Optimal Regulation of Blood Glucose Level in Type I Diabetes using Insulin and Glucagon

The Glucose-Insulin-Glucagon nonlinear model [1-4] accurately describes how the body responds to exogenously supplied insulin and glucagon in patients affected by Type I diabetes. Based on this model, we design infusion rates of either insulin (monotherapy) or insulin and glucagon (dual therapy) that can optimally maintain the blood glucose level within desired limits after consumption of a meal and prevent the onset of both hypoglycemia and hyperglycemia. This problem is formulated as a nonlinear optimal control problem, which we solve using the numerical optimal control package PSOPT. Interestingly, in the case of monotherapy, we find the optimal solution is close to the standard method of insulin based glucose regulation, which is to assume a variable amount of insulin half an hour before each meal. We also find that the optimal dual therapy (that uses both insulin and glucagon) is better able to regulate glucose as compared to using insulin alone. We also propose an ad-hoc rule for both the dosage and the time of delivery of insulin and glucagon.Comment: Accepted for publication in PLOS ON

Predictive Control of Diabetic Glycemia

Diabetes Mellitus is a chronic disease, where the blood glucose concentration of the patient is elevated. This is either because of missing insulin production due to failure of the β-cells in the pancreas (Type 1) or because of reduced sensitivity of the cells in the body to insulin (Type 2). The therapy for Type 1 diabetic patients usually consists of insulin injections to substitute for the missing insulin. The decision about the amount of insulin to be taken has to be made by the patient, based on empirically developed rules of thumb. To help the patient with this task, advanced mathematical algorithms were used in this thesis to determine intakes of insulin and counteracting glucose that can bring the blood glucose concentration back to normoglycemia. The focus in this work was to determine insulin and glucose intakes around mealtimes. These algorithms used optimization methods together with predictions of the blood glucose concentration and mathematical models describing the patient dynamics to determine the insulin and glucose doses. For evaluation, the control algorithms were tested insilico using a virtual patient and are compared to a simple bolus calculator from the literature. The aim was to increase the time spent in the safe range of blood glucose values of 70 − 180 [mg/dL]

A Survey of Insulin-Dependent Diabetes—Part II: Control Methods

We survey blood glucose control schemes for insulin-dependent diabetes therapies and systems. These schemes largely rely on mathematical models of the insulin-glucose relations, and these models are typically derived in an empirical or fundamental way. In an empirical way, the experimental insulin inputs and resulting blood-glucose outputs are used to generate a mathematical model, which includes a couple of equations approximating a very complex system. On the other hand, the insulin-glucose relation is also explained from the well-known facts of other biological mechanisms. Since these mechanisms are more or less related with each other, a mathematical model of the insulin-glucose system can be derived from these surrounding relations. This kind of method of the mathematical model derivation is called a fundamental method. Along with several mathematical models, researchers develop autonomous systems whether they involve medical devices or not to compensate metabolic disorders and these autonomous systems employ their own control methods. Basically, in insulin-dependent diabetes therapies, control methods are classified into three categories: open-loop, closed-loop, and partially closed-loop controls. The main difference among these methods is how much the systems are open to the outside people

Enhancing automatic closed-loop glucose control in type 1 diabetes with an adaptive meal bolus calculator - in silico evaluation under intra- day variability

[EN] Background and Objective: Current prototypes of closed-loop systems for glucose control in type 1 diabetes mellitus, also referred to as artificial pancreas systems, require a pre-meal insulin bolus to compensate for delays in subcutaneous insulin absorption in order to avoid initial post-prandial hyperglycemia. Computing such a meal bolus is a challenging task due to the high intra-subject variability of insulin requirements. Most closed-loop systems compute this pre-meal insulin dose by a standard bolus calculation, as is commonly found in insulin pumps. However, the performance of these calculators is limited due to a lack of adaptiveness in front of dynamic changes in insulin requirements. Despite some initial attempts to include adaptation within these calculators, challenges remain. Methods: In this paper we present a new technique to automatically adapt the meal-priming bolus within an artificial pancreas. The technique consists of using a novel adaptive bolus calculator based on Case-Based Reasoning and Run-To-Run control, within a closed-loop controller. Coordination between the adaptive bolus calculator and the controller was required to achieve the desired performance. For testing purposes, the clinically validated Imperial College Artificial Pancreas controller was employed. The proposed system was evaluated against itself but without bolus adaptation. The UVa-Padova T1DM v3.2 system was used to carry out a three-month in silico study on 11 adult and 11 adolescent virtual subjects taking into account inter-and intra-subject variability of insulin requirements and uncertainty on carbohydrate intake. Results: Overall, the closed-loop controller enhanced by an adaptive bolus calculator improves glycemic control when compared to its non-adaptive counterpart. In particular, the following statistically significant improvements were found (non-adaptive vs. adaptive). Adults: mean glucose 142.2 ± 9.4 vs. 131.8 ± 4.2 mg/dl; percentage time in target [70, 180] mg/dl, 82.0 ± 7.0 vs. 89.5 ± 4.2; percentage time above target 17.7 ± 7.0 vs. 10.2 ± 4.1. Adolescents: mean glucose 158.2 ± 21.4 vs. 140.5 ± 13.0 mg/dl; percentage time in target, 65.9 ± 12.9 vs. 77.5 ± 12.2; percentage time above target, 31.7 ± 13.1 vs. 19.8 ± 10.2. Note that no increase in percentage time in hypoglycemia was observed.This project has been funded by the Welcome Trust.Herrero, P.; Bondía Company, J.; Adewuji, O.; Pesl, P.; El-Sharkawy, M.; Reddy, M.; Toumazou, C.... (2017). Enhancing automatic closed-loop glucose control in type 1 diabetes with an adaptive meal bolus calculator - in silico evaluation under intra- day variability. Computer Methods and Programs in Biomedicine. 146:125-131. https://doi.org/10.1016/j.cmpb.2017.05.010S12513114

