Mathematical models of diabetes progression

A simplified longitudinal model for the development of Type 2 Diabetes Mellitus

Obesity and diabetes are a progressively more and more deleterious hallmark of modern, well fed societies. In order to study the potential impact of strategies designed to obviate the pathological consequences of detrimental lifestyles, a model for the development of Type 2 diabetes geared towards large population simulations would be useful. The present work introduces such a model, representing in simplified fashion the interplay between average glycemia, average insulinemia and functional beta-cell mass, and incorporating the effects of excess food intake or, conversely, of physical activity levels. Qualitative properties of the model are formally established and simulations are shown as examples of its use.

An extended minimal model of OGTT: estimation of α- and β-cell dysfunction, insulin resistance, and the incretin effect

Loss of insulin sensitivity, α- and β-cell dysfunction, and impairment in incretin effect have all been implicated in the pathophysiology of type 2 diabetes (T2D). Parsimonious mathematical models are useful in quantifying parameters related to the pathophysiology of T2D. Here, we extend the minimum model developed to describe the glucose-insulin-glucagon dynamics in the isoglycemic intravenous glucose infusion (IIGI) experiment to the oral glucose tolerance test (OGTT). The extended model describes glucose and hormone dynamics in OGTT including the contribution of the incretin hormones, glucose-dependent insulinotropic polypeptide (GIP), and glucagon-like peptide-1 (GLP-1), to insulin secretion. A new function describing glucose arrival from the gut is introduced. The model is fitted to OGTT data from eight individuals with T2D and eight weight-matched controls (CS) without diabetes to obtain parameters related to insulin sensitivity, β- and α-cell function. The parameters, i.e., measures of insulin sensitivity, a1, suppression of glucagon secretion, k1, magnitude of glucagon secretion, γ2, and incretin-dependent insulin secretion, γ3, were found to be different between CS and T2D with P values < 0.002, <0.017, <0.009, <0.004, respectively. A new rubric for estimating the incretin effect directly from modeling the OGTT is presented. The average incretin effect correlated well with the experimentally determined incretin effect with a Spearman rank test correlation coefficient of 0.67 (P < 0.012). The average incretin effect was found to be different between CS and T2D (P < 0.032). The developed model is shown to be effective in quantifying the factors relevant to T2D pathophysiology.NEW & NOTEWORTHY A new extended model of oral glucose tolerance test (OGTT) has been developed that includes glucagon dynamics and incretin contribution to insulin secretion. The model allows the estimation of parameters related to α- and β-cell dysfunction, insulin sensitivity, and incretin action. A new function describing the influx of glucose from the gut has been introduced. A new rubric for estimating the incretin effect directly from the OGTT experiment has been developed. The effect of glucose dose was also investigated.

Dynamical modeling the effect of glucagon-like peptide on glucose-insulin regulatory system based on mice experimental observation

As an emerging global epidemic, type 2 diabetes mellitus (T2DM) represents one of the leading causes of morbidity and mortality worldwide. Existing evidences demonstrated that glucagon-like peptide-1 (GLP-1) modulate the glucose regulatory system by enhancing the β-cell function. However, the detailed process of GLP-1 in glycaemic regulator for T2DM remains to be clarified. Thus, in this study, we propose an Institute of Cancer Research (ICR) mice high fat and cholesterol dietary experimental data-driven mathematical model to investigate the secretory effect of GLP-1 on the dynamics of glucose-insulin regulatory system. Specifically, we develop a mathematical model of GLP-1 dynamics as part of the interaction model of β-cell, insulin, and glucose dynamics. The parameter estimation and data fitting are in agreement with the data in mice experiments In addition, uncertainty quantification is performed to explore the possible factors that influence the pathways leading to the pathological state. Model analyses reveal that the high fat or high cholesterol diet stimulated GLP-1 plays an important role in the dynamics of glucose, insulin and β cells in short-term. These results show that enhanced GLP-1 may mitigate the dysregulation of glucose-insulin regulatory system via promoting the β cells function and stimulating secretion of insulin, which offers an in-depth insights into the mechanistic of hyperglycemia from dynamical approach and provide the theoretical basis for GLP-1 served as a potential clinical targeted drug for treatment of T2DM.

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 data-driven computational model for obesity-driven diabetes onset and remission through weight loss

Obesity is a major risk factor for the development of type 2 diabetes (T2D), where a sustained weight loss may result in T2D remission in individuals with obesity. To design effective and feasible intervention strategies to prevent or reverse T2D, it is imperative to study the progression of T2D and remission together. Unfortunately, this is not possible through experimental and observational studies. To address this issue, we introduce a data-driven computational model and use human data to investigate the progression of T2D with obesity and remission through weight loss on the same timeline. We identify thresholds for the emergence of T2D and necessary conditions for remission. We explain why remission is only possible within a window of opportunity and the way that window depends on the progression history of T2D, individual's metabolic state, and calorie restrictions. These findings can help to optimize therapeutic intervention strategies for T2D prevention or treatment.

Modeling the progression of Type 2 diabetes with underlying obesity

Environmentally induced or epigenetic-related beta-cell dysfunction and insulin resistance play a critical role in the progression to diabetes. We developed a mathematical modeling framework capable of studying the progression to diabetes incorporating various diabetogenic factors. Considering the heightened risk of beta-cell defects induced by obesity, we focused on the obesity-diabetes model to further investigate the influence of obesity on beta-cell function and glucose regulation. The model characterizes individualized glucose and insulin dynamics over the span of a lifetime. We then fit the model to the longitudinal data of the Pima Indian population, which captures both the fluctuations and long-term trends of glucose levels. As predicted, controlling or eradicating the obesity-related factor can alleviate, postpone, or even reverse diabetes. Furthermore, our results reveal that distinct abnormalities of beta-cell function and levels of insulin resistance among individuals contribute to different risks of diabetes. This study may encourage precise interventions to prevent diabetes and facilitate individualized patient treatment.

