血糖-胰島素之動態模式建立與胰島素療法設計研究

本論文旨在建構一個能夠描述人體內分泌血糖－胰島素濃度之動態模式，並且以上述模式為基礎，提出協助糖尿病患者維持血糖濃度調控正常的胰島素注射規劃與外部自動控制系統，以期盼在合理的胰島素使用量下，能夠協助病患體內血糖濃度的正常化，擁有更佳的生活品質。本論文可分為以下三個部分。第一部份進行血糖－胰島素內分泌動態模式以及胰島素皮下組織吸收模式的建立。首先根據觀察一般人與多組病患的臨床血糖數據以及內分泌知識，了解生理上所表現出之脈動行為和特性，以帶時延數學微分方程式結構來建立模式，其中包含五個特定可調整參數。再以數學觀點分析此特定可調整參數對於血糖與胰島素濃度之影響與其合理範圍。藉著可調整參數之改變，尋找最能夠描述每一病患臨床數據之特定參數組合，此為一非線性動態規劃(NDP)問題。利用公開之血糖臨床數據庫進行上述問題求解，所提出的模式與臨床數據得到良好的匹配效果，解得之特定參數與病患嚴重程度的相依關係，亦有所探討。另外研究以注射方式之外部胰島素製劑，建立胰島素皮下組織吸收模式，皮下組織所吸收的胰島素濃度變化，隨各種劑型劑量之胰島素製劑產生不同變化。藉著三個特定可調整參數變化，利用此模式進行市售六種胰島素製劑之描述。最後利用另一血糖－胰島素臨床數據庫，搭配醫師之胰島素製劑指示，同時使用上述兩模式進行求解，在56組數據測試下，所提出的模式與臨床數據亦得到良好的匹配效果。根據上述兩模式進行第二、第三部分之胰島素療法研究。第二部份，進行胰島素製劑皮下施打排程規劃。研究傳統胰島素製劑施打方式，依據患者一般進食時間與碳水化合物攝取量組合，配合醫師的規劃為基礎，血糖控制為目標，進行三種施打方式組合，決定施打胰島素製劑的時間排程、劑量規劃與藥劑種類選擇，可具體構成為一混合整數非線性動態規劃問題(MINDP)。本文提出之三種施打方式組合，血糖控制成效皆優於醫生建議之方式，雖然胰島素藥劑總使用量較大，但仍在安全範圍之內。此外，本文深入探討非常態的用餐情況，或是不精確之胰島素施打時間與劑量對於原規劃所造成的敏感性與容忍性測試，血糖控制成效亦皆在可接受範圍。第三部份，研究使用血糖感測器與胰島素幫浦之閉環路自動控制方式。為強化血糖控制效率，減少多次注射的痛苦，另一胰島素療法為利用血糖監測儀器回饋訊號與胰島素幫浦施加胰島素製劑之連續式閉環路自動控制。本文探討其控制策略問題，採用比例(P)與比例積分(PI)控制器驅動胰島素幫浦施加胰島素進入體內。並考慮實際狀況既有的回饋訊號時延與胰島素傳送之輸入時延，以及避免出現低血糖之限制等，本控制策略問題可具體構成一非線性動態規劃問題(NDP)，解得之控制器皆可表現較佳之血糖控制效果，優於目前以醫生建議治療之方式。此外，本文深入探討其控制器對於非常態用餐量，或是血糖監測回饋訊號時延大小之容忍性測試，以及進行回饋訊號雜訊與胰島素幫浦干擾測試。血糖控制成效亦皆在可接受範圍。本研究提出對於高血糖患者的胰島素控制策略，可以安全、有效穩定血糖，提供治療師或醫師對於糖尿病控制的參考，讓患者保有更好的生活品質。

關鍵字

血糖-胰島素動態系統；生理內分泌系統；時延微分方程式；比例控制器；比例積分控制器；混合整數非線性動態規劃

並列摘要

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, we proposed a GID model consists of two delay differential equations (DDEs) wherein five adjustable parameters are used to characterize the respective dynamics and oscillation 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 the glucose behavior on normal and diabetic subjects. Moreover, the corresponding parameters are fairly persuasive to identify the patient's conditions of major physiological functions. For the SCAI model, the subcutaneous (SC) absorption behaviors of available insulin preparations for diabetes are investigated. The three adjustable parameters in SCAI model are used to characterize the pharmcodynamics of six types of insulin. Based 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). According 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) controllers 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 patients to take better glucose control on a daily basis.

並列關鍵字

Glucose-insulin dynamics ； Physiological endocrine system ； Delay differential equations (DDEs) ； Proportional (P) controller ； Proportional plus integral (PI) controller ； Mixed-integer nonlinear dynamic programming (MINDP)

參考文獻

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血糖-胰島素之動態模式建立與胰島素療法設計研究

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