Cited by 349Pancreatic function and diabetesDiabetes Management and ResearchDiabetes, Cardiovascular Risks, and Lipoproteins

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Coefficients of normal blood glucose regulation

Bolie, Victor W.·1961·Journal of Applied Physiology

DOI 10.1152/jappl.1961.16.5.783

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Abstract

A previously formulated glucose-insulin feed-back theory was simplified with appropriate assumptions for the purpose of determining which physiological sensitivity coefficients dominate the mathematical characteristics of the normal insulin and glucose tolerance curves. It was found from experimental data that these physiological coefficients approximate the well-known critical damping criteria of servomechanism theory. Correlations between theoretical and experimental results were made with some particular solutions of the necessary differential equations, obtained with the aid of an electronic analogue computer. Using a distribution volume of 17.5 liters for the 70-kg adult in three different methods of approach, it was found that the average coefficients of the insulin and glucose responses of the liver, pancreas, and peripheral tissues are approximately ⍺ = 0.780 unit/hr/unit, β = 0.208 unit/hr/g, γ = 4.34 g/hr/unit, and δ = 2.92 g/hr/g. Submitted on December 27, 1960

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“Beginning with a model using ordinary diﬀerential equations by Bolie (1961), mathematicians and scientists have been developing models for over the past ﬁve decades.”
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Sokol, Y., Лапта, С., Chmykhova, O., et al. (2018) · IEEE International Conference on Electronics and Nanotechnology (ELNANO) · doi:10.1109/elnano.2018.8477505 · Cited by 4
“Bolie episodically investigated [5], his model has the following form:”
BackgroundMethod
Modeling and Control of the Glucose‐Insulin‐Glucagon System in Type I Diabetis Mellitus
Sangeetha, S., Sreepradha, C., Sobana, S., Bidisha, P., & Panda, R. C. (2020) · ChemBioEng Reviews · doi:10.1002/cben.201900015 · Cited by 4
Proportional Insulin Infusion in Closed-Loop Control of Blood Glucose
Grasman, J., Callender, H. L., & Mensink, M. (2017) · PLoS ONE · doi:10.1371/journal.pone.0169135 · Cited by 4
Finite-time control of plasma glucose in insulin therapies for diabetes
Liu, S., Huang, M., Song, X., & Shi, X. (2018) · Advances in Difference Equations · doi:10.1186/s13662-018-1532-z · Cited by 4
The glucose control mechanism viewed as a regulator
Zelin, S., Jun, G. H., & Norwich, K. H. (1975) · Medical & Biological Engineering & Computing · doi:10.1007/bf02477126 · Cited by 4
Evaluation of the Bolie model describing blood glucose response for the application to continuous subcutaneous insulin infusion.
HIRAYAMA, H., Kasuya, Y., YAGISHITA, A., & Katakura, T. (1985) · Journal of Pharmacobio-Dynamics · doi:10.1248/bpb1978.8.808 · Cited by 4
Perturbation-Iteration Method for Solving Mathematical Model of Glucose and Insulin in Diabetic Human during Physical Activity
Gahamanyi, M., Ntaganda, J. M., & Haggar, M. S. D. (2016) · Open Journal of Applied Sciences · doi:10.4236/ojapps.2016.612072 · Cited by 3
“828 the 1960s, researches in the direction of solving mathematical models have been developed to describe glucose-insulin dynamic systems [1] [13].”
Background
A biological rhythm in the hypothalamic system links sleep-wake cycles with feeding-fasting cycles
Tamayo-Molina, Y. S., Giraldo, M. A., Rodríguez, B. A., & Machado, G. (2024) · Scientific Reports · doi:10.1038/s41598-024-77915-4 · Cited by 6
Breadth of Pharmacology Modeling: Fundamentals of Pharmacokinetics, Pharmacodynamics, and Mechanistic Modeling
Mager, D. E. (2025) · Handbook of experimental pharmacology · doi:10.1007/164_2025_746 · Cited by 3
Robust glucose control via μ-synthesis in type 1 diabetes mellitus
Morales-Contreras, J., Ruiz-Velazquez, E., & García-Rodríguez, J. A. (2017) · IEEE International Autumn Meeting on Power, Electronics and Computing (ROPEC) · doi:10.1109/ropec.2017.8261671 · Cited by 3
“Simple linear models have been proposed in [6], [7].”
Method
Modelado matemático de ingestas de alimento e infusión de insulina en un paciente con diabetes tipo 1 en lazo cerrado
Manrique-Córdoba, J., Romero-Ante, J. D., Albán, Ó. A. V., Vicente-Samper, J. M., & Sabater-Navarro, J. M. (2020) · Revista Iberoamericana de Automática e Informática Industrial RIAI · doi:10.4995/riai.2019.11161 · Cited by 3
“Uno de los pioneros en este campo fue Bolie, quien en 1961 (Bolie, 1961) propuso un modelo usando ecuaciones diferenciales ordinarias que con la ayuda de un computador análogo electrónico realizó correlaciones entre resultados teóricos y experimentales.”
Background
Nonlinear modeling of oral glucose tolerance test response to evaluate associations with aging outcomes
Schumock, G., Bandeen‐Roche, K., Chia, C. W., Kalyani, R. R., Ferrucci, L., & Varadhan, R. (2024) · PLoS ONE · doi:10.1371/journal.pone.0302381 · Cited by 3

Authors: Bolie, V. W.
Affiliations: Iowa State University (US)
Corresponding author: Bolie, Victor W.
Venue: Journal of Applied Physiology
Publisher: American Physiological Society
Published: 1961-09-01
Volume: 16
Issue: 5
Pages: 783-788
ISSN: 0161-7567 (ISSN-L)
8750-7587
1522-1601
DOI: 10.1152/jappl.1961.16.5.783
OpenAlex: W2337101260
Cited by: 349
References: 0
Citations by year: 2026: 12 · 2025: 25 · 2024: 18 · 2023: 14 · 2022: 10 · 2021: 13 · 2020: 18 · 2019: 13 · 2018: 13 · 2017: 16 · 2016: 8 · 2015: 15 · 2014: 12 · 2013: 12 · 2012: 10
FWCI: 2.58
Type: journal article
Language: en
Open access: closed
Locations: Journal of Applied Physiology (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
Health Sciences › Medicine › Endocrinology, Diabetes and Metabolism › Diabetes, Cardiovascular Risks, and Lipoproteins
Keywords: blood glucose regulation, glucose tolerance curve, critical damping, volume of distribution, glucose-insulin dynamics
MeSH terms: Blood Glucose, Humans, Carbohydrate Metabolism

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Coefficients of normal blood glucose regulation

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