Dynamic modeling of free fatty acid, glucose, and insulin: an extended "minimal model"

Blood Glucose Prediction from Nutrition Analytics in Type 1 Diabetes: A Review

INTRODUCTION

Type 1 Diabetes (T1D) affects over 9 million worldwide and necessitates meticulous self-management for blood glucose (BG) control. Utilizing BG prediction technology allows for increased BG control and a reduction in the diabetes burden caused by self-management requirements. This paper reviews BG prediction models in T1D, which include nutritional components.

METHOD

A systematic search, utilizing the PRISMA guidelines, identified articles focusing on BG prediction algorithms for T1D that incorporate nutritional variables. Eligible studies were screened and analyzed for model type, inclusion of additional aspects in the model, prediction horizon, patient population, inputs, and accuracy.

RESULTS

The study categorizes 138 blood glucose prediction models into data-driven (54%), physiological (14%), and hybrid (33%) types. Prediction horizons of ≤30 min are used in 36% of models, 31-60 min in 34%, 61-90 min in 11%, 91-120 min in 10%, and >120 min in 9%. Neural networks are the most used data-driven technique (47%), and simple carbohydrate intake is commonly included in models (data-driven: 72%, physiological: 52%, hybrid: 67%). Real or free-living data are predominantly used (83%).

CONCLUSION

The primary goal of blood glucose prediction in T1D is to enable informed decisions and maintain safe BG levels, considering the impact of all nutrients for meal planning and clinical relevance.

Model selection reveals selective regulation of blood amino acid and lipid metabolism by insulin in humans

Insulin plays a crucial role in regulating the metabolism of blood glucose, amino acids (aa), and lipids in humans. However, the mechanisms by which insulin selectively regulates these metabolites are not fully understood. To address this question, we used mathematical modeling to identify the selective regulatory mechanisms of insulin on blood aa and lipids. Our study revealed that insulin negatively regulates the influx and positively regulates the efflux of lipids, consistent with previous findings. By contrast, we did not observe the previously reported insulin's negative regulation of branched-chain aa (BCAA) influx; instead, we found that insulin positively regulates BCAA efflux. We observed that the earlier peak time of lipids compared to BCAA is dependent on insulin's negative regulation of their influx. Overall, our findings shed new light on how insulin selectively regulates the levels of different metabolites in human blood, providing insights into the metabolic disorder pathogenesis and potential therapies.

Mathematical modeling reveals differential dynamics of insulin action models on glycerol and glucose in adolescent girls with obesity

Under healthy conditions, the pancreas responds to a glucose challenge by releasing insulin. Insulin suppresses lipolysis in adipose tissue, thereby decreasing plasma glycerol concentration, and it regulates plasma glucose concentration through action in muscle and liver. Insulin resistance (IR) occurs when more insulin is required to achieve the same effects, and IR may be tissue-specific. IR emerges during puberty as a result of high concentrations of growth hormone and is worsened by youth-onset obesity. Adipose, liver, and muscle tissue exhibit distinct dose-dependent responses to insulin in multi-phase hyperinsulinemic-euglycemic (HE) clamps, but the HE clamp protocol does not address potential differences in the dynamics of tissue-specific insulin responses. Changes to the dynamics of insulin responses would alter glycemic control in response to a glucose challenge. To investigate the dynamics of insulin acting on adipose tissue, we developed a novel differential-equations based model that describes the coupled dynamics of glycerol concentrations and insulin action during an oral glucose tolerance test in female adolescents with obesity and IR. We compared these dynamics to the dynamics of insulin acting on muscle and liver as assessed with the oral minimal model applied to glucose and insulin data collected under the same protocol. We found that the action of insulin on glycerol peaks approximately 67 min earlier (p < 0.001) and follows the dynamics of plasma insulin more closely compared to insulin action on glucose as assessed by the parameters representing the time constants for insulin action on glucose and glycerol (p < 0.001). These findings suggest that the dynamics of insulin action show tissue-specific differences in our IR adolescent population, with adipose tissue responding to insulin more quickly compared to muscle and liver. Improved understanding of the tissue-specific dynamics of insulin action may provide novel insights into the progression of metabolic disease in patient populations with diverse metabolic phenotypes.

Minimally-Invasive and Efficient Method to Accurately Fit the Bergman Minimal Model to Diabetes Type 2

Introduction

Diabetes mellitus is a global burden that is expected to grow 25 % by 2030. This will increase the need for prevention, diagnosis and treatment of diabetes. Animal and individualized in silico models will allow understanding and compensation for inter and intra-individual differences in treatment and management strategies for diabetic patients. The method presented here can advance the concept of personalized medicine.

Methods

Twenty experiments were performed with Sprague-Dawley rats with streptozotocin induced experimental diabetes in which the insulin-glucose response curve was recorded over 60-100 min using only an insulin pump and a percutaneous glucose sensor. The information was used to fit the five-parameter Bergman Minimal Model to the experimental results using a genetic algorithm with a root-mean-squared optimization rule.

Results

The Bergman Minimal Model parameters were estimated with high accuracy, low prediction bias, and low average root-mean-squared error of 15.27 mg/dl glucose.

Conclusions

This study demonstrates a simple method to accurately parameterize the Bergman Minimal Model. We used Sprague-Dawley rats since their physiology is close to that of humans. The parameters can be used to objectively characterize the physiological severity of diabetes. In this way, planned treatments can compensate for natural variations of conditions both inter and intra patients. Changes in parameters indicate the patient's diabetic condition using values of glucose effectiveness (S G = p 1 ) and insulin sensitivity (S I = p 3 / p 2 ). Quantifying the diabetic patient's condition is consistent with the trend toward personalized medicine. Parameter values can also be used to explain atypical research results of other studies and increase understanding of diabetes.