A glucose-insulin-glucagon coupled model of the isoglycemic intravenous glucose infusion experiment

Type 2 diabetes (T2D) is a pathophysiology that is characterized by insulin resistance, beta- and alpha-cell dysfunction. Mathematical models of various glucose challenge experiments have been developed to quantify the contribution of insulin and beta-cell dysfunction to the pathophysiology of T2D. There is a need for effective extended models that also capture the impact of alpha-cell dysregulation on T2D. In this paper a delay differential equation-based model is developed to describe the coupled glucose-insulin-glucagon dynamics in the isoglycemic intravenous glucose infusion (IIGI) experiment. As the glucose profile in IIGI is tailored to match that of a corresponding oral glucose tolerance test (OGTT), it provides a perfect method for studying hormone responses that are in the normal physiological domain and without the confounding effect of incretins and other gut mediated factors. The model was fit to IIGI data from individuals with and without T2D. Parameters related to glucagon action, suppression, and secretion as well as measures of insulin sensitivity, and glucose stimulated response were determined simultaneously. Significant impairment in glucose dependent glucagon suppression was observed in patients with T2D (duration of T2D: 8 (6–36) months) relative to weight matched control subjects (CS) without diabetes (k1 (mM)−1: 0.16 ± 0.015 (T2D, n = 7); 0.26 ± 0.047 (CS, n = 7)). Insulin action was significantly lower in patients with T2D (a1 (10 pM min)−1: 0.000084 ± 0.0000075 (T2D); 0.00052 ± 0.00015 (CS)) and the Hill coefficient in the equation for glucose dependent insulin response was found to be significantly different in T2D patients relative to CS (h: 1.4 ± 0.15; 1.9 ± 0.14). Trends in parameters with respect to fasting plasma glucose, HbA1c and 2-h glucose values are also presented. Significantly, a negative linear relationship is observed between the glucagon suppression parameter, k1, and the three markers for diabetes and is thus indicative of the role of glucagon in exacerbating the pathophysiology of diabetes (Spearman Rank Correlation: (n = 12; (−0.79, 0.002), (−0.73,.007), (−0.86,.0003)) respectively).

Dynamics of thyroid diseases and thyroid-axis gland masses

Thyroid disorders are common and often require lifelong hormone replacement. Treating thyroid disorders involves a fascinating and troublesome delay, in which it takes many weeks for serum thyroid‐stimulating hormone (TSH) concentration to normalize after thyroid hormones return to normal. This delay challenges attempts to stabilize thyroid hormones in millions of patients. Despite its importance, the physiological mechanism for the delay is unclear. Here, we present data on hormone delays from Israeli medical records spanning 46 million life‐years and develop a mathematical model for dynamic compensation in the thyroid axis, which explains the delays. The delays are due to a feedback mechanism in which peripheral thyroid hormones and TSH control the growth of the thyroid and pituitary glands; enlarged or atrophied glands take many weeks to recover upon treatment due to the slow turnover of the tissues. The model explains why thyroid disorders such as Hashimoto's thyroiditis and Graves' disease have both subclinical and clinical states and explains the complex inverse relation between TSH and thyroid hormones. The present model may guide approaches to dynamically adjust the treatment of thyroid disorders.

Ultimate Bounds for a Diabetes Mathematical Model Considering Glucose Homeostasis

This paper deals with a recently reported mathematical model formulated by five first-order ordinary differential equations that describe glucoregulatory dynamics. As main contributions, we found a localization domain with all compact invariant sets; we settled on sufficient conditions for the existence of a bounded positively-invariant domain. We applied the localization of compact invariant sets and Lyapunov’s direct methods to obtain these results. The localization results establish the maximum cell concentration for each variable. On the other hand, Lyapunov’s direct method provides sufficient conditions for the bounded positively-invariant domain to attract all trajectories with non-negative initial conditions. Further, we illustrate our analytical results with numerical simulations. Overall, our results are valuable information for a better understanding of this disease. Bounds and attractive domains are crucial tools to design practical applications such as insulin controllers or in silico experiments. In addition, the model can be used to understand the long-term dynamics of the system.

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.

The progression of secondary diabetes: A review of modeling studies

Mathematical modeling has provided quantitative information consistent with experimental data, greatly improving our understanding of the progression of type 1 and type 2 diabetes. However, diabetes is a complex metabolic disease and has been found to be involved in crosstalk interactions with diverse endocrine diseases. Mathematical models have also been developed to investigate the quantitative impact of various hormonal disorders on glucose imbalance, advancing the precision treatment for secondary diabetes. Here we review the models established for the study of dysglycemia induced by hormonal disorders, such as excessive glucocorticoids, epinephrine, and growth hormone. To investigate the influence of hyperthyroidism on the glucose regulatory system, we also propose a hyperthyroid-diabetes progression model. Model simulations indicate that timely thyroid treatment can halt the progression of hyperglycemia and prevent beta-cell failure. This highlights the diagnosis of hormonal disorders, together withblood sugar tests, as significant measures for the early diagnosis and treatment of diabetes. The work recapitulates updated biological research on the interactions between the glucose regulatory system and other endocrine axes. Further mathematical modeling of secondary diabetes is desired to promote the quantitative study of the disease and the development of individualized diabetic therapies.

