  We present mathematical models, computational algorithms and software, which
can be used for prediction of results of prosthetic 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 of dentures. 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 and strain fields
in periodontal ligament and jawbone. The input parameters for the developed
model can be divided into two groups. The first group of parameters describes
the mechanical properties of periodontal ligament, teeth and jawbone (for
example, elasticity of periodontal ligament etc.). The second group
characterized the geometric properties of objects: the size of the teeth, their
spatial coordinates, the size of periodontal ligament etc. The mechanical
properties are the same for almost all, but the input of geometrical data is
complicated because of their individual characteristics. In this connection, we
develop algorithms and software for processing of images obtained by computed
tomography (CT) scanner and for constructing individual digital model of the
tooth-periodontal ligament-jawbone system of the patient. Integration of models
and algorithms described allows to carry out biomechanical analysis on
three-dimensional digital model and to select prosthesis design.
