Examining Type 1 Diabetes Mathematical Models Using Experimental Data

Hannah Al Ali, Alireza Daneshkhah, Abdesslam Boutayeb and Zindoga Mukandavire
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Hannah Al Ali: Computational Science and Mathematical Modelling, Coventry University, Coventry CV1 5FB, UK
Alireza Daneshkhah: Computational Science and Mathematical Modelling, Coventry University, Coventry CV1 5FB, UK
Abdesslam Boutayeb: Department of Mathematics, Faculty of Sciences, University Mohamed Premier, P.O. Box 524, Oujda 60000, Morocco
Zindoga Mukandavire: Institute of Applied Research and Technology, Emirates Aviation University, Dubai 53044, United Arab Emirates

IJERPH, 2022, vol. 19, issue 2, 1-20

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 capability 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.

Keywords: diabetes; thresholds; model selection; model calibration (search for similar items in EconPapers)
JEL-codes: I I1 I3 Q Q5 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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