Sparse System Identification of Leptin Dynamics in Women With Obesity

The prevalence of obesity is increasing around the world at an alarming rate. The interplay of the hormone leptin with the hypothalamus-pituitary-adrenal axis plays an important role in regulating energy balance, thereby contributing to obesity. This study presents a mathematical model, which describes hormonal behavior leading to an energy abnormal equilibrium that contributes to obesity. To this end, we analyze the behavior of two neuroendocrine hormones, leptin and cortisol, in a cohort of women with obesity, with simplified minimal state-space modeling. Using a system theoretic approach, coordinate descent method, and sparse recovery, we deconvolved the serum leptin-cortisol levels. Accordingly, we estimate the secretion patterns, timings, amplitudes, number of underlying pulses, infusion, and clearance rates of hormones in eighteen premenopausal women with obesity. Our results show that minimal state-space model was able to successfully capture the leptin and cortisol sparse dynamics with the multiple correlation coefficients greater than 0.83 and 0.87, respectively. Furthermore, the Granger causality test demonstrated a negative prospective predictive relationship between leptin and cortisol, 14 of 18 women. These results indicate that increases in cortisol are prospectively associated with reductions in leptin and vice versa, suggesting a bidirectional negative inhibitory relationship. As dysregulation of leptin may result in an abnormality in satiety and thereby associated to obesity, the investigation of leptin-cortisol sparse dynamics may offer a better diagnostic methodology to improve better treatments plans for individuals with obesity.

CKD subpopulations defined by risk-factors: A longitudinal analysis of electronic health records

Chronic kidney disease (CKD) is a progressive disease that evades early detection and is associated with various comorbidities. Although clinical comprehension and control of these comorbidities is crucial for CKD management, complex pathophysiological interactions and feedback loops make this a formidable task. We have developed a hybrid semimechanistic modeling methodology to investigate CKD progression. The model is represented as a system of ordinary differential equations with embedded neural networks and takes into account complex disease progression pathways, feedback loops, and effects of 53 medications to generate time trajectories of eight clinical biomarkers that capture CKD progression due to various risk factors. The model was applied to real world data of US patients with CKD to map the available longitudinal information onto a set of time‐invariant patient‐specific parameters with a clear biological interpretation. These parameters describing individual patients were used to segment the cohort using a clustering approach. Model‐based simulations were conducted to investigate cluster‐specific treatment strategies. The model was able to reliably reproduce the variability in biomarkers across the cohort. The clustering procedure segmented the cohort into five subpopulations – four with enhanced sensitivity to a specific risk factor (hypertension, hyperlipidemia, hyperglycemia, or impaired kidney) and one that is largely insensitive to any of the risk factors. Simulation studies were used to identify patient‐specific strategies to restrain or prevent CKD progression through management of specific risk factors. The semimechanistic model enables identification of disease progression phenotypes using longitudinal data that aid in prioritizing treatment strategies at individual patient level.

A new model for the HPA axis explains dysregulation of stress hormones on the timescale of weeks

Stress activates a complex network of hormones known as the hypothalamic-pituitary-adrenal (HPA) axis. The HPA axis is dysregulated in chronic stress and psychiatric disorders, but the origin of this dysregulation is unclear and cannot be explained by current HPA models. To address this, we developed a mathematical model for the HPA axis that incorporates changes in the total functional mass of the HPA hormone-secreting glands. The mass changes are caused by HPA hormones which act as growth factors for the glands in the axis. We find that the HPA axis shows the property of dynamical compensation, where gland masses adjust over weeks to buffer variation in physiological parameters. These mass changes explain the experimental findings on dysregulation of cortisol and ACTH dynamics in alcoholism, anorexia, and postpartum. Dysregulation occurs for a wide range of parameters and is exacerbated by impaired glucocorticoid receptor (GR) feedback, providing an explanation for the implication of GR in mood disorders. These findings suggest that gland-mass dynamics may play an important role in the pathophysiology of stress-related disorders.

Bayesian analysis of Glucose dynamics during the Oral Glucose Tolerance Test (OGTT)

This paper proposes a model that considers the action and timing of insulin and glucagon in glucose homeostasis after an oral stimulus. We use the Bayesian paradigm to infer kinetic rates, namely insulin and glucagon secretion, gastrointestinal emptying, and basal glucose concentration in blood. We identify two insulin scores related to glucose concentration in both blood and the gastrointestinal tract. The scores allow us to suggest a classification for individuals with impaired insulin sensitivity.

A mathematical model of food intake

The metabolic, hormonal and psychological determinants of the feeding behavior in humans are numerous and complex. A plausible model of the initiation, continuation and cessation of meals taking into account the most relevant such determinants would be very useful in simulating food intake over hours to days, thus providing input into existing models of nutrient absorption and metabolism. In the present work, a meal model is proposed, incorporating stomach distension, glycemic variations, ghrelin dynamics, cultural habits and influences on the initiation and continuation of meals, reflecting a combination of hedonic and appetite components. Given a set of parameter values (portraying a single subject), the timing and size of meals are stochastic. The model parameters are calibrated so as to reflect established medical knowledge on data of food intake from the National Health and Nutrition Examination Survey (NHANES) database during years 2015 and 2016.

Mathematical Modeling for the Physiological and Clinical Investigation of Glucose Homeostasis and Diabetes

Mathematical modeling in the field of glucose metabolism has a longstanding tradition. The use of models is motivated by several reasons. Models have been used for calculating parameters of physiological interest from experimental data indirectly, to provide an unambiguous quantitative representation of pathophysiological mechanisms, to determine indices of clinical usefulness from simple experimental tests. With the growing societal impact of type 2 diabetes, which involves the disturbance of the glucose homeostasis system, development and use of models in this area have increased. Following the approaches of physiological and clinical investigation, the focus of the models has spanned from representations of whole body processes to those of cells, i.e., from in vivo to in vitro research. Model-based approaches for linking in vivo to in vitro research have been proposed, as well as multiscale models merging the two areas. The success and impact of models has been variable. Two kinds of models have received remarkable interest: those widely used in clinical applications, e.g., for the assessment of insulin sensitivity and β-cell function and some models representing specific aspects of the glucose homeostasis system, which have become iconic for their efficacy in describing clearly and compactly key physiological processes, such as insulin secretion from the pancreatic β cells. Models are inevitably simplified and approximate representations of a physiological system. Key to their success is an appropriate balance between adherence to reality, comprehensibility, interpretative value and practical usefulness. This has been achieved with a variety of approaches. Although many models concerning the glucose homeostasis system have been proposed, research in this area still needs to address numerous issues and tackle new opportunities. The mathematical representation of the glucose homeostasis processes is only partial, also because some mechanisms are still only partially understood. For in vitro research, mathematical models still need to develop their potential. This review illustrates the problems, approaches and contribution of mathematical modeling to the physiological and clinical investigation of glucose homeostasis and diabetes, focusing on the most relevant and stimulating models.

