Journal of Mathematical Biology

, Volume 66, Issue 7, pp 1409–1462 | Cite as

A review of spatial computational models for multi-cellular systems, with regard to intestinal crypts and colorectal cancer development

  • Giovanni De Matteis
  • Alex GraudenziEmail author
  • Marco Antoniotti


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 is 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 devoted to the survey of so-called in-lattice (or grid) models and off-lattice (off-grid) models. The current work 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.


Cell sorting Crypt dynamics Colorectal cancer Cell adhesion Modeling Simulation 

Mathematics Subject Classification

MSC 37N25 MSC 92-08 MSC 92B05 MSC 92C15 MSC 92C17 MSC 92C42 


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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • Giovanni De Matteis
    • 1
  • Alex Graudenzi
    • 2
    Email author
  • Marco Antoniotti
    • 2
  1. 1.Department of Mathematics “F. Enriques”University of MilanMilanItaly
  2. 2.Department of Informatics, Systems and CommunicationUniversity of Milan BicoccaMilanItaly

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