Swarm hybrid optimization for a piecewise model fitting applied to a glucose model

[EN] Purpose ¿ The purpose of this paper is to study insulin pump therapy and accurate monitoring of glucose levels in diabetic patients, which are current research trends in diabetology. Both problems have a wide margin for improvement and promising applications in the control of parameters and levels involved. Design/methodology/approach ¿ The authors have registered data for the levels of glucose in diabetic patients throughout a day with a temporal resolution of 5 minutes, the amount and time of insulin administered and time of ingestion. The estimated quantity of carbohydrates is also monitored. A mathematical model for Type 1 patients was fitted piecewise to these data and the evolution of the parameters was analyzed. Findings ¿ They have found that the parameters for the model change abruptly throughout a day for the same patient, but this set of parameters account with precision for the evolution of the glucose levels in the test patients. This fitting technique could be used to personalize treatments for specific patients and predict the glucose-level variations in terms of hours or even shorter periods of time. This way more effective insulin pump therapies could be developed. Originality/value ¿ The proposed model could allow for the development of improved schedules on insulin pump therapiesAcedo Rodríguez, L.; Botella, M.; Cortés, J.; Hidalgo, J.; Maqueda, E.; Villanueva Micó, RJ. (2018). Swarm hybrid optimization for a piecewise model fitting applied to a glucose model. Journal of Systems and Information Technology. 20(4):9618-9627. https://doi.org/10.1108/JSIT-10-2017-0103S9618962720

PATIENT-SPECIFIC CONTROLLER FOR AN IMPLANTABLE ARTIFICIAL PANCREAS

Ph.DDOCTOR OF PHILOSOPH

Contributions to modelling and control for improved hypoglycaemia and variability mitigation by dual-hormone artificial pancreas systems