Type 2 diabetes progression: A regulatory network approach

In order to elucidate central elements underlying type 2 diabetes, we constructed a regulatory network model involving 37 components (molecules, receptors, processes, etc.) associated to signaling pathways of pancreatic beta-cells. In a first approximation, the network topology was described by Boolean rules whose interacting dynamics predicted stationary patterns broadly classified as health, metabolic syndrome, and diabetes stages. A subsequent approximation based on a continuous logic analysis allowed us to characterize the progression of the disease as transitions between these states associated to alterations of cell homeostasis due to exhaustion or exacerbation of specific regulatory signals. The method allowed the identification of key transcription factors involved in metabolic stress as essential for the progression of the disease. Integration of the present analysis with existent mathematical models designed to yield accurate account of experimental data in human or animal essays leads to reliable predictions for beta-cell mass, insulinemia, glycemia, and glycosylated hemoglobin in diabetic fatty rats.

Type 2 diabetes: one disease, many pathways

Diabetes is a chronic, progressive disease that calls for longitudinal data and analysis. We introduce a longitudinal mathematical model that is capable of representing the metabolic state of an individual at any point in time during their progression from normal glucose tolerance to type 2 diabetes (T2D) over a period of years. As an application of the model, we account for the diversity of pathways typically followed, focusing on two extreme alternatives, one that goes through impaired fasting glucose (IFG) first and one that goes through impaired glucose tolerance (IGT) first. These two pathways are widely recognized to stem from distinct metabolic abnormalities in hepatic glucose production and peripheral glucose uptake, respectively. We confirm this but go beyond to show that IFG and IGT lie on a continuum ranging from high hepatic insulin resistance and low peripheral insulin resistance to low hepatic resistance and high peripheral resistance. We show that IFG generally incurs IGT and IGT generally incurs IFG on the way to T2D, highlighting the difference between innate and acquired defects and the need to assess patients early to determine their underlying primary impairment and appropriately target therapy. We also consider other mechanisms, showing that IFG can result from impaired insulin secretion, that non-insulin-dependent glucose uptake can also mediate or interact with these pathways, and that impaired incretin signaling can accelerate T2D progression. We consider whether hyperinsulinemia can cause insulin resistance in addition to being a response to it and suggest that this is a minor effect.

'Turning the tide' on hyperglycemia in pregnancy: insights from multiscale dynamic simulation modeling

INTRODUCTION

Hyperglycemia in pregnancy (HIP, including gestational diabetes and pre-existing type 1 and type 2 diabetes) is increasing, with associated risks to the health of women and their babies. Strategies to manage and prevent this condition are contested. Dynamic simulation models (DSM) can test policy and program scenarios before implementation in the real world. This paper reports the development and use of an advanced DSM exploring the impact of maternal weight status interventions on incidence of HIP.

METHODS

A consortium of experts collaboratively developed a hybrid DSM of HIP, comprising system dynamics, agent-based and discrete event model components. The structure and parameterization drew on a range of evidence and data sources. Scenarios comparing population-level and targeted prevention interventions were simulated from 2018 to identify the intervention combination that would deliver the greatest impact.

RESULTS

Population interventions promoting weight loss in early adulthood were found to be effective, reducing the population incidence of HIP by 17.3% by 2030 (baseline ('business as usual' scenario)=16.1%, 95% CI 15.8 to 16.4; population intervention=13.3%, 95% CI 13.0 to 13.6), more than targeted prepregnancy (5.2% reduction; incidence=15.3%, 95% CI 15.0 to 15.6) and interpregnancy (4.2% reduction; incidence=15.5%, 95% CI 15.2 to 15.8) interventions. Combining targeted interventions for high-risk groups with population interventions promoting healthy weight was most effective in reducing HIP incidence (28.8% reduction by 2030; incidence=11.5, 95% CI 11.2 to 11.8). Scenarios exploring the effect of childhood weight status on entry to adulthood demonstrated significant impact in the selected outcome measure for glycemic regulation, insulin sensitivity in the short term and HIP in the long term.

DISCUSSION

Population-level weight reduction interventions will be necessary to 'turn the tide' on HIP. Weight reduction interventions targeting high-risk individuals, while beneficial for those individuals, did not significantly impact forecasted HIP incidence rates. The importance of maintaining interventions promoting healthy weight in childhood was demonstrated.

