Simple Linear Model of Tumor Growth in a Changing Environment

Abstract

In an environment that is neither static nor in equilibrium, but is dynamic and changing, the kinetics of the reactions that cause the growth of a tumor, which depend on the state of the evolving environment, cannot be parametrized in terms of constant rates. We propose a simple model for describing the growth on an untreated tumor in such environments, which is characterized by a minimal number of parameters and is generalizable to include the effects of various types of therapies. In the simplest version that we consider here, it consists of a linear equation with a time-dependent growth rate, which we interpret as the coupling of the system with a dynamic environment. A complete solution is given in terms of the integral of the growth rate. The essential features of the general solution are illustrated with a few examples, and comparison is made with the models that have been proposed to describe recent data.