NEW APPROACH TO APPLICATION OF MATHEMATICAL APPARATUS FOR THE CONSTRUCTION OF THREE-DIMENSIONAL SPINE MODEL

Abstract

The paper presents a mathematical model with graphic visualization, which describes spine geometric parameters and conditions of their changes in time and space. Reduction of data file size necessary for reproduction of vertebra shape and storage of this structure in a computer with the least losses is achieved with algorithm of geometrical interpolation and vertebral body shape reconstruction – with trigonometric interpolation sums (TIS). The developed spine model is based on three concepts. A spline interpolation is used for reproduction of the whole spine. The spline polynomial is built on data received by calculation of transition matrices. This requires the parameters of not each point, but only of three key ones (in the basic spine levels). Application of spline interpolation considerably reduces time expenses for transition matrices calculation. The developed model takes into account the geometrical features of human vertebra, and changes of its kinematic characteristics in space and time. The model will allow observation of deformation of the whole spine caused by change of one or several randomly chosen parameters. Thus the geometrical characteristics necessary to calculate matrix chain of the second model are the results of the first model calculations. Having a set of the statistical data, the given model can be used for observation of spine response to various disturbing factors. After assigning initial spine parameters a graphic interpretation of the model will enable to receive a three-dimensional spine image, to shift and rotate it, to assign a direction of load application, to trace the changes in the spine shape during physiological movements and walking.