A stochastic model of mutant growth due to mutation in tumors,based on stem cell considerations

A stochastic model of the evolution of mutant subpopulations from stem cells in a human tumor system is derived. From the model, the growth of mutants (both stem cell mutants and overall mutants) due to mutation of tumor stem cells during growth is explored in detail. This allows one to relate the mutant stem cell and overall tumor mutant cell population sizes. The relation of these average sizes is derived for large tumor size and confirms the result of the model due to MacKillop et al. [4], which is based on three tumor cell subpopulations: stem, transitional, and end cells. Furthermore, the results of the stem cell statistics obtained are the same as those obtained from the filtered Poisson process approach [2].