Examining Type 1 Diabetes Mathematical Models Using Experimental Data

Hannah Al Ali, Alireza Daneshkhah, Abdesslam Boutayeb, Zindoga Mukandavire

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Abstract

Type 1 diabetes requires treatment with insulin injections and monitoring glucose levels in affected individuals. We explored the utility of two mathematical models in predicting glucose concentration levels in type 1 diabetic mice and determined disease pathways. We adapted two mathematical models, one with β-cells and the other with no β-cell component to determine their ca-pability in predicting glucose concentration and determine type 1 diabetes pathways using published glucose concentration data for four groups of experimental mice. The groups of mice were numbered Mice Group 1–4, depending on the diabetes severity of each group, with severity increasing from group 1–4. A Markov Chain Monte Carlo method based on a Bayesian framework was used to fit the model to determine the best model structure. Akaike information criteria (AIC) and Bayesian information criteria (BIC) approaches were used to assess the best model structure for type 1 diabetes. In fitting the model with no β-cells to glucose level data, we varied insulin absorption rate and insulin clearance rate. However, the model with β-cells required more parameters to match the data and we fitted the β-cell glucose tolerance factor, whole body insulin clearance rate, glucose production rate, and glucose clearance rate. Fitting the models to the blood glucose concentration level gave the least difference in AIC of 1.2, and a difference in BIC of 0.12 for Mice Group 4. The estimated AIC and BIC values were highest for Mice Group 1 than all other mice groups. The models gave substantial differences in AIC and BIC values for Mice Groups 1–3 ranging from 2.10 to 4.05. Our results suggest that the model without β-cells provides a more suitable structure for modelling type 1 diabetes and predicting blood glucose concentration for hypoglycaemic episodes.

Original languageEnglish
Article number737
Number of pages20
JournalInternational Journal of Environmental Research and Public Health
Volume19
Issue number2
DOIs
Publication statusPublished - 10 Jan 2022

Bibliographical note

Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland.
This article is an open access article distributed under the terms and
conditions of the Creative Commons Attribution (CC BY) license (https://
creativecommons.org/licenses/by/4.0/).

Keywords

  • Diabetes
  • Model calibration
  • Model selection
  • Thresholds

ASJC Scopus subject areas

  • Pollution
  • Public Health, Environmental and Occupational Health
  • Health, Toxicology and Mutagenesis

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