Regression Analysis of Geometric Parameters of “Screw Implant – Maxillary Segment” Biomechanical System

A series of finite element calculations was performed to evaluate the impact of the geometric parameters of the reconstructive structures for “screw implant – maxillary segment” biomechanical system on the stress state of the cancellous tissue. To generate the model, we used high-order 10-node tetrahedral finite elements with the quadratic approximation of displacements that provided high modeling accuracy, in particular, in the areas of the implant thread - bone tissue joint, characterized by a high gradient of components of the stress-strain behavior. The finite element model is represented by 102231 elements. Biomechanical system was rigidly fixed at the frontal sections of the maxillary segment, thus preventing its displacement. The regression analysis of the results of a series of biomechanical system finite element calculations performed by us allowed establishing an analytical relationship between its geometric parameters (implant length and diameter, abutment slope angle) and factor of safety of the cancellous bone. Its linear model with the low coefficient of determination (0.584) and quadratic model providing high enough value of the coefficient (0.875) were used. It is obvious that at the next stages of research, when certain improvements in this direction could be achieved, it will be possible to consider nonlinear phenomena in the regression models in order to obtain the better precision of results. The results of the work will allow us to reveal the main trends in changes of the factor of safety of cancellous tissue relative to the value of traumatic stresses, depending on the implant length and diameter, and abutment slope angle.