A critical review of mathematical models and data used in diabetology

Analysis and dynamical structure of glucose insulin glucagon system with Mittage-Leffler kernel for type I diabetes mellitus

In this paper, we propose a fractional-order mathematical model to explain the role of glucagon in maintaining the glucose level in the human body by using a generalised form of a fractal fractional operator. The existence, boundedness, and positivity of the results are constructed by fixed point theory and the Lipschitz condition for the biological feasibility of the system. Also, global stability analysis with Lyapunov's first derivative functions is treated. Numerical simulations for fractional-order systems are derived with the help of Lagrange interpolation under the Mittage-Leffler kernel. Results are derived for normal and type 1 diabetes at different initial conditions, which support the theoretical observations. These results play an important role in the glucose-insulin-glucagon system in the sense of a closed-loop design, which is helpful for the development of artificial pancreas to control diabetes in society.

Steady solution and its stability of a mathematical model of diabetic atherosclerosis

Atherosclerosis is a leading cause of death worldwide. Making matters worse, nearly 463 million people have diabetes, which increases atherosclerosis-related inflammation. Diabetic patients are twice as likely to have a heart attack or stroke. In this paper, we consider a simplified mathematical model for diabetic atherosclerosis involving LDL, HDL, glucose, insulin, free radicals (ROS), β cells, macrophages and foam cells, which satisfy a system of partial differential equations with a free boundary, the interface between the blood flow and the plaque. We establish the existence of small radially symmetric stationary solutions to the model and study their stability. Our analysis shows that the plague will persist due to hyperglycemia even when LDL and HDL are in normal range, hence confirms that diabetes increase the risk of atherosclerosis.

A methodical survey of mathematical model-based control techniques based on open and closed loop control approach for diabetes management

Disturbance of blood sugar level is controlled through well-known biomechanical feedback loops: high levels of glucose in blood facilitate to release insulin from the pancreas which accelerates the absorption rate of cellular glucose. Low glucose levels encourage to release pancreatic glucagon which induces glycogen breakdown to glucose in the liver. These bio-control systems do not function properly in diabetic patients. Though the control of disease seems intuitively easy, in real life, due to many differences in structure by diet and fasting, exercise, medications, patient’s profile and other stressors, it is not that easy. The mathematical models of the glucose-insulin regulatory system follow the patient’s physiological conditions which make it difficult to identify and estimate all the model parameters. In this paper, we have given a systematic literature review on mathematical models of the diabetic patients, and various kinds of disease control techniques through the development of open and closed loop insulin deliver command system and optimization of exogenous insulin rate. It demonstrates the open and closed loop type model-based control strategies underlying the assumptions of the concerned models. The combination of mathematical model with control strategies such as genetic algorithm (GA), neural network (NN), sliding mode controller (SMC), model predictive controller (MPC), and fuzzy logic control (FLC) has been considered, which provides an overview of this area, highlighting the control profile over the diabetic model with promising clinical results, outlining key challenges, and identifying needs for the future research. Also, the significance of these control algorithms has been discussed in the presence of the noises, the controller’s robustness and various other disturbances. It provides substantial information on diabetes management through various control techniques.

WELL-POSEDNESS OF A MATHEMATICAL MODEL OF DIABETIC ATHEROSCLEROSIS WITH ADVANCED GLYCATION END-PRODUCTS

Atherosclerosis is a leading cause of death worldwide; it emerges as a result of multiple dynamical cell processes including hemodynamics, endothelial damage, innate immunity and sterol biochemistry. Making matters worse, nearly 463 million people have diabetes, which increases atherosclerosis-related inflammation, diabetic patients are twice as likely to have a heart attack or stroke. The pathophysiology of diabetic vascular disease is generally understood. Dyslipidemia with increased levels of atherogenic LDL, hyperglycemia, oxidative stress and increased inflammation are factors that increase the risk and accelerate development of atherosclerosis. In a recent paper [53], we have developed mathematical model that includes the effect of hyperglycemia and insulin resistance on plaque growth. In this paper, we propose a more comprehensive mathematical model for diabetic atherosclerosis which include more variables; in particular it includes the variable for Advanced Glycation End-Products (AGEs)concentration. Hyperglycemia trigger vascular damage by forming AGEs, which are not easily metabolized and may accelerate the progression of vascular disease in diabetic patients. The model is given by a system of partial differential equations with a free boundary. We also establish local existence and uniqueness of solution to the model. The methodology is to use Hanzawa transformation to reduce the free boundary to a fixed boundary and reduce the system of partial differential equations to an abstract evolution equation in Banach spaces, and apply the theory of analytic semigroup.

WELL-POSEDNESS OF A MATHEMATICAL MODEL OF DIABETIC ATHEROSCLEROSIS

Atherosclerosis is a leading cause of death in the United States and worldwide; it emerges as a result of multiple dynamical cell processes including hemodynamics, endothelial damage, innate immunity and sterol biochemistry. Making matters worse, nearly 21 million Americans have diabetes, a disease where patients' cells cannot efficiently take in dietary sugar, causing it to build up in the blood. In part because diabetes increases atherosclerosis-related inflammation, diabetic patients are twice as likely to have a heart attack or stroke. Past work has shown that hyperglycemia and insulin resistance alter function of multiple cell types, including endothelium, smooth muscle cells and platelets, indicating the extent of vascular disarray in this disease. Although the pathophysiology of diabetic vascular disease is generally understood, there is no mathematical model to date that includes the effect of diabetes on plaque growth. In this paper, we propose a mathematical model for diabetic atherosclerosis; the model is given by a system of partial differential equations with a free boundary. We establish local existence and uniqueness of solution to the model. The methodology is to use Hanzawa transformation to reduce the free boundary to a fixed boundary and reduce the system of partial differential equations to an abstract evolution equation in Banach spaces, and apply the theory of analytic semigroup.