Mathematical model of diabetes and lipid metabolism linked to diet, leptin sensitivity, insulin sensitivity and VLDLTG clearance predicts paths to health and type II diabetes

An original model of diabetes linked to carbohydrate and lipid intake is presented and applied to predict the effects on biomarkers of various diets. The variables (biomarkers) are concentrations of fasting plasma glucose, insulin, leptin, glucagon, non-esterified fatty acids (NEFA) and very low density lipoprotein triglyceride (VLDLTG), as well as muscle lipids, hepatic lipids, pancreatic lipids, fat mass and mass of β-cells. The model predicts isocaloric high carbohydrate low fat (HCLF) diet and low carbohydrate high fat (LCHF) diet trajectories to health which vary in fat mass by at most a few kilograms at steady state. The LCHF trajectories to health are faster than isocaloric HCLF trajectories with respect to fat mass loss, although these trajectories may be slower initially if parameters are adjusting from HCLF values. On LC diets, leptin sensitivity and VLDLTG clearance are thought to increase. Increasing leptin sensitivity and VLDLTG clearance is predicted to lower lipids including fat mass and VLDLTG. The model predicts that changes in VLDLTG due to a change in diet happen rapidly, approaching steady state values after a few weeks, reflecting leptin sensitivity and VLDLTG clearance which are much harder to measure. The model predicts that if only insulin sensitivity increases on a LC diet, steady state fat mass would increase slightly. If leptin and insulin sensitivities increase concurrently, the combined effect could be a decrease in fat mass, consistent with the fact that increasing insulin sensitivity is often associated with fat mass loss in trials. The model predicts trajectories to fat type II diabetes with hypertriglyceridemia due to high carbohydrate moderate fat diets, on which insulin rises before falling, as ectopic fat deposits increase; made fatter and more diabetic by higher lipid consumption. It predicts trajectories to non-diabetic states with raised fat mass, VLDLTG and muscle, hepatic and pancreatic lipids due to moderate carbohydrate high fat diets. The model predicts paths to lean type II diabetes, on a diet of moderate energy but low β-cell replication rate or high death rate.

A novel fast-slow model of diabetes progression: Insights into mechanisms of response to the interventions in the Diabetes Prevention Program

Several models for the long-term development of T2DM already exist, focusing on the dynamics of the interaction between glycemia, insulinemia and β-cell mass. Current models consider representative (fasting or daily average) glycemia and insulinemia as characterizing the compensation state of the subject at some instant in slow time. This implies that only these representative levels can be followed through time and that the role of fast glycemic oscillations is neglected. An improved model (DPM15) for the long-term progression of T2DM is proposed, introducing separate peripheral and hepatic (liver and kidney) insulin actions. The DPM15 model no longer uses near-equilibrium approximation to separate fast and slow time scales, but rather describes, at each step in slow time, a complete day in the life of the virtual subject in fast time. The model can thus represent both fasting and postprandial glycemic levels and describe the effect of interventions acting on insulin-enhanced tissue glucose disposal or on insulin-inhibited hepatic glucose output, as well as on insulin secretion and β-cell replicating ability. The model can simulate long-term variations of commonly used clinical indices (HOMA-B, HOMA-IR, insulinogenic index) as well as of Oral Glucose Tolerance or Euglycemic Hyperinsulinemic Clamp test results. The model has been calibrated against observational data from the Diabetes Prevention Program study: it shows good adaptation to observations as a function of very plausible values of the parameters describing the effect of such interventions as Placebo, Intensive LifeStyle and Metformin administration.

A Mathematical Model for DC Vaccine Treatment of Type I Diabetes

Type I diabetes (T1D) is an autoimmune disease that can be managed, but for which there is currently no cure. Recent discoveries, particularly in mouse models, indicate that targeted modulation of the immune response has the potential to move an individual from a diabetic to a long-term, if not permanent, healthy state. In this paper we develop a single compartment mathematical model that captures the dynamics of dendritic cells (DC and tDC), T cells (effector and regulatory), and macrophages in the development of type I diabetes. The model supports the hypothesis that differences in macrophage clearance rates play a significant role in determining whether or not an individual is likely to become diabetic subsequent to a significant immune challenge. With this model we are able to explore the effects of strengthening the anti-inflammatory component of the immune system in a vulnerable individual. Simulations indicate that there are windows of opportunity in which treatment intervention is more likely to be beneficial in protecting an individual from entering a diabetic state. This model framework can be used as a foundation for modeling future T1D treatments as they are developed.

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 fasting glucose-insulin dynamics from sparse data

With the fast growth of diabetes prevalence, the disease is now considered an epidemic. Diabetes is characterized by elevated glucose levels, that may be treated with insulin. Tight control of glucose is essential for prevention of complications and patients' well-being. In this paper we model the fasting glucose-insulin dynamics in type 2 diabetes, aiming at controlling the glucose level. Relevant clinical data are typically sparse and have a sampling period much greater than the fast dynamics in the glucose-insulin dynamics in humans. We adapt a physiological model such that important slow non-linear dynamics are identifiable and test the resulting model on deterministic simulated data and sparse, slow sampled clinical data.

A long-term mechanistic computational model of physiological factors driving the onset of type 2 diabetes in an individual

A computational model of the physiological mechanisms driving an individual's health towards onset of type 2 diabetes (T2D) is described, calibrated and validated using data from the Diabetes Prevention Program (DPP). The objective of this model is to quantify the factors that can be used for prevention of T2D. The model is energy and mass balanced and continuously simulates trajectories of variables including body weight components, fasting plasma glucose, insulin, and glycosylated hemoglobin among others on the time-scale of years. Modeled mechanisms include dynamic representations of intracellular insulin resistance, pancreatic beta-cell insulin production, oxidation of macronutrients, ketogenesis, effects of inflammation and reactive oxygen species, and conversion between stored and activated metabolic species, with body-weight connected to mass and energy balance. The model was calibrated to 331 placebo and 315 lifestyle-intervention DPP subjects, and one year forecasts of all individuals were generated. Predicted population mean errors were less than or of the same magnitude as clinical measurement error; mean forecast errors for weight and HbA1c were ~5%, supporting predictive capabilities of the model. Validation of lifestyle-intervention prediction is demonstrated by synthetically imposing diet and physical activity changes on DPP placebo subjects. Using subject level parameters, comparisons were made between exogenous and endogenous characteristics of subjects who progressed toward T2D (HbA1c > 6.5) over the course of the DPP study to those who did not. The comparison revealed significant differences in diets and pancreatic sensitivity to hyperglycemia but not in propensity to develop insulin resistance. A computational experiment was performed to explore relative contributions of exogenous versus endogenous factors between these groups. Translational uses to applications in public health and personalized healthcare are discussed.

