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A review of spatial computational models for multi-cellular systems, with regard to intestinal crypts and colorectal cancer development. (English) Zbl 1275.37039
Colon rectal cancers (CRC) are the result of sequences of mutations which lead the intestinal tissue to develop in a carcinoma following a “progression” of observable phenotypes. The actual modeling and simulation of the key biological structures involved in this process are of interest to biologists and physicians and, at the same time, it poses significant challenges from the mathematics and computer science viewpoints. In this report, we give an overview of some mathematical models for cell sorting (a basic phenomenon that underlies several dynamical processes in an organism), intestinal crypt dynamics, and related problems and open questions. In particular, major attention is paid to the survey of so-called “in-lattice” (or grid) models and “off-lattice (off-grid) models. This paper is the groundwork for future research on semi-automated hypotheses formation and testing about the behavior of the various actors taking part in the adenoma-carcinoma progression, from regulatory processes to cell-cell signaling pathways. Some future directions, e.g., multi-scale modeling and noisy random boolean networks are mentioned.

MSC:
37N25 Dynamical systems in biology
92B05 General biology and biomathematics
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