LSTMs and Deep Residual Networks for Carbohydrate and Bolus Recommendations in Type 1 Diabetes Management

To avoid serious diabetic complications, people with type 1 diabetes must keep their blood glucose levels (BGLs) as close to normal as possible. Insulin dosages and carbohydrate consumption are important considerations in managing BGLs. Since the 1960s, models have been developed to forecast blood glucose levels based on the history of BGLs, insulin dosages, carbohydrate intake, and other physiological and lifestyle factors. Such predictions can be used to alert people of impending unsafe BGLs or to control insulin flow in an artificial pancreas. In past work, we have introduced an LSTM-based approach to blood glucose level prediction aimed at “what-if” scenarios, in which people could enter foods they might eat or insulin amounts they might take and then see the effect on future BGLs. In this work, we invert the “what-if” scenario and introduce a similar architecture based on chaining two LSTMs that can be trained to make either insulin or carbohydrate recommendations aimed at reaching a desired BG level in the future. Leveraging a recent state-of-the-art model for time series forecasting, we then derive a novel architecture for the same recommendation task, in which the two LSTM chain is used as a repeating block inside a deep residual architecture. Experimental evaluations using real patient data from the OhioT1DM dataset show that the new integrated architecture compares favorably with the previous LSTM-based approach, substantially outperforming the baselines. The promising results suggest that this novel approach could potentially be of practical use to people with type 1 diabetes for self-management of BGLs.

Characterizing the type 2 diabetes mellitus epidemic in Jordan up to 2050

We aimed to characterize the type 2 diabetes mellitus (T2DM) epidemic and the role of key risk factors in Jordan between 1990-2050, and to forecast the T2DM-related costs. A recently-developed population-level T2DM mathematical model was adapted and applied to Jordan. The model was fitted to six population-based survey data collected between 1990 and 2017. T2DM prevalence was 14.0% in 1990, and projected to be 16.0% in 2020, and 20.6% in 2050. The total predicted number of T2DM cases were 218,326 (12,313 were new cases) in 1990, 702,326 (36,941 were new cases) in 2020, and 1.9 million (79,419 were new cases) in 2050. Out of Jordan's total health expenditure, 19.0% in 1990, 21.1% in 2020, and 25.2% in 2050 was forecasted to be spent on T2DM. The proportion of T2DM incident cases attributed to obesity was 55.6% in 1990, 59.5% in 2020, and 62.6% in 2050. Meanwhile, the combined contribution of smoking and physical inactivity hovered around 5% between 1990 and 2050. Jordan's T2DM epidemic is predicted to grow sizably in the next three decades, driven by population ageing and high and increasing obesity levels. The national strategy to prevent T2DM needs to be strengthened by focusing it on preventive interventions targeting T2DM and key risk factors.

A Glucose-Insulin Mixture Model and Application to Short-Term Hypoglycemia Prediction in the Night Time

OBJECTIVE

Insulin-induced hypoglycemia is recognized as a critical problem for diabetic patients, especially at night. To give glucose prediction and advance warning of hypoglycemia of at least 30 minutes, various glucose-insulin models have been proposed. Recognizing the complementary nature of the models, this research proposes a Glucose-Insulin Mixture (GIM) model to predict the glucose values for hypoglycemia detection, by optimally fusing different models with its adjusted parameters to address the inter- and intra-individual variability.

METHODS

Two types of classic glucose-insulin models, the Ruan model, with single-compartment glucose kinetics, and the Hovorka model, with two-compartment glucose kinetics, are selected as two candidate models. Based on Bayesian inference, GIM is introduced with quantified contributions from the models with the associated parameters. GIM is then applied to predict the glucose values and hypoglycemia events.

RESULTS

The proposed model is validated by the nocturnal glucose data collected from 12 participants with type 1 diabetes. The GIM model has promising fitting of RMSE within 0.3465 mmol/L and predicting of RMSE within 0.5571 mmol/L. According to the literature, the hypoglycemia is defined as 3.9 mmol/L, and the GIM model shows good short-term hypoglycemia prediction performance with the data collected within the last hour (accuracy: 95.97%, precision: 91.77%, recall: 95.60%). In addition, the probability of hypoglycemia event in 30 minutes is inferred.

CONCLUSION

GIM, by fusing various glucose-insulin models via Bayesian inference, has the promise to capture glucose dynamics and predict hypoglycemia.

SIGNIFICANCE

GIM based short-term hypoglycemia prediction has potential clinical utility for timely intervention.

A Novel Synthetic Model of the Glucose-Insulin System for Patient-Wise Inference of Physiological Parameters From Small-Size OGTT Data

Existing mathematical models for the glucose-insulin (G-I) dynamics often involve variables that are not susceptible to direct measurement. Standard clinical tests for measuring G-I levels for diagnosing potential diseases are simple and relatively cheap, but seldom give enough information to allow the identification of model parameters within the range in which they have a biological meaning, thus generating a gap between mathematical modeling and any possible physiological explanation or clinical interpretation. In the present work, we present a synthetic mathematical model to represent the G-I dynamics in an Oral Glucose Tolerance Test (OGTT), which involves for the first time for OGTT-related models, Delay Differential Equations. Our model can represent the radically different behaviors observed in a studied cohort of 407 normoglycemic patients (the largest analyzed so far in parameter fitting experiments), all masked under the current threshold-based normality criteria. We also propose a novel approach to solve the parameter fitting inverse problem, involving the clustering of different G-I profiles, a simulation-based exploration of the feasible set, and the construction of an information function which reshapes it, based on the clinical records, experimental uncertainties, and physiological criteria. This method allowed an individual-wise recognition of the parameters of our model using small size OGTT data (5 measurements) directly, without modifying the routine procedures or requiring particular clinical setups. Therefore, our methodology can be easily applied to gain parametric insights to complement the existing tools for the diagnosis of G-I dysregulations. We tested the parameter stability and sensitivity for individual subjects, and an empirical relationship between such indexes and curve shapes was spotted. Since different G-I profiles, under the light of our model, are related to different physiological mechanisms, the present method offers a tool for personally-oriented diagnosis and treatment and to better define new health criteria.

Modelling the effects of glucagon during glucose tolerance testing

Background

Glucose tolerance testing is a tool used to estimate glucose effectiveness and insulin sensitivity in diabetic patients. The importance of such tests has prompted the development and utilisation of mathematical models that describe glucose kinetics as a function of insulin activity. The hormone glucagon, also plays a fundamental role in systemic plasma glucose regulation and is secreted reciprocally to insulin, stimulating catabolic glucose utilisation. However, regulation of glucagon secretion by α-cells is impaired in type-1 and type-2 diabetes through pancreatic islet dysfunction. Despite this, inclusion of glucagon activity when modelling the glucose kinetics during glucose tolerance testing is often overlooked. This study presents two mathematical models of a glucose tolerance test that incorporate glucose-insulin-glucagon dynamics. The first model describes a non-linear relationship between glucagon and glucose, whereas the second model assumes a linear relationship.

