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Most human tumors result from the accumulation of multiple genetic and epigenetic alterations in a single cell. Mutations that confer a fitness advantage to the cell are known as driver mutations and are causally related to tumorigenesis. Other mutations, however, do not change the phenotype of the cell or even decrease cellular fitness. While much experimental effort is being devoted to the identification of the different functional effects of individual mutations, mathematical modeling of tumor progression generally considers constant fitness increments as mutations are accumulated. In this paper we study a mathematical model of tumor progression with random fitness increments. We analyze a multi-type branching process in which cells accumulate mutations whose fitness effects are chosen from a distribution. We determine the effect of the fitness distribution on the growth kinetics of the tumor. This work contributes to a quantitative understanding of the accumulation of mutations leading to cancer phenotypes.
Darwinian evolution can be modeled in general terms as a flow in the space of fitness (i.e. reproductive rate) distributions. In the diffusion approximation, Tsimring et al. have showed that this flow admits fitness wave solutions: Gaussian-shape fit
We present a numerical scheme for solving an inverse problem for parameter estimation in tumor growth models for glioblastomas, a form of aggressive primary brain tumor. The growth model is a reaction-diffusion partial differential equation (PDE) for
We generalize the evolution model introduced by Guiol, Machado and Schinazi (2010). In our model at odd times a random number X of species is created. Each species is endowed with a random fitness with arbitrary distribution on $[0, 1]$. At even time
In this article, we present a multispecies reaction-advection-diffusion partial differential equation (PDE) coupled with linear elasticity for modeling tumor growth. The model aims to capture the phenomenological features of glioblastoma multiforme o
Malignant brain tumors are among the deadliest neoplasms with the lowest survival rates of any cancer type. In considering surgical tumor resection, suboptimal extent of resection is linked to poor clinical outcomes and lower overall survival rates.