Time-dependent subpopulation induction in heterogeneous tumors
Time-dependent induction of clonal heterogeneity in the neoplastic micro- environment is analysed within the context of a competitive ecology. A model that describes a constant source for clonal emergence was analysed by the last two authors, \textit{B. E. Miller} and \textit{A. S. Glicksman}, J. Theor. Biol. 128, 233-346 as an extension of a model proposed by \textit{B. Jansson} and \textit{L. Revesz} [Math. Biosci. 19, 131-154 (1974; Zbl 0272.92005)]. The extended model has been termed the JRE Model. This paper extends these analyses to time-dependent emergence rates which may represent induction in the presence of a cytotoxic agent. If the analysis is constrained to the tumor microenvironment, and if the emergent subpopulation is drug resistant, then the model may describe the induction and emergence of drug resistant subclones in a growing neoplasm. Asymptotic closed form solutions are derived for a class of emergence rate functions which decay asymptotically to a constant mutation rate. This underlying mutation rate may represent spontaneous mutation to the resistant phenotype, and has been analysed stochastically. The asymptotic solutions to the time-dependent model approach the steady state solution for the JRE Model which represents the dynamics observed in the presence of a constant, spontaneous mutation rate. The clinical and biological implications of these results are discussed.
Time-dependent induction of clonal heterogeneity
scientific article; zbMATH DE number 4072759