Results

Both models are validated against insulin-modified and glucose infusion intravenous glucose tolerance test (IVGTT) data, as well as insulin infusion data, and are capable of estimating patient glucose effectiveness (s_G) and insulin sensitivity (s_I). Inclusion of glucagon dynamics proves to provide a more detailed representation of the metabolic portrait, enabling estimation of two new diagnostic parameters: glucagon effectiveness (s_E) and glucagon sensitivity (δ).

Conclusions

The models are used to investigate how different degrees of pax‘tient glucagon sensitivity and effectiveness affect the concentration of blood glucose and plasma glucagon during IVGTT and insulin infusion tests, providing a platform from which the role of glucagon dynamics during a glucose tolerance test may be investigated and predicted.

LSTMs and Neural Attention Models for Blood Glucose Prediction: Comparative Experiments on Real and Synthetic Data

We have shown in previous work that LSTM networks are effective at predicting blood glucose levels in patients with type I diabetes, outperforming human experts and an SVR model trained with features computed by manually engineered physiological models. In this paper we present the results of a much larger set of experiments on real and synthetic datasets in what-if, agnostic, and inertial scenarios. Experiments on a more recent real-patient dataset, which we are releasing to the research community, demonstrate that LSTMs are robust to noise and can easily incorporate additional features, such as skin temperature, heart rate and skin conductance, without any change in the architecture. A neural attention module that we designed specifically for time series prediction improves prediction performance on synthetic data; however, the improvements do not transfer to real data. Conversely, using time of day as an additional input feature consistently improves the LSTM performance on real data but not on synthetic data. These and other differences show that behavior on synthetic data cannot be assumed to always transfer to real data, highlighting the importance of evaluating physiological models on data from real patients.

A Population Dynamic Model to Assess the Diabetes Screening and Reporting Programs and Project the Burden of Undiagnosed Diabetes in Thailand

Diabetes mellitus (DM) is rising worldwide, exacerbated by aging populations. We estimated and predicted the diabetes burden and mortality due to undiagnosed diabetes together with screening program efficacy and reporting completeness in Thailand, in the context of demographic changes. An age and sex structured dynamic model including demographic and diagnostic processes was constructed. The model was validated using a Bayesian Markov Chain Monte Carlo (MCMC) approach. The prevalence of DM was predicted to increase from 6.5% (95% credible interval: 6.3-6.7%) in 2015 to 10.69% (10.4-11.0%) in 2035, with the largest increase (72%) among 60 years or older. Out of the total DM cases in 2015, the percentage of undiagnosed DM cases was 18.2% (17.4-18.9%), with males higher than females (p-value < 0.01). The highest group with undiagnosed DM was those aged less than 39 years old, 74.2% (73.7-74.7%). The mortality of undiagnosed DM was ten-fold greater than the mortality of those with diagnosed DM. The estimated coverage of diabetes positive screening programs was ten-fold greater for elderly compared to young. The positive screening rate among females was estimated to be significantly higher than those in males. Of the diagnoses, 87.4% (87.0-87.8%) were reported. Targeting screening programs and good reporting systems will be essential to reduce the burden of disease.

Glucose-responsive insulin by molecular and physical design

The concept of a glucose-responsive insulin (GRI) has been a recent objective of diabetes technology. The idea behind the GRI is to create a therapeutic that modulates its potency, concentration or dosing relative to a patient's dynamic glucose concentration, thereby approximating aspects of a normally functioning pancreas. From the perspective of the medicinal chemist, the GRI is also important as a generalized model of a potentially new generation of therapeutics that adjust potency in response to a critical therapeutic marker. The aim of this Perspective is to highlight emerging concepts, including mathematical modelling and the molecular engineering of insulin itself and its potency, towards a viable GRI. We briefly outline some of the most important recent progress toward this goal and also provide a forward-looking viewpoint, which asks if there are new approaches that could spur innovation in this area as well as to encourage synthetic chemists and chemical engineers to address the challenges and promises offered by this therapeutic approach.

Modeling of Diabetes and Its Clinical Impact

Understanding all aspects of diabetes treatment is hindered by the complexity of this chronic disease and its multifaceted complications and comorbidities, including social and financial impacts. In vivo studies as well as clinical trials provided invaluable information for unraveling not only metabolic processes but also risk estimations of, for example, complications. These approaches are often time- and cost-consuming and have frequently been supported by simulation models. Simulation models provide the opportunity to investigate diabetes treatment from additional viewpoints and with alternative objectives. This review presents selected models focusing either on metabolic processes or risk estimations and financial outcomes to provide a basic insight into this complex subject. It also discusses opportunities and challenges of modeling diabetes.

Labile haemoglobin as a glycaemic biomarker for patient-specific monitoring of diabetes: mathematical modelling approach

Diabetes mellitus constitutes a major health problem and its clinical presentation and progression may vary considerably. A number of standardized diagnostic and monitoring tests are currently used for diabetes. They are based on measuring either plasma glucose, glycated haemoglobin or both. Their main goal is to assess the average blood glucose concentration. There are several sources of interference that can lead to discordances between measured plasma glucose and glycated haemoglobin levels. These include haemoglobinopathies, conditions associated with increased red blood cell turnover or the administration of some therapies, to name a few. Therefore, there is a need to provide new diagnostic tools for diabetes that employ clinically accessible biomarkers which, at the same time, can offer additional information allowing us to detect possible conflicting cases and to yield more reliable evaluations of the average blood glucose level concentration. We put forward a biomathematical model to describe the kinetics of two patient-specific glycaemic biomarkers to track the emergence and evolution of diabetes: glycated haemoglobin and its labile fraction. Our method incorporates erythrocyte age distribution and utilizes a large cohort of clinical data from blood tests to support its usefulness for diabetes monitoring.