Insulin Action, Glucose Homeostasis and Free Fatty Acid Metabolism: Insights From a Novel Model

Glucose and free fatty acids (FFA) are essential nutrients that are both partly regulated by insulin. Impaired insulin secretion and insulin resistance are hallmarks of aberrant glucose disposal, and type 2 diabetes (T2DM). In the current study, a novel model of FFA kinetics is proposed to estimate the role insulin action on FFA lipolysis and oxidation allowing estimation of adipose tissue insulin sensitivity (S_IFFA ). Twenty-five normal volunteers were recruited for the current study. To participate, volunteers had to be less than 40 years of age and have a body mass index (BMI) < 30 kg/m², and be free of medical comorbidity. The proposed model of FFA kinetics was used to analyze the data derived from the insulin-modified FSIGT. Mean fractional standard deviations of the parameter estimates were all less than 20%. Standardized residuals of the fit of the model to the FFA temporal data were randomly distributed, with only one estimated point lying outside the 2-standard deviation range, suggesting an acceptable fit of the model to the FFA data. The current study describes a novel one-compartment non-linear model of FFA kinetics during an FSIGT that provides an FFA metabolism insulin sensitivity parameter (S_IFFA ). Furthermore, the models suggest a new role of glucose as the modulator of FFA disposal. Estimates of S_IFFA confirmed previous findings that FFA metabolism is more sensitive to changes in insulin than glucose metabolism. Novel derived indices of insulin sensitivity of FFA (S_IFFA ) were correlated with minimal model indices. These associations suggest a cooperative rather than competitive interplay between the two primary nutrients (glucose and FFA) and allude to the FFA acting as the buffer, such that glucose homeostasis is maintained.

Alterations in plasma non-esterified fatty acid (NEFA) kinetics and relationship with insulin resistance in polycystic ovary syndrome

STUDY QUESTION

Are non-esterified fatty acid (NEFA) kinetics altered in women with polycystic ovary syndrome (PCOS)?

SUMMARY ANSWER

Women with PCOS, particularly obese subjects, have dysregulated plasma NEFA kinetics in response to changes in plasma insulin and glucose levels, which are associated with insulin resistance (IR) independently of the fasting plasma NEFA levels.

WHAT IS KNOWN ALREADY

Elevated plasma NEFA levels are associated with IR in many disorders, although the homeostasis of NEFA kinetics and its relationship to IR in women with PCOS is unknown.

STUDY DESIGN, SIZE, DURATION

We prospectively compared insulin sensitivity and NEFA kinetics in 29 PCOS and 29 healthy controls women matched for BMI.

PARTICIPANTS/MATERIALS, SETTING, METHODS

This study was conducted in a tertiary institution. Plasma NEFA, glucose and insulin levels were assessed during a modified frequently sampled intravenous glucose tolerance test (mFSIVGTT). Minimal models were used to assess insulin sensitivity (Si) and NEFA kinetics (i.e. model-derived initial plasma NEFA level [NEFA0], phi constant [Φ], reflecting glucose-mediated inhibition of lipolysis and measures of maximum rate of lipolysis [SFFA] and NEFA uptake from plasma [KFFA]).

MAIN RESULTS AND THE ROLE OF CHANCE

The study provides new evidence that women with PCOS have defective NEFA kinetics characterized by: (i) lower basal plasma NEFA levels, measured directly and modeled (NEFA0), and (ii) a greater glucose-mediated inhibition of lipolysis in the remote or interstitial space (reflected by a lower affinity constant [Φ]). There were no differences, however, in the maximal rates of adipose tissue lipolysis (SFFA) and the rate at which NEFA leaves the plasma pool (KFFA). The differences observed in NEFA kinetics were exacerbated, and almost exclusively observed, in the obese PCOS subjects.

LIMITATIONS, REASONS FOR CAUTION

Our study did not study NEFA subtypes. It was also cross-sectional and based on women affected by PCOS as defined by the 1990 National Institutes of Health (NIH) criteria (i.e. Phenotypes A and B) and identified in the clinical setting. Consequently, extrapolation of the present data to other phenotypes of PCOS should be made with caution. Furthermore, our data is exploratory and therefore requires validation with a larger sample size.

WIDER IMPLICATIONS OF THE FINDINGS

Dysfunction in NEFA kinetics may be a marker of metabolic dysfunction in nondiabetic obese women with PCOS and may be more important than simply assessing circulating NEFA levels at a single point in time for understanding the mechanism(s) underlying the IR of PCOS.

STUDY FUNDING/COMPETING INTEREST(S)

This work was supported by NIH grants R01-DK073632 and R01-HD29364 to R.A.; a Career Development Award from MD Medical Group, Moscow, RF, to D.L. and Augusta University funds to Y.-H.C. RA serves as consultant to Ansh Labs, Medtronics, Spruce Biosciences and Latitude Capital. U.E., Z.A., D.L., R.M., Y.-H.C., R.C.B. and Y.D.I.C. have no competing interests to declare.

TRIAL REGISTRATION NUMBER

Not applicable.

