Authors: Cristian Tomasetti
Publish Date: 2012/02/07
Volume: 74, Issue: 6, Pages: 1379-1395
Abstract
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exponentially In contrast we are able to obtain analytical results for cases where the exponential growth of cancer has been replaced by other arguably more realistic types of growth of a heterogeneous tumor cell population Our main result is that the probability that a given random mutation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 presentThe author wishes to thank Professor Dmitry Dolgopyat for his helpful discussions and the reviewers for their valuable comments The work of CT was supported in part by the National Institute of Health under Grant T32 CA009337 by the joint National Science Foundation/National Institute of General Medical Sciences program under Grant DMS0758374 and by the National Cancer Institute under Grant R01CA130817
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