Dissecting Long-Term Glucose Metabolism Identifies New Susceptibility Period for Metabolic Dysfunction in Aged Mice

Metabolic disorders, like diabetes and obesity, are pathogenic outcomes of imbalance in glucose metabolism. Nutrient excess and mitochondrial imbalance are implicated in dysfunctional glucose metabolism with age. We used conplastic mouse strains with defined mitochondrial DNA (mtDNA) mutations on a common nuclear genomic background, and administered a high-fat diet up to 18 months of age. The conplastic mouse strain B6-mt^FVB, with a mutation in the mt-Atp8 gene, conferred β-cell dysfunction and impaired glucose tolerance after high-fat diet. To our surprise, despite of this functional deficit, blood glucose levels adapted to perturbations with age. Blood glucose levels were particularly sensitive to perturbations at the early age of 3 to 6 months. Overall the dynamics consisted of a peak between 3–6 months followed by adaptation by 12 months of age. With the help of mathematical modeling we delineate how body weight, insulin and leptin regulate this non-linear blood glucose dynamics. The model predicted a second rise in glucose between 15 and 21 months, which could be experimentally confirmed as a secondary peak. We therefore hypothesize that these two peaks correspond to two sensitive periods of life, where perturbations to the basal metabolism can mark the system for vulnerability to pathologies at later age. Further mathematical modeling may perspectively allow the design of targeted periods for therapeutic interventions and could predict effects on weight loss and insulin levels under conditions of pre-diabetic obesity.

Experimental evaluation and computational modeling of the effects of encapsulation on the time-profile of glucose-stimulated insulin release of pancreatic islets

Background

In type 1 diabetic patients, who have lost their ability to produce insulin, transplantation of pancreatic islet cells can normalize metabolic control in a manner that is not achievable with exogenous insulin. To be successful, this procedure has to address the problems caused by the immune and autoimmune responses to the graft. Islet encapsulation using various techniques and materials has been and is being extensively explored as a possible approach. Within this framework, it is of considerable interest to characterize the effect encapsulation has on the insulin response of pancreatic islets.

Methods

To improve our ability to quantitatively describe the glucose-stimulated insulin release (GSIR) of pancreatic islets in general and of micro-encapsulated islets in particular, we performed dynamic perifusion experiments with frequent sampling. We used unencapsulated and microencapsulated murine islets in parallel and fitted the results with a complex local concentration-based finite element method (FEM) computational model.

Results

The high-resolution dynamic perifusion experiments allowed good characterization of the first-phase and second-phase insulin secretion, and we observed a slightly delayed and blunted first-phase insulin response for microencapsulated islets when compared to free islets. Insulin secretion profiles of both free and encapsulated islets could be fitted well by a COMSOL Multiphysics model that couples hormone secretion and nutrient consumption kinetics with diffusive and convective transport. This model, which was further validated and calibrated here, can be used for arbitrary geometries and glucose stimulation sequences and is well suited for the quantitative characterization of the insulin response of cultured, perifused, transplanted, or encapsulated islets.

Conclusions

The present high-resolution GSIR experiments allowed for direct characterization of the effect microencapsulation has on the time-profile of insulin secretion. The multiphysics model, further validated here with the help of these experimental results, can be used to increase our understanding of the challenges that have to be faced in the design of bioartificial pancreas-type devices and to advance their further optimization.

Electronic supplementary material

The online version of this article (doi:10.1186/s12938-015-0021-9) contains supplementary material, which is available to authorized users.

Probing the binding affinity of amyloids to reduce toxicity of oligomers in diabetes

MOTIVATION

Amyloids play a role in the degradation of β-cells in diabetes patients. In particular, short amyloid oligomers inject themselves into the membranes of these cells and create pores that disrupt the strictly controlled flow of ions through the membranes. This leads to cell death. Getting rid of the short oligomers either by a deconstruction process or by elongating them into longer fibrils will reduce this toxicity and allow the β-cells to live longer.

RESULTS

We develop a computational method to probe the binding affinity of amyloid structures and produce an amylin analog that binds to oligomers and extends their length. The binding and extension lower toxicity and β-cell death. The amylin analog is designed through a parsimonious selection of mutations and is to be administered with the pramlintide drug, but not to interact with it. The mutations (T9K L12K S28H T30K) produce a stable native structure, strong binding affinity to oligomers, and long fibrils. We present an extended mathematical model for the insulin-glucose relationship and demonstrate how affecting the concentration of oligomers with such analog is strictly coupled with insulin release and β-cell fitness.

AVAILABILITY AND IMPLEMENTATION

SEMBA, the tool to probe the binding affinity of amyloid proteins and generate the binding affinity scoring matrices and R-scores is available at: http://amyloid.cs.mcgill.ca

A therapy parameter-based model for predicting blood glucose concentrations in patients with type 1 diabetes

In this paper, the problem of predicting blood glucose concentrations (BG) for the treatment of patients with type 1 diabetes, is addressed. Predicting BG is of very high importance as most treatments, which consist in exogenous insulin injections, rely on the availability of BG predictions. Many models that can be used for predicting BG are available in the literature. However, it is widely admitted that it is almost impossible to perfectly model blood glucose dynamics while still being able to identify model parameters using only blood glucose measurements. The main contribution of this work is to propose a simple and identifiable linear dynamical model, which is based on the static prediction model of standard therapy. It is shown that the model parameters are intrinsically correlated with physician-set therapy parameters and that the reduction of the number of model parameters to identify leads to inferior data fits but to equivalent or slightly improved prediction capabilities compared to state-of-the-art models: a sign of an appropriate model structure and superior reliability. The validation of the proposed dynamic model is performed using data from the UVa simulator and real clinical data, and potential uses of the proposed model for state estimation and BG control are discussed.

Effects of diet and exercise interventions on diabetes risk factors in adults without diabetes: meta-analyses of controlled trials

BACKGROUND AND AIMS

Fasting insulin (FI), fasting glucose (FG), systolic blood pressure (SBP), high density lipoproteins (HDL), triacylglycerides (TAG), and body mass index (BMI) are well-known risk factors for type 2 diabetes. Reliable estimates of lifestyle intervention effects on these factors allow diabetes risk to be predicted accurately. The present meta-analyses were conducted to quantitatively summarize effects of diet and exercise intervention programs on FI, FG, SBP, HDL, TAG and BMI in adults without diabetes.

