Simple Linear Model of Tumor Growth in a Changing Environment

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...

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Veröffentlicht in:Applied mathematics (Irvine, Calif.) Calif.), 2015-06, Vol.6 (7), p.1139-1147
Hauptverfasser: Nieves, Jose F., Ubriaco, Marcelo R.
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:2152-7385
2152-7393
DOI:10.4236/am.2015.67104