Simple Linear Model of Tumor Growth in a Changing Environment

Jose F. Nieves, Marcelo R. Ubriaco

Department of Physics, Laboratory of Theoretical Physics, University of Puerto Rico, San Juan, Puerto Rico.

DOI: 10.4236/am.2015.67104                

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.

Keywords

Tumor Growth, Mathematical Modeling, Linear Models, Dynamic Environment, Minimal Parametrizations

Conflicts of Interest

The authors declare no conflicts of interest.

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