Skip to main content
SpringerLink
Log in
SpringerLink
Log in

The Minimal Model of Glucose Regulation: A Biography

  • Chapter
Mathematical Modeling in Nutrition and the Health Sciences

Part of the book series: Advances in Experimental Medicine and Biology ((AEMB,volume 537))

Abstract

The life history of the so-called “minimal model” of glucose regulation can be traced back over two decades. During the decades after World War II, the science of cybernet-ics was introduced by Norbert Weiner at MIT (Weiner,1965). Weiner recognized the importance of the rapidly developing fields of control theory and systems analysis to problems in biology and medicine. During the ensuing decade, much was written about the potential benefits of applying mathematical analysis to biology (Yates et al., 1972).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Ader, M., Pacini, G., Yang, Y.J., and Bergman, R.N., 1985, Importance of glucose per se to intravenous glucose tolerance: comparison of the minimal model prediction with direct measurements, Diabetes 34:1092–1103.

    Article  Google Scholar 

  • Ader, M., and Bergman, R.N., 1987, Insulin sensitivity in the intact organism, in: Bailliere’s Clinics in Endocrinology and Metabolism, K.G.M.M. Alberti, P.D. Home, and R. Taylor eds., Bailliere Tindall, London.

    Google Scholar 

  • Ader, M., Ni, T.-C, and Bergman, R.N., 1997, Glucose effectiveness assessed under dynamic and steady state conditions: comparability of uptake versus production components, J. Clin. Invest. 99:1187–1199.

    Article  Google Scholar 

  • Andres, R., Swerdloff, R., Pozefsky, T., and Coleman, D., 1966, Manual feedback technique for the control of blood glucose concentration, in: Automation in Analytical Chemistry, J. Skeggs, ed., Mediad, Inc., New York.

    Google Scholar 

  • Basu, A., Caumo, A., Bettini, F., Gelisio, A., Alzaid, A., Cobelli, C, and Rizza, R.A., 1997, Impaired basal glucose effectiveness in NIDDM: contribution of defects in glucose disappearance and production, measured using an optimized minimal model independent protocol, Diabetes 46:421–432.

    Article  Google Scholar 

  • Beard, J. C, Ward, W.K., Halter, J.B., Wallum, B.J., and Porte, D., Jr., 1987, Relationship of islet function to insulin action in human obesity, J. Clin. Endocrinol. Metab. 65:59–64.

    Article  Google Scholar 

  • Bergman, R.N., 1989, Toward physiological understanding of glucose tolerance: minimal-model approach (Lilly Lecture), Diabetes 38:1512–1527.

    Article  Google Scholar 

  • Bergman, R.N., 1995, Insulin sensitivity from the minimal model, in: Research Methodologies in Human Diabetes -- Part 2, Walter de Gruyter, Berlin.

    Google Scholar 

  • Bergman, R.N., and Ader, M., 1993, Concepts emerging from the minimal model approach, in: Current Topics in Diabetes Research, F. Belfiore, R.N. Bergman, and G.M. Molinatti, eds., Karger, Basel.

    Google Scholar 

  • Bergman, R.N., and Cobelli, C, 1980, Minimal modeling, partition analysis and the estimation of insulin sensitivity, Fed. Proc. 39:110–115.

    Google Scholar 

  • Bergman, R.N., Finegood, D.T., and Ader, M., 1985, Assessment of insulin sensitivity in vivo, Endocr. Rev. 6:45–86.

    Article  Google Scholar 

  • Bergman, R.N., Phillips, L.S., and Cobelli, C, 1981, Physiologic evaluation of factors controlling glucose tolerance in man: measurement of insulin sensitivity and B-cell glucose sensitivity from the response to intravenous glucose, J. Clin. Invest. 68:1456–1467.

    Article  Google Scholar 

  • Bergman, R.N., Prager, R., Volund, A., and Olefsky, J.M., 1987, Equivalence of the insulin sensitivity index in man derived by the minimal model method and the euglycemic glucose clamp, J. Clin. Invest. 79:790–800.