A closed-loop multi-level model of glucose homeostasis

BACKGROUND

The pathophysiologic processes underlying the regulation of glucose homeostasis are considerably complex at both cellular and systemic level. A comprehensive and structured specification for the several layers of abstraction of glucose metabolism is often elusive, an issue currently solvable with the hierarchical description provided by multi-level models. In this study we propose a multi-level closed-loop model of whole-body glucose homeostasis, coupled with the molecular specifications of the insulin signaling cascade in adipocytes, under the experimental conditions of normal glucose regulation and type 2 diabetes.

METHODOLOGY/PRINCIPAL FINDINGS

The ordinary differential equations of the model, describing the dynamics of glucose and key regulatory hormones and their reciprocal interactions among gut, liver, muscle and adipose tissue, were designed for being embedded in a modular, hierarchical structure. The closed-loop model structure allowed self-sustained simulations to represent an ideal in silico subject that adjusts its own metabolism to the fasting and feeding states, depending on the hormonal context and invariant to circadian fluctuations. The cellular level of the model provided a seamless dynamic description of the molecular mechanisms downstream the insulin receptor in the adipocytes by accounting for variations in the surrounding metabolic context.

CONCLUSIONS/SIGNIFICANCE

The combination of a multi-level and closed-loop modeling approach provided a fair dynamic description of the core determinants of glucose homeostasis at both cellular and systemic scales. This model architecture is intrinsically open to incorporate supplementary layers of specifications describing further individual components influencing glucose metabolism.

Biphasic response as a mechanism against mutant takeover in tissue homeostasis circuits

Tissues use feedback circuits in which cells send signals to each other to control their growth and survival. We show that such feedback circuits are inherently unstable to mutants that misread the signal level: Mutants have a growth advantage to take over the tissue, and cannot be eliminated by known cell-intrinsic mechanisms. To resolve this, we propose that tissues have biphasic responses in and the signal is toxic at both high and low levels, such as glucotoxicity of beta cells, excitotoxicity in neurons, and toxicity of growth factors to T cells. This gives most of these mutants a frequency-dependent selective disadvantage, which leads to their elimination. However, the biphasic mechanisms create a new unstable fixed point in the feedback circuit beyond which runaway processes can occur, leading to risk of diseases such as diabetes and neurodegenerative disease. Hence, glucotoxicity, which is a dangerous cause of diabetes, may have a protective anti-mutant effect. Biphasic responses in tissues may provide an evolutionary stable strategy that avoids invasion by commonly occurring mutants, but at the same time cause vulnerability to disease.

Dynamical compensation in physiological circuits

Biological systems can maintain constant steady-state output despite variation in biochemical parameters, a property known as exact adaptation. Exact adaptation is achieved using integral feedback, an engineering strategy that ensures that the output of a system robustly tracks its desired value. However, it is unclear how physiological circuits also keep their output dynamics precise-including the amplitude and response time to a changing input. Such robustness is crucial for endocrine and neuronal homeostatic circuits because they need to provide a precise dynamic response in the face of wide variation in the physiological parameters of their target tissues; how such circuits compensate their dynamics for unavoidable natural fluctuations in parameters is unknown. Here, we present a design principle that provides the desired robustness, which we call dynamical compensation (DC). We present a class of circuits that show DC by means of a nonlinear feedback loop in which the regulated variable controls the functional mass of the controlling endocrine or neuronal tissue. This mechanism applies to the control of blood glucose by insulin and explains several experimental observations on insulin resistance. We provide evidence that this mechanism may also explain compensation and organ size control in other physiological circuits.

Requirements for multi-level systems pharmacology models to reach end-usage: the case of type 2 diabetes

We are currently in the middle of a major shift in biomedical research: unprecedented and rapidly growing amounts of data may be obtained today, from in vitro, in vivo and clinical studies, at molecular, physiological and clinical levels. To make use of these large-scale, multi-level datasets, corresponding multi-level mathematical models are needed, i.e. models that simultaneously capture multiple layers of the biological, physiological and disease-level organization (also referred to as quantitative systems pharmacology-QSP-models). However, today's multi-level models are not yet embedded in end-usage applications, neither in drug research and development nor in the clinic. Given the expectations and claims made historically, this seemingly slow adoption may seem surprising. Therefore, we herein consider a specific example-type 2 diabetes-and critically review the current status and identify key remaining steps for these models to become mainstream in the future. This overview reveals how, today, we may use models to ask scientific questions concerning, e.g., the cellular origin of insulin resistance, and how this translates to the whole-body level and short-term meal responses. However, before these multi-level models can become truly useful, they need to be linked with the capabilities of other important existing models, in order to make them 'personalized' (e.g. specific to certain patient phenotypes) and capable of describing long-term disease progression. To be useful in drug development, it is also critical that the developed models and their underlying data and assumptions are easily accessible. For clinical end-usage, in addition, model links to decision-support systems combined with the engagement of other disciplines are needed to create user-friendly and cost-efficient software packages.

A Mathematical Model of the Pathogenesis, Prevention, and Reversal of Type 2 Diabetes

Type 2 diabetes (T2D) is generally thought to result from the combination of 2 metabolic defects, insulin resistance, which increases the level of insulin required to maintain glucose within the normal range, and failure of insulin-secreting pancreatic β-cells to compensate for the increased demand. We build on a mathematical model pioneered by Topp and colleagues to elucidate how compensation succeeds or fails. Their model added a layer of slow negative feedback to the classic insulin-glucose loop in the form of a slow, glucose-dependent birth and death law governing β-cell mass. We add to that model regulation of 2 aspects of β-cell function on intermediate time scales. The model quantifies the relative contributions of insulin action and insulin secretion defects to T2D and explains why prevention is easier than cure. The latter is a consequence of a threshold separating the normoglycemic and diabetic states (bistability), which also underlies the success of bariatric surgery and acute caloric restriction in rapidly reversing T2D. The threshold concept gives new insight into "Starling's Law of the Pancreas," whereby insulin secretion is higher for prediabetics and early diabetics than for normal individuals.

