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

A dual-attention based coupling network for diabetes classification with heterogeneous data

Diabetes Mellitus (DM) is a group of metabolic disorders characterized by hyperglycaemia in the absence of treatment. Classification of DM is essential as it corresponds to the respective diagnosis and treatment. In this paper, we propose a new coupling network with hierarchical dual-attention that utilizes heterogeneous data, including Flash Glucose Monitoring (FGM) data and biomarkers in electronic medical records. The long short-term memory-based FGM sub-network extracts the time-dependent features of dynamic FGM sequences, while the biomarkers sub-network learns the features of static biomarkers. The convolutional block attention module (CBAM) for dispersing the feature weights of the spatial and channel dimensions is implemented into the FGM sub-network to endure the variability of FGM and allows us to extract high-level discriminative features more accurately. To better adjust the importance weights of the characteristics of the two sub-networks, self-attention is introduced to integrate the characteristics of heterogeneous data. Based on the dataset provided by Peking University People's Hospital, the proposed method is evaluated through factorial experiments of multi-source heterogeneous data, ablation studies of various attention strategies, time consumption evaluation and quantitative evaluation. The benchmark tests reveal the proposed network achieves a type 1 and 2 diabetes classification accuracy of 95.835% and the comprehensive performance metrics, including Matthews correlation coefficient, F1-score and G-mean, are 91.333%, 94.939% and 94.937% respectively. In the factorial experiments, the proposed method reaches the maximum area under the receiver operating characteristic curve of 0.9428, which indicates the effectiveness of the coupling between the nominated sub-networks. The coupling network with a dual-attention strategy performs better than the one without or only with a single-attention strategy in the ablation study as well. In addition, the model is also tested on another data set, and the accuracy of the test reaches 94.286%, reflecting that the model is robust when it is transferred to untrained diabetes data. The experimental results show that the proposed method is feasible in the classification of diabetes types. The code is available at https://github.com/bitDalei/Diabetes-Classification-with-Heterogeneous-Data.

Quantitative system pharmacology as a legitimate approach to examine extrapolation strategies used to support pediatric drug development

Extrapolation strategies from adult data for designing pediatric drug development programs are explored using the quantitative systems pharmacology (QSP) modeling approach, a mechanistic drug and disease modeling framework that can predict clinical response and guide pediatric drug development in general. This innovative model‐informed drug discovery and development approach can leverage adult‐pediatric pharmacology and disease similarity metrics to validate extrapolation assumptions. We describe the QSP model strategy and framework for extrapolation to design pediatric drug development programs by leveraging adult data across a wide range of therapeutic areas and illustrating stage‐gate decisions informed by such an approach.

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.

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.

Mathematical model of blood glucose dynamics by emulating the pathophysiology of glucose metabolism in type 2 diabetes mellitus

Mathematical modelling has established itself as a theoretical tool to understand fundamental aspects of a variety of medical-biological phenomena. The predictive power of mathematical models on some chronic conditions has been helpful in its proper prevention, diagnosis, and treatment. Such is the case of the modelling of glycaemic dynamics in type 2 diabetes mellitus (T2DM), whose physiology-based mathematical models have captured the metabolic abnormalities of this disease. Through a physiology-based pharmacokinetic-pharmacodynamic approach, this work addresses a mathematical model whose structure starts from a model of blood glucose dynamics in healthy humans. This proposal is capable of emulating the pathophysiology of T2DM metabolism, including the effect of gastric emptying and insulin enhancing effect due to incretin hormones. The incorporation of these effects lies in the implemented methodology since the mathematical functions that represent metabolic rates, with a relevant contribution to hyperglycaemia, are adjusting individually to the clinical data of patients with T2DM. Numerically, the resulting model successfully simulates a scheduled graded intravenous glucose test and oral glucose tolerance tests at different doses. The comparison between simulations and clinical data shows an acceptable description of the blood glucose dynamics in T2DM. It opens the possibility of using this model to develop model-based controllers for the regulation of blood glucose in T2DM.

'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.

Translational Quantitative Systems Pharmacology in Drug Development: from Current Landscape to Good Practices

Systems pharmacology approaches have the capability of quantitatively linking the key biological molecules relevant to a drug candidate's mechanism of action (drug-induced signaling pathways) to the clinical biomarkers associated with the proposed target disease, thereby quantitatively facilitating its development and life cycle management. In this review, the model attributes of published quantitative systems pharmacology (QSP) modeling for lowering cholesterol, treating salt-sensitive hypertension, and treating rare diseases as well as describing bone homeostasis and related pharmacological effects are critically reviewed with respect to model quality, calibration, validation, and performance. We further reviewed the common practices in optimizing QSP modeling and prediction. Notably, leveraging genetics and genomic studies for model calibration and validation is common. Statistical and quantitative assessment of QSP prediction and handling of model uncertainty are, however, mostly lacking as are the quantitative and statistical criteria for assessing QSP predictions and the covariance matrix of coefficients between the parameters in a validated virtual population. To accelerate advances and application of QSP with consistent quality, a list of key questions is proposed to be addressed when assessing the quality of a QSP model in hopes of stimulating the scientific community to set common expectations. The common expectations as to what constitutes the best QSP modeling practices, which the scientific community supports, will advance QSP modeling in the realm of informed drug development. In the long run, good practices will extend the life cycles of QSP models beyond the life cycles of individual drugs.

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 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.

Determination of personalized diabetes treatment plans using a two-delay model

Diabetes cases worldwide have risen steadily over the past few decades, lending urgency to the search for more efficient, effective, and personalized ways to treat the disease. Current treatment strategies, however, may fail to maintain oscillations in blood glucose concentration that naturally occur multiple times per day, an important element of normal human physiology. Building upon recent successes in mathematical modeling of the human glucose-insulin system, we show that both food intake and insulin therapy likely demand increasingly precise control over insulin sensitivity if oscillations at a healthy average glucose concentration are to be maintained. We then model and describe personalized treatment options for patients with diabetes that maintain these oscillations. We predict that for a person with type II diabetes, both blood glucose levels can be controlled and healthy oscillations maintained when the patient gets an hour of daily exercise and is placed on a combination of Metformin and sulfonylurea drugs. We note that insulin therapy and an additional hour of exercise will reduce the patient׳s need for sulfonylureas. Results of a modeling analysis suggest that, with constant nutrition and controlled exercise, the blood glucose levels of a person with type I diabetes can be properly controlled with insulin infusion between 0.45 and 0.7μU/mlmin. Lastly, we note that all suggested strategies rely on existing clinical techniques and established treatment measures, and so could potentially be of immediate use in the design of an artificial pancreas.

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.