Migration and proliferation dichotomy in tumor cell invasion

Abstract

We propose a two-component reaction-transport model for the migration-proliferation dichotomy in the spreading of tumor cells. By using a continuous time random walk (CTRW) we formulate a system of the balance equations for the cancer cells of two phenotypes with random switching between cell proliferation and migration. The transport process is formulated in terms of the CTRW with an arbitrary waiting time distribution law. Proliferation is modeled by a standard logistic growth. We apply hyperbolic scaling and Hamilton-Jacobi formalism to determine the overall rate of tumor cell invasion. In particular, we take into account both normal diffusion and anomalous transport (subdiffusion) in order to show that the standard diffusion approximation for migration leads to overestimation of the overall cancer spreading rate.

9 pages

References in corpus (4)

• Simulating the Impact of a Molecular 'Decision-Process' on Cellular Phenotype and Multicellular Patterns in Brain Tumors
• Robust formation of morphogen gradients
• Dynamics and pattern formation in invasive tumor growth
• Simulating the time series of a selected gene expression profile in an agent-based tumor model

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