Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30135
Variational Evolutionary Splines for Solving a Model of Temporomandibular Disorders

Authors: Alberto Hananel

Abstract:

The aim of this work is to modelize the occlusion of a person with temporomandibular disorders as an evolutionary equation and approach its solution by the construction and characterizing of discrete variational splines. To formulate the problem, certain boundary conditions have been considered. After showing the existence and the uniqueness of the solution of such a problem, a convergence result of a discrete variational evolutionary spline is shown. A stress analysis of the occlusion of a human jaw with temporomandibular disorders by finite elements is carried out in FreeFem++ in order to prove the validity of the presented method.

Keywords: Approximation, evolutionary PDE, finite element method, temporomandibular disorders, variational spline.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1127573

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 942

References:


[1] M. L. Rodr´ıguez, Aproximaci´on de curvas y superficies a partir de problemas de contorno mediante m´etodos variacionales. Aplicaciones. Tesis Doctoral en Matem´aticas de la Universidad de Granada, 2005.
[2] E. Ohashi and D. A. Paredes, “Factorial analysis of the diagnosis of temporomandibular disorders criteria’s: Articular evaluation,” Journal of Dental Research, vol. 81, pp. A458–A458, 2002.
[3] A. Hananel, “Sistema experto difuso para el pron´ostico y diagn´ostico de des´ordenes temporomandibulares utilizando an´alisis factorial y elementos finitos,” Revista MACI, vol. 3, pp. 303–306, 2011.
[4] A. Hananel, Sistema Experto Difuso para el Pron´ostico y Diagn´ostico de Des´ordenes Temporomandibulares utilizando An´alisis Factorial y Elemento Finito. Tesis de Maestr´ıa en Ciencias con Menci´on en Matem´atica Aplicada de la Universidad Nacional de Piura, 2011.
[5] T. W. Korioth, D. P. Romilly, and A. G. Hannam, “Three-dimensional finite element stress analysis of the dentate human mandible,” American Journal of Physical Anthropology, vol. 88, pp. 69–96, 1992.
[6] M. P. Do Carmo, Geometr´ıa Diferencial de Curvas y Superficies. Alianza Universidad Textos, 1990.
[7] T. W. Korioth, D. P. Romilly, and A. G. Hannam, “3-D finite element modelling of human jaw deformation during clenching,” Journal of Dental Research, vol. 72, p. 195, 1993.
[8] M. Beek, J. Koolstra, L. V. Ruijven, and T. V. Eijden, “Three–dimensional finite element analysis of the human temporomandibular joint disc,” Journal of Biomechanics, vol. 33, pp. 307–316, 2000.
[9] D. Kubein, H. Nagerl, R. Schwestka, K. Thieme, J. Faghanel, and B. Miehe, “Funtional conditions of the mandible: theory and physiology,” Annals of anatomy, vol. 181, pp. 27–32, 1999.
[10] T. W. Korioth and A. G. Hannam, “Finite element fe modelling of the human mandible during unilateral molar clenching,” Journal of Dental Research, vol. 70, p. 334, 1991.
[11] A. Doubova and F. Guill´en, Un curso de c´alculo num´erico, interpolaci´on, aproximaci´on, integraci´on y resoluci´on de problemas diferenciales. Universidad de Sevilla–Departamento de ecuaciones diferenciales y an´alisis num´erico, 2007.
[12] P. A. Raviart and J. M. Thomas, Introduction `a l’Analyse Num´erique des ´equations aux D´eriv´ees Partielles. Masson, 1983.
[13] O. Chau and V. V. Motreanu, “Dynamic contact problems with velocity conditions,” International Journal of applied mathematics and computer science, vol. 12, no. 1, pp. 17–26, 2002.
[14] W. V. Chaves, Mec´anica del medio continuo. Conceptos b´asicos. Centro Internacional de M´etodos Num´ericos en Ingenier´ıa, 2010.
[15] T. W. Korioth and A. G. Hannam, “Deformation of the human mandible during simulated tooth clenching,” Journal of Dental Research, vol. 73, pp. 56–66, 1994.
[16] M. Koseki, N. Inou, and K. Maki, “Estimation of masticatory forces for patient-specific analysis of the human mandible,” Transactions of the Japan Society of Mechanical Engineers Series C, vol. 74, no. 743, pp. 1857–1864, 2008.
[17] D. Dragulescu, D. Stanciu, and M. Toth-Tascau, “Modeling and dynamic study of human mandible,” Seria Mecanica-Transaccions on Mechanics, vol. 47, no. 61, pp. 49–54, 2002.
[18] M. C. L´opez de Silanes and R. Arcang´eli, “Sur la convergence des Dm-splines d’ajustement pour des donn´ees exactes ou bruit´ees,” Revista Matem´atica de la Universidad Complutense de Madrid, vol. 4, no. 2–3, pp. 279–284, 1991.
[19] J. Farah, R. Craig, and K. Meroueh, “Finite element analysis of a mandibular model,” Journal of Oral Rehabilitation, vol. 15, pp. 615–624, 1998.
[20] A. Kouibia, Aproximaci´on de curvas y superficies param´etricas mediante splines variacionales. Tesis Doctoral de la Universidad de Granada, 1999.
[21] P. M. Prenter, Splines and Variational Methods. A Wiley–Interscience Publication, 1989.
[22] J. Viao, M. Burguera, J. Fern´andez, A. Rodr´ıguez, M. Campo, D. Su´arez, T. Abeleira, and M. Gallas, “Simulaci´on num´erica en odontolog´ıa y ortodoncia,” Bolet´ın SeMA, vol. 33, pp. 113–147, 2005.
[23] A. P´erez, J. Cegoino, J. L´opez, J. D. Vicente, and M. Doblar´e, “Simulaci´on por elementos finitos de la articulaci´on temporomandibular,” Biomec´anica, vol. 11, pp. 10–22, 2003.
[24] T. W. Korioth, P. C. Dechow, and A. G. Hannam, “3-D finite element modelling and validation of a dentate human mandible,” Journal of Dental Research, vol. 71, p. 203, 1992.
[25] J. Gal, L. Gallo, G. Murray, I. Klineberg, C. Johnson, and S. Palla, “Screw axes and wrenches in the study of human jaw mechanics,” Critical reviews in oral biology and Medicine, vol. 13, no. 4, pp. 366–376, 2002.
[26] T. W. Korioth, Finite element modelling of human mandibular biomechanics. The University of British Columbia, 1992.
[27] Y. Zhang, M. Wang, and W. Ling, “Influence of teeth contact alternation to TMJ stress distribution. Three-dimensional finite element study,” World Journal of Modelling and Simulation, pp. 60–64, 2005.
[28] K. Atkinson and W. Han, Theoretical Numerical Analysis: A Functional Analysis Framework. Nueva York: Springer–Verlag, 2001.