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

Development of a Clinical Type 1 Diabetes Metabolic System Model and in Silico Simulation Tool

Invited journal symposium paperObjectives: To develop a safe and effective protocol for the clinical control of Type 1 diabetes using conventional self-monitoring blood glucose (SMBG) measurements, and multiple daily injection (MDI) with insulin analogues. To develop an in silico simulation tool of Type 1 diabetes to predict long-term glycaemic control outcomes of clinical interventions. Methods: The virtual patient method is used to develop a simulation tool for Type 1 diabetes using data from a Type 1 diabetes patient cohort (n=40). The tool is used to test the adaptive protocol (AC) and a conventional intensive insulin therapy (CC) against results from a representative control cohort. Optimal and suboptimal basal insulin replacement are evaluated as a function of self-monitoring blood glucose (SMBG) frequency in conjunction with the (AC and CC) prandial control protocols. Results: In long-term glycaemic control, the AC protocol significantly decreases HbA1c in conditions of suboptimal basal insulin replacement for SMBG frequencies =6/day, and reduced the occurrence of mild and severe hypoglycaemia by 86-100% over controls over all SMBG frequencies in conditions of optimal basal insulin. Conclusions: A simulation tool to predict long-term glycaemic control outcomes from clinical interventions is developed to test a novel, adaptive control protocol for Type 1 diabetes. The protocol is effective and safe compared to conventional intensive insulin therapy and controls. As fear of hypoglycaemia is a large psychological barrier to glycaemic control, the AC protocol may represent the next evolution of intensive insulin therapy to deliver increased glycaemic control with increased safety. Further clinical or experimental validation is needed to fully prove the concept

Continuous glucose monitoring sensors: Past, present and future algorithmic challenges

Continuous glucose monitoring (CGM) sensors are portable devices that allow measuring and visualizing the glucose concentration in real time almost continuously for several days and are provided with hypo/hyperglycemic alerts and glucose trend information. CGM sensors have revolutionized Type 1 diabetes (T1D) management, improving glucose control when used adjunctively to self-monitoring blood glucose systems. Furthermore, CGM devices have stimulated the development of applications that were impossible to create without a continuous-time glucose signal, e.g., real-time predictive alerts of hypo/hyperglycemic episodes based on the prediction of future glucose concentration, automatic basal insulin attenuation methods for hypoglycemia prevention, and the artificial pancreas. However, CGM sensors’ lack of accuracy and reliability limited their usability in the clinical practice, calling upon the academic community for the development of suitable signal processing methods to improve CGM performance. The aim of this paper is to review the past and present algorithmic challenges of CGM sensors, to show how they have been tackled by our research group, and to identify the possible future ones

A critical review of mathematical models and data used in diabetology

The literature dealing with mathematical modelling for diabetes is abundant. During the last decades, a variety of models have been devoted to different aspects of diabetes, including glucose and insulin dynamics, management and complications prevention, cost and cost-effectiveness of strategies and epidemiology of diabetes in general. Several reviews are published regularly on mathematical models used for specific aspects of diabetes. In the present paper we propose a global overview of mathematical models dealing with many aspects of diabetes and using various tools. The review includes, side by side, models which are simple and/or comprehensive; deterministic and/or stochastic; continuous and/or discrete; using ordinary differential equations, partial differential equations, optimal control theory, integral equations, matrix analysis and computer algorithms

Towards a Model-Based Meal Detector for Type I Diabetics

Blood glucose management systems are an important class of Medical Cyber-Physical Systems that provide vital everyday decision support service to diabetics. An artificial pancreas, which integrates a continuous glucose monitor, a wearable insulin pump, and control algorithms running on embedded computing devices, can significantly improve the quality of life for millions of Type 1 diabetics. A primary problem in the development of an artificial pancreas is the accurate detection and estimation of meal carbohydrates, which cause significant glucose system disturbances. Meal carbohydrate detection is challenging since post-meal glucose responses greatly depend on patient-specific physiology and meal composition. In this paper, we develop a novel meal-time detector that leverages a linearized physiological model to realize a (nearly) constant false alarm rate (CFAR) performance despite unknown model parameters and uncertain meal inputs. Insilico evaluations using 10, 000 virtual subjects on an FDA-accepted maximal physiological model illustrate that the proposed CFAR meal detector significantly outperforms a current state-of-the-art meal detector that utilizes a voting scheme based on rate-of-change (RoC) measures. The proposed detector achieves 99.6% correct detection rate while averaging one false alarm every 24 days (a 1.4% false alarm rate), which represents an 84% reduction in false alarms and a 95% reduction in missed alarms when compared to the RoC approach

Adipose tissue dynamics: Cellular and lipid turnover in health and disease

The alarming increase in obesity and its related metabolic health complications, such as type 2 diabetes, has evolved into a global pandemic. Obesity is mainly characterized by excessive accumulation of adipose tissue, primarily due to an imbalance between energy intake and expenditure. Prolonged positive energy balance leads to the expansion of existing adipocytes (hypertrophy) and/or an increase in preadipocyte and adipocyte number (hyperplasia) to accommodate excess energy intake. However, obesity is not solely defined by increases in adipocyte size and number. The turnover of adipose tissue cells also plays a crucial role in the development and progression of obesity. Cell turnover encompasses the processes of cell proliferation, differentiation, and apoptosis, which collectively regulate the overall cell population within adipose tissue. Lipid turnover represents another critical factor that influences how adipose tissue stores and releases energy. Our understanding of adipose tissue lipid turnover in humans remains limited due to the slow rate of turnover and methodological constraints. Nonetheless, disturbances in lipid metabolism are strongly associated with altered adipose tissue lipid turnover. In obesity, there is a decreased rate of triglyceride removal (lipolysis followed by oxidation), leading to the accumulation of triglycerides over time. This review provides a comprehensive summary of findings from both in vitro and in vivo methods used to study the turnover of adipose cells and lipids in metabolic health and disease. Understanding the mechanisms underlying cellular and lipid turnover in obesity is essential for developing strategies to mitigate the adverse effects of excess adiposity

Reflections on some mathematical modeling in endocrinology

This is an expository paper which explores a variety of epidemiological and other quantitative approaches to research in endocrinology. It is a sample of some of the projects in which the author and his colleagues, including doctoral students, have been involved over a number of years. The medical and mathematical theories have been tested on consenting patients in clinical environments