Linear model of tumor growth in a changing environment

Abstract

We propose a model for describing the growth on an untreated tumor, which is characterized in a simple way by a minimal number of parameters with a well-defined physical interpretation. The model is motivated by invoking the Master Equation and the Principle of Detailed Balance in the present context, and it is easily generalizable to include the effects of various types of therapies. In the simplest version that we consider here, it leads to a linear equation that describes the population growth in a dynamic environment, for which a complete solution can be given in terms of the integral of the growth rate. The essential features of the general solution for this case are illustrated with a few examples.