Dynamic Modeling of Free Fatty Acid, Glucose, and Insulin During Rest and Exercise in Insulin Dependent Diabetes Mellitus Patients

Malfunctioning of the beta-cells of the pancreas leads to the metabolic disease known as diabetes mellitus (DM), which is characterized by significant glucose variation due to lack of insulin secretion, lack of insulin action, or both. DM can be broadly classified into two types: type 1 diabetes mellitus (T1DM) - which is caused mainly due to lack of insulin secretion; and type 2 diabetes mellitus (T2DM) - which is caused due to lack of insulin action. The most common intensive insulin treatment for T1DM requires administration of insulin subcutaneously 3 - 4 times daily in order to maintain normoglycemia (blood glucose concentration at 70 to 120 mg/dl). Although the effectiveness of this technique is adequate, wide glucose fluctuations persist depending upon individual daily activity, such as meal intake, exercise, etc. For tighter glucose control, the current focus is on the development of automated closed-loop insulin delivery systems. In a model-based control algorithm, model quality plays a vital role in controller performance. In order to have a reliable model-based automatic insulin delivery system operating under various physiological conditions, a model must be synthesized that has glucose-predicting ability and includes all the major energy-providing substrates at rest, as well as during physical activity. Since the 1960s, mathematical models of metabolism have been proposed in the literature. The majority of these models are glucose-based and have ignored the contribution of free fatty acid (FFA) metabolism, which is an important source of energy for the body. Also, significant interactions exist among FFA, glucose, and insulin. It is important to consider these metabolic interactions in order to characterize the endogenous energy production of a healthy or diabetic patient. In addition, physiological exercise induces fundamental metabolic changes in the body; this topic has also been largely overlooked by the diabetes modeling community.This dissertation takes a more lipocentric (lipid-based) approach in metabolic modeling for diabetes by combining FFA dynamics with glucose and insulin dynamics in the existing glucocentric models. A minimal modeling technique was used to synthesize a FFA model, and this was coupled with the Bergman minimal model to yield an extended minimal model. The model predictions of FFA, glucose, and insulin were validated with experimental data obtained from the literature. A mixed meal model was developed to capture the absorption of carbohydrates (CHO), proteins, and FFA from the gut into the circulatory system. The mixed meal model served as a disturbance to the extended minimal model. In a separate study, an exercise minimal model was developed to incorporate the effects of exercise on glucose and insulin dynamics. Here, the Bergman minimal model was modified by adding equations and terms to capture the changes in glucose and insulin dynamics during and after mild-to-moderate exercise.A single composite model for predicting FFA-glucose-insulin dynamics during rest and exercise was developed by combining the extended and exercise minimal models. To make the composite model more biologically relevant, modifications were made to the original model structures. The dynamical effects of insulin on glucose and FFA were divided into three parts: (i) insulin-mediated glucose uptake by the tissues, (ii) insulin-mediated suppression of endogenous glucose production, and (iii) anti-lipolytic effects of insulin. Labeled and unlabeled intra-venous glucose tolerance test data were used to estimate the parameters of the glucose model which facilitated separation of insulin action on glucose utilization and production. The model successfully captured the FFA-glucose interactions at the systemic level. The model also successfully predicted mild-to-moderate exercise effects on glucose and FFA dynamics. A detailed physiologically-based compartmental model of FFA was synthesized and integrated with the existing physiologically-based glucose-insulin model developed by Sorensen. Distribution of FFA in the circulatory system was evaluated by developing mass balance equations across the major FFA-utilizing tissues/organs. Rates of FFA production or consumption were added to each of the physiologic compartments. In order to incorporate the FFA effects on glucose, modifications were made to the existing mass balance equations in the Sorensen model. The model successfully captured the FFA-glucose-insulin interactions at the organ/tissue levels.Finally, the loop was closed by synthesizing model predictive controllers (MPC) based on the extended minimal model and the composite model. Both linear and nonlinear MPC algorithms were formulated to maintain glucose homeostasis by rejecting disturbances from mixed meal ingestion. For comparison purposes, MPC algorithms were also synthesized based on the Bergman minimal model which does not account for the FFA dynamics. The closed-loop simulation results indicated a tighter blood glucose control in the post-prandial period with the MPC formulations based on the lipocentric (extended minimal and composite) models