MATERIALS AND METHODS

MEDLINE and EMBASE were searched to find studies involving diet plus exercise interventions. Studies were required to use adults not diagnosed with type 2 diabetes, involve both dietary and exercise counseling, and include changes in diabetes risk factors as outcome measures. Data from 18, 24, 23, 30, 29 and 29 studies were used for the analyses of FI, FG, SBP, HDL, TAG and BMI, respectively. About 60% of the studies included exclusively overweight or obese adults. Mean age and BMI of participants at baseline were 48 years and 30.1 kg/m(2). Heterogeneity of intervention effects was first estimated using random-effect models and explained further with mixed-effects models.

RESULTS

Adults receiving diet and exercise education for approximately one year experienced significant (P <0.001) reductions in FI (-2.56 ± 0.58 mU/L), FG (-0.18 ± 0.04 mmol/L), SBP (-2.77 ± 0.56 mm Hg), TAG (-0.258 ± 0.037 mmol/L) and BMI (-1.61 ± 0.13 kg/m(2)). These risk factor changes were related to a mean calorie intake reduction of 273 kcal/d, a mean total fat intake reduction of 6.3%, and 40 minutes of moderate intensity aerobic exercise four times a week. Lifestyle intervention did not have an impact on HDL. More than 99% of total variability in the intervention effects was due to heterogeneity. Variability in calorie and fat intake restrictions, exercise type and duration, length of the intervention period, and the presence or absence of glucose, insulin, or lipid abnormalities explained 23-63% of the heterogeneity.

CONCLUSIONS

Calorie and total fat intake restrictions coupled with moderate intensity aerobic exercises significantly improved diabetes risk factors in healthy normoglycemic adults although normoglycemic adults with glucose, insulin, and lipid abnormalities appear to benefit more.

Undiagnosed diabetes from cross-sectional GP practice data: an approach to identify communities with high likelihood of undiagnosed diabetes

OBJECTIVES

To estimate undiagnosed diabetes prevalence from general practitioner (GP) practice data and identify areas with high levels of undiagnosed and diagnosed diabetes.

DESIGN

Data from the North-West Adelaide Health Survey (NWAHS) were used to develop a model which predicts total diabetes at a small area. This model was then applied to cross-sectional data from general practices to predict the total level of expected diabetes. The difference between total expected and already diagnosed diabetes was defined as undiagnosed diabetes prevalence and was estimated for each small area. The patterns of diagnosed and undiagnosed diabetes were mapped to highlight the areas of high prevalence.

SETTING

North-West Adelaide, Australia.

PARTICIPANTS

This study used two population samples-one from the de-identified GP practice data (n=9327 active patients, aged 18 years and over) and another from NWAHS (n=4056, aged 18 years and over).

MAIN OUTCOME MEASURES

Total diabetes prevalence, diagnosed and undiagnosed diabetes prevalence at GP practice and Statistical Area Level 1.

RESULTS

Overall, it was estimated that there was one case of undiagnosed diabetes for every 3-4 diagnosed cases among the 9327 active patients analysed. The highest prevalence of diagnosed diabetes was seen in areas of lower socioeconomic status. However, the prevalence of undiagnosed diabetes was substantially higher in the least disadvantaged areas.

CONCLUSIONS

The method can be used to estimate population prevalence of diabetes from general practices wherever these data are available. This approach both flags the possibility that undiagnosed diabetes may be a problem of less disadvantaged social groups, and provides a tool to identify areas with high levels of unmet need for diabetes care which would enable policy makers to apply geographic targeting of effective interventions.

Glucose-insulin regulation model with subcutaneous insulin injection and evaluation using diabetic inpatients data

Closed-loop insulin delivery systems often implement glucose measurement and insulin administration in the subcutis. However some existing models for glucose-insulin system ignored the dynamics of subcutaneous glucose and subcutaneously-injected insulin. This paper reports a two-compartment model that includes glucose and insulin dynamics in subcutis, and its evaluation using patient data. Clinical information such as glucose level, insulin dosage, insulin injection time and meals of anonymous diabetes inpatients was collected. Measured glucose level of the diabetic inpatients agrees with that of computer simulation. Due to the lack of glucose-insulin model with subcutaneously-injected insulin for type 2 diabetic patients, our model was compared with existing model for type 1 subjects. The new glucose-insulin model can mimic dynamics of glucose and insulin under the disturbance of insulin injections and meals. Model parameters were estimated using nonlinear least square method and their effect on pathology and physiology of diabetes were analyzed.

The impact of mathematical modeling on the understanding of diabetes and related complications

Diabetes is a chronic and complex multifactorial disease caused by persistent hyperglycemia and for which underlying pathogenesis is still not completely understood. The mathematical modeling of glucose homeostasis, diabetic condition, and its associated complications is rapidly growing and provides new insights into the underlying mechanisms involved. Here, we discuss contributions to the diabetes modeling field over the past five decades, highlighting the areas where more focused research is required.

A mathematical model for determining age-specific diabetes incidence and prevalence using body mass index

PURPOSE

Few models have been developed specifically for the epidemiology of diabetes. Diabetes incidence is critical in predicting diabetes prevalence. However, reliable estimates of disease incidence rates are difficult to obtain. The aim of this study was to propose a mathematical framework for predicting diabetes prevalence using incidence rates estimated within the model using body mass index (BMI) data.

METHODS

A generic mechanistic model was proposed considering birth, death, migration, aging, and diabetes incidence dynamics. Diabetes incidence rates were determined within the model using their relationships with BMI represented by the Hill equation. The Hill equation parameters were estimated by fitting the model to National Health and Nutrition Examination Survey (NHANES) 1999-2010 data and used to predict diabetes prevalence pertaining to each NHANES survey year. The prevalences were also predicted using diabetes incidence rates calculated from the NHANES data themselves. The model was used to estimate death rate parameters and to quantify sensitivities of prevalence to each population dynamic.

