Feedback patterns in simulating intestinal wall motions: interdisciplinary approach to the motility mechanisms

TL;DR

This paper models intestinal wall motions using a system of differential equations and algebraic structures, revealing the roles of feedback patterns in gastrointestinal motility regulation.

Contribution

It introduces a novel interdisciplinary approach combining dynamical systems and coquaternion algebra to describe GI tract regulation mechanisms.

Findings

Identification of positive, negative feedback, and reciprocal links in intestinal regulation

Development of a mathematical model with six ODEs for GI segment dynamics

Proposal of coquaternion algebra as a framework for self-regulatory structures

Abstract

Ability of smooth muscles to contract in response to distension plays a crucial role in motor function of intestine. Qualitative analysis of dynamical models using myogenic active property of smooth muscles has shown well agreement with physiologic data. Considered as a self-regulatory unit, function of gastrointestinal (GI) segment is assumed to be regulated by integration of basis patterns providing accumulation and propagation of intestinal content. By implementing external, depending on neural system, variable to the previous model, and considering two attaches to one another reservoirs as a physical analogue of the segmental partition of intestine, a system of six ODE equations, three for each reservoir, describes coordinated wall motions and propagation of the content from one reservoir to another. It was shown that besides negative feedback (NFB), other functional patterns, namely positive feedback (PFB) and reciprocal links (RL) are involved in regulations of filling-emptying cycle. Being integrated in a whole functional system these three patterns expressed in a matrix form represent basis elements of imaginary part of coquaternion which with identity basis component is an algebraically closed structure under addition and multiplication of its elements. A coquaternion ring may be considered as a model of inner self-regulatory functional structure providing coordinated wall motions of GI tract portions.