Nonlinear Modeling of the Dynamic Effects of Free Fatty Acids on Insulin Sensitivity

  • Vasilis Z. Marmarelis
  • Dae C. Shin
  • Georgios D. Mitsis
Chapter
Part of the Lecture Notes in Bioengineering book series (LNBE)

Abstract

This chapter presents a nonlinear model of the combined dynamic effects of spontaneous variations of plasma insulin and free fatty acids on glucose concentration in a fasting dog. The model is based on the general nonparametric modeling methodology that employs the concept of Principal Dynamic Modes (PDMs) to obtain a Volterra-equivalent nonlinear dynamic model with two inputs (insulin and free fatty acids) and one output (glucose) that are measured experimentally every 3 min in a fasting dog as time-series data over 10 hr. This model is deemed valid and predictive for all input waveforms within the experimental dynamic range. The obtained model is composed of two PDMs for each input and cubic Associated Nonlinear Functions (ANFs), in addition to two cross-terms. The waveform of the obtained PDMs offers potentially valuable interpretation of the implicated physiological mechanisms. The system nonlinearities are described, in turn, by the obtained ANFs. The evaluation of the overall model performance is facilitated by the use of specialized inputs, such as pulses or impulses. For instance, the use of insulin input pulses can yield estimates of “dynamic insulin sensitivity” (as the ratio of the steady-state glucose response to the input pulse amplitude) for various levels of free fatty acids. The obtained result indicates (in a quantitative manner) the widely held view that insulin sensitivity decreases with rising levels of free fatty acids. Furthermore, it indicates that this effect depends on the input insulin strength (dose-dependent insulin sensitivity). Drastic reduction of insulin sensitivity is predicted by the model above a critical level of free fatty acids for low-to-moderate values of plasma insulin. This result demonstrates the potential utility of the proposed modeling approach for advancing our quantitative understanding of the processes underpinning obesity and Type II diabetes.

Keywords

Obesity Posit Convolution Glucagon 

Notes

Acknowledgments

This work was supported in part by the NIH/NIBIB center grant No. P41- EB001978 to the Biomedical Simulations Resource at the University of Southern California and by the University of Cyprus Internal Research Grant “Nonlinear, data-driven modeling and model-based control of blood glucose”. The authors acknowledge thankfully Dr. R. Bergman and Dr. K. Hücking for making available the experimental data.

References

  1. 1.
    Bergman RN, Lovejoy JC (1997) The minimal model approach and determinants of glucose tolerance. Louisiana State University Press, Baton RougeGoogle Scholar
  2. 2.
    Vicini P, Caumo A, Cobelli C (1997) The hot IVGTT two-compartment minimal model: indexes of glucose effectiveness and insulin sensitivity. Am J Physiol 273:E1024–E1032Google Scholar
  3. 3.
    Cobelli C, Mari A (1983) Validation of mathematical models of complex endocrine-metabolic systems. A case study on a model of glucose regulation. Med Biol Eng Compu 21:390–399CrossRefGoogle Scholar
  4. 4.
    Roy A, Parker RS (2006) Dynamic modeling of free fatty acid, glucose, and insulin: an extended “minimal model”. Diab Technol Ther 8:617–626CrossRefGoogle Scholar
  5. 5.
    Mitsis GD, Markakis MG, Marmarelis VZ (2009) Nonlinear modeling of the dynamic effects of infused insulin on glucose: comparison of compartmental with Volterra models. IEEE Trans Biomed Eng 56(10):2347–2358CrossRefGoogle Scholar
  6. 6.
    Marmarelis VZ, Mitsis GD, Huecking K, Bergman RN (2002) Nonlinear modeling of the insulin-glucose dynamic relationship in dogs. In: Proceedings of the second joint EMBS/BMES conference, Houston, TX, pp 224–225Google Scholar
  7. 7.
    Rebrin K, Steil GM, Getty L, Bergman RN (1995) Free fatty acid as a link in the regulation of hepatic glucose output by peripheral insulin. Diabetes 44:1038–1045CrossRefGoogle Scholar
  8. 8.
    Boden G (2002) Interaction between free fatty acids and glucose metabolism. Curr Opin Clin Nutr Metab Care 5(5):545–549CrossRefGoogle Scholar
  9. 9.
    Boden G (2003) Effects of free fatty acids (FFA) on glucose metabolism: significance for insulin resistance and type 2 diabetes. Exp Clin Endocrinol Diab 111(3):121–124CrossRefGoogle Scholar
  10. 10.
    Delarue J, Magnan C (2007) Free fatty acids and insulin resistance. Curr Opin Clin Nutr Metab Care 10(2):142–148CrossRefGoogle Scholar
  11. 11.
    Kraegen EW, Cooney GJ (2008) Free fatty acids and skeletal muscle insulin resistance. Curr Opin Lipidol 19(3):235–241CrossRefGoogle Scholar
  12. 12.
    Marmarelis VZ (2004) Nonlinear dynamic modeling of physiological systems. IEEE-Wiley, PiscatawayCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Vasilis Z. Marmarelis
    • 1
  • Dae C. Shin
    • 1
  • Georgios D. Mitsis
    • 2
  1. 1.Department of Biomedical EngineeringUniversity of Southern CaliforniaLos AngelesUSA
  2. 2.Department of Electrical and Computer EngineeringUniversity of CyprusNicosiaCyprus

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