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Coefficients of normal blood glucose regulation
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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Quantitative estimation of insulin sensitivity.
Bergman, R. N., Ider, Y. Z., Bowden, C. R., & Cobelli, C. (1979) · American Journal of Physiology-Endocrinology and Metabolism · doi:10.1152/ajpendo.1979.236.6.e667 · Cited by 1,874
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“Many approaches to modeling the human glucose-insulin system have been taken [9], [17]–[19], starting from the initial glucose modeling work of Bolie [20].”
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“One of the pioneering papers in this field is Bolie (1961) [19] according to Derouich and Boutayeb (2002, p.”
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“Pioneering work on modeling the glucose–insulin regulatory system and the ultradian insulin secretory oscillations can be traced back to Bolie (1961), in which the linearized system of the glucose–insulin regulation in terms of the differential equations of feedback was analysed with the so-called…”
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“G G d B (B), B G dB J(B, ) d K K (B) dB η η ∂λ Γ ∂λ ⎡ ⎤ + λ Γ η ⎢ ⎥ ∂ ∂η ⎢ ⎥ η = Γ ⎢ ⎥ − η − Γ ⎢ ⎥ ⎣ ⎦ (8)”
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“One of the earliest “minimal” representations of the glucose-insulin system was published in the early 1960’s (Bolie, 1961).”
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“If it is not possible to measure insulin, a structurally identifiable model can be obtained by reducing the number of unknown parameters to three, e.g. by fixing the values of two of them (“Bolie C”).”
InfluentialA mathematical model of brain glucose homeostasis
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BackgroundPharmacokinetic-Pharmacodynamic Modeling of Metformin for the Treatment of Type II Diabetes Mellitus
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“Victor Bolie 26 pioneered the filed by proposing a linear model to describe the plasma glucose and insulin concentrations in an intravenous glucose tolerance test (IVGTT).”
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BackgroundMathematical Modeling of the Blood Glucose Regulation System in Diabetes Mellitus Patients
Александрович, К. В., Philippov, Y. I., Tarasov, Y. V., Boyarsky, M. D., Mayorov, A. Y., Shestakova, M. V., & Dedov, I. I. (2015) · Annals of the Russian academy of medical sciences · doi:10.15690/vramn.v70.i5.1441 · Cited by 18
“он предложил линейную модель, основанную на собственной теории [31], с двумя обыкновенными дифференциальными уравнениями (ОДУ), описывающими закономерности изменений концентрации ГК и инсулина.”
A Closed-Loop Artificial Pancreas Based on MPC: Human-Friendly Identification and Automatic Meal Dis
Lee, H., & Bequette, B. (2008) · IFAC Proceedings Volumes · doi:10.3182/20080706-5-kr-1001.00715 · Cited by 19
A physical activity-intensity driven glycemic model for type 1 diabetes
Hobbs, N., Samadi, S., Rashid, M. M., Shahidehpour, A., Askari, M. R., Park, M., Quinn, L., & Çınar, A. (2022) · Computer Methods and Programs in Biomedicine · doi:10.1016/j.cmpb.2022.107153 · Cited by 18
Modelling the regulatory system for diabetes mellitus with a threshold window
Yang, J., Tang, S., & Cheke, R. (2014) · Communications in Nonlinear Science and Numerical Simulation · doi:10.1016/j.cnsns.2014.08.012 · Cited by 17
“insulin therapies, a number of research papers have appeared on the topic [2, 3, 10, 13, 15, 16, 39, 40].”
Background
Metadata
- 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
- 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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