RESULTS

The model using incidence rate estimates from the Hill equations successfully predicted diabetes prevalence of younger, middle-aged, and older adults (prediction error, 20.0%, 9.64%, and 7.58% respectively). Diabetes prevalence was positively associated with diabetes incidence in every age group, but the associations among younger adults were stronger. In contrast, diabetes prevalence was more sensitive to death rates in older adults than younger adults. Both diabetes incidence and prevalence were strongly sensitive to BMI at younger ages, but sensitivity gradually declined as age progressed. Younger and middle aged adults diagnosed with diabetes had at least a two-fold greater risk of death than their nondiabetic counterparts. Nondiabetic older adults were found to be under slightly higher death risk (0.079) than those diagnosed with diabetes (0.073).

CONCLUSIONS

The proposed model predicts diagnosed diabetes incidence and prevalence reasonably well using the link between BMI and diabetes development risk. Ethnic group and gender-specific model parameter estimates could further improve predictions. Model prediction accuracy and applicability need to be comprehensively evaluated with independent data sets.

Dynamics of glucose and insulin concentration connected to the β-cell cycle: model development and analysis

Background

Diabetes mellitus is a group of metabolic diseases with increased blood glucose concentration as the main symptom. This can be caused by a relative or a total lack of insulin which is produced by the β‐cells in the pancreatic islets of Langerhans. Recent experimental results indicate the relevance of the β‐cell cycle for the development of diabetes mellitus.

Methods

This paper introduces a mathematical model that connects the dynamics of glucose and insulin concentration with the β‐cell cycle. The interplay of glucose, insulin, and β‐cell cycle is described with a system of ordinary differential equations. The model and its development will be presented as well as its mathematical analysis. The latter investigates the steady states of the model and their stability.

Results

Our model shows the connection of glucose and insulin concentrations to the β‐cell cycle. In this way the important role of glucose as regulator of the cell cycle and the capability of the β‐cell mass to adapt to metabolic demands can be presented. Simulations of the model correspond to the qualitative behavior of the glucose‐insulin regulatory system showed in biological experiments.

Conclusions

This work focusses on modeling the physiological situation of the glucose‐insulin regulatory system with a detailed consideration of the β‐cell cycle. Furthermore, the presented model allows the simulation of pathological scenarios. Modification of different parameters results in simulation of either type 1 or type 2 diabetes.

Structural identifiability and indistinguishability analyses of the minimal model and a euglycemic hyperinsulinemic clamp model for glucose-insulin dynamics

Many mathematical models have been developed to describe glucose-insulin kinetics as a means of analysing the effective control of diabetes. This paper concentrates on the structural identifiability analysis of certain well-established mathematical models that have been developed to characterise glucose-insulin kinetics under different experimental scenarios. Such analysis is a pre-requisite to experiment design and parameter estimation and is applied for the first time to these models with the specific structures considered. The analysis is applied to a basic (original) form of the Minimal Model (MM) using the Taylor Series approach and a now well-accepted extended form of the MM by application of the Taylor Series approach and a form of the Similarity Transformation approach. Due to the established inappropriate nature of the MM with regard to glucose clamping experiments an alternative model describing the glucose-insulin dynamics during a Euglycemic Hyperinsulinemic Clamp (EIC) experiment was considered. Structural identifiability analysis of the EIC model is also performed using the Taylor Series approach and shows that, with glucose infusion as input alone, the model is structurally globally identifiable. Additional analysis demonstrates that the two different model forms are structurally distinguishable for observation of both glucose and insulin.

A local glucose-and oxygen concentration-based insulin secretion model for pancreatic islets

BACKGROUND

Because insulin is the main regulator of glucose homeostasis, quantitative models describing the dynamics of glucose-induced insulin secretion are of obvious interest. Here, a computational model is introduced that focuses not on organism-level concentrations, but on the quantitative modeling of local, cellular-level glucose-insulin dynamics by incorporating the detailed spatial distribution of the concentrations of interest within isolated avascular pancreatic islets.

METHODS

All nutrient consumption and hormone release rates were assumed to follow Hill-type sigmoid dependences on local concentrations. Insulin secretion rates depend on both the glucose concentration and its time-gradient, resulting in second-and first-phase responses, respectively. Since hypoxia may also be an important limiting factor in avascular islets, oxygen and cell viability considerations were also built in by incorporating and extending our previous islet cell oxygen consumption model. A finite element method (FEM) framework is used to combine reactive rates with mass transport by convection and diffusion as well as fluid-mechanics.

RESULTS

The model was calibrated using experimental results from dynamic glucose-stimulated insulin release (GSIR) perifusion studies with isolated islets. Further optimization is still needed, but calculated insulin responses to stepwise increments in the incoming glucose concentration are in good agreement with existing experimental insulin release data characterizing glucose and oxygen dependence. The model makes possible the detailed description of the intraislet spatial distributions of insulin, glucose, and oxygen levels. In agreement with recent observations, modeling also suggests that smaller islets perform better when transplanted and/or encapsulated.

CONCLUSIONS

An insulin secretion model was implemented by coupling local consumption and release rates to calculations of the spatial distributions of all species of interest. The resulting glucose-insulin control system fits in the general framework of a sigmoid proportional-integral-derivative controller, a generalized PID controller, more suitable for biological systems, which are always nonlinear due to the maximum response being limited. Because of the general framework of the implementation, simulations can be carried out for arbitrary geometries including cultured, perifused, transplanted, and encapsulated islets.

Review: Starch Matrices and the Glycemic Response

Starch is the most important source of energy for humans, and it is present in many products derived from cereals, legumes and tubers. Interestingly, some of these food products can have different metabolic effects (e.g. change of postprandial blood glucose concentration) although the total amount of starch is the same. This review focuses on a microstructural perspective of the glycemic response, in search of an alternative and complementary explanation of this phenomenon. Several starch and food microstructures are responsible for the change in starch bioaccessibility. Aspects such as the characterization of the microstructure of starchy products and, its relation to the metabolic problem, the crucial role of the food matrix and other components in the ingested meal, and the gaps in our present knowledge are discussed.

