Delay-Induced Uncertainty for a Paradigmatic Glucose-Insulin Model

TL;DR

This paper demonstrates that delays in the glucose-insulin system can cause sustained chaos, leading to unpredictability, and provides a diagnostic approach for delay-induced uncertainty applicable to various physiological models.

Contribution

It introduces a theoretical framework to diagnose delay-induced uncertainty in oscillatory systems, validated on the glucose-insulin model and extended to infinite-dimensional delay systems.

Findings

Delay causes sustained chaos in the glucose-insulin model.

The DIU recipe applies to both finite and infinite-dimensional systems.

Delay-induced chaos implies fundamental unpredictability in physiological models.

Abstract

Medical practice in the intensive care unit is based on the supposition that physiological systems such as the human glucose-insulin system are predictable. We demonstrate that delay within the glucose-insulin system can induce sustained temporal chaos, rendering the system unpredictable. Specifically, we exhibit such chaos for the Ultradian glucose-insulin model. This well-validated, finite-dimensional model represents feedback delay as a three-stage filter. Using the theory of rank one maps from smooth dynamical systems, we precisely explain the nature of the resulting delay-induced uncertainty (DIU). We develop a recipe one may use to diagnose DIU in a general oscillatory dynamical system. For infinite-dimensional delay systems, no analog of the theory of rank one maps exists. Nevertheless, we show that the geometric principles encoded in our DIU recipe apply to such systems by exhibiting sustained temporal chaos for a linear shear flow. Our results are potentially broadly applicable because delay is ubiquitous throughout mathematical physiology.