Numerical Simulation of the Stress-Strain State of the Dental

Abstract

We present mathematical models, computational algorithms and software,which can be used for prediction of results of orthopedic treatment. More interest issue is biomechanics of the periodontal complex because any prosthesis is accompanied by a risk of overloading the supporting elements. Such risk can be avoided by the proper load distribution and prediction of stresses that occur during the use ofdentures. In this regard, we developed the mathematical model of the periodontal complex and its software implementation. This model is based on linear elasticity theory and allows to calculate the stress tensor and displacement fields in periodont and jaw bone. The input parameters for the developed model can be divided into two groups. The first group of parameters describes the mechanical properties of periodont, teeth and jaw (for example, elasticity of periodontal ligament etc.). The second group characterized the geometric properties of objects: the size of the teeth, their spatialcoordinates, the size of periodont etc. The mechanical properties are the same for almost all, but the inputof geometrical data is complicated because of their individualcharacteristics. In this connection, we develop algorithms andsoftware for processing of images obtained by computed tomography scanand for constructing individual digital model of thetooth-periodont-jaw system of the patient.Integration of models and algorithms described allows to carry outbiomechanical analysis on three-dimensional digital model and toselect denture design.