A hybrid Decision Support System for the risk assessment of retinopathy development as a long term complication of Type 1 Diabetes Mellitus

The aim of the present study is to design and develop a Decision Support System (DSS) closely coupled with an Electronic Medical Record (EMR), able to predict the risk of a Type 1 Diabetes Mellitus (T1DM) patient to develop retinopathy. The proposed system is able to store a wealth of information regarding the clinical state of the T1DM patient and continuously provide the health experts with predictions regarding the possible future complications that he may present. The DSS is a hybrid infrastructure combining a Feedforward Neural Network (FNN), a Classification and Regression Tree (CART) and a Rule Induction C5.0 classifier, with an improved Hybrid Wavelet Neural Network (iHWNN). A voting mechanism is utilized to merge the results from the four classification models. The proposed DSS has been trained and evaluated using data from 55 T1DM patients, acquired by the Athens Hippokration Hospital in close collaboration with the EURODIAB research team. The DSS has shown an excellent performance resulting in an accuracy of 98%. Care has been taken to design and implement a consistent and continuously evolving Information Technology (IT) system by utilizing technologies such as smart agents periodically triggered to retrain the DSS with new cases added in the data repository.

Real-time forecasting of an epidemic using a discrete time stochastic model: a case study of pandemic influenza (H1N1-2009)

Background

Real-time forecasting of epidemics, especially those based on a likelihood-based approach, is understudied. This study aimed to develop a simple method that can be used for the real-time epidemic forecasting.

Methods

A discrete time stochastic model, accounting for demographic stochasticity and conditional measurement, was developed and applied as a case study to the weekly incidence of pandemic influenza (H1N1-2009) in Japan. By imposing a branching process approximation and by assuming the linear growth of cases within each reporting interval, the epidemic curve is predicted using only two parameters. The uncertainty bounds of the forecasts are computed using chains of conditional offspring distributions.

Results

The quality of the forecasts made before the epidemic peak appears largely to depend on obtaining valid parameter estimates. The forecasts of both weekly incidence and final epidemic size greatly improved at and after the epidemic peak with all the observed data points falling within the uncertainty bounds.

Conclusions

Real-time forecasting using the discrete time stochastic model with its simple computation of the uncertainty bounds was successful. Because of the simplistic model structure, the proposed model has the potential to additionally account for various types of heterogeneity, time-dependent transmission dynamics and epidemiological details. The impact of such complexities on forecasting should be explored when the data become available as part of the disease surveillance.

Estimated incidence of cardiovascular complications related to type 2 diabetes in Mexico using the UKPDS outcome model and a population-based survey

BACKGROUND

To estimate the incidence of complications, life expectancy and diabetes related mortality in the Mexican diabetic population over the next two decades using data from a nation-wide, population based survey and the United Kingdom Prospective Diabetes Study (UKPDS) outcome model.

METHODS

The cohort included all patients with type 2 diabetes evaluated during the National Health and Nutrition Survey (ENSANut) 2006. ENSANut is a probabilistic multistage stratified survey whose aim was to measure the prevalence of chronic diseases. A total of 47,152 households were visited. Results are shown stratified by gender, time since diagnosis (> or ≤ to 10 years) and age at the time of diagnosis (> or ≤ 40 years).

RESULTS

The prevalence of diabetes in our cohort was 14.4%. The predicted 20 year-incidence for chronic complications per 1000 individuals are: ischemic heart disease 112, myocardial infarction 260, heart failure 113, stroke 101, and amputation 62. Furthermore, 539 per 1000 patients will have a diabetes-related premature death. The average life expectancy for the diabetic population is 10.9 years (95%CI 10.7-11.2); this decreases to 8.3 years after adjusting for quality of life (CI95% 8.1-8.5). Male sex and cases diagnosed after age 40 have the highest risk for developing at least one major complication during the next 20 years.

CONCLUSIONS

Based on the current clinical profile of Mexican patients with diabetes, the burden of disease related complications will be tremendous over the next two decades.

A computational model of the human glucose-insulin regulatory system

OBJECTIVE

A computational model of insulin secretion and glucose metabolism for assisting the diagnosis of diabetes mellitus in clinical research is introduced. The proposed method for the estimation of parameters for a system of ordinary differential equations (ODEs) that represent the time course of plasma glucose and insulin concentrations during glucose tolerance test (GTT) in physiological studies is presented. The aim of this study was to explore how to interpret those laboratory glucose and insulin data as well as enhance the Ackerman mathematical model.

METHODS

Parameters estimation for a system of ODEs was performed by minimizing the sum of squared residuals (SSR) function, which quantifies the difference between theoretical model predictions and GTT's experimental observations. Our proposed perturbation search and multiple-shooting methods were applied during the estimating process.

RESULTS

Based on the Ackerman's published data, we estimated the key parameters by applying R-based iterative computer programs. As a result, the theoretically simulated curves perfectly matched the experimental data points. Our model showed that the estimated parameters, computed frequency and period values, were proven a good indicator of diabetes.

CONCLUSION

The present paper introduces a computational algorithm to biomedical problems, particularly to endocrinology and metabolism fields, which involves two coupled differential equations with four parameters describing the glucose-insulin regulatory system that Ackerman proposed earlier. The enhanced approach may provide clinicians in endocrinology and metabolism field insight into the transition nature of human metabolic mechanism from normal to impaired glucose tolerance.

Economic models in type 2 diabetes

OBJECTIVE

To identify and critically appraise cost-effectiveness models developed to evaluate type 2 diabetes (T2D) treatments and to assess which types of treatment effects they capture.

RESEARCH DESIGN AND METHODS

A systematic search was performed in MEDLINE, EMBASE, Centre for Reviews and Dissemination databases at the University of York, and Health Economic Evaluation Database for the period to September 2008. The websites of Health Technology Assessment (HTA) bodies in different countries were also screened for relevant models. For each of the identified original models, details of the structure, data in- and outputs were extracted and the overall quality of the model in terms of the combination of structure, assumptions and data inputs were appraised using published criteria.

RESULTS

Seventy-eight articles and 41 HTAs reporting relevant economic evaluations were identified. There were ten models with multiple publications, and a further ten models with one associated publication. The critical review demonstrated that most had the same fundamental structure, used similar micro-simulation techniques and were based on the same key data sources. However, the process for identification of relevant data and their synthesis, and the selection of outcomes lacked transparency. The models differed according to the extent and type of interventions they evaluated and which diabetes complications and treatment-related adverse events were captured. For example, just one model incorporated changes in patient weight, despite the fact that weight gain can be a side-effect of some treatments, and weight loss a potential benefit of others.

