Towards a Mathematical Formalism for Semi-stochastic Cell-Level Computational Modeling of Tumor Initiation

F. J. Vermolen, R. P. van der Meijden, M. Van Es, A. Gefen, D. Weihs

Research output: Contribution to journalArticlepeer-review

Abstract

A phenomenological model is formulated to model the early stages of tumor formation. The model is based on a cell-based formalism, where each cell is represented as a circle or sphere in two-and three dimensional simulations, respectively. The model takes into account constituent cells, such as epithelial cells, tumor cells, and T-cells that chase the tumor cells and engulf them. Fundamental biological processes such as random walk, haptotaxis/chemotaxis, contact mechanics, cell proliferation and death, as well as secretion of chemokines are taken into account. The developed formalism is based on the representation of partial differential equations in terms of fundamental solutions, as well as on stochastic processes and stochastic differential equations. We also take into account the likelihood of seeding of tumors. The model shows the initiation of tumors and allows to study a quantification of the impact of various subprocesses and possibly even of various treatments.

Original languageEnglish
Pages (from-to)1680-1694
Number of pages15
JournalAnnals of Biomedical Engineering
Volume43
Issue number7
DOIs
StatePublished - 22 Jul 2015

Keywords

  • Cell migration
  • Cell proliferation
  • Cell-based modeling
  • Fundamentalsolutions
  • Immune system response
  • Mutation
  • Tumor initiation

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