Summary
In this chapter we evaluate the ability of the minimal model of glucose disappearance to describe experimental data collected from 9 diabetic patients controlled subcutaneously by an insulin pump. Two versions of the minimal model are used: the nonlinear classic minimal model developed by Bergman et al. (MM) and the linear approximation proposed by Fernandez et al. (LMM). All data windows (n = 13) show residuals that are correlated for both the LMM and MM (p-value < 0.01). The results also show that both the LMM and MM provide an equivalent goodness of fit with R 2 values that are statistically equivalent (p-value > 0.05). This study confirms that the minimal model of glucose disappearance, either the classic or linear version, is unable to describe the observed experimental data possibly as a result of the physiological constraints imposed by the minimal model approach on the system dynamics, together with possible errors derived from the unmeasured insulin dynamics. Further testing on more complex models should be performed.
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References
Anderson, T.W.: An Introduction to Multivariate Statistical Analysis, 3rd edn. Wiley Series in Probability and Statistics. Wiley-Interscience, Hoboken (2003)
Anderson, T.W., Darling, D.A.: A test of goodness of fit. J. Am. Stat. Assoc. 49, 765–769 (1954)
Bergman, R.N., Ider, Y.Z., Bowden, C.R., Cobelli, C.: Quantitative estimation of insulin sensitivity. Am. J. Physiol. 236(6), E667–E677 (1979)
Carson, E.R., Cobelli, C., Finkelstein, L.: The Mathematical Modeling of Metabolic and Endocrine Systems. John Wiley & Sons, New York (1983)
Caumo, A., Bergman, R.N., Cobelli, C.: Insulin sensitivity studies from meal tolerance tests in normal subjects: a minimal model index. J. Clin. Endocrinol. Metab. 85(11), 4396–4402 (2000)
Cobelli, C., Mari, A.: Validation of mathematical models of complex endocrine-metabolic systems. A case study on a model of glucose regulation. Med. Biol. Eng. Comput. 21, 390–399 (1983)
Cobelli, C., Ruggeri, A.: Evaluation of portal/peripheral route and of algorithms for insulin delivery in the closed-loop control of glucose in diabetes. A modeling study. IEEE. Trans. Biomed. Eng. BME-30(2), 93–103 (1983)
Cobelli, C., Vicini, P., Toffolo, G., Caumo, A.: The hot IVGTT minimal models: simultaneous assessment of disposal indices and hepatic glucose release. In: Lovejoy, J., Bergman, R.N. (eds.) The minimal model approach and determinants of glucose tolerance, vol. 262, pp. E968–E975. Louisiana State University Press, Baton Rouge (1997)
Fernandez, M., Acosta, D., Quiroz, A.: Improving the precision of model parameters using model based signal enhancement and the linear minimal model following an IVGTT in the healthy man. Appl. Math. Comput. 196(1), 185–192 (2008)
Fernandez, M., Acosta, D., Villasana, M., Streja, D.: Enhancing parameter precision and the minimal modeling approach in type I diabetes. In: Proceedings of the 26th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, pp. 797–800. IEEE Press, Los Alamitos (2004)
Fernandez, M., Atherton, D.P.: Linearisation and simplification of a nonlinear model of the glucose regulatory system. Diabetes Nutr. Metab. 11(1), 86 (1998); Abstracts, Symposium on Computers in Diabetes 1998
Fernandez, M., Atherton, D.P.: Analysis of insulin sensitivity estimates from linear models of glucose disappearance. Appl. Math. Comput. 167(1), 528–538 (2005)
Fernandez, M., Villasana, M.: Letter to the editor: on a model of glucose absorption. Med. Eng. Phys. 30(4), 538–540 (2008)
Fernandez, M., Villasana, M., Streja, D.: Glucose dynamics in type I diabetes: insights from the classic and linear minimal models. Comput. Biol. Med. 37(5), 611–627 (2007)
Fernandez-Chas, M.: Insulin sensitivity estimates from a linear model of glucose disappearance. Ph.D. thesis, University of Sussex, Brighton, UK (2001)
Lehmann, E.D., Deutsch, T.: A physiological model of glucose-insulin interaction in type 1 diabetes mellitus. J. Biomed. Eng. 14, 235–242 (1992)
Radziuk, J., McDonald, T., Rubentein, D., Dupre, J.: Initial splanchnic extraction of ingested glucose in normal man. Metabolism 27(6), 657–669 (1978)
Shichiri, M., Sakakida, M., Nishida, K., Shimoda, S.: Enhanced, simplified glucose sensors: long-term clinical application of wearable artificial pancreas. Artif. Organs 22(1), 32–42 (1998)
Willinska, M.E., Chassin, L.J., Schaller, H.C., Schaupp, L., Pieber, T.R., Hovorka, R.: Insulin kinetics in Type-1 diabetes: Continuous and bolus delivery of rapid acting insulin. IEEE. Trans. Biomed. Eng. 52(1), 3–12 (2005)
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Fernandez, M., Villasana, M., Streja, D. (2009). The Minimal Model of Glucose Disappearance in Type I Diabetes. In: Sidhu, A.S., Dillon, T.S. (eds) Biomedical Data and Applications. Studies in Computational Intelligence, vol 224. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02193-0_13
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DOI: https://doi.org/10.1007/978-3-642-02193-0_13
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