Liver regeneration after partial hepatectomy: the upper optimality estimate

Abstract

This publication investigates one of the fundamental problems of mathematical biology, specifically the development of mathematical models for the dynamics of complex biosystems that have a satisfactory explanatory and predictable power. A necessary condition for the development of such models is to find a solution for the problem of identifying the objective principles and rules of regulation of the "cellular system", which determines among all the possibilities exactly the "real path" of its dynamics observed in the experiment. One of the promising approaches to solving this problem is based on the hypothesis that the regulation of processes for support/restoration of the dynamic homeostasis of tissues and organs of the body occurs according to certain principles, and criteria of optimality, which have developed due to the natural selection of the body during its previous evolution. It is quite difficult to solve this problem at the current time due to the many uncertainties in the paths of the previous evolution of the organism, the dynamics of changes in external conditions, as well as the high computational complexity of solving such a problem. Instead of this, we have proposed a simplified formulation of the problem of searching for regulation control strategies, which gives us an upper estimate of optimality for the processes of maintaining/restoring dynamic homeostasis of the liver. The upper estimate of the optimality of regulation and testing of hypotheses for the model of liver regeneration was considered in the case of partial hepatectomy and was solved by Python software methods. The result shows that in the case of partial hepatectomy, the liver regeneration strategies obtained in numerous experiments for the problem of the upper optimality estimate qualitatively coincide with the processes of liver regeneration that can be observed during biological experiments. In plenty of experiments following hypotheses were also tested: how significant is the contribution of the process of controlled apoptosis, and how other processes (polyploidy, division, and formation of binuclear hepatocytes) affect the strategy of liver regeneration.