CarbMetSim: A discrete-event simulator for carbohydrate metabolism in humans

This paper describes CarbMetSim, a discrete-event simulator that tracks the blood glucose level of a person in response to a timed sequence of diet and exercise activities. CarbMetSim implements broader aspects of carbohydrate metabolism in human beings with the objective of capturing the average impact of various diet/exercise activities on the blood glucose level. Key organs (stomach, intestine, portal vein, liver, kidney, muscles, adipose tissue, brain and heart) are implemented to the extent necessary to capture their impact on the production and consumption of glucose. Key metabolic pathways (glucose oxidation, glycolysis and gluconeogenesis) are accounted for in the operation of different organs. The impact of insulin and insulin resistance on the operation of various organs and pathways is captured in accordance with published research. CarbMetSim provides broad flexibility to configure the insulin production ability, the average flux along various metabolic pathways and the impact of insulin resistance on different aspects of carbohydrate metabolism. The simulator does not yet have a detailed implementation of protein and lipid metabolism. This paper contains a preliminary validation of the simulator's behavior. Significant additional validation is required before the simulator can be considered ready for use by people with Diabetes.

Control strategies in systemic metabolism

Metabolic control systems coordinate myriad processes across the cellular, tissue and organismal levels to optimize the allocation of limited supplies across multiple, often competing, metabolic demands. As such, the regulation of metabolism can be analysed from the perspective of the economic theory of supply and demand. Here, we discuss how such analyses can provide new insights into the logic of metabolic control. In particular, we suggest that, in addition to being subject to well-appreciated homeostatic control, metabolism is subject to supply-driven and demand-driven controls, each operated by a dedicated set of signals throughout various physiological states, including inflammation. Furthermore, we argue that systemic homeostasis is a derived feature that evolved from the control systems that monitor metabolic supply and demand.

Control Limitations in Models of T1DM and the Robustness of Optimal Insulin Delivery

BACKGROUND

In insulin therapy, the blood glucose level is constrained from below by the hypoglycemic threshold, that is, the blood glucose level must remain above this threshold. It has been shown that this constraint fundamentally limits the ability to lower the maxima of the blood glucose level predicted by many mathematical models of glucose metabolism. However, it is desirable to minimize hyperglycemia as well. Hence, a desirable insulin input is one that minimizes the maximum glucose concentration while causing it to remain above the hypoglycemic, or higher, threshold. It has been shown that this input, which we call optimal, is characterized by glucose profiles for which either each maximum of the glucose concentration is followed by a minimum or each minimum is followed by a maximum.

METHODS

We discuss the implication of this inherent control limitation for clinical practice and test, through simulation, the robustness of the optimal input to a number of different model and parameter uncertainties. We further develop guidelines on how to design an optimal insulin input that is robust to such uncertainties.

RESULTS

The optimal input is in general not robust to uncertainties. However, a number of strategies may be used to ensure the blood glucose level remains above the hypoglycemic threshold and the maximum blood glucose level achieved is less than that achieved by standard therapy.

CONCLUSIONS

An understanding of the limitations on the controllability of the blood glucose level is important for future treatment improvements and the development of artificial pancreas systems.

In vivo and in silico dynamics of the development of Metabolic Syndrome

The Metabolic Syndrome (MetS) is a complex, multifactorial disorder that develops slowly over time presenting itself with large differences among MetS patients. We applied a systems biology approach to describe and predict the onset and progressive development of MetS, in a study that combined in vivo and in silico models. A new data-driven, physiological model (MINGLeD: Model INtegrating Glucose and Lipid Dynamics) was developed, describing glucose, lipid and cholesterol metabolism. Since classic kinetic models cannot describe slowly progressing disorders, a simulation method (ADAPT) was used to describe longitudinal dynamics and to predict metabolic concentrations and fluxes. This approach yielded a novel model that can describe long-term MetS development and progression. This model was integrated with longitudinal in vivo data that was obtained from male APOE*3-Leiden.CETP mice fed a high-fat, high-cholesterol diet for three months and that developed MetS as reflected by classical symptoms including obesity and glucose intolerance. Two distinct subgroups were identified: those who developed dyslipidemia, and those who did not. The combination of MINGLeD with ADAPT could correctly predict both phenotypes, without making any prior assumptions about changes in kinetic rates or metabolic regulation. Modeling and flux trajectory analysis revealed that differences in liver fluxes and dietary cholesterol absorption could explain this occurrence of the two different phenotypes. In individual mice with dyslipidemia dietary cholesterol absorption and hepatic turnover of metabolites, including lipid fluxes, were higher compared to those without dyslipidemia. Predicted differences were also observed in gene expression data, and consistent with the emergence of insulin resistance and hepatic steatosis, two well-known MetS co-morbidities. Whereas MINGLeD specifically models the metabolic derangements underlying MetS, the simulation method ADAPT is generic and can be applied to other diseases where dynamic modeling and longitudinal data are available.

Quantitative approaches to energy and glucose homeostasis: machine learning and modelling for precision understanding and prediction

Obesity is a major global public health problem. Understanding how energy homeostasis is regulated, and can become dysregulated, is crucial for developing new treatments for obesity. Detailed recording of individual behaviour and new imaging modalities offer the prospect of medically relevant models of energy homeostasis that are both understandable and individually predictive. The profusion of data from these sources has led to an interest in applying machine learning techniques to gain insight from these large, relatively unstructured datasets. We review both physiological models and machine learning results across a diverse range of applications in energy homeostasis, and highlight how modelling and machine learning can work together to improve predictive ability. We collect quantitative details in a comprehensive mathematical supplement. We also discuss the prospects of forecasting homeostatic behaviour and stress the importance of characterizing stochasticity within and between individuals in order to provide practical, tailored forecasts and guidance to combat the spread of obesity.

