### 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 In contrast, we are able to obtain analytical results for cases where the exponential growth of cancer has been replaced by other, arguably more realistic types of growth of a heterogeneous tumor cell population.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 language | English (US) |
---|---|

Pages (from-to) | 1379-1395 |

Number of pages | 17 |

Journal | Bulletin of Mathematical Biology |

Volume | 74 |

Issue number | 6 |

DOIs | |

State | Published - Jun 2012 |

Externally published | Yes |

### Fingerprint

### 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.

Research output: Contribution to journal › Article

*Bulletin of Mathematical Biology*, vol. 74, no. 6, pp. 1379-1395. https://doi.org/10.1007/s11538-012-9717-1

}

TY - JOUR

T1 - On the Probability of Random Genetic Mutations for Various Types of Tumor Growth

AU - Tomasetti, Cristian

PY - 2012/6

Y1 - 2012/6

N2 - 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 In contrast, we are able to obtain analytical results for cases where the exponential growth of cancer has been replaced by other, arguably more realistic types of growth of a heterogeneous tumor cell population.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.

AB - 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.

KW - Branching processes

KW - Drug resistance

KW - Genetic mutations

KW - Ordinary differential equations

KW - Stem cells

KW - Tumor growth

UR - http://www.scopus.com/inward/record.url?scp=84861480120&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84861480120&partnerID=8YFLogxK

U2 - 10.1007/s11538-012-9717-1

DO - 10.1007/s11538-012-9717-1

M3 - Article

C2 - 22311065

AN - SCOPUS:84861480120

VL - 74

SP - 1379

EP - 1395

JO - Bulletin of Mathematical Biology

JF - Bulletin of Mathematical Biology

SN - 0092-8240

IS - 6

ER -