    Article  Google Scholar 

  • Best, J.D., Kahn, S.E., Ader, M., Watanabe, R.M., Ni, T.-C., and Bergman, R.N., 1996, Role of glucose effectiveness in the determination of glucose tolerance, Diab. Care 19:1018–1030.

    Google Scholar 

  • Bradley, D.C., Poulin, R.A., and Bergman, R.N., 1992, Dynamics of hepatic and peripheral insulin effects suggest common rate-limiting step in vivo, Diabetes 42:296–306.

    Article  Google Scholar 

  • Brownlee, M., 1994, Glycation and diabetic complications, Diabetes 43:836–841.

    Google Scholar 

  • Buchanan, T.A., Metzger, B.E., Freinkel, N., and Bergman, R.N., 1990, Insulin sensitivity and B-cell responsiveness to glucose during late pregnancy in lean and moderately obese women with normal glucose tolerance or mild gestational diabetes, Am. J. Obstet. Gynecol. 162:1008–1014.

    Google Scholar 

  • Buchanan, T.A., Xiang, A.H., Peters, R.K., Kjos, S.L., Berkowitz, K., Marroquin, A., Goico, J., Ochoa, C, and Azen, S.P., 2000, Response of pancreatic b-cells to improved insulin sensitivity in women at high risk for type 2 diabetes, Diabetes 49:782–788.

    Article  Google Scholar 

  • Cahill, G.F., Jr., Herrera, M.G., Morgan, A.P., Soeldner, J.S., Steinke, J., Levy, P.L., Reichard, G.A., and Kipnis, D.M., 1966, Hormone-fuel interrelationships during fasting, J. Clin. Invest. 45:1751–1769.

    Article  Google Scholar 

  • Caumo, A., Vicini, P., and Cobelli, C., 1996, Is the minimal model too minimal? Diabetologia 39:997–1000.

    Article  Google Scholar 

  • Cobelli, C., Vicini, P., and Caumo, A., 1997, If the minimal model is too minimal, who suffers more: SG or SI? Diabetologia 40:362–364.

    Google Scholar 

  • Cobelli, C, Bettini, F., Caumo, A., and Quon, M.J., 1998, Overestimation of minimal model glucose effectiveness in presence of insulin response is due to undermodeling, Am. J. Physiol. 275:E1031–E1036.

    Google Scholar 

  • Dea, M., Hamilton-Wessler, M., Ader, M., Poulin, R.A., Moore, D., and Markussen, J., 1997, Long-acting insulin analogue NN304 has similar transendothelial transport to porcine insulin, Diabetes 46:164A.

    Google Scholar 

  • DeFronzo, R.A., Tobin, J.D., and Andres, R., 1979, Glucose clamp technique: a method for quantifying insulin secretion and resistance, Am. J. Physiol. 237:E214–E223.

    Google Scholar 

  • Donner, C.C., Fraze, E., Chen, Y.D.I., Hollenbeck, C.B., Foley, J.E., and Reaven, G.M., 1985, Presentation of a new method for specific measurement of in vivo insulin-stimulated glucose disposal in humans: comparison of this approach with the insulin clamp and minimal model techniques, J. Clin. Endocrinol Metab. 60:723–726.

    Article  Google Scholar 

  • Dunaif, A., and Finegood, D.T., 1996, b-Cell dysfunction independent of obesity and glucose intolerance in the polycystic ovary syndrome, J. Clin. Endocrinol. Metab. 81:942–947.

    Article  Google Scholar 

  • Finegood, D.T., Pacini, G., and Bergman, R.N., 1984, The insulin sensitivity index: correlation in dogs between values determined from the intravenous glucose tolerance test and the euglycemic glucose clamp, Diabetes 33:362–368.