Chronic intermittent hypoxia and obstructive sleep apnea: an experimental and clinical approach

Obstructive sleep apnea (OSA) is a prevalent sleep disorder considered as an independent risk factor for cardiovascular consequences, such as systemic arterial hypertension, ischemic heart disease, cardiac arrhythmias, metabolic disorders, and cognitive dysfunction. The pathogenesis of OSA-related consequence is assumed to be chronic intermittent hypoxia (IH) inducing alterations at the molecular level, oxidative stress, persistent systemic inflammation, oxygen sensor activation, and increase of sympathetic activity. Overall, these mechanisms have an effect on vessel permeability and are considered to be important factors for explaining vascular, metabolic, and cognitive OSA-related consequences. The present review attempts to examine together the research paradigms and clinical studies on the effect of acute and chronic IH and the potential link with OSA. We firstly describe the literature data on the mechanisms activated by acute and chronic IH at the experimental level, which are very helpful and beneficial to explaining OSA consequences. Then, we describe in detail the effect of IH in patients with OSA that we can consider "the human model" of chronic IH. In this way, we can better understand the specific pathophysiological mechanisms proposed to explain the consequences of IH in OSA.

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.

Modeling glucose and free fatty acid kinetics in glucose and meal tolerance test

BACKGROUND

Quantitative evaluation of insulin regulation on plasma glucose and free fatty acid (FFA) in response to external glucose challenge is clinically important to assess the development of insulin resistance (World J Diabetes 1:36-47, 2010). Mathematical minimal models (MMs) based on insulin modified frequently-sampled intravenous glucose tolerance tests (IM-FSIGT) are widely applied to ascertain an insulin sensitivity index (IEEE Rev Biomed Eng 2:54-96, 2009). Furthermore, it is important to investigate insulin regulation on glucose and FFA in postprandial state as a normal physiological condition. A simple way to calculate the appearance rate (Ra) of glucose and FFA would be especially helpful to evaluate glucose and FFA kinetics for clinical applications.

METHODS

A new MM is developed to simulate the insulin modulation of plasma glucose and FFA, combining IM-FSIGT with a mixed meal tolerance test (MT). A novel simple functional form for the appearance rate (Ra) of glucose or FFA in the MT is developed. Model results are compared with two other models for data obtained from 28 non-diabetic women (13 African American, 15 white).

RESULTS

The new functional form for Ra of glucose is an acceptable empirical approximation to the experimental Ra for a subset of individuals. When both glucose and FFA are included in FSIGT and MT, the new model is preferred using the Bayes Information Criterion (BIC).

CONCLUSIONS

Model simulations show that the new MM allows consistent application to both IM-FSIGT and MT data, balancing model complexity and data fitting. While the appearance of glucose in the circulation has an important effect on FFA kinetics in MT, the rate of appearance of FFA can be neglected for the time-period modeled.

Real-Time Model-Based Fault Detection of Continuous Glucose Sensor Measurements

OBJECTIVE

Faults in subcutaneous glucose concentration readings with a continuous glucose monitoring (CGM) may affect the computation of insulin infusion rates that can lead to hypoglycemia or hyperglycemia in artificial pancreas control systems for patients with type 1 diabetes (T1D).

METHODS

Multivariable statistical monitoring methods are proposed for detection of faults in glucose concentration values reported by a subcutaneous glucose sensor. A nonlinear first principle glucose/insulin/meal dynamic model is developed. An unscented Kalman filter is used for state and parameter estimation of the nonlinear model. Principal component analysis models are developed and used for detection of dynamic changes. K-nearest neighbor classification algorithm is used for diagnosis of faults. Data from 51 subjects are used to assess the performance of the algorithm.

RESULTS

The results indicate that the proposed algorithm works successfully with 84.2% sensitivity. Overall, 155 (out of 184) of the CGM failures are detected with a 2.8-min average detection time.

CONCLUSION

A novel algorithm that integrates data-driven and model-based methods is developed. The proposed method is able to detect CGM failures with a high rate of success.

SIGNIFICANCE

The proposed fault detection algorithm can decrease the effects of faults on insulin infusion rates and reduce the potential for hypo- or hyperglycemia for patients with T1D.

Model-Based Quantification of the Systemic Interplay between Glucose and Fatty Acids in the Postprandial State

In metabolic diseases such as Type 2 Diabetes and Non-Alcoholic Fatty Liver Disease, the systemic regulation of postprandial metabolite concentrations is disturbed. To understand this dysregulation, a quantitative and temporal understanding of systemic postprandial metabolite handling is needed. Of particular interest is the intertwined regulation of glucose and non-esterified fatty acids (NEFA), due to the association between disturbed NEFA metabolism and insulin resistance. However, postprandial glucose metabolism is characterized by a dynamic interplay of simultaneously responding regulatory mechanisms, which have proven difficult to measure directly. Therefore, we propose a mathematical modelling approach to untangle the systemic interplay between glucose and NEFA in the postprandial period. The developed model integrates data of both the perturbation of glucose metabolism by NEFA as measured under clamp conditions, and postprandial time-series of glucose, insulin, and NEFA. The model can describe independent data not used for fitting, and perturbations of NEFA metabolism result in an increased insulin, but not glucose, response, demonstrating that glucose homeostasis is maintained. Finally, the model is used to show that NEFA may mediate up to 30–45% of the postprandial increase in insulin-dependent glucose uptake at two hours after a glucose meal. In conclusion, the presented model can quantify the systemic interactions of glucose and NEFA in the postprandial state, and may therefore provide a new method to evaluate the disturbance of this interplay in metabolic disease.