CONCLUSIONS

Whilst many economic models exist in T2D, most share common features such as the model type. Identified shortcomings are lack of transparency in data identification and evidence synthesis as well as the selection of the modelled outcomes. Future models should aim to include all relevant treatment outcomes, whether these relate to effects on underlying diabetes and its complications or to short- or long-term side effects of treatment.

Pancreatic islet cells: a model for calcium-dependent peptide release

In mammals the concentration of blood glucose is kept close to 5 mmol∕l. Different cell types in the islet of Langerhans participate in the control of glucose homeostasis. β-cells, the most frequent type in pancreatic islets, are responsible for the synthesis, storage, and release of insulin. Insulin, released with increases in blood glucose promotes glucose uptake into the cells. In response to glucose changes, pancreatic α-, β-, and δ-cells regulate their electrical activity and Ca(2+) signals to release glucagon, insulin, and somatostatin, respectively. While all these signaling steps are stimulated in hypoglycemic conditions in α-cells, the activation of these events require higher glucose concentrations in β and also in δ-cells. The stimulus-secretion coupling process and intracellular Ca(2+) ([Ca(2+)](i)) dynamics that allow β-cells to secrete is well-accepted. Conversely, the mechanisms that regulate α- and δ-cell secretion are still under study. Here, we will consider the glucose-induced signaling mechanisms in each cell type and the mathematical models that explain Ca(2+) dynamics.

A mathematical model of brain glucose homeostasis

BACKGROUND

The physiological fact that a stable level of brain glucose is more important than that of blood glucose suggests that the ultimate goal of the glucose-insulin-glucagon (GIG) regulatory system may be homeostasis of glucose concentration in the brain rather than in the circulation.

METHODS

In order to demonstrate the relationship between brain glucose homeostasis and blood hyperglycemia in diabetes, a brain-oriented mathematical model was developed by considering the brain as the controlled object while the remaining body as the actuator. After approximating the body compartmentally, the concentration dynamics of glucose, as well as those of insulin and glucagon, are described in each compartment. The brain-endocrine crosstalk, which regulates blood glucose level for brain glucose homeostasis together with the peripheral interactions among glucose, insulin and glucagon, is modeled as a proportional feedback control of brain glucose. Correlated to the brain, long-term effects of psychological stress and effects of blood-brain-barrier (BBB) adaptation to dysglycemia on the generation of hyperglycemia are also taken into account in the model.

RESULTS

It is shown that simulation profiles obtained from the model are qualitatively or partially quantitatively consistent with clinical data, concerning the GIG regulatory system responses to bolus glucose, stepwise and continuous glucose infusion. Simulations also revealed that both stress and BBB adaptation contribute to the generation of hyperglycemia.

CONCLUSION

Simulations of the model of a healthy person under long-term severe stress demonstrated that feedback control of brain glucose concentration results in elevation of blood glucose level. In this paper, we try to suggest that hyperglycemia in diabetes may be a normal outcome of brain glucose homeostasis.

Mathematical models of diabetes progression

Few attempts have been made to model mathematically the progression of type 2 diabetes. A realistic representation of the long-term physiological adaptation to developing insulin resistance is necessary for effectively designing clinical trials and evaluating diabetes prevention or disease modification therapies. Writing a good model for diabetes progression is difficult because the long time span of the disease makes experimental verification of modeling hypotheses extremely awkward. In this context, it is of primary importance that the assumptions underlying the model equations properly reflect established physiology and that the mathematical formulation of the model give rise only to physically plausible behavior of the solutions. In the present work, a model of the pancreatic islet compensation is formulated, its physiological assumptions are presented, some fundamental qualitative characteristics of its solutions are established, the numerical values assigned to its parameters are extensively discussed (also with reference to available cross-sectional epidemiologic data), and its performance over the span of a lifetime is simulated under various conditions, including worsening insulin resistance and primary replication defects. The differences with respect to two previously proposed models of diabetes progression are highlighted, and therefore, the model is proposed as a realistic, robust description of the evolution of the compensation of the glucose-insulin system in healthy and diabetic individuals. Model simulations can be run from the authors' web page.

Mathematical models of energy homeostasis

Diabetes and obesity present a mounting global challenge. Clinicians are increasingly turning to mechanism-based mathematical models for a quantitative definition of physiological defects such as insulin resistance, glucose intolerance and elevated obesity set points, and for predictions of the likely outcomes of therapeutic interventions. However, a very large range of such models is available, making a judicious choice difficult. To better inform this choice, here we present the most important models published to date in a uniform format, discussing similarities and differences in terms of the decisions faced by modellers. We review models for glucostasis, based on the glucose-insulin feedback control loop, and consider extensions to long-term energy balance, dislipidaemia and obesity.

Use of case-based reasoning to enhance intensive management of patients on insulin pump therapy

BACKGROUND

This study was conducted to develop case-based decision support software to improve glucose control in patients with type 1 diabetes mellitus (T1DM) on insulin pump therapy. While the benefits of good glucose control are well known, achieving and maintaining good glucose control remains a difficult task. Case-based decision support software may assist by recalling past problems in glucose control and their associated therapeutic adjustments.

METHODS

Twenty patients with T1DM on insulin pumps were enrolled in a 6-week study. Subjects performed self-glucose monitoring and provided daily logs via the Internet, tracking insulin dosages, work, sleep, exercise, meals, stress, illness, menstrual cycles, infusion set changes, pump problems, hypoglycemic episodes, and other events. Subjects wore a continuous glucose monitoring system at weeks 1, 3, and 6. Clinical data were interpreted by physicians, who explained the relationship between life events and observed glucose patterns as well as treatment rationales to knowledge engineers. Knowledge engineers built a prototypical system that contained cases of problems in glucose control together with their associated solutions.

RESULTS

Twelve patients completed the study. Fifty cases of clinical problems and solutions were developed and stored in a case base. The prototypical system detected 12 distinct types of clinical problems. It displayed the stored problems that are most similar to the problems detected, and offered learned solutions as decision support to the physician.

CONCLUSIONS

This software can screen large volumes of clinical data and glucose levels from patients with T1DM, identify clinical problems, and offer solutions. It has potential application in managing all forms of diabetes.