A glycemia-structured population model

Structured models are population models in which the individuals are characterized with respect to the value of some variable of interest, called the structure variable. In the present paper, we propose a glycemia-structured population model, based on a linear partial differential equation with variable coefficients. The model is characterized by three rate functions: a new-adult population glycemic profile, a glycemia-dependent mortality rate and a glycemia-dependent average worsening rate. First, we formally analyze some properties of the solution, the transient behavior and the equilibrium distribution. Then, we identify the key parameters and functions of the model from real-life data and we hypothesize some plausible modifications of the rate functions to obtain a more beneficial steady-state behavior. The interest of the model is that, while it summarizes the evolution of diabetes in the population in a completely different way with respect to previously published Monte Carlo aggregations of individual-based models, it does appear to offer a good approximation of observed reality and of the features expected in the clinical setting. The model can offer insights in pharmaceutical research and be used to assess possible public health intervention strategies.

Insulin resistance or hypersecretion? The βIG picture revisited

Mathematical models of glucose, insulin and pancreatic beta-cell mass dynamics are essential to our understanding of the physiological basis of the development of type 2 diabetes. The classical view of diabetes is that the disease develops due to insulin insufficiency. An alternate viewpoint that has recently staged a revival is that diabetogenesis is a hypersecretion disorder. A prominent model of diabetes progression is the βIG model due to Topp and coworkers. Here we study two new variants of the Topp model, which we name "Topp-IR" and "Topp-HS". Topp-IR is a model in which increasing insulin resistance is sufficient to drive a system away from health towards hyperglycemia. Topp-HS describes the hypersecretion model in mathematical terms. We thus show that the hypersecretion hypothesis is theoretically sound, and is therefore a potential route to diabetes. On the basis of insights derived from modeling, we clarify several subtleties of that argument, including postulating a central role for transient insulin peaks in driving insulin resistance.

Possible role of interleukin-1β in type 2 diabetes onset and implications for anti-inflammatory therapy strategies

Increasing evidence of a role of chronic inflammation in type 2 diabetes progression has led to the development of therapies targeting the immune system. We develop a model of interleukin-1β dynamics in order to explain principles of disease onset. The parameters in the model are derived from in vitro experiments and patient data. In the framework of this model, an IL-1β switch is sufficient and necessary to account for type 2 diabetes onset. The model suggests that treatments targeting glucose bear the potential of stopping progression from pre-diabetes to overt type 2 diabetes. However, once in overt type 2 diabetes, these treatments have to be complemented by adjuvant anti-inflammatory therapies in order to stop or decelerate disease progression. Moreover, the model suggests that while glucose-lowering therapy needs to be continued all the way, dose and duration of the anti-inflammatory therapy needs to be specifically controlled. The model proposes a framework for the discussion of clinical trial outcomes.

Effects of IL-1β-Blocking Therapies in Type 2 Diabetes Mellitus: A Quantitative Systems Pharmacology Modeling Approach to Explore Underlying Mechanisms

Recent clinical studies suggest sustained treatment effects of interleukin-1β (IL-1β)–blocking therapies in type 2 diabetes mellitus. The underlying mechanisms of these effects, however, remain underexplored. Using a quantitative systems pharmacology modeling approach, we combined ex vivo data of IL-1β effects on β-cell function and turnover with a disease progression model of the long-term interactions between insulin, glucose, and β-cell mass in type 2 diabetes mellitus. We then simulated treatment effects of the IL-1 receptor antagonist anakinra. The result was a substantial and partly sustained symptomatic improvement in β-cell function, and hence also in HbA1C, fasting plasma glucose, and proinsulin–insulin ratio, and a small increase in β-cell mass. We propose that improved β-cell function, rather than mass, is likely to explain the main IL-1β–blocking effects seen in current clinical data, but that improved β-cell mass might result in disease-modifying effects not clearly distinguishable until >1 year after treatment.

Long-term models of oxidative stress and mitochondrial damage in insulin resistance progression

Insulin resistance, characterized by a reduced cellular response to insulin, is a major factor in type 2 diabetes pathogenesis, with a complex etiology consisting of a combination of environmental and genetic factors. Oxidative stress, which develops through an accumulation of toxic reactive oxygen species generated by mitochondria, is believed to contribute to insulin resistance in certain tissues. We develop mathematical models of feedback between reactive oxygen species production and dysfunction in mitochondria to provide insight into the role of oxidative stress in insulin resistance. Our models indicate that oxidative stress generated by glucose overload accelerates irreversible mitochondrial dysfunction. These models provide a foundation for understanding the long-term progression of insulin resistance and type 2 diabetes.

A drug and disease model for lixisenatide, a GLP-1 receptor agonist in type 2 diabetes

Incretin hormone analogs such as glucagon-like peptide-1 (GLP-1) receptor agonists have emerged as promising new options for the treatment of type 2 diabetes mellitus (T2DM), targeting several of its pathophysiological traits, including reduced insulin sensitivity, inadequate insulin secretion, and loss of β-cell mass (BCM). This article describes the semi-mechanistic modeling of lixisenatide dose-response over time using fasting plasma glucose (FPG), fasting serum insulin (FSI) and glycated hemoglobin (HbA1c) data from two Phase II and four Phase III clinical trials, for a total of 2470 T2DM patients. Previously published models for FPG, FSI, and BCM as well as HbA1c were adapted and expanded to describe the available data. The model incorporated aspects describing disease progression, standard-of-care, FPG-dependent and -independent HbA1c synthesis, and covariate effects of body size, race, and sex. The final model described lixisenatide effects on β-cell responsiveness, insulin sensitivity and FPG-independent HbA1c synthesis, was able to describe the observed FPG, FSI, and HbA1c data accurately, and was successful in predicting data from an unseen Phase III clinical study.

