Modeling the Glucose-Insulin Dynamics and the PSE Approach for Insulin Therapy Design
Date Issued
2009
Date
2009
Author(s)
Tsai, Hong-Wen
Abstract
This dissertation aims to develop the overall glucose-insulin model with exogenous injected insulin and implement the glycemia control by therapy of insulin injection scheduling and therapy of insulin pump for diabetics having a better quality of life. The first part in this dissertation is to build the model, which can describe the endogenous glucose-insulin dynamics (GID), and the subcutaneous absorption model by exogenous insulin injection (SCAI). According the glucose dynamics from clinical data and physiological literatures, e proposed a GID model consists of two delay differential equations (DDEs) wherein five adjustable parameters are used to characterize the respective dynamics and scillation behavior of normal and diabetic subjects. The effects of these adjustable parameters are further analyzed. The parametric estimation of the proposed GID model by several clinical data can be formulated as a nonlinear dynamic program (NDP). With the optimized results, the suggested model has the capability to approach he glucose behavior on normal and diabetic subjects. Moreover, the corresponding parameters are fairly persuasive to identify the patient''s conditions of major hysiological functions. For the SCAI model, the subcutaneous (SC) absorption behaviors of available nsulin preparations for diabetes are investigated. The three adjustable parameters in SCAI model are used to characterize the pharmcodynamics of six types of insulin.ased on the accurate dynamic models, the glycemia control with different therapies can be implemented and further improved. The second part in this dissertation aims at developing an efficient insulin injection scheduling strategy for diabetics. The problems of searching the optimal injected time, type, and dosage of insulin could be formulated as mixed-integer nonlinear dynamic programs (MINDPs).ccording to the subjects'' time and the amount of food uptake and physician''s suggestions to insulin injections, the optimal injection schedules are implemented in three scenarios by adjusting either the insulin injection times, or insulin types, or insulin dosage, or other combinations of these factors. The corresponding results of glucose control in each scenario is demonstrated and perform efficiently than physician''s suggestions. Even the insulin consumption is more than physician''s suggestions, the optimized insulin usages are still within the therapeutic window for ensuring safety and efficacy. The robustness of suggested therapy to unscheduled situations is also exemplified. The third part is concentrated on designing an external automatic feedback controllers for regulating the glycemia within a normal physiological range and eliminating the influence by exogenous disturbance for diabetics. Due to the discomfort and infection by the therapy of multiple injections on the skin, insulin pump therapy has been developed to reduce the risks of needle sticks. Based on the proposed GID and SCAI models, the glycemia control on diabetics via insulin pump and glucose sensor can be therefore regarded as a closed-loop control problem. The proportional (P) and the proportional plus integral (PI) ontrollers are adopted to implement this control to create an efficient insulin injection sequences. We further consider the practical delayed feedback signal by glucose sensor, insulin delivery time by insulin pump, the effects of subcutaneous absorption by fast-acting insulin, and reduce the emergency of hypoglycemia. The problems of searching the optimal parameters of controllers could be formulated as nonlinear dynamic programs (NDPs). The simulation results have presented the proposed controllers could achieve a efficient glucose control under the clinically acceptable insulin dosage. Not only the robustness for variations of carbohydrate infuse and sensor delay are discussed but also the uncertainties by glucose measurement noise and pump deliver disturbance are moreover testified. It is expected that the proposed optimal injection scheduling and closed-loop control to glycemia can be served as a valuable reference for physicians and atients to take better glucose control on a daily basis.
Subjects
Glucose-insulin dynamics
Physiological endocrine system
Delay differential equations (DDEs)
Proportional (P) controller
Proportional plus integral (PI) controller
Mixed-integer nonlinear dynamic programming (MINDP)
SDGs
Type
thesis
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