TITLE:
Simple Linear Model of Tumor Growth in a Changing Environment
AUTHORS:
Jose F. Nieves, Marcelo R. Ubriaco
KEYWORDS:
Tumor Growth, Mathematical Modeling, Linear Models, Dynamic Environment, Minimal Parametrizations
JOURNAL NAME:
Applied Mathematics,
Vol.6 No.7,
June
17,
2015
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.