A parsimonious model of blood glucose homeostasis

TL;DR

This paper introduces a simple, minimal mathematical model of blood glucose regulation that effectively captures key dynamics and can aid in diagnosing pre-diabetes, using only three parameters and validated with real-world data.

Contribution

The paper presents a novel minimal model of glucose homeostasis as a control system, simplifying complex biological interactions into a planar dynamical system with practical diagnostic potential.

Findings

Model with only 3 parameters fits glucose data well

Parameters show consistent distribution across different glycemic episodes

Model can potentially be used for pre-diabetes diagnostics

Abstract

The mathematical modelling of biological systems has historically followed one of two approaches: comprehensive and minimal. In comprehensive models, the involved biological pathways are modelled independently, then brought together as an ensemble of equations that represents the system being studied, most often in the form of a large system of coupled differential equations. This approach often contains a very large number of tuneable parameters (> 100) where each describes some physical or biochemical subproperty. As a result, such models scale very poorly when assimilation of real world data is needed. Furthermore, condensing model results into simple indicators is challenging, an important difficulty in scenarios where medical diagnosis is required. In this paper, we develop a minimal model of glucose homeostasis with the potential to yield diagnostics for pre-diabetes. We model glucose homeostasis as a closed control system containing a self-feedback mechanism that describes the collective effects of the physiological components involved. The model is analyzed as a planar dynamical system, then tested and verified using data collected with continuous glucose monitors (CGMs) from healthy individuals in four separate studies. We show that, although the model has only a small number (3) of tunable parameters, their distribution across subjects has a consistent distribution both for hyperglycemic and for hypoglycemic episodes.