Creation of a three-dimensional model of the mandible and the TMJ in vivo by means of the finite element method.

Abstract

The aim of this study was to develop a three-dimensional finite element model of the mandible, including its TMJ. The model consisted of 7942 nodes and 41,010 elements, which were obtained from a convergence test, done to minimize the result error. It included cancellous and cortical bone, periodontal ligament, masticatory muscles (masseters, temporalis, lateral and internal pterygoids), teeth and the articular disk. All characteristics such as dental, mandibular, and muscle geometry were obtained from a computerized tomography (CT) of a living person. CT sections were scanned and digitized with a CAD software program. After images were adequately assembled, a vertical tracing was done which allowed the definition of a three-dimensional mesh. Modeling of teeth was carried out independently and the periodontal ligament was later included, limiting the alveolar area. Muscles were modeled based on flat-scale photographs and total muscle force was distributed in multiple vectors. The articular disk was generated having 2 mm of thickness with the combination of spring-type (axial stiffness) and gap-type (contact) elements. The model was then analyzed with finite element method (FEM) software where a mesh was generated and values for Poisson's ratio, elasticity, and shear modulus were assigned. These were orthotropic for cancellous and cortical bone, and isotropic for dentin, periodontal ligament, articular disk, and temporal bone. The boundary conditions were defined restricting the nodes on the periphery of the temporal bone. It was therefore possible to generate a three-dimensional finite element model based on information obtained in vivo.