A conceptual review on systems biology in health and diseases: from biological networks to modern therapeutics

Human physiology is an ensemble of various biological processes spanning from intracellular molecular interactions to the whole body phenotypic response. Systems biology endures to decipher these multi-scale biological networks and bridge the link between genotype to phenotype. The structure and dynamic properties of these networks are responsible for controlling and deciding the phenotypic state of a cell. Several cells and various tissues coordinate together to generate an organ level response which further regulates the ultimate physiological state. The overall network embeds a hierarchical regulatory structure, which when unusually perturbed can lead to undesirable physiological state termed as disease. Here, we treat a disease diagnosis problem analogous to a fault diagnosis problem in engineering systems. Accordingly we review the application of engineering methodologies to address human diseases from systems biological perspective. The review highlights potential networks and modeling approaches used for analyzing human diseases. The application of such analysis is illustrated in the case of cancer and diabetes. We put forth a concept of cell-to-human framework comprising of five modules (data mining, networking, modeling, experimental and validation) for addressing human physiology and diseases based on a paradigm of system level analysis. The review overtly emphasizes on the importance of multi-scale biological networks and subsequent modeling and analysis for drug target identification and designing efficient therapies.

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.

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.

Evaluation of a mathematical model of diabetes progression against observations in the Diabetes Prevention Program

The seminal publication of the Diabetes Prevention Program (DPP) results in 2002 has provided insight into the impact of major therapies on the development of diabetes over a time span of a few years. In the present work, the publicly available DPP data set is used to calibrate and evaluate a recently developed mechanistic mathematical model for the long-term development of diabetes to assess the model's ability to predict the natural history of disease progression and the effectiveness of preventive interventions. A general population is generated from which virtual subject samples corresponding to the DPP enrollment criteria are selected. The model is able to reproduce with good fidelity the observed time courses of both diabetes incidence and average glycemia, under realistic hypotheses on evolution of disease and efficacy of the studied therapies, for all treatment arms. Model-based simulations of the long-term evolution of the disease are consistent with the transient benefits observed with conventional therapies and with promising effects of radical improvement of insulin sensitivity (as by metabolic surgery) or of β-cell protection. The mechanistic diabetes progression model provides a credible tool by which long-term implications of antidiabetic interventions can be evaluated.

Modeling diabetes disease progression and salsalate intervention in Goto-Kakizaki rats

Type 2 diabetes mellitus (T2DM) arises owing to insulin resistance and β-cell dysfunction. Chronic inflammation is widely identified as a cause of T2DM. The Goto-Kakizaki (GK) rat is a spontaneous rodent model for T2DM with chronic inflammation. The purpose of this study was to characterize diabetes progression in GK rats and evaluate the potential role of the anti-inflammatory agent salsalate. The GK rats were divided into control groups (n = 6) and salsalate treatment groups (n = 6), which were fed a salsalate-containing diet from 5 to 21 weeks of age. Blood glucose and salicylate concentrations were measured once a week. Glucose concentrations showed a biphasic increase in which the first phase started at approximately 5 weeks, resulting in an increase by 15 to 25 mg/dl and a second phase at 14 to 15 weeks with an upsurge of more than 100 mg/dl. A mechanism-based model was proposed to describe the natural diabetes progression and salsalate pharmacodynamics by using a population method in S-ADAPT. Two transduction cascades were applied to mimic the two T2DM components: insulin resistance and β-cell dysfunction. Salsalate suppressed both disease factors by a fraction of 0.622 on insulin resistance and 0.134 on β-cell dysfunction. The substantial alleviation of diabetes by salsalate supports the hypothesis that chronic inflammation is a pathogenic factor of diabetes in GK rats. In addition, body weight and food intake were measured and further modeled by a mechanism-based growth model. Modeling results suggest that salsalate reduces weight gain by enhancing metabolic rate and energy expenditure in both GK and Wister-Kyoto rats.

A model for glucose, insulin, and beta-cell dynamics in subjects with insulin resistance and patients with type 2 diabetes

Type 2 diabetes mellitus (T2DM) is a progressive, metabolic disorder characterized by reduced insulin sensitivity and loss of beta-cell mass (BCM), resulting in hyperglycemia. Population pharmacokinetic-pharmacodynamic (PKPD) modeling is a valuable method to gain insight into disease and drug action. A semi-mechanistic PKPD model incorporating fasting plasma glucose (FPG), fasting insulin, insulin sensitivity, and BCM in patients at various disease stages was developed. Data from 3 clinical trials (phase II/III) with a peroxisome proliferator-activated receptor agonist, tesaglitazar, were used to develop the model. In this, a modeling framework proposed by Topp et al was expanded to incorporate the effects of treatment and impact of disease, as well as variability between subjects. The model accurately described FPG and fasting insulin data over time. The model included a strong relation between insulin clearance and insulin sensitivity, predicted 40% to 60% lower BCM in T2DM patients, and realistic improvements of BCM and insulin sensitivity with treatment. The treatment response on insulin sensitivity occurs within the first weeks, whereas the positive effects on BCM arise over several months. The semi-mechanistic PKPD model well described the heterogeneous populations, ranging from nondiabetic, insulin-resistant subjects to long-term treated T2DM patients. This model also allows incorporation of clinical-experimental studies and actual observations of BCM.