Sounding the metabolic orchestra: A delay dynamical systems perspective on the glucose-insulin regulatory response to on-off glucose infusion

TL;DR

This study models the glucose-insulin system with delays to understand how periodic glucose infusion affects its oscillations and response, offering insights for potential diagnostic strategies.

Contribution

It introduces a delay differential equation model to analyze the effects of on-off glucose infusion on glucose-insulin dynamics, highlighting the role of ultradian oscillations and system entrainment.

Findings

Infusion patterns influence glucose and insulin levels.

Ultradian oscillations interact with infusion timing.

Model suggests new testing strategies for abnormal glucose responses.

Abstract

We investigate the consequences of periodic, on-off glucose infusion on the glucose-insulin regulatory system on the basis of a system-level mathematical model with two explicit time delays. Studying the effects of such infusion protocols is mathematically challenging yet a promising direction for probing the system response to infusion. We pay special attention to the interplay of the infusion with intermediate-time-scale, ultradian oscillations that arise as a results of the physiological response of glucose uptake and back-release into the bloodstream. By using numerical solvers and numerical continuation software, we investigate the response of the model to different infusion patterns, and explore how these patterns affect the overall levels of glucose and insulin, and can lead to entrainment. By doing so, we provide a road-map of system responses that can potentially help identify new test strategies for detecting abnormal responses to glucose uptake.