Skip to main content
SpringerLink
Log in

Mathematical Modelling of the Control of Blood Glucose Levels in Diabetics by Insulin Infusion

  • Chapter
Dynamics of Complex Interconnected Biological Systems

Part of the book series: Mathematical Modelling ((MMO,volume 6))

  • 309 Accesses

Abstract

Mathematical optimization techniques are applied to two simple mathematical models of blood glucose dynamics to derive insulin infusion programs for the control of blood glucose levels in diabetic individuals. Based on the results of the mathematical optimization a semiclosed loop algorithm is proposed for continuous insulin delivery to diabetic patients. The algorithm is based on three hourly plasma glucose samples. A theoretical evaluation of the effectiveness of this algorithm shows that it is superior to two existing algorithms in controlling hyperglycemia.

A glucose infusion term representing the effect of glucose intake resulting from a meal is then introduced into both model equations. A theoretical analysis is then undertaken to determine the most effective insulin infusion programs for the control of plasma glucose levels following a meal.

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 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight 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

  1. E. Ackerman, L.C. Gatewood, J.W. Rosevear, and G.D. Molnar, (1965). Model studies of blood glucose regulation. Bull. Math. Biophys. 27, pp. 21–37.

    Article  Google Scholar 

  2. R. N. Bergman, L. S. Phillips, and C. Cobelli, (1981). Measurement of insulin sensitivity and β-cell glucose sensitivity from the response to intraveous glucose. J. Clin. Invest. 68, pp. 1456–1467.

    Article  Google Scholar 

  3. R. N. Bergman, D. T. Finegood, and M. Ader, (1985). Assessment of insulin sensitivity in vivo. Endocrine Reviews 6, pp. 45–86.

    Article  Google Scholar 

  4. J.A. Campbell and P.H. Abbrecht, (1968). An analysis of the control of insulin secretion. Proc. 21st Annual Conference Eng. Med. Biol. 10, pp. 29.

    Google Scholar 

  5. D. J. Chisolm, E. W. Kraegen, D. J. Bell, and D. R Chipps, (1984). A semi-closed loop computer-assisted insulin infusion system. Med. J. Aust. 141, pp. 784–789.

    Google Scholar 

  6. M. E. Fisher and K. L. Teo, (1989). Optimal insulin infusion resulting from a mathematical model of blood glucose dynamics. IEEE Trans. Biomed. Eng. 36, pp. 479–486.

    Article  Google Scholar 

  7. S. M. Furier, E. W. Kraegen, R. H. Smallwood, and D. J. Chisolm, (1985). Blood glucose control by intermittent loop closure in the basal mode: Computer simulation with a diabetic model. Diabetes Care 8, pp. 553–561.

    Article  Google Scholar 

  8. R.V. Gamkrelidze, (1975). Principles of Optimal Control Theory, Plenum Press, New York.

    Google Scholar 

  9. L.C. Gatewood, E. Ackerman, J.W. Rosevear, and G.D. Molnar, (1968). Simulation studies of blood-glucose regulation: Effect of intestinal glucose absorption. Comp. Biomed. Res. 2, pp. 15–27.

    Article  Google Scholar 

  10. L.C. Gatewood, E. Ackerman, J.W. Rosevear, and G.D. Molnar, (1970). Modeling blood glucose dynamics. Behav. Science 15, pp. 72–87.

    Article  Google Scholar 

  11. C.J. Goh and K.L. Teo, (1987). MISER, An Optimal Control Software, Applied Research Corporation, National University of Singapore.

    Google Scholar 

  12. M. Kikuchi, E. Machiyama, N. Kabei, A. Yamada, Y. Sakurai, Y. Hara, and A. Sano, (1980). Adaptive control system of blood glucose regulation. In MEDINFO 80, pp. 96–100. ed. A.B. Lindberg and S. Kaihara.

    Google Scholar 

  13. R.L. Ollerton, (1988). An application of optimal control theory to diabetes mellitus, preprint.

    Google Scholar 

  14. G.W. Swan, (1983). Applications of Optimal Control Theory in Biomedicine, Marcel Dekker, New York.

    Google Scholar 

  15. T. Yipintsoi, L.C. Gatewood, E. Ackerman, P.L. Spivak, G.D. Molnar, G.W. Rosevear, and F.C. Service, (1973). Mathematical analysis of blood glucose and plasma insulin responses to insulin infusion in healthy and diabetic subjects. Comput. Biol. Med. 3, pp. 71–78.

    Article  Google Scholar 

Download references

Authors
  1. Michael E. Fisher
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Aerospace and Mechanical Engineering, University of Arizona, Tucson, AZ, 85721, USA

    Thomas L. Vincent

  2. Mathematics Department, University of Western Australia, Nedlands, 6009, Western Australia, Australia

    Alistair I. Mees  & Leslie S. Jennings  & 

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Birkhäuser Boston

About this chapter

Cite this chapter

Fisher, M.E. (1990). Mathematical Modelling of the Control of Blood Glucose Levels in Diabetics by Insulin Infusion. In: Vincent, T.L., Mees, A.I., Jennings, L.S. (eds) Dynamics of Complex Interconnected Biological Systems. Mathematical Modelling, vol 6. Birkhäuser Boston. https://doi.org/10.1007/978-1-4684-6784-0_5

Download citation

  • DOI: https://doi.org/10.1007/978-1-4684-6784-0_5

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-1-4684-6786-4

  • Online ISBN: 978-1-4684-6784-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation