Mathematical principle of cellular accommodation: A Schmitt trigger approach

Abstract

Hysteresis usage was occupied to many physical problems. Up to today, there is a limited contributions to describe 3D bone remodeling algorithm. Many theories were developed to light mechanotranduction of bone tissue. Unfortunately current models are very far from explaining the situation of bone remodeling at loadless condition such as neutral axis of long bones and skull. They are supposed to resorp due to disuse atrophy according to background algorithms. At this point, Schmitt triggerbistable circuit approach can be considered as a novel concept. It may establish a conceptual backbone as a process memory. It assumes the density retains its value until the input changes sufficiently to switch a change. In the load-carrying configuration, when the strain is higher than a certain threshold according to bone's strain history factor (SHF), the density is supposed to be high. However, in the loadless condition, the density rate is supposed to be low due to moderate strain history factor values, the density will retain its value. This system is very appropriate to solve bone remodeling. The purpose of this manuscript is to folds: first to consolidate a novel mathematical model for cellular accomodation, second to develop graphical representation for novel hysteresis functions.