PMID: 1933032Jan 1, 1991Paper

Autocrine and paracrine growth factors in tumor growth: a mathematical model

Bulletin of Mathematical Biology
S Michelson, J T Leith

Abstract

A mathematical model of tumor growth including autocrine and paracrine control has been developed. The model starts with the logistic equation of Verhulst: dV/dt = rV (1-V/K). Autocrine controls are described as modifiers of the Malthusian growth rate (r), while paracrine controls modify the carrying capacity (K) of the system. The control mechanisms are expressed in terms of "candidate" functions, which are based upon the dynamic distribution of TGF-alpha TGF-beta in the local tumor environment. Three paradigms of tissue growth have been modeled: normal tissue wound repair, unrestricted, unperturbed tumor growth, and tumor growth in a (radiation) damaged environment (the Tumor Bed Effect, TBE). These scenarios were used to test the dynamics of the system against known phenomena. Computer simulations are presented for each case. The mode is being extended to include the description of heterogeneous tumors, within which subpopulations can express differential degrees of growth activity. Heterogeneous tumor models, with and without emergent subpopulations, and models of terminal differentiation are also discussed.

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Citations

Dec 1, 1995·Acta Biotheoretica·M A Chaplain
Sep 1, 1993·Bulletin of Mathematical Biology·S Michelson, J T Leith
Sep 1, 1995·Bulletin of Mathematical Biology·S Michelson, J T Leith
Mar 1, 1997·Bulletin of Mathematical Biology·S Michelson, J T Leith
Mar 23, 2012·Bulletin of Mathematical Biology·Shelby Wilson, Doron Levy
Mar 1, 1995·Bulletin of Mathematical Biology·S Michelson, J T Leith
Oct 13, 2001·European Journal of Cancer : Official Journal for European Organization for Research and Treatment of Cancer (EORTC) [and] European Association for Cancer Research (EACR)·L A BachF B Christiansen
Oct 7, 2006·Free Radical Biology & Medicine·Kenji HyoudouMitsuru Hashida
Sep 24, 2019·PLoS Computational Biology·Gregory J KimmelPhilipp M Altrock
Jun 22, 1992·Proceedings. Biological Sciences·J A Sherratt, M A Nowak
Dec 3, 2008·Physics in Medicine and Biology·Adrienne CampbellEugene Wong

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