Bulletin of Mathematical Biology

, Volume 74, Issue 6, pp 1379–1395

On the Probability of Random Genetic Mutations for Various Types of Tumor Growth

Original Article


In this work, we consider the problem of estimating the probability for a specific random genetic mutation to be present in a tumor of a given size. Previous mathematical models have been based on stochastic methods where the tumor was assumed to be homogeneous and, on average, growing exponentially. In contrast, we are able to obtain analytical results for cases where the exponential growth of cancer has been replaced by other, arguably more realistic types of growth of a heterogeneous tumor cell population. Our main result is that the probability that a given random mutation will be present by the time a tumor reaches a certain size, is independent of the type of curve assumed for the average growth of the tumor, at least for a general class of growth curves. The same is true for the related estimate of the expected number of mutants present in a tumor of a given size, if mutants are indeed present.


Tumor growth Genetic mutations Drug resistance Stem cells Ordinary differential equations Branching processes 

Copyright information

© Society for Mathematical Biology 2012

Authors and Affiliations

  1. 1.Department of Biostatistics, Harvard University and Department of Biostatistics and Computational BiologyDana-Farber Cancer InstituteBostonUSA

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