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Optimizing inputs for diagnosis of diabetes. I. Fitting a minimal model to data

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Abstract

A glucose tolerance test was performed on dogs by injecting glucose intravenously and measuring the plasma glucose and insulin concentrations versus time. Various analytical and computational techniques were utilized to fit the data to a minimal model and to estimate the parameters of the blood glucose regulation process. A relatively good fit was obtained in spite of the rather simple model.

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References

  1. Bolie, V. W.,Coefficients of Normal Blood Glucose Regulation, Journal of Applied Physiology, Vol. 16, pp. 783–788, 1961.

    Google Scholar 

  2. Bergman, R. N., Kalaba, R. E., andSpingarn, K.,Optimal Inputs for Blood Glucose Regulation Parameter Estimation, Clinical Data and Analysis (to appear).

  3. Bergman, R. N., Kalaba, R. E., andSpingarn, K.,Optimal Inputs for Blood Glucose Regulation Parameter Estimation, II, Clinical Data and Analysis (to appear).

  4. Kalaba, R. E., andSpingarn, K.,Optimal Inputs and Sensitivities for Parameter Estimation, Journal of Optimization Theory and Applications, Vol. 11, No. 1, 1973.

  5. Kalaba, R. E., andSpingarn, K.,Optimal Inputs for Nonlinear Process Parameter Estimation, IEEE Transactions on Aerospace and Electronic Systems, Vol. 10, No. 3, 1974.

  6. Kalaba, R. E., andSpingarn, K.,Optimal Input System Indentification for Homogeneous and Non-Homogeneous Boundary Conditions, Journal of Optimization Theory and Applications, Vol. 16, Nos. 5/6, 1975.

  7. Mehra, R. K.,Optimal Inputs for Linear System Identification, IEEE Transactions on Automatic Control, Vol. 19, No. 3, 1974.

  8. Nahi, N. E., andWallis, D. E., Jr.,Optimal Inputs for Parameter Estimation in Dynamic Systems with White Observation Noise, Joint Automatic Control Conference Preprints, Boulder, Colorado, 1969.

    Google Scholar 

  9. Aoki, M., andStaley, R. M.,On Input Signal Synthesis in Parameter Identification, Automatica, Vol. 6, pp. 431–440, 1970.

    Google Scholar 

  10. Ackerman, E., Rosevear, J. W., andMcGuckin, W. F.,A Mathematical Model of the Glucose-Tolerance Test, Physics in Medicine and Biology, Vol. 9, No. 2, 1964.

  11. Ackerman, E., Gatewood, L. C., Rosevear, J. W., andMolnar, G. D.,Model Studies of Blood-Glucose Regulation, Bulletin of Mathematical Biophysics, Vol. 27, pp. 21–37, 1965.

    Google Scholar 

  12. Ceresa, F., Ghemi, F., Martini, P. F., Martino, P., Segre, G., andVitelli, A.,Control of Blood Glucose in Normal and Diabetic Subjects, Diabetes, Vol. 17, No. 9, 1968.

  13. Segre, G., Turco, G. L., andVercellone, G.,Modeling Blood Glucose and Insulin Kinetics in Normal, Diabetic, and Obese Subjects, Diabetes, Vol. 22, No. 2, 1973.

  14. Curry, D., Bennet, L., andGrodsky, G.,Dynamics of Insulin Secretion from the Isolated Pancreas, Endocrinology, Vol. 83, No. 3, 1968.

  15. Bergman, R. N., andUrquhart, J.,The Pilot Gland Approach to the Study of Insulin Secretory Dynamics, Recent Progress in Hormone Research, Vol. 27, pp. 583–605, 1971.

    Google Scholar 

  16. Srinivasan, R., Kadish, A. H., andSridhar, R.,A Mathematical Model for the Control Mechanism of Free Fatty Acid-Glucose Metabolism in Normal Humans, Computers and Biomedical Research, Vol. 3, No. 2, 1970.

  17. Grodsky, G. M.,A Threshold Distribution Hypothesis for Packet Storage of Insulin and its Mathematical Modelling, Journal of Clinical Investigation, Vol. 51, No. 8, 1972.

  18. Bergman, R. N., andBucolo, R. J.,Nonlinear Metabolic Dynamics of the Pancreas and Liver, ASME Journal of Dynamic Systems, Measurement, and Control, Vol. 95, pp. 296–300, 1973.

    Google Scholar 

  19. Giese, C., andMcGhee, R. B.,Estimation of Nonlinear System States and Parameters by Regression Methods, Joint Automatic Control Conference, Troy, New York, 1965.

  20. Bellman, R. E., andKalaba, R. E.,Quasilinearization and Nonlinear Boundary-Value Problems, American Elsevier Publishing Company, New York, New York, 1965.

    Google Scholar 

  21. Buell, J., andKalaba, R. E.,Quasilinearization and the Fitting of Nonlinear Models of Drug Metabolism to Experimental Kinetic Data, University of Southern California, Report No. USCEE-316, 1968.

  22. Sage, A. P., andMelsa, J. L.,System Identification, p. 157, Academic Press, New York, New York, 1971.

    Google Scholar 

  23. Kagiwada, H. H.,System Identification, Methods and Applications, Addison-Wesley Publishing Company, Reading, Massachussetts, 1974.

    Google Scholar 

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Animal experiments were funded by the National Institute of Health Grant No. AM-17236 awarded to Dr. R. N. Bergman at U.S.C.

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Bergman, R.N., Kalaba, R.E. & Spingarn, K. Optimizing inputs for diagnosis of diabetes. I. Fitting a minimal model to data. J Optim Theory Appl 20, 47–63 (1976). https://doi.org/10.1007/BF00933347

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