Mathematical modelling of regulatory mechanisms of cell groups functioning at norm and at unregulated cell division

Abstract

This paper presents a method for modeling organs and tissues based on the equations of the functional unit of organs and tissues (FUOT) and mathematical models for the main cellular functions: division, growth, differentiation, performance of specific functions, aging, apoptosis and natural death. The elements of FUOT are cells. The analysis shows that there are short circuits of regulation, which in specific realizations of cell development correspond to stable or partially stable cellular structures. This can occur as a normal phenomenon in the form of an adaptive response to stressful influences, and as an abnormal pathological condition. Such partial FUOT can be called minifuot. The study of the proliferative minifuot equations show the presence of a nonzero stable equilibrium position, and a stable limit cycle in the first quadrant. The results of these studies can be useful in studying the mechanisms of cell groups functioning at norm and at unregulated cell division.