4.4 Article

A Turing mechanism in order to explain the patchy nature of Crohn's disease

Journal

JOURNAL OF MATHEMATICAL BIOLOGY
Volume 83, Issue 2, Pages -

Publisher

SPRINGER HEIDELBERG
DOI: 10.1007/s00285-021-01635-w

Keywords

Inflammatory diseases; Turing pattern; Reaction-diffusion system; Activator-inhibitor

Funding

  1. Inflamex Laboratory of Excellence
  2. Galilee PhD College

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Crohn's disease is an inflammatory bowel disease with a patchy inflammatory pattern that is not well understood. A toy-model introduced in this study explains the appearance of such patterns through a reaction-diffusion system involving bacteria and phagocyte, demonstrating the occurrence of Turing-type instabilities. This study is the first to investigate Turing patterns in inflammatory models.
Crohn's disease is an inflammatory bowel disease (IBD) that is not well understood. In particular, unlike other IBDs, the inflamed parts of the intestine compromise deep layers of the tissue and are not continuous but separated and distributed through the whole gastrointestinal tract, displaying a patchy inflammatory pattern. In the present paper, we introduce a toy-model which might explain the appearance of such patterns. We consider a reaction-diffusion system involving bacteria and phagocyte and prove that, under certain conditions, this system might reproduce an activator-inhibitor dynamic leading to the occurrence of Turing-type instabilities. In other words, we prove the existence of stable stationary solutions that are spatially periodic and do not vanish in time. We also propose a set of parameters for which the system exhibits such phenomena and compare it with realistic parameters found in the literature. This is the first time, as far as we know, that a Turing pattern is investigated in inflammatory models.

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