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Mathematical and Computer Modelling, 2001:1297-1305
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Next: Introduction

Simple ODE models of tumor growth
and anti-angiogenic or radiation treatment
R.K. SACHS$ ^{\ddag }$, L.R. HLATKY$ ^{\dag }$ and P. HAHNFELDT$ ^{\dag }$
$ ^{\ddag}$Department of Mathematics University of California, Berkeley, CA 94720;
$ ^{\dag}$DFCI, Harvard Medical School, Boston, MA 02115.
Abstract
Models of tumor growth and treatment based on one or two ordinary differential equations are heavily used in practice because they are simple but can often still capture the essence of complicated interactions. Currently relevant examples of such models are given here: some classic growth equations; an ODE pair for the interplay between tumor and neovascularization during cancer growth or therapy; and an ODE pair for response to ionizing radiation. Mathematically more sophisticated generalizations of various kinds, usually more realistic but less practical, are mentioned very briefly.

Indexing Phrases. Radiotherapy and chemotherapy; tumor growth kinetics; angiogenic inhibitors; time factors.

Correspondence to: R.K. Sachs, Dept. Mathematics, Evans Hall, UCB, Berkeley, CA 94720. Voice: 510-642-4384; Fax: 510-642-6726.

Email: sachs@math.berkeley.edu; Internet: /$ \sim$sachs/



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