubara S, Sakuda M. Stress distributions in the naxillary complex form orthopedic headgear forces. Angle Orthod 1993; 63:111-118.

[92] Beek M, Koolstra JH, Van Ruijven LJ, Van Eijden TMGJ. Three-dimensional finite element analysis of the human trmporomandibular joint disc. J Biomec 2000; 33:307-316.

[93] Ferrario VF, Sforza C. Biomechanical model of the human mandible in unilateral clench: distribution of temporomandibular joint reaction forces between working and balancing sides. J Prosth Dent 1994; 72:169-176.

[94] Kanematsu S. Dentofacial changes produced by extraoral posterior force on the mandible of Macaca irus. J Jpn Orhtod Soc 1988; 47:1-36.

[95] Deguchi T, Kitsugi A. Stability of changes associated with chin cup treatment. Angle Orthod 1996; 66:139-146.

[96] Gower JC. Generalized Procrustes analysis. Psychometrika 1975; 40:33-50.

[97] Rohlf FJ, Slice D. Extensions of the Procrustes method for the optimal superimposition of landmarks. Syst Zool 1990; 39:40-59.

[98] Goodall CR. Procrustes methods in the statistical analysis of shape. J Royal Stat Soc B 1991; 53:285-339.

[99] Liu PH, Chang CH, Chang HP. Investigation of midfacial and mandibular morphology: Strain tensor analysis. J Chinese Inst Eng 2003; 26:771-780.

[100]Chang CH. Computer aided analysis of femoral stem prosthesis. PhD Thesis, Rice University, USA, 1990.

[101]Chang HP, Kinoshita Z, Kawamoto T. Craniofacial pattern of Class III deciduous dentition. Angle Orthodontics 1992; 62:139-144.

[102]Miyajima K, McNamara JA Jr., Sana M, Murata S. An estimation of craniofacial growth in the untreated Class III female with anterior crossbite. Am J Orthod Dentofac Orthop 1997; 112: 425-434.

[103]Susami R. A cephalometric study of dentofacial growth in mandibular prognathism. J Japan Orthod Soc 1967; 26:1-34.

[104]Rohlf FJ. Relationships among eigenshape analysis, Fourier analysis, and analysis of coordinates. Math Geol 1986; 18:845-854.

[105]Lele S, Richtsmeier JT. Euclidean distance matrix analysis: A coordinate free approach for comparing biological shapes and using landmark data. Am J Phys Anthropol 1991; 86:415-28.

[106]Richtsmeier JT, Cheverud JM, Jele S. Advances in anthropological morphometrics. Ann Rev Anthropol. 1992; 21:283-305.

[107]Rohlf FJ, Marcus LF. A revolution in morphometrics. Trends Ecol Evol. 1993; 8:129-132.

[106]Sugawara J, Mitani H. Facial growth of skeletal Class III malocclusion and the effects, limitations, and long-term dentofacial adaptations to chincap therapy. Semin Orthod 1997; 3:244-254.

[107]Karlsen AT. Longitudinal changes in Class I subjects with moderate mandibular skeletal protrusion. Angle Orthod 1998; 68:431-438.

[108]Kerr WJ, Miller S, Ayme B, Wihelm N. Mandibular form and position in 10-year-old boys. Am J Orthod Dentofac Orthop 1994; 106:115-120.

[109]Ishikawa H, Nakamura S, Kim C, Iwasaki, H, Satoh Y, Yoshida S. Individual growth in Class III malocclusions and its relationship to the chin cap effects. Am J Orthod Dentofac Orthop 1998; 114:337–346.

[110]Chang Hong-Po, Wu Yih-Ming. A roentgenographic cephalometric study of Class III malocclusion among Chinese children. Formosan Science 1985; 39:1-14.

[111]Courant R. Variational methods for the solution of problems of equilibrium and vibrations. Bulletin Am Mathe Socie 1943; 49:1-23.

[112]Knoell AC. A mathematical model of an in vitro human mandible. J Biomechan 1977; 10:159-166.

[113]Meijer HJA, Starmans FJM, Steen WHA, Bosman F. A three-dimensional finite element study on two versus four implants in an edentulous mandible. 1994; 7:271-279.

[114]Benzing UR, Gall H, Weber H. Biomechanical aspects of two different implant-prosthetic concepts for edentulous maxillae. Int J Oral Maxillofac Implants 1995; 10:188-198.

[115]Nedoma J, Stehlik J. Mathematical simulation of osteotomy. Numerical analysis and results. J Comp Appl Math 1995; 63:421-438.

[116]Cowin SC, Mehrabadi M. Identification of elastic symmetry of bone and other materials. J Biomechan 1989; 22:503-515.

[117]Kregde M. Amethod of selecting the best implant prosthesis design option using three-dimensional finite element analysis. In J Oral Maxillofac Implants 1993; 8:662-673.

[118]Deguchi T. Force distribution of the temporomandibular joint and temporal bone surface subjected to the head-chincup force. Am J Orthod Dentofac Orthop 1998; 114:277-282.

[119]Vollmer D, Meyer U, Joos U, Vègh A, Piffkò J. Experimental and finite element study of a human mandible. J Cranio Maxillofac Surg 2000; 28:91-96.

[120]Chen J, Akyuz U, Xu L, Pidaparti RMV. Stress analysis of the human temporomandibular joint. Med Eng Phys 1998; 20:565-572.

[121]Barbenel JC. The biomechanics of the temporomandibular joint:a theoretical study. J Biomechan 1972; 5:251-256.

[122]Boyd RL, Gibbs CH, Mahan PE, Tichmond AF Laskin JL. Temporomandibular joint forces measured at the condyle of macaca arctoides. Am J Orthod dentofac Orthop 1990; 97:471-479.

[123]Katona T. The effect of cusp and jaw morphology on the forces on teeth and temporomandibular joint. J Oral Rehab 1989; 16:211-219.

[124Rubin C, Krishnamurthy N, Caoliouto E, Yi H. Stress analysis of the human tooth using a three-dimensional finite element model. J Dent Res 1983; 62:82-86.

[125]Benzing UR, Gall H, Weber H. Biomechanical aspects of two different implant-prosthetic concepts for edentulous maxillae. Int J Oral Maxillofac Implants 1995; 10:188-198.