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

Research output: Contribution to journalArticle

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 In contrast, we are able to obtain analytical results for cases where the exponential growth of cancer has been replaced by other, arguably more realistic types of growth of a heterogeneous tumor cell population.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

Original languageEnglish (US)
Pages (from-to)1379-1395
Number of pages17
JournalBulletin of Mathematical Biology
Volume74
Issue number6
DOIs
StatePublished - Jun 2012
Externally publishedYes

Fingerprint

Tumor Growth
tumor
Tumors
mutation
Tumor
Mutation
neoplasms
Growth
Neoplasms
Mutant
mutants
Growth Curve
Cell Population
growth curve
Stochastic Methods
Exponential Growth
cancer
Cancer
mathematical models
Cells

Keywords

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

ASJC Scopus subject areas

  • Neuroscience(all)
  • Computational Theory and Mathematics
  • Mathematics(all)
  • Pharmacology
  • Immunology
  • Biochemistry, Genetics and Molecular Biology(all)
  • Agricultural and Biological Sciences(all)
  • Environmental Science(all)

Cite this

On the Probability of Random Genetic Mutations for Various Types of Tumor Growth. / Tomasetti, Cristian.

In: Bulletin of Mathematical Biology, Vol. 74, No. 6, 06.2012, p. 1379-1395.

Research output: Contribution to journalArticle

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