Progress in Mathematical Modeling of Gastrointestinal Slow Wave Abnormalities

Abstract

Gastrointestinal (GI) motility is regulated in part by electrophysiological events called slow waves, which are generated by the interstitial cells of Cajal (ICC). Slow waves propagate by a process of “entrainment,” which occurs over a decreasing gradient of intrinsic frequencies in the antegrade direction across much of the GI tract. Abnormal initiation and conduction of slow waves have been demonstrated in, and linked to, a number of GI motility disorders. A range of mathematical models have been developed to study abnormal slow waves and applied to propose novel methods for non-invasive detection and therapy. This review provides a general outline of GI slow wave abnormalities and their recent classification using multi-electrode (high-resolution) mapping methods, with a particular emphasis on the spatial patterns of these abnormal activities. The recently-developed mathematical models are introduced in order of their biophysical scale from cellular to whole-organ levels. The modeling techniques, main findings from the simulations, and potential future directions arising from notable studies are discussed.

Computational model of gastric motility with active‐strain electromechanics

“…In the presence of pathologies, abnormal slow waves are observed and associated with different gastric motility disorders. In particular, the physiological entrainment regulated by ICC may degenerate leading to ectopic initiations, conduction blocks etc., usually named dysrhythmias . Most of these phenomena appear astonishingly similar to what is known from cardiac tissue, e.g., in the form of cardiac arrhythmias, further emphasizing the shared biophysical features between different active biological media …”

On the electro‐chemo‐mechanical modelling of stomach smooth muscle contraction

“…Several cell and tissue models are available describing parts of the gastric contraction process, see [2] and [5]. However, little has been documented on stomach smooth muscle contraction regarding three-dimensional boundary problems and the whole mechano-electrochemical process.…”

Phase waves and trigger waves: emergent properties of oscillating and excitable networks in the gut

“…; Lammers, ; Du et al . ). These waves circle (spiral) continuously around a point which may be fixed or not and can be induced by temporary or chronic blocks in coupling.…”

“…High spatial resolution arrays of recording electrodes applied to the surface of the small intestine and stomach have revealed re-entrant spiral waves, the poster child of cardiac arrhythmia (Lammers, 2013;O'Grady et al 2014;Lammers, 2015;Du et al 2017). These waves circle (spiral) continuously around a point which may be fixed or not and can be induced by temporary or chronic blocks in coupling.…”