    Article  Google Scholar 

  • Foster, D.M., Boston, R.C., Jacquez, J.A., and Zech, L., 1989, A resource facility for kinetic analysis: modeling using the SAAM computer programs, Health Phys. 57 (Suppl 1):457–466.

    Article  Google Scholar 

  • Garcia, G.V., Freeman, R.V., Supiano, M.A., Smith, M.J., Galecki, A.T., and Halter, J.B., 1997, Glucose metabolism in older adults: a study including subjects more than 80 years of age, J. Am. Geriatr. Soc. 45:813–817.

    Google Scholar 

  • Getty, L., Hamilton-Wessler, M., Ader, M., Dea, M.K., and Bergman, R.N., 1998, Biphasic insulin secretion during intravenous glucose tolerance test promotes optimal interstitial insulin profile, Diabetes 47:1941–1947.

    Article  Google Scholar 

  • Greif, P., Wastney, M., Linares, O., and Boston, R., 1998, Balancing needs, efficiency, and functionality in the provision of modeling software: a perspective of the NIH WinSAAM project, in: Mathematical Modeling in Experimental Nutrition, A.J. Clifford and H.-G. Müller, eds., Plenum Press, New York.

    Google Scholar 

  • Grodsky, G.M., 1972, A threshold distribution hypothesis for packet storage of insulin and its mathematical modeling, J. Clin. Invest. 51:2047–2059.

    Article  Google Scholar 

  • Hamilton-Wessler, M., Ader, M., Dea, M., Moore, D., Jorgensen, P.N., Markussen, J., and Bergman, R.N., 1999, Mechanism of protracted metabolic effects of fatty acid acylated insulin, NN304, in dogs: retention of NN304 by albumin, Diabetologia 42:1254–1263.

    Article  Google Scholar 

  • Hamilton-Wessler, M., Ellmerer, M., Dea, M.K., Mittelman, S.D., van Citters, G.W., and Kim, S.P., 2000, Insulin resistance in dogs with transendothelial transport defect, Diabetes 49 (Suppl 1), A59.

    Google Scholar 

  • Hodgkin, A.L., 1951, The ionic basis of electrical activity in nerve and muscle, Biol. Rev. 26: 339–401.

    Article  Google Scholar 

  • Howard, G., O’Leary, D.H., Zaccaro, D., Haffner, S., Rewers, M., Hamman, R., Selby, J.V., Saad, M.F., Savage, P., and Bergman, R. for the IRAS Investigators, 1996, Insulin sensitivity and atherosclerosis: the Insulin Resistance Atherosclerosis Study (IRAS), Circulation 93:1809–1817.

    Article  Google Scholar 

  • Jansson, P.A., Fowelin, J.P., von Schenck, H.P., Smith, U.P., and Lonnroth, P.N., 1993, Measurement by microdialysis of the insulin concentration in subcutaneous interstitial fluid: Importance of the endothelial barrier for insulin, Diabetes 42:1469–1473.

    Article  Google Scholar 

  • Kahn, S. E., Beard, J.C., Schwartz, M.W., Ward, W.K., Ding, H.L., Bergman, R.N., Taborsky, G.J., Jr., and Porte, D., Jr., 1989, Increased B-cell secretory capacity as mechanism for islet adaptation to nicotinic-acid-induced insulin resistance, Diabetes 38:562–568.

    Article  Google Scholar 

  • Kahn, S.E., Prigeon, R.L., McCulloch, D.K., Boyko, E.J., Bergman, R.N., Schwartz, M.W., Neifing, J.L., Ward, W.K., Beard, J.C., Palmer, J.P., and Porte, D., Jr., 1993, Quantification of the relationship between insulin sensitivity and B-cell function in human subjects: evidence for a hyperbolic function, Diabetes 42:1663–1672.

    Article  Google Scholar 

  • King, G.L., and Johnson, S.M., 1985, Receptor-mediated transport of insulin across endothelial cells, Science 227:1583–1586.

