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

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

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

Electrical Engineering, Mathematics and Computer Science

Delft Institute of Applied Mathematics

2015-02-11

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.

tumor initiation
cell-based modeling
immune system response
fundamental solutions
cell proliferation
mutation
cell migration

http://resolver.tudelft.nl/uuid:b5b0dec3-4d0d-44bc-aac8-2d70a6f7cdfc

Springer

0090-6964

https://doi.org/10.1007/s10439-015-1271-1

Annals of Biomedical Engineering, 2015

Institutional Repository

journal article

© 2015 The Author(s)
This article is published with open access at Springerlink.com