MATHEMATICAL MODELING OF THE ELASTIC PROPERTIES OF THE MUCOUS FLAPS IN CONDUCTING PATCHWORK OPERATIONS OF THE ORAL CAVITY

Abstract

Introduction: To date, there are techniques that allow dental surgeons to restore the lost volume of bone mass, but the level of complications during augmentation remains consistently high. One of the main types of postoperative complications is the exposure of bone augmentate and its infection as a result of ischemic or destructive processes in the mucous shreds, which cover the augmentate, resulting from their overgrowth. The aim: The purpose of our research was to increase bone augmentation effectiveness in patients with secondary edentulism and to reduce risk of postoperative complications caused by ischemia of the mucous membranes because of their tension by mathematical simulation of tensile limits and permissible deformation for the mucous membranes of the oral cavity. Materials and methods: As a research method was selected a two-component Mooney-Rivlin model, taking into account the indicators of elasticity and static strength of flat samples in tension, which allows them to perform hyperprime behavior at small and moderate deformations. For computer simulation of epithelial flap deformation during operation by finite element method we used ANSYS software environment. Results: Since elastic forces are potential, the work of forces does not depend on the way of tension. Only the initial and final states of the sample, i.e. its initial and final forms, play a role. Conclusions: The flap of 30 × 25 mm can be stretched and thus it is necessary to eliminate the deficit of fabric up to 5 mm wide in the direction of the Y axis (vertical axis). The relative elongation is λ = 25/20 = 1.25. The flap tension first occurs in the y direction.