Mixed model of dietary fat effect on postprandial glucose-insulin metabolism from carbohydrates in type 1 diabetes

In this study we introduce an extension of a previously developed model of glucose-insulin metabolism in type 1 diabetes (T1D) from carbohydrates that includes the effect of dietary fat on postprandial glycemia. We include two compartments that represent plasma triglyceride and nonesterified fatty acid (NEFA) concentration, in addition to a mathematical representation of delayed gastric emptying and insulin resistance, which are the most well-known effects of dietary fat metabolism. Simulation results show that postprandial glucose as well as lipid levels in our model approximates clinical data from T1D patients.

Meal Detection in Patients With Type 1 Diabetes: A New Module for the Multivariable Adaptive Artificial Pancreas Control System

A novel meal-detection algorithm is developed based on continuous glucose measurements. Bergman's minimal model is modified and used in an unscented Kalman filter for state estimations. The estimated rate of appearance of glucose is used for meal detection. Data from nine subjects are used to assess the performance of the algorithm. The results indicate that the proposed algorithm works successfully with high accuracy. The average change in glucose levels between the meals and the detection points is 16(±9.42) [mg/dl] for 61 successfully detected meals and snacks. The algorithm is developed as a new module of an integrated multivariable adaptive artificial pancreas control system. Meal detection with the proposed method is used to administer insulin boluses and prevent most of postprandial hyperglycemia without any manual meal announcements. A novel meal bolus calculation method is proposed and tested with the UVA/Padova simulator. The results indicate significant reduction in hyperglycemia.

Modeling glucose and free fatty acid kinetics during insulin-modified intravenous glucose tolerance test in healthy humans: role of counterregulatory response

Insulin administration during insulin-modified intravenous glucose tolerance test (IM-IVGTT) can induce transient hypoglycemia in healthy insulin-sensitive subjects. This triggers counterregulatory reflex (CRR) responses, which influence the kinetics of glucose and nonesterified fatty acids (NEFA), and undermines the accuracy of mathematical modeling methods that do not explicitly account for CRR. The aim of this study is to evaluate mathematical models of glucose and NEFA kinetics against experimental data in the presence or absence of CRR. Thirteen healthy nondiabetic subjects underwent a standard IM-IVGTT and a modified test (GC-IM-IVGTT) with a variable glucose infusion preventing hypoglycemia. While model predictions fit very well with glucose and NEFA data from GC-IM-IVGTT, they lagged behind observations from IM-IVGTT during recovery from hypoglycemia, independently of insulinemia, which did not differ significantly between protocols. A modification to the glucose minimal model, using the glucose concentration below a threshold as a signal for CRR, improves model predictions for both glucose and NEFA. The associated increase in endogenous glucose production correlates, among various CRR hormones, mainly with the dynamics of glucagon concentration. The modified minimal models introduce new parameters that quantify strength and duration of CRR following hypoglycemia. Although CRR represents an unwanted side-effect in IM-IVGTT occurring only in insulin-sensitive subjects, this study provides new insights leading to improved procedures for estimating insulin sensitivity from IM-IVGTT, which may also allow for assessing the individual capacity of recovery from hypoglycemic events in patients treated with insulin or insulin-releasing drugs.

A novel mathematical model detecting early individual changes of insulin resistance

BACKGROUND

Insulin resistance (IR) and hyperinsulinemia as well as obesity play a key role in the metabolic syndrome (MetS), type 2 diabetes (T2D), and associated cardiovascular disease. Unfortunately, IR and hyperinsulinemia are often diagnosed late (i.e., when the MetS is already clinically evident). An earlier diagnosis of IR would be desirable to reduce its clinical consequences, in particular in view of the increasing prevalence of obesity and diabetes conditions. For this purpose, we developed a mathematical model capable of detecting early onset of IR through small variations of insulin sensitivity, glucose effectiveness, and first- or second-phase responses.

MATERIALS AND METHODS

Murine models provide controlled conditions to study various stages of IR. Various degrees of hypercholesterolemia, obesity, IR, and atherosclerosis were induced in low-density lipoprotein receptor-deficient mice by feeding them cholesterol- or sucrose-rich diets. IR was assessed by oral glucose tolerance tests. Controls included animals fed exclusively, or switched back to, regular chow. A nonlinear mathematical model of the order of 5 was developed by refining Bergman's "Minimal Model" and then applied to experimental data.

RESULTS

Different metabolic constellations consistently corresponded to specific and close-meshed changes in model parameters. Reduced second-phase glucose sensitivity characterized an early impaired glucose tolerance. Later stages showed an increased first-phase glucose sensitivity compensating for decreased insulin sensitivity. Finally, T2D was associated with both first- and second-phase sensitivities close to zero.

CONCLUSIONS

The new mathematical model detected various insulin-sensitive or -resistant metabolic stages of IR. It can therefore be implemented for quantitative metabolic risk assessment and may be of therapeutic value by anticipating the start of therapeutic interventions.

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.

Understanding the metabolic syndrome: a modeling perspective

The prevalence of obesity is growing at an alarming rate, placing many at risk for developing diabetes, hypertension, sleep apnea, or a combination of disorders known as "metabolic syndrome". The evidence to date suggests that metabolic syndrome results from an imbalance in the mechanisms that link diet, physical activity, glucose-insulin control, and autonomic cardiovascular control. There is also growing recognition that sleep-disordered breathing and other forms of sleep disruption can contribute significantly to autonomic dysfunction and insulin resistance. Chronic sleep deprivation resulting from sleep-disordered breathing or behavioral causes can lead to excessive daytime sleepiness and lethargy, which in turn contribute to increasing obesity. Analysis of this complex dynamic system using a model-based approach can facilitate the delineation of the causal pathways that lead to the emergence of the metabolic syndrome. In this paper, we provide an overview of the main physiological mechanisms associated with obesity and sleep-disordered breathing that are believed to result in metabolic and autonomic dysfunction, and review the models and modeling approaches that are relevant in characterizing the interplay among the multiple factors that underlie the development of the metabolic syndrome.