    Article  Google Scholar 

  • Knott, G.D., 1979, MLAB -- a mathematical modeling tool, Comput. Progr. Biomed. 10:271–280.

    Article  Google Scholar 

  • Korytkowski, M.T., Berga, S.L., and Horwitz, M.J., 1995, Comparison of the minimal model and the hyperglycemic clamp for measuring insulin sensitivity and acute insulin response to glucose, Metabolism 44:1121–1125.

    Article  Google Scholar 

  • Lewis, G.F., Vranic, M., Harley, P., and Giacca, A., 1997, Fatty acids mediate the acute extrahepatic effects of insulin on hepatic glucose production in humans, Diabetes 46:1111–1119.

    Article  Google Scholar 

  • Manning, R.D., Jr., and Guyton, A.C., 1982, Control of blood volume, Rev. Physiol Biochem. Pharmacol. 93:70–114.

    Google Scholar 

  • Martin, B.C., Warram, J.H., Krolewski, A.S., Bergman, R.N., Soeldner, J.S., and Kahn, C.R., 1992, Role of glucose and insulin resistance in development of type 2 diabetes mellitus: results of a 25-year follow-up study, Lancet 340:925–929.

    Article  Google Scholar 

  • McDonald, C, Dunaif, A., and Finegood, D.T., 2000, Minimal-model estimates of insulin sensitivity are insensitive to errors in glucose effectiveness, J. Clin. Endocrinol. Metab. 85: 2504–2508.

    Article  Google Scholar 

  • Miles, P.D.G., Levisetti, M., Reichart, D., Khoursheed, M., Moossa, A.R., and Olefsky, J.M., 1995, Kinetics of insulin action in vivo: identification of rate-limiting steps, Diabetes 44:947–953.

    Article  Google Scholar 

  • Mittelman, S.D., and Bergman, R.N., 2000, Inhibition of lipolysis causes suppression of endogenous glucose production independent of changes in insulin, Am. J. Physiol. 279: E630–E637.

    Google Scholar 

  • Ni, T.-C., Ader, M., and Bergman, R.N., 1997, Reassessment of glucose effectiveness and insulin sensitivity from minimal model analysis: a theoretical evaluation of the single-compartment glucose distribution assumption, Diabetes 43:1813–1821.

    Article  Google Scholar 

  • Poulin, R.A., Steil, G.M., Moore, D.M., Ader, M., and Bergman, R.N., 1994, Dynamics of glucose production and uptake are more closely related to insulin in hindlimb lymph than in thoracic duct lymph, Diabetes 43:180–190.

    Article  Google Scholar 

  • Quon, M.J., Cochran, C, Taylor, S.I., and Eastman, R.C., 1994, Non-insulin-mediated glucose disappearance in subjects with IDDM: discordance between experimental results and minimal model analysis, Diabetes 43:890–896.

    Article  Google Scholar 

  • Rashevsky, N., 1940, Advances and Applications of Mathematical Biology, University of Chicago Press, Chicago.

    Google Scholar 

  • Rebrin, K., Steil, G.M., Getty, L., and Bergman, R.N., 1995, Free fatty acid as a link in the regulation of hepatic glucose output by peripheral insulin, Diabetes 44:1038–1045.

    Article  Google Scholar 

  • Rebrin, K., Steil, G.M., Mittelman, S., and Bergman, R.N., 1996, Causal linkage between insulin regulation of lipolysis and liver glucose output, J. Clin. Invest. 98:741–749.

    Article  Google Scholar 

  • Turing, A.M., 1936, On computable numbers, with an application to the Entscheidungsproblem, Proc. London Math. Soc. 2:230–265.

    MathSciNet  Google Scholar 

  • Steil, G. M., Ader, M., Moore, D.M., Rebrin, K., and Bergman, R.N., 1996, Transendothelial insulin transport is not saturable in vivo: no evidence for a receptor-mediated process, J. Clin. Invest. 97:1497–1503.

