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.
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Cobelli, C., & Man, C. D. (2021) · Journal of Diabetes Science and Technology · doi:10.1177/19322968211015268 · Cited by 21 · see citing works
“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).”
BackgroundMathematical models of the kinetics of glucose and insulin in plasma
Norwich, K. H. (1969) · Bulletin of Mathematical Biology · doi:10.1007/bf02478212 · Cited by 19 · see citing works
Gallardo-Hernández, A. G., Fridman, L. M., Islas‐Andrade, S., & Shtessel, Y. B. (2008) · IEEE Conference on Decision and Control (CDC) · doi:10.1109/cdc.2008.4739450 · Cited by 17 · see citing works
“Biological models are quite complicated, since the 70’s there have been several published model that have evoluted [4],[5], [6],[7].”
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 · see citing works
“он предложил линейную модель, основанную на собственной теории [31], с двумя обыкновенными дифференциальными уравнениями (ОДУ), описывающими закономерности изменений концентрации ГК и инсулина.”
Lee, H., & Bequette, B. W. (2008) · IFAC Proceedings Volumes · doi:10.3182/20080706-5-kr-1001.00715 · Cited by 18 · see citing works
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 · see citing works
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 · see citing works
“insulin therapies, a number of research papers have appeared on the topic [2, 3, 10, 13, 15, 16, 39, 40].”
Background
- 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 › Surgery › 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
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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