Insulin activation of plasma nonesterified fatty acid uptake in metabolic syndrome

OBJECTIVE

Insulin control of fatty acid metabolism has long been deemed dominated by suppression of adipose lipolysis. The goal of the present study was to test the hypothesis that this single role of insulin is insufficient to explain observed fatty acid dynamics.

METHODS AND RESULTS

Fatty acid kinetics were measured during a meal tolerance test and insulin sensitivity assessed by intravenous glucose tolerance test in overweight human subjects (n=15; body mass index, 35.8 ± 7.1 kg/m(2)). Non-steady state tracer kinetic models were formulated and tested using ProcessDB software. Suppression of adipose fatty acid release, by itself, could not account for postprandial nonesterified fatty acid concentration changes, but adipose suppression combined with insulin activation of fatty acid uptake was consistent with the measured data. The observed insulin K(m) for nonesterified fatty acid uptake was inversely correlated with both insulin sensitivity of glucose uptake (intravenous glucose tolerance test insulin sensitivity; r=-0.626; P=0.01) and whole body fat oxidation after the meal (r=-0.538; P=0.05).

CONCLUSIONS

These results support insulin regulation of fatty acid turnover by both release and uptake mechanisms. Activation of fatty acid uptake is consistent with the human data, has mechanistic precedent in cell culture, and highlights a new potential target for therapies aimed at improving the control of fatty acid metabolism in insulin-resistant disease states.

Modeling the autonomic and metabolic effects of obstructive sleep apnea: a simulation study

Long-term exposure to intermittent hypoxia and sleep fragmentation introduced by recurring obstructive sleep apnea (OSA) has been linked to subsequent cardiovascular disease and Type 2 diabetes. The underlying mechanisms remain unclear, but impairment of the normal interactions among the systems that regulate autonomic and metabolic function is likely involved. We have extended an existing integrative model of respiratory, cardiovascular, and sleep-wake state control, to incorporate a sub-model of glucose-insulin-fatty acid regulation. This computational model is capable of simulating the complex dynamics of cardiorespiratory control, chemoreflex and state-related control of breath-to-breath ventilation, state-related and chemoreflex control of upper airway potency, respiratory and circulatory mechanics, as well as the metabolic control of glucose-insulin dynamics and its interactions with the autonomic control. The interactions between autonomic and metabolic control include the circadian regulation of epinephrine secretion, epinephrine regulation on dynamic fluctuations in glucose and free-fatty acid in plasma, metabolic coupling among tissues and organs provided by insulin and epinephrine, as well as the effect of insulin on peripheral vascular sympathetic activity. These model simulations provide insight into the relative importance of the various mechanisms that determine the acute and chronic physiological effects of sleep-disordered breathing. The model can also be used to investigate the effects of a variety of interventions, such as different glucose clamps, the intravenous glucose tolerance test, and the application of continuous positive airway pressure on OSA subjects. As such, this model provides the foundation on which future efforts to simulate disease progression and the long-term effects of pharmacological intervention can be based.

Dynamic modeling of methylprednisolone effects on body weight and glucose regulation in rats

Influences of methylprednisolone (MPL) and food consumption on body weight (BW), and the effects of MPL on glycemic control including food consumption and the dynamic interactions among glucose, insulin, and free fatty acids (FFA) were evaluated in normal male Wistar rats. Six groups of animals received either saline or MPL via subcutaneous infusions at the rate of 0.03, 0.1, 0.2, 0.3 and 0.4 mg/kg/h for different treatment periods. BW and food consumption were measured twice a week. Plasma concentrations of MPL and corticosterone (CST) were determined at animal sacrifice. Plasma glucose, insulin, and FFA were measured at various times after infusion. Plasma MPL concentrations were simulated by a two-compartment model and used as the driving force in the pharmacodynamic (PD) analysis. All data were modeled using ADAPT 5. The MPL treatments caused reduction of food consumption and body weights in all dosing groups. The steroid also caused changes in plasma glucose, insulin, and FFA concentrations. Hyperinsulinemia was achieved rapidly at the first sampling time of 6 h; significant elevations of FFA were observed in all drug treatment groups; whereas only modest increases in plasma glucose were observed in the low dosing groups (0.03 and 0.1 mg/kg/h). Body weight changes were modeled by dual actions of MPL: inhibition of food consumption and stimulation of weight loss, with food consumption accounting for the input of energy for body weight. Dynamic models of glucose and insulin feedback interactions were extended to capture the major metabolic effects of FFA: stimulation of insulin secretion and inhibition of insulin-stimulated glucose utilization. These models of body weight and glucose regulation adequately captured the experimental data and reflect significant physiological interactions among glucose, insulin, and FFA. These mechanism-based PD models provide further insights into the multi-factor control of this essential metabolic system.

The Unscented Kalman Filter estimates the plasma insulin from glucose measurement

Understanding the simultaneous interaction within the glucose and insulin homeostasis in real-time is very important for clinical treatment as well as for research issues. Until now only plasma glucose concentrations can be measured in real-time. To support a secure, effective and rapid treatment e.g. of diabetes a real-time estimation of plasma insulin would be of great value. A novel approach using an Unscented Kalman Filter that provides an estimate of the current plasma insulin concentration is presented, which operates on the measurement of the plasma glucose and Bergman's Minimal Model of the glucose insulin homeostasis. We can prove that process observability is obtained in this case. Hence, a successful estimator design is possible. Since the process is nonlinear we have to consider estimates that are not normally distributed. The symmetric Unscented Kalman Filter (UKF) will perform best compared to other estimator approaches as the Extended Kalman Filter (EKF), the simplex Unscented Kalman Filter (UKF), and the Particle Filter (PF). The symmetric UKF algorithm is applied to the plasma insulin estimation. It shows better results compared to the direct (open loop) estimation that uses a model of the insulin subsystem.

