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

TL;DR

This paper introduces a reaction-diffusion model to explain the patchy inflammatory patterns in Crohn's disease, demonstrating how Turing instabilities can produce stable, spatially periodic solutions.

Contribution

It is the first to investigate Turing patterns in inflammatory disease models, providing a theoretical framework for understanding Crohn's disease patchiness.

Findings

Reaction-diffusion system can produce Turing patterns

Existence of stable spatially periodic solutions

Parameter sets align with biological data

Abstract

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.