A parsimonious model of blood glucose homeostasis

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 distributions are consistent across subjects and studies both for hyperglycemic and for hypoglycemic episodes.

Evaluation of a continuous glucose monitor-derived homeostasis metric for type 2 diabetes screening

“…Around 80 -100 data segments that exhibit peaks in blood glucose over 60 to 300 minutes are extracted automatically [19]. Each segment yields one set of optimized parameters, and their distribution is the basis of The parameter distribution for each individual was then compared to the representative parameter distributions.…”

“…The model was shown to accurately reproduce both positive (hyperglycemic) and negative (hypoglycemic) excursions of blood sugar levels when combined with a lightweight procedure to conform it to segments of CGM data. Moreover, pilot studies suggested that the tuned model parameters have the potential to be used as biomarkers for diabetic status [18,19].…”