- Email: [email protected]
Muscular guidance of human jaw laterodeviations
DEVELOPMENT ELEMENT MODEL
OF A THREE DIMENSIONAL FINITE OF THE HUMAN TEMPOROMANDIBULAR JOINT M. Beek, L.J. van Ruijven, E. Donker, J.H. Koolstra, T.M.G.J. van Eijden Department of Functional Anatomy, Academic Centre for Dentistry Amsterdam-ACTA INTRODUCTION: The human temporomandibular joint consists of two incongruent articular surfaces, coveted with a cartilage layer and separated by a cartilaginous articular disc. The finite element method is capable of determining stresses and deformations in such complex geometries. However, relevant research is still limited to two dimensional (2D) geometries (Chen et al.. 1994). Therefore, a method to create a tetrahedral mesh representing a three dimensional (3D) cartilage layer was developed. METHODS: The 3D geometry of the articulating surface was measured using a magnetic tracking device (An et al., 1988). The coordinates, obtained in random order, were arranged into an orthogonal grid and then fitted to polynomials. The algorithm was tested using known mathematical surfaces. A 2D Delaunay triangulation was applied to points on the grid. Their spatial coordinates were calculated using the polygons. A volume could be created using an approximate thickness of the cartilage. This volume was tilled with tetrahedral elements. A polyquad surface was modelled to represent the bony surface. The contact between the rigid surface and the elements was modelled to be fixed. RESULTS: For all surfaces tested the algorithm converged to a satisfying solution. The error was largest near the edge of the surface. The mesh generated from the fitted polynomials consisted of fairly well shaped elements, except for those near the border. Simulating free movement of the model without any loads resulted in Cauchy stresses of less than 30 N/m2. DISCUSSION: The fitting algorithm depends greatly on the fact whether an articular surface can be described by polynomials. The mesh can be improved by a controlled placement of the points on the grid, a more sophisticated method of smoothing, and by triangulating directly in three dimensions. The model can be made more realistic by measuring the thickness of the cartilage. CONCLUSION: The method we developed, can be used to transform the 3D geometrical data of a cartilage layer into a tetrahedral mesh for finite element analysis. REFERENCES: 1. An et al., J. Biomech., 21, 613-620. 1988. 2. Chen et al., .I. Biomech. Eng.. I 16, 401-407, 1994. ACKNOWLEDGEMENT: This work was sponsored by the National Computing Facilities Foundation (NCF) for the use of supercomputer facilities, with financial support from the Netherlands Organization for Scientific Research (NWO). CORRESPONDENCE: M. Beek Dept. of Functional Anatomy - ACTA, Meibergdreef 15, 1105 AZ, Amsterdam, The Netherlands, tel: +31 20 5665355, fax: +31 20 6911856, [email protected]
I I'"
Conference
of the
ESB, July
MUSCULAR
Department
GUIDANCE OF HUMAN JAW LATERODEVIATIONS J.H. Koolstra, T.M.G.J. van Bijden of Functional Anatomy, Academic Centre for Dentistry Amsterdam-ACTA
INTRODUCTION: The contribution of the masticatory muscles to jaw movements is still not completely understood. Not only the forces of active muscles are involved but also forces generated by passive structures like ligaments, inactive muscles and joints. Biomechanical models have been of assistence to analyse symmetrical jaw movements (Koolstra et al., 1997). Many habitual movements (chewing, grinding) are non-symmetrically. They all include laterodeviations. Therefore, the objective of the present study was to analyse the contribution of the various masticatoty muscles to these laterodeviations. METHODS: A dynamical 6 degrees-of-fmedom biomechanical model of the human masticatoty system was developed. This model was able to predict jaw movements as the result of arbitrary muscle activation patterns by solving ordinary differential equations. Its geometrical data were obtained by dissection (Van Eijden et al., 1997). Jaw movement simulations resulting from activation of the masticatory muscles separately and unilaterally were performed to analyse their contribution to laterodeviations. Also the result of combined muscle activation was predicted. RESULTS: It was found that various muscles were able to perform laterodeviations individually. Such movement was mostly combined with an opening or closing movement. The movements were dependent on the amount of jaw opening and consequently with the position of the condyles on the articular eminence. Jaw movement simulations as the result of combined muscle activity were according to naturally observed ones, including an anteriorly directed translation of the contralateral condyle and an ipsilateral shift of the ipsilateral condyle. DISCUSSION: For masticatory muscles with a strong medio-lateral component possible unilateral performance was predicted (Williams et al., 1989) based upon their orientation only. Many movements resulting from the simulations generally were in accordance with these predictions, and with responses evoked by muscle stimulation (Zwijnenburg et al., 1996). The influence of the jaw position on the movement could be attributed to the joint reaction forces. CONCLUSION: Analysis of the simulated movements revealed that apart from the muscle forces also the joint forces play a dominant role in non-symmetrical jaw movements. REFERENCES: 1. Koolstra et al., J.Biomech., 30, 943-950, 1997. 2. Van Eijden et al., Anat. Rec., 248, 464-474, 1997. 3. Wiliams et al. Gray’s Anatomy, Churchill Livingstone, Edinburgh, 1989. 4. Zwijnenburg et al., J. Dent. Res, 75, 1798-1803.1996. CORRESPONDENCE: J.H. Koolstra Dept. Functional Anatomy - ACTA, Meibergdmef 15, 1105 AZ Amsterdam, The Netherlands tel: +31 20 5665370, fax: +31 20 6911856, [email protected]
