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Zbl 1251.92022
Tomasetti, Cristian
On the probability of random genetic mutations for various types of tumor growth. (English)
[J] Bull. Math. Biol. 74, No. 6, 1379-1395 (2012). ISSN 0092-8240; ISSN 1522-9602/e

Summary: 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 In contrast, we are able to obtain analytical results for cases where the exponential growth of cancer has been replaced by other, arguably more realistic types of growth of a heterogeneous tumor cell population.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.

MSC 2000:: *92C50 Medical appl. of mathematical biology
60J85 Appl. of branching processes
37N25 Dynamical systems in biology
92C37 Cell biology

Keywords: drug resistance; stem cells; ordinary differential equations; branching processes

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Zentralblatt MATH Berlin [Germany]