Abstract
Mathematical models afford a procedure of unifying concepts and hypotheses by expressing quantitative relationships between observables. The model presented indicates the roles of both insulin and glucagon as regulators of blood glucose, albeit in different ranges of the blood glucose concentrations. Insulin secretion is induced during hyperglycemia, while glucagon secretion results during hypoglycemia. These are demonstrated by simulations of a mathematical model conformed to data from the oral glucose tolerance test and the insulin infusion test in normal control subjects and stable and unstable diabetic patients. The model studies suggest the parameters could prove of value in quantifying the diabetic condition by indicating the degree of instability.
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Literature
Ackerman, E., L. C. Gatewood, J. W. Rosevear and G. D. Molnar. 1965. “Model Studies of Blood-Glucose Regulation.”Bull. Math. Biophys.,27, 21–38.
Bolie, V. W. 1961. “Coefficients of Normal Blood-Glucose Regulation.”J. Appl. Physiol.,16, 783–788.
Brent, R. P. 1973.Algorithms for Minimization Without Derivatives. Englewood Cliffs, New Jersey: Prentice-Hall.
Cerasi, E. 1967. “An Analogue Computer Model for the Insulin Response to Glucose Infusion.”Acta. Endocrinol.,5, 163–183.
Ceresa, F., F. Ghemi, P. F. Martini, P. Martino, G. Segre and A. Vitelli. 1968. “Control of Blood Glucose in Normal and in Diabetic Subjects.”Diabetes,17, 570–578.
Curry, D. L., L. L. Bennett and G. M. Grodsky. 1968. “Dynamics of Insulin Secretion by the Perfused Rat Pancreas.”Endocrinology,83, 572–584.
Della Corte, M., S. Romano, M. R. Voeghelin and M. Serio. 1970. “On a Mathematical Model for the Analysis of the Glucose Tolerance Curve.”Diabetes,19, 445–449.
Gatewood, L. C., E. Ackerman, G. D. Molnar and J. W. Rosevear. 1967. “Simulation Studies of Some Etiologic Relationships in Diabetic Instability.”Fedn. Proc.,26, 257 (abstract).
——, J. W. Rosevear and G. D. Molnar. 1967. “Modeling Blood Glucose Dynamics.”Behav. Sci.,15, 72–87.
Fineberg, S. E. and T. J. Merimee. 1974. “Acute Metabolic Effects of Human Growth Hormone.”Diabetes,23, 499–504.
Hisanaga, R. G. 1975.MIMO User Manual. Minneapolis: Health Computer Sciences, University of Minnesota.
Horwitz, D. L., A. H. Rubenstein, C. Reynolds, G. D. Molnar and N. Yanaihara. 1975. “Prolonged Suppression of Insulin Release by Insulin-Induced Hyperglycemia: Demonstration by C-Peptide Assay.”Hormon. Metab. Res.,7, 449–452.
Kraegen, E. W. 1969. “The Blood Glucose Feedback Control System.” Ph.D. thesis, University of New South Wales, Kensington, NSW.
Molnar, G. D., C. F. Gastineau, J. W. Rosevear and K. E. Moxness. 1965. “Quantitative Aspects of Labile Diabetes.”Diabetes,14, 279–288.
—, V. Fatourechi, E. Ackerman, W. F. Taylor, J. W. Rosevear, L. C. Gatewood, F. J. Service and K. E. Moxness. 1971. “Growth Hormone and Glucose Interrelationships in Diabetes: Studies of Inadvertent Hypoglycemic Episodes During Continuous Glucose Analysis.”J. Clin. Endocr.,32, 426–437.
Palumbo, P. J., W. F. Taylor, G. D. Molnar and W. N. Tauxe. 1972. “Disappearance of Bovine Insulin from Plasma in Diabetic and Normal Subjects.”Metabolism,21, 787–798.
Reynolds, C. 1974. “Glucagon-insulin-glucose Relationships in Diabetes Mellitus and Correlation of Glucagon and Insulin Abnormalities with Degree of Diabetic Instability.” M.S. thesis, University of Minnesota, Minneapolis.
—, G. D. Molnar, D. J. Horwitz, A. H. Rubenstein, W. F. Taylor and N.-S. Jiang. 1977. “Abnormalities of Endogenous Glucagon and Insulin in Unstable Diabetes.”Diabetes,26, 36–45.
Samols, E., G. Marri and V. Marks. 1966. “Interrelationships of Glucagon, Insulin and Glucose: The Insulinogenic Effect of Glucagon.”Diabetes,15, 855–866.
Service, F. J., G. D. Molnar, J. W. Rosevear, E. Ackerman, L. C. Gatewood and W. F. Taylor. 1970. “Mean Amplitude of Glycemic Excursions, a Measure of Diabetic Instability.”Diabetes,19, 644–655.
Unger, R. H. 1973. “Pancreatic Glucagon in Health and Disease.”Metabolism,22, 265–288.
— and L. Orci. 1976. “Physiology and Pathophysiology of Glucagon.”Physiol. Rev.,56, 778–826.
Yipintsoi, T., L. C. Gatewood, E. Ackerman, P. L. Spivak, G. D. Molnar, J. W. Rosevear and F. J. Service. 1973. “Mathematical Analysis of Blood Glucose and Plasma Insulin Responses to Insulin Infusion in Healthy and Diabetic Subjects.”Comput. Biol. Med.,3, 71–78.
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Celeste, R., Ackerman, E., Gatewood, L.C. et al. The role of glucagon in the regulation of blood glucose: Model studies. Bltn Mathcal Biology 40, 59–77 (1978). https://doi.org/10.1007/BF02463130
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DOI: https://doi.org/10.1007/BF02463130