Modeling the effects of subcutaneous insulin administration and carbohydrate consumption on blood glucose

BACKGROUND

Estimation of the magnitude and duration of effects of carbohydrate (CHO) and subcutaneously administered insulin on blood glucose (BG) is required for improved BG regulation in people with type 1 diabetes mellitus (T1DM). The goal of this study was to quantify these effects in people with T1DM using a novel protocol.

METHODS

The protocol duration was 8 hours: a 1-3 U subcutaneous (SC) insulin bolus was administered and a 25-g CHO meal was consumed, with these inputs separated by 3-5 hours. The DexCom SEVEN® PLUS continuous glucose monitor was used to obtain SC glucose measurements every 5 minutes and YSI 2300 Stat Plus was used to obtain intravenous glucose measurements every 15 minutes.

RESULTS

The protocol was tested on 11 subjects at Sansum Diabetes Research Institute. The intersubject parameter coefficient of variation for the best identification method was 170%. The mean percentages of output variation explained by the bolus insulin and meal models were 68 and 69%, respectively, with root mean square error of 14 and 10 mg/dl, respectively. Relationships between the model parameters and clinical parameters were observed.

CONCLUSION

Separation of insulin boluses and meals in time allowed unique identification of model parameters. The wide intersubject variation in parameters supports the notion that glucose-insulin models and thus insulin delivery algorithms for people with T1DM should be personalized. This experimental protocol could be used to refine estimates of the correction factor and the insulin-to-carbohydrate ratio used by people with T1DM.

Systems engineering medicine: engineering the inflammation response to infectious and traumatic challenges

The complexity of the systemic inflammatory response and the lack of a treatment breakthrough in the treatment of pathogenic infection demand that advanced tools be brought to bear in the treatment of severe sepsis and trauma. Systems medicine, the translational science counterpart to basic science's systems biology, is the interface at which these tools may be constructed. Rapid initial strides in improving sepsis treatment are possible through the use of phenomenological modelling and optimization tools for process understanding and device design. Higher impact, and more generalizable, treatment designs are based on mechanistic understanding developed through the use of physiologically based models, characterization of population variability, and the use of control-theoretic systems engineering concepts. In this review we introduce acute inflammation and sepsis as an example of just one area that is currently underserved by the systems medicine community, and, therefore, an area in which contributions of all types can be made.

Hostility and minimal model of glucose kinetics in African American women

OBJECTIVE

To explore the underlying physiology of hostility (HOST) and to test the hypothesis that HOST has a greater impact on fasting glucose in African American (AA) women than it does on AA men or white men or women, using an intravenous glucose tolerance test (IVGTT) and the minimal model of glucose kinetics.

METHODS

A total of 115 healthy subjects selected for high or low scores on the 27 item Cook Medley HOST Scale underwent an IVGTT. Fasting nonesterified fatty acids (NEFA) levels were measured before the IVGTT. Catecholamine levels were measured 10 minutes into the IVGTT.

RESULTS

Moderation by group (AA women versus others) of HOST was found for glucose effectiveness (Sg, p = .02), acute insulin response (AIRg, p = .02), and disposition index (DI, p = .02). AA women showed a negative association between HOST and both Sg (beta = -0.45, p = .04) and DI (beta = -0.49, p = .02), controlling for age and body mass index. HOST was also associated with changes in epinephrine (beta = 0.39, p = .05) and fasting NEFA (beta = 0.44, p = .02) in the AA women. Controlling for fasting NEFA reduced the effect of HOST on both Sg and DI.

CONCLUSIONS

This study shows that HOST is related to decreased DI, a measure of pancreatic compensation for increased insulin resistance as well as decreased Sg, a measure of noninsulin-mediated glucose transport compared in AA women. These effects are partly mediated by the relationship of HOST to fasting NEFA.

Nonlinear modeling of the dynamic effects of infused insulin on glucose: comparison of compartmental with Volterra models

This paper presents the results of a computational study that compares simulated compartmental (differential equation) and Volterra models of the dynamic effects of insulin on blood glucose concentration in humans. In the first approach, we employ the widely accepted "minimal model" and an augmented form of it, which incorporates the effect of insulin secretion by the pancreas, in order to represent the actual closed-loop operating conditions of the system, and in the second modeling approach, we employ the general class of Volterra-type models that are estimated from input-output data. We demonstrate both the equivalence between the two approaches analytically and the feasibility of obtaining accurate Volterra models from insulin-glucose data generated from the compartmental models. The results corroborate the proposition that it may be preferable to obtain data-driven (i.e., inductive) models in a more general and realistic operating context, without resorting to the restrictive prior assumptions and simplifications regarding model structure and/or experimental protocols (e.g., glucose tolerance tests) that are necessary for the compartmental models proposed previously. These prior assumptions may lead to results that are improperly constrained or biased by preconceived (and possibly erroneous) notions-a risk that is avoided when we let the data guide the inductive selection of the appropriate model within the general class of Volterra-type models, as our simulation results suggest.

Computational study of an augmented minimal model for glycaemia control

In this paper we introduce a new model structure for the metabolic effects of intravenous insulin on blood glucose in man and derive its parameter values from the widely used model of Sorensen. The proposed model attempts to combine the advantages of the existing comprehensive and minimal models. Validation of the new model is done through deriving equivalent nonparametric nonlinear models in the form of Principal Dynamic Modes. We show that the new structure can represent the insulin-glucose dynamics of healthy subjects as well as Type 1 and Type 2 diabetics, with appropriate adjustment in its parameters.

