Cited by 330Pancreatic function and diabetesDiabetes Management and ResearchDiabetes and associated disorders

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A model of β-cell mass, insulin, and glucose kinetics: pathways to diabetes

TOPP, BRIAN, PROMISLOW, KEITH, DEVRIES, GERDA, MIURA, ROBERT M, FINEGOOD, DIANE T·2000·Journal of Theoretical Biology

DOI 10.1006/jtbi.2000.2150

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Abstract

Diabetes is a disease of the glucose regulatory system that is associated with increased morbidity and early mortality. The primary variables of this system are beta-cell mass, plasma insulin concentrations, and plasma glucose concentrations. Existing mathematical models of glucose regulation incorporate only glucose and/or insulin dynamics. Here we develop a novel model of beta -cell mass, insulin, and glucose dynamics, which consists of a system of three nonlinear ordinary differential equations, where glucose and insulin dynamics are fast relative to beta-cell mass dynamics. For normal parameter values, the model has two stable fixed points (representing physiological and pathological steady states), separated on a slow manifold by a saddle point. Mild hyperglycemia leads to the growth of the beta -cell mass (negative feedback) while extreme hyperglycemia leads to the reduction of the beta-cell mass (positive feedback). The model predicts that there are three pathways in prolonged hyperglycemia: (1) the physiological fixed point can be shifted to a hyperglycemic level (regulated hyperglycemia), (2) the physiological and saddle points can be eliminated (bifurcation), and (3) progressive defects in glucose and/or insulin dynamics can drive glucose levels up at a rate faster than the adaptation of the beta -cell mass which can drive glucose levels down (dynamical hyperglycemia).

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A mathematical model for ketosis-prone diabetes suggests the existence of multiple pancreatic β-cell inactivation mechanismsPreprint
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Authors: TOPP, B., PROMISLOW, K., DEVRIES, G., MIURA, R. M., & FINEGOOD, D. T.
Affiliations: Simon Fraser University (CA)
University of Alberta (CA)
University of British Columbia (CA)
ORCID: PROMISLOW, KEITH
FINEGOOD, DIANE T
Venue: Journal of Theoretical Biology
Publisher: Elsevier BV
Published: 2000-10
Volume: 206
Issue: 4
Pages: 605-619
ISSN: 0022-5193 (ISSN-L)
DOI: 10.1006/jtbi.2000.2150
OpenAlex: W2002062638
Cited by: 330
References: 60
Citations by year: 2026: 25 · 2025: 30 · 2024: 23 · 2023: 17 · 2022: 22 · 2021: 20 · 2020: 21 · 2019: 13 · 2018: 11 · 2017: 5 · 2016: 16 · 2015: 19 · 2014: 13 · 2013: 12 · 2012: 9
FWCI: 3.60
Type: journal article
Language: en
Open access: closed
Licence: www.elsevier.com/tdm/userlicense/1.0/ (tdm)
Locations: Journal of Theoretical Biology (publishedVersion)
PubMed (publishedVersion)
Topics: Health Sciences › Medicine › Endocrinology, Diabetes and Metabolism › Pancreatic function and diabetes
Health Sciences › Medicine › Endocrinology, Diabetes and Metabolism › Diabetes Management and Research
Life Sciences › Biochemistry, Genetics and Molecular Biology › Genetics › Diabetes and associated disorders
Keywords: beta-cell mass, insulin dynamics, glucose kinetics, diabetes mellitus, glucose regulation, hyperglycemia, slow manifold, saddle points, bifurcation, negative feedback, positive feedback, nonlinear ordinary differential equations
MeSH terms: Blood Glucose, Diabetes Mellitus, Humans, Insulin, Islets of Langerhans, Models, Biological, Nonlinear Dynamics, Cell Size

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A model of β-cell mass, insulin, and glucose kinetics: pathways to diabetes

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