Exploration of bimodal kinetics in marker digesta outflows using compartmental models

Abstract

A deterministic compartmental model is developed for examining the dynamics of digesta marker outflows in animals, focussing on models which will simulate bimodal kinetics with two peaks in the time course of marker outflow. First, to establish the background to the subsequent modelling of bimodal flow, we examine the compartmental scheme which gives rise mechanistically to the gamma function, and derive or describe various useful properties. This is illustrated by varying two key parameters of the gamma function, n (the number of compartments), and k (the rate constant for compartment emptying). Next, a more articulated compartmental scheme is constructed, and by progressive parameter changes, it is shown how bimodal faecal marker outflow can be achieved. Last, progressive simplification is applied to this scheme to arrive at what is (hopefully) the simplest compartmental scheme which can be used to simulate bimodal kinetics. This may be used mechanistically to describe the role of digesta flow in animals which exhibit such characteristics.

Keywords: Bimodal kinetics; Compartmental models; Digesta; Dynamics; Gamma functions; Marker.