Modeling of glucose regulation and insulin-signaling pathways

A model of glucose regulation system was combined with a model of insulin-signaling pathways in this study. A feedback loop was added to link the transportation of glucose into cells (by GLUT4 in the insulin-signaling pathways) and the insulin-dependent glucose uptake in the glucose regulation model using the Michaelis-Menten kinetic model. A value of K(m) for GLUT4 was estimated using Genetic Algorithm. The estimated value was found to be 25.3 mM, which was in the range of K(m) values found experimentally from in vivo and in vitro human studies. Based on the results of this study, the combined model enables us to understand the overall dynamics of glucose at the systemic level, monitor the time profile of components in the insulin-signaling pathways at the cellular level and gives a good estimate of the K(m) value of glucose transportation by GLUT4. In conclusion, metabolic modeling such as displayed in this study provides a good predictive method to study the step-by-step reactions in an organism at different levels and should be used in combination with experimental approach to increase our understanding of metabolic disorders such as type 2 diabetes.

Mathematical models of energy homeostasis

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

Evaluation of quantitative models of the effect of insulin on lipolysis and glucose disposal

The effects of insulin on the suppression of lipolysis are neither fully understood nor quantified. We examined a variety of mathematical models analogous to the minimal model of glucose disposal (MMG) to quantify the combined influence of insulin on lipolysis and glucose disposal during an insulin-modified frequently sampled intravenous glucose tolerance test. The tested models, which include two previously published ones, consisted of separate compartments for plasma free fatty acids (FFA), glucose, and insulin. They differed in the number of compartments and in the action of insulin to suppress lipolysis that decreased the plasma FFA level. In one category of models, a single insulin compartment acted on both glucose and FFA simultaneously. In a second category, there were two insulin compartments, each acting on FFA and glucose independently. For each of these two categories, we tested 11 variations of how insulin suppressed lipolysis. We also tested a model with an additional glucose compartment that acted on FFA. These 23 models were fit to the plasma FFA and glucose concentrations of 102 subjects individually. Using Bayesian model comparison methods, we selected the model that best balanced fit and minimized model complexity. In the best model, insulin suppressed lipolysis via a Hill function through a remote compartment that acted on both glucose and FFA simultaneously, and glucose dynamics obeyed the classic MMG.

The future of open- and closed-loop insulin delivery systems

We have analysed several aspects of insulin-dependent diabetes mellitus, including the glucose metabolic system, diabetes complications, and previous and ongoing research aimed at controlling glucose in diabetic patients. An expert review of various models and control algorithms developed for the glucose homeostasis system is presented, along with an analysis of research towards the development of a polymeric insulin infusion system. Recommendations for future directions in creating a true closed-loop glucose control system are presented, including the development of multivariable models and control systems to more accurately describe and control the multi-metabolite, multi-hormonal system, as well as in-vivo assessments of implicit closed-loop control systems.

A novel minimal model to describe NEFA kinetics following an intravenous glucose challenge

Dynamics of nonesterified fatty acid (NEFA) metabolism in humans requires quantification if we are to understand the etiology of such diseases as type 1 and 2 diabetes, as well as metabolic syndrome and obesity, or if we are to elucidate the mechanism of action of various interventions. We present a new compartmental model that employs the pattern of plasma glucose concentrations in healthy young adults to predict dynamic changes that occur in plasma NEFA concentrations during either a glucose-only intravenous glucose tolerance test, or an insulin-modified intravenous tolerance test, or a modified protocol during which variable-rate glucose infusions were administered to prevent plasma glucose from declining below 100 mg/dl. The model described all of the major features of NEFA response to an intravenous glucose tolerance test, including an initial latency phase, a phase during which plasma NEFA concentrations plummet to a nadir, and a rebound phase during which plasma NEFA concentrations may rise to a plateau concentration, which may be substantially higher than the initial basal NEFA concentration. This model is consistent with physiological processes and provides seven adjustable parameters that can be used to quantify NEFA production (lipolysis) and utilization (oxidation). When tested on data from the scientific literature, the range in estimated rate of lipolysis was 24-36 micromol.l(-1).min(-1) and for NEFA oxidation rate was 25-54 micromol.l(-1).min(-1). All model parameters were well identified and had coefficients of variation < 15% of their estimated values. It is concluded that this model is suitable to describe NEFA kinetics in human subjects.

Pharmacokinetic Modeling of the Glucoregulatory System

A pharmacokinetic model is proposed to describe the glucoregulatory process. The model describes the dynamics of glucose, amino acids, and fatty acids, as well as both the hormonal actions and dynamics of insulin, glucagon, epinephrine, and glucagon-like peptide-one. The model was developed assuming that the dynamics of each species occurrs in only one compartment. Several forms of the metabolic absorption and elimination rates, along with possibilities for increasing the complexity of each compartmental model are discussed. Once properly identified and validated, the novel model has the potential to be more descriptive than other models describing glucose dynamics in the body.

A novel minimal model to describe non-esterified fatty acid kinetics in Holstein dairy cows

The dynamics of non-esterified fatty acid (NEFA) metabolism in lactating dairy cows requires quantification if we are to understand how dietary treatments and disease influence changes in body condition (adipose reserves) and the production of milk fat. We present here a novel compartmental model that employs the pattern of plasma glucose concentrations to predict the dynamic changes that occur in plasma NEFA concentrations during an