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.
journal_name
Bull Math Bioljournal_title
Bulletin of mathematical biologyauthors
Michelson S,Ito K,Tran HT,Leith JTdoi
10.1007/BF02459658subject
Has Abstractpub_date
1989-01-01 00:00:00pages
731-47issue
6eissn
0092-8240issn
1522-9602pii
S0092-8240(89)80060-6journal_volume
51pub_type
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