    Article  Google Scholar 

  • Taniguchi, A., Nakai, Y., Fukushima, M., Imura, H., Kawamura, H., Nagata, I., Florant, G.L., and Tokuyama, K., 1994, Insulin sensitivity, insulin secretion, and glucose effectiveness in subjects with impaired glucose tolerance: a minimal model analysis, Metabolism 43:714–718.

    Article  Google Scholar 

  • Valle, T., Tuomilehto, J., Bergman, R.N., Ghosh, S., Hauser, E.R., Eriksson, J., Nylund, S.J., Kohtamaki, K, Toivanen, L., Vidgren, G., Tuomilehto-Wolf, E., Ehnholm, C, Blaschak, J., Langefeld, C.D., Watanabe, R.M., Magnuson, V., Ally, D.S., Hagopian, W.A., Ross, E., Buchanan, T.A., Collins, F., and Boenke, M., 1998, Mapping genes for NIDDM: design of the Finland-United States investigation of NIDDM genetics (FUSION) study, Diab. Care 21: 949–958.

    Article  Google Scholar 

  • Vicini, P., Caumo, A., and Cobelli, C, 1997. The hot IVGTT two-compartment minimal model: indexes of glucose effectiveness and insulin sensitivity, Am. J. Physiol. 273:E1024–E1032.

    Google Scholar 

  • Weiner, N., 1965, Cybernetics or Control and Communication in the Animal, MIT Press, Boston.

    Google Scholar 

  • Weyer, C., Bogardus, C., Mott, D.M., and Pratley, R.E., 1999, The natural history of insulin secretory dysfunction and insulin resistance in the pathogenesis of type 2 diabetes mellitus, J. Clin. Invest. 104:787–794.

    Article  Google Scholar 

  • Wing, R.R., Blair, E.H., Bononi, P., Marcus, M.D., Watanabe, R., and Bergman, R.N., 1994, Caloric restriction per se is a significant factor in improvements in glycemic control and insulin sensitivity during weight loss in obese NIDDM patients, Diab. Care 17:30–36.

    Article  Google Scholar 

  • Yang, Y.J., Hope, I.D., Ader, M., and Bergman, R.N., 1989, Insulin transport across capillaries is rate limiting for insulin action in dogs, J. Clin. Invest. 84:1620–1628.

    Article  Google Scholar 

  • Yates, F.E., Marsh, D.J., and Iberall, A.S., 1972, Integration of the whole organism: a foundation for a theoretical biology, in: Challenging Biological Problems: Directions Towards Their Solution, J.A. Behnke, ed., Oxford University Press, New York.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physiology and Biophysics and USC Diabetes Research Center, University of Southern California, Los Angeles, CA, 90033

    Richard N. Bergman

  2. Department of Physiology and Biophysics, Keck-USC School of Medicine, 1333 San Pablo Street, Los Angeles, CA, 90033

    Richard N. Bergman

Authors
  1. Richard N. Bergman
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. U.S. Department of Agriculture, Beltsville Human Nutrition Research Center, Beltsville, Maryland

    Janet A. Novotny

  2. Department of Nutrition, Pennsylvania State University, State College, Pennsylvania

    Michael H. Green

  3. School of Veterinary Medicine, University of Pennsylvania, Kennett Square, Pennsylvania

    Ray C. Boston

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer Science+Business Media New York

About this chapter

Cite this chapter

Bergman, R.N. (2003). The Minimal Model of Glucose Regulation: A Biography. In: Novotny, J.A., Green, M.H., Boston, R.C. (eds) Mathematical Modeling in Nutrition and the Health Sciences. Advances in Experimental Medicine and Biology, vol 537. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-9019-8_1

Download citation

  • DOI: https://doi.org/10.1007/978-1-4419-9019-8_1

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-4759-0

  • Online ISBN: 978-1-4419-9019-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation