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

Consistency of compact and extended models of glucose-insulin homeostasis: The role of variable pancreatic reserve

Published compact and extended models of the glucose-insulin physiologic control system are compared, in order to understand why a specific functional form of the compact model proved to be necessary for a satisfactory representation of acute perturbation experiments such as the Intra Venous Glucose Tolerance Test (IVGTT). A spectrum of IVGTT’s of virtual subjects ranging from normal to IFG to IGT to frank T2DM were simulated using an extended model incorporating the population-of-controllers paradigm originally hypothesized by Grodsky, and proven to be able to capture a wide array of experimental results from heterogeneous perturbation procedures. The simulated IVGTT’s were then fitted with the Single-Delay Model (SDM), a compact model with only six free parameters, previously shown to be very effective in delivering precise estimates of insulin sensitivity and secretion during an IVGTT. Comparison of the generating, extended-model parameter values with the obtained compact model estimates shows that the functional form of the nonlinear insulin-secretion term, empirically found to be necessary for the compact model to satisfactorily fit clinical observations, captures the pancreatic reserve level of the simulated virtual patients. This result supports the validity of the compact model as a meaningful analysis tool for the clinical assessment of insulin sensitivity

Modelling of glycaemia dynamics: impact of physical exercises

In this article the authors performed linear, nonlinear and numerical analysis of glycemic regulation mathematical model described by two differential equations with one delay argument. The results obtained in the linear analysis were used in numeric analysis while constructing stable periodic solutions applying the Runge–Kuto IV successive method in normal and diabetes cases. Impact of physical exercise on the dynamics of glucose and insulin was modelled as well while introducing two external periodical functions defining diet and physical exercise into the above mentioned model. We applied the simulation modelling program “Model Maker” for modelling

The role of Computer Aided Process Engineering in physiology and clinical medicine

This paper discusses the potential role for Computer Aided Process Engineering (CAPE) in developing engineering analysis and design approaches to biological systems across multiple levels—cell signalling networks, gene, protein and metabolic networks, cellular systems, through to physiological systems. The 21st Century challenge in the Life Sciences is to bring together widely dispersed models and knowledge in order to enable a system-wide understanding of these complex systems. This systems level understanding should have broad clinical benefits. Computer Aided Process Engineering can bring systems approaches to (i) improving understanding of these complex chemical and physical (particularly molecular transport in complex flow regimes) interactions at multiple scales in living systems, (ii) analysis of these models to help to identify critical missing information and to explore the consequences on major output variables resulting from disturbances to the system, and (iii) ‘design’ potential interventions in in vivo systems which can have significant beneficial, or potentially harmful, effects which need to be understood. This paper develops these three themes drawing on recent projects at UCL. The first project has modeled the effects of blood flow on endothelial cells lining arteries, taking into account cell shape change resulting in changes in the cell skeleton which cause consequent chemical changes. A second is a project which is building an in silico model of the human liver, tieing together models from the molecular level to the liver. The composite model models glucose regulation in the liver and associated organs. Both projects involve molecular transport, chemical reactions, and complex multiscale systems, tackled by approaches from CAPE. Chemical Engineers solve multiple scale problems in manufacturing processes – from molecular scale through unit operations scale to plant-wide and enterprise wide systems – so have an appropriate skill set for tackling problems in physiology and clinical medicine, in collaboration with life and clinical scientists

The thermodynamics of metabolism, cardiovascular performance and exercise, in health and diabetes: The objective of clinical markers

Extensive experience in UK National Health Service metabolic syndrome/type 2 diabetes clinics highlights the need for convenient clinical marker(s) which can be readily used to indicate the success or otherwise of alternative therapies. In this paper we study the metabolic context of the healthy and diseased states, which points to the haemodynamics being a possible key in identifying candidate markers. Human metabolism relates to two elemental thermodynamic systems, the individual cell and the human body in its entirety. The fundamental laws of thermodynamics apply to humans, animals, and their individual cells for both healthy and diseased conditions. as they are to classic heat engines. In compliance with the second law enhanced levels of heat are generated under exercise, heat itself being another factor modulating the cardiovascular response to physical exercise. Nutrients and oxygen uptake occurs via the digestive system and lungs, respectively, leading to ATP production by the established metabolic pathways: this is controlled by insulin. These are then delivered to the cells via the haemodynamic system to satisfy local metabolic need. The supply and demand of oxygen are finely regulated, in part, via oxygen-dependent release of ATP from the circulating erythrocytes. Energy supply and demand are regulated to sustain muscle activity resulting in the body’s output of measurable thermodynamic work—i.e. exercise. Recently a dynamic pathway model allowing quantification of ATP release from the erythrocytes and its contribution to oxygen supply regulation has been published. However, metabolic uptake is well known to be greatly affected by disease such as the highly prevalent diabetes type 2 with insulin resistance and beta cell dysfunction having mechanistic roles. In 2010, over 25% of residents above 65 in the USA had diabetes 2. The complexity of the metabolic pathways means that monitoring of patient-specific treatment would be beneficial from a diabetic marker which may be haemodynamic-related and traceable via the local fluid dynamics

Projection of Diabetes Population Size and Associated Economic Burden through 2030 in Iran : Evidence from Micro-Simulation Markov Model and Bayesian Meta-Analysis

Acknowledgments The authors would like to thank kindly all advisors and colleagues, for their valuable technical support. We would like to thank you Ms Laura Marie Dysart for editing the paper.Peer reviewedPublisher PD

Mathematical modelling of blood glucose regulation

Exercise is beneficial for all individuals; it lowers blood pressure, keeps the heart healthy and increases insulin sensitivity. Recent studies have shown the power that regular exercise has to improve metabolic health, which in turn works to prevent and to reverse the onset of the widespread epidemics of type 2 diabetes (T2DM). However, diabetics taking insulin are required to meticulously plan exercise around meals and intake of insulin as they face an increased risk of hypoglycaemia from physical activity, which can discourage them from taking part. This thesis describes the use of systems of ordinary differential equations to model the effects of exercise on the glucose regulatory system, for both healthy and diabetic individuals. A particular focus is given to the role of glucagon, whose role is often neglected in glucoregulatory models, and its ability to enhance hepatic glucose production and so to prevent hypoglycaemia. Models of glucose-insulin-glucagon dynamics are first developed to describe an Intravenous glucose tolerance test (IVGTT), as the processes involved are simpler than in exercise and already widely modelled for glucose and insulin, thus is a good basis for validating the incorporation of glucagon. Mathematical models are used as tools within biological applications as they allow for an investigation into the dynamics that are involved in complex regulatory processes. The mathematical models in this thesis serve as accurate tools to predict blood glucose levels during exercise for both a non-diabetic and type 1 diabetic individual (T1DM) and emphasise exercise as a key element in the prevention of T2DM. By mathematically modelling the system and the mechanisms that occur to maintain glucose homeostasis an insight is gained into what the principal factors are for the greatest increase in insulin sensitivity and for the reduction in the likelihood of either hypoglycaemic or hyperglycaemic episodes. This may lead to recommendations for exercise plans which not only provide the greatest benefits for everyday health ant to assist with preventing the onset of diabetes but also to offer safer regimes for individuals with T1DM