8-I I 98, Toulouse,
France
43
OF A THREE DIMENSIONAL FINITE OF THE HUMAN TEMPOROMANDIBULAR JOINT M. Beek, L.J. van Ruijven, E. Donker, J.H. Koolstra, T.M.G.J. van Eijden Department of Functional Anatomy, Academic Centre for Dentistry Amsterdam-ACTA INTRODUCTION: The human temporomandibular joint consists of two incongruent articular surfaces, coveted with a cartilage layer and separated by a cartilaginous articular disc. The finite element method is capable of determining stresses and deformations in such complex geometries. However, relevant research is still limited to two dimensional (2D) geometries (Chen et al.. 1994). Therefore, a method to create a tetrahedral mesh representing a three dimensional (3D) cartilage layer was developed. METHODS: The 3D geometry of the articulating surface was measured using a magnetic tracking device (An et al., 1988). The coordinates, obtained in random order, were arranged into an orthogonal grid and then fitted to polynomials. The algorithm was tested using known mathematical surfaces. A 2D Delaunay triangulation was applied to points on the grid. Their spatial coordinates were calculated using the polygons. A volume could be created using an approximate thickness of the cartilage. This volume was tilled with tetrahedral elements. A polyquad surface was modelled to represent the bony surface. The contact between the rigid surface and the elements was modelled to be fixed. RESULTS: For all surfaces tested the algorithm converged to a satisfying solution. The error was largest near the edge of the surface. The mesh generated from the fitted polynomials consisted of fairly well shaped elements, except for those near the border. Simulating free movement of the model without any loads resulted in Cauchy stresses of less than 30 N/m2. DISCUSSION: The fitting algorithm depends greatly on the fact whether an articular surface can be described by polynomials. The mesh can be improved by a controlled placement of the points on the grid, a more sophisticated method of smoothing, and by triangulating directly in three dimensions. The model can be made more realistic by measuring the thickness of the cartilage. CONCLUSION: The method we developed, can be used to transform the 3D geometrical data of a cartilage layer into a tetrahedral mesh for finite element analysis. REFERENCES: 1. An et al., J. Biomech., 21, 613-620. 1988. 2. Chen et al., .I. Biomech. Eng.. I 16, 401-407, 1994. ACKNOWLEDGEMENT: This work was sponsored by the National Computing Facilities Foundation (NCF) for the use of supercomputer facilities, with financial support from the Netherlands Organization for Scientific Research (NWO). CORRESPONDENCE: M. Beek Dept. of Functional Anatomy - ACTA, Meibergdreef 15, 1105 AZ, Amsterdam, The Netherlands, tel: +31 20 5665355, fax: +31 20 6911856, [email protected]
I I'"
Conference
of the
ESB, July
MUSCULAR
Department
GUIDANCE OF HUMAN JAW LATERODEVIATIONS J.H. Koolstra, T.M.G.J. van Bijden of Functional Anatomy, Academic Centre for Dentistry Amsterdam-ACTA
INTRODUCTION: The contribution of the masticatory muscles to jaw movements is still not completely understood. Not only the forces of active muscles are involved but also forces generated by passive structures like ligaments, inactive muscles and joints. Biomechanical models have been of assistence to analyse symmetrical jaw movements (Koolstra et al., 1997). Many habitual movements (chewing, grinding) are non-symmetrically. They all include laterodeviations. Therefore, the objective of the present study was to analyse the contribution of the various masticatoty muscles to these laterodeviations. METHODS: A dynamical 6 degrees-of-fmedom biomechanical model of the human masticatoty system was developed. This model was able to predict jaw movements as the result of arbitrary muscle activation patterns by solving ordinary differential equations. Its geometrical data were obtained by dissection (Van Eijden et al., 1997). Jaw movement simulations resulting from activation of the masticatory muscles separately and unilaterally were performed to analyse their contribution to laterodeviations. Also the result of combined muscle activation was predicted. RESULTS: It was found that various muscles were able to perform laterodeviations individually. Such movement was mostly combined with an opening or closing movement. The movements were dependent on the amount of jaw opening and consequently with the position of the condyles on the articular eminence. Jaw movement simulations as the result of combined muscle activity were according to naturally observed ones, including an anteriorly directed translation of the contralateral condyle and an ipsilateral shift of the ipsilateral condyle. DISCUSSION: For masticatory muscles with a strong medio-lateral component possible unilateral performance was predicted (Williams et al., 1989) based upon their orientation only. Many movements resulting from the simulations generally were in accordance with these predictions, and with responses evoked by muscle stimulation (Zwijnenburg et al., 1996). The influence of the jaw position on the movement could be attributed to the joint reaction forces. CONCLUSION: Analysis of the simulated movements revealed that apart from the muscle forces also the joint forces play a dominant role in non-symmetrical jaw movements. REFERENCES: 1. Koolstra et al., J.Biomech., 30, 943-950, 1997. 2. Van Eijden et al., Anat. Rec., 248, 464-474, 1997. 3. Wiliams et al. Gray’s Anatomy, Churchill Livingstone, Edinburgh, 1989. 4. Zwijnenburg et al., J. Dent. Res, 75, 1798-1803.1996. CORRESPONDENCE: J.H. Koolstra Dept. Functional Anatomy - ACTA, Meibergdmef 15, 1105 AZ Amsterdam, The Netherlands tel: +31 20 5665370, fax: +31 20 6911856, [email protected]
8-I I 98, Toulouse,
France
43