Abstract
A stochastic analog to a deterministic model describing subpopulation emergence in heterogeneous tumors is developed. The resulting system is described by the Fokker-Planck or forward Kolmogorov equation. A finite element approach for the numerical solution to this equation is described. Four biological and clinical scenarios are simulated (emergence of heterogeneity, exclusion of a subpopulation, and induction of drug resistance in both pure and heterogeneous tumors). The results of the simulations show that the stochastic model describes the same basic dynamics as its deterministic counterpart via a convective component, but that for each simulation a distribution of tumor sizes and mixes can also be derived from a diffusive component in the model. These distributions yield estimates for subpopulation extinction probabilities. The biological and clinical relevance of these results are discussed.
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Research support provided in part by ACS Grant IN45-Z and ACS PDT 243 B.
Research support provided in part by the National Science Foundation under NSF Grant MCS-8504316, and by the Air Force Office of Scientific Research under Contract F49620-86-C-0111.
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Michelson, S., Ito, K., Tran, H.T. et al. Stochastic models for subpopulation emergence in heterogeneous tumors. Bltn Mathcal Biology 51, 731–747 (1989). https://doi.org/10.1007/BF02459658
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DOI: https://doi.org/10.1007/BF02459658