Data-driven Modeling for Diabetes pp 223-237 | Cite as

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

## 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.

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