[ES] Las personas con diabetes tipo 1 carecen de la capacidad de secretar insulina y, por lo tanto, necesitan regular su glucosa en sangre con la administración de insulina exógena. El páncreas artificial se presenta como la solución tecnológica ideal para alcanzar los objetivos terapéuticos de la normoglucemia, liberando al paciente de la carga actual de autocontrol y manejo. Sin embargo, el riesgo de hipoglucemia y la variabilidad glucémica siguen siendo factores limitantes en los algoritmos de control actuales integrados en el páncreas artificial. El propósito de la presente tesis es profundizar en el conocimiento de la hipoglucemia y avanzar los algoritmos de control del páncreas artificial para minimizar la incidencia de hipoglucemia y reducir la variabilidad glucémica. Después de proporcionar una visión general del estado del arte del control de la glucosa y el páncreas artificial, esta tesis aborda temas relacionados con el modelado y el control, con las siguientes contribuciones: Se presenta una extensión del modelo de Bergman Minimal que tiene en cuenta la respuesta contrarreguladora a la hipoglucemia. Este modelo explica la relación entre los diversos cambios fisiológicos producidos durante la hipoglucemia, con la adrenalina y los ácidos grasos libres como actores principales. Como resultado, se obtiene una mejor comprensión de la hipoglucemia, lo que permite explicar una auto-potenciación paradójica de la hipoglucemia como se modela a través de enfoques funcionales en el ampliamente utilizado simulador de diabetes tipo 1 UVA-Padova, que se utilizará en esta tesis para la validación in silico de los controladores desarrollados. Se realiza una evaluación de las métricas de variabilidad de la glucosa y los índices de calidad de control. La evaluación de la variabilidad glucémica en el desempeño de los controladores es necesaria; pero todavía no hay un conjunto de métricas de variabilidad glucémica que sea considerado como el "gold estándar". Por tanto, se lleva a cabo un análisis de las métricas de variabilidad disponibles en la literatura para definir un conjunto de indicadores recomendables. Debido a las limitaciones de los sistemas de páncreas artificiales unihormonales para mitigar la hipoglucemia en escenarios difíciles como el ejercicio, esta tesis se centra en el desarrollo de nuevos algoritmos de control bihormonales, con infusión simultanea de insulina y glucagón. Se propone un controlador coordinado bihormonal con estructuras de control paralelas como un algoritmo de control factible para la mitigación de la hipoglucemia y la reducción de la variabilidad glucémica, demostrando un rendimiento superior al de las estructuras de control utilizadas actualmente con lazos de control independientes de insulina y glucagón. Los controladores están diseñados y evaluados in silico en escenarios desafiantes y su rendimiento se evalúa principalmente con el conjunto de métricas definidas previamente como las recomendables.[CA] Les persones amb diabetis tipus 1 no tenen la capacitat de secretar insulina secreta i per tant, necessiten regular la seva glucosa en sang amb l'administració d'insulina exògena. El Pàncrees Artificial es presenta com la solució tecnològica ideal per assolir els objectius terapèutics de la normoglucèmia, alliberant al pacient de la càrrega actual d'autocontrol. No obstant, el risc d'hipoglucèmia i l'alta variabilitat glucèmica continuen sent un factor limitant en els algoritmes de control actuals integrats en el Pàncrees Artificials. El propòsit de la present tesi és aprofundir en el coneixement de la hipoglucèmia i millorar els algoritmes de control per corregir amb antelació la dosi excessiva d'insulina, minimitzant la incidència d'hipoglucèmia i reduint la variabilitat glucèmica. Després de donar una visió general de l'estat de l'art del control de la glucosa i el pàncrees artificial, aquesta tesi aborda aspectes de modelització i control, amb les següents contribucions: Es presenta una extensió del model Minimal de Bergman amb la contrarregulació. Aquest model explica la relació entre els diversos canvis siològics produïts durant la hipoglucèmia. Així, permet comprendre millor la hipoglucèmia i comparar els resultats amb els proporcionats per l'enfocament funcional del simulador de diabetis tipus 1 més utilitzat a la comunitat científica. Es realitza una avaluació de les mètriques de variabilitat glucèmica i dels índexs de qualitat de control. Es necessària l'avaluació de la variabilitat glucèmica en el rendiment dels controladors; però encara no hi ha un conjunt de mètriques considerades com les "gold standard". Per tant, es realitza una anàlisi de les mètriques de variabilitat disponibles a la literatura per definir un conjunt d'indicadors recomanables. Es proposa un controlador bi-hormonal coordinat amb estructures de control paral.leles com un algoritme de control viable per a la mitigació d'hipoglucèmia i la reducció de la variabilitat glucèmica. Els controladors estan dissenyats i avaluats in-silico en escenaris desafiadors i el seu rendiment es valora principalment amb el conjunt de mètriques definides prèviament com les mètriques recomanables.[EN] People with Type 1 Diabetes lack the ability to secrete insulin and therefore need to regulate their blood glucose with exogenous insulin delivery. The Artificial Pancreas is presented as the ideal technological solution to reach the therapeutic goals of normoglycaemia, freeing the patient from the current burden of self-control and management. Nevertheless, the risk of hypoglycaemia and the high glycaemic variability are still a limiting factors in the current control algorithms integrated in the Artificial Pancreas. The purpose of the present thesis is to delve into knowledge of hypoglycaemia and to advance in the artificial pancreas control algorithms in order to minimise hypoglycaemia incidence and reduce glycaemic variability. After providing an overview of the state of the art in the eld of glucose control and articial pancreas, this thesis addresses issues on modelling and control, with the following contributions: An extension of the Bergman Minimal model accounting for counterregulatory response to hypoglycaemia is presented. This model explains the relationship between the several physiological changes produced during hypoglycaemia, with adrenaline and free fatty acids as main players. As a result, a better understanding of hypoglycaemia is gained, allowing to explain a paradoxical auto-potentiation of hypoglycaemia as modeled through functional approaches in the widespread used UVA-Padova Type 1 Diabetes simulator, which will be used in this thesis for in silico validation of the developed controllers. An assessment of glucose variability metrics and control quality indices is carried out. The evaluation of the glycaemic variability on the controllers performance is necessary; but there is not a gold standard variability metrics yet. Therefore, an analysis of the variability metrics available in literature is conducted in order to define a recommendable set of indicators. Due to the limitations of single-hormone artificial pancreas systems in mitigating hypoglycaemia in challenging scenarios such as exercise, this thesis focuses on the developement of new dual-hormone control algorithms, with concomitant infusion of insulin and glucagon. A coordinated dual-hormone controller with parallel control structures is proposed as a feasible control algorithm for hypoglycaemia mitigation and glycaemic variability reduction, demonstrating superior performance as currently used control structures with independent insulin and glucagon control loops. The controllers are designed and evaluated in-silico under challenging scenarios and their performance are assessed mainly with the set of metrics defined previously as the recommendable ones.Moscardó García, V. (2019). Contributions to modelling and control for improved hypoglycaemia and variability mitigation by dual-hormone artificial pancreas systems [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/120456TESI