Sparse System Identification of Leptin Dynamics in Women With Obesity

The prevalence of obesity is increasing around the world at an alarming rate. The interplay of the hormone leptin with the hypothalamus-pituitary-adrenal axis plays an important role in regulating energy balance, thereby contributing to obesity. This study presents a mathematical model, which describes hormonal behavior leading to an energy abnormal equilibrium that contributes to obesity. To this end, we analyze the behavior of two neuroendocrine hormones, leptin and cortisol, in a cohort of women with obesity, with simplified minimal state-space modeling. Using a system theoretic approach, coordinate descent method, and sparse recovery, we deconvolved the serum leptin-cortisol levels. Accordingly, we estimate the secretion patterns, timings, amplitudes, number of underlying pulses, infusion, and clearance rates of hormones in eighteen premenopausal women with obesity. Our results show that minimal state-space model was able to successfully capture the leptin and cortisol sparse dynamics with the multiple correlation coefficients greater than 0.83 and 0.87, respectively. Furthermore, the Granger causality test demonstrated a negative prospective predictive relationship between leptin and cortisol, 14 of 18 women. These results indicate that increases in cortisol are prospectively associated with reductions in leptin and vice versa, suggesting a bidirectional negative inhibitory relationship. As dysregulation of leptin may result in an abnormality in satiety and thereby associated to obesity, the investigation of leptin-cortisol sparse dynamics may offer a better diagnostic methodology to improve better treatments plans for individuals with obesity

A System-Theoretic Investigation of Hormone Dynamics in Chronic Fatigue Syndrome, Fibromyalgia Syndrome, and Obesity

Fibromyalgia syndrome (FMS), chronic fatigue syndrome (CFS), and obesity are complicated medical disorders with little known etiologies. The purpose of this research is to characterize FMS, CFS, and obesity by studying the variations in hormonal secretion patterns, timings, amplitudes, the number of underlying pulses, as well as infusion and clearance rates of hormones such as cortisol, and leptin. Employing a physiological state-space model with plausible constraints, we estimate the hormonal secretory events and the physiological system parameters (i.e., infusion and clearance rates). The first outcome of our research shows that the clearance rate of cortisol is lower in FMS patients as compared to their matched healthy individuals based on a simplified cortisol secretion model. Moreover, the number, magnitude, and the energy levels of cortisol secretory events are lower in FMS patients. During early morning hours, the magnitude and the energy levels of the cortisol secretory events are higher in CFS patients. Due to the lower cortisol clearance rate, there is a higher accumulation of cortisol in FMS patients as compared to their matched healthy subjects. As the FMS patients accumulate higher cortisol residues, internal inhibitory feedback regulates the hormonal secretory events. Therefore, the FMS patients show a lower number, magnitude, and the energy levels of hormonal secretory events. Though CFS patients have the same number of secretory events, the secretion quantity is lower during early morning hours. When we compare the results for CFS patients against FMS patients, we observe different cortisol alteration patterns. In the second part of this thesis, we propose a simplified minimal leptin secretion model and study the correlation between estimated parameters of leptin and cortisol. The hunger hormone leptin and stress hormone cortisol are closely associated with obesity. Traditionally, a leptin-cortisol antagonism is observed in obese patients. We also observe a leptin-cortisol antagonism when we compare the reconstructed leptin and cortisol levels, hence, further validating the model. The proposed model can potentially be employed to study leptin variations in obese patients against their matched healthy subjects. Characterizing CFS, FMS, and obesity based on the hormonal alterations will help us develop effective methods for treating these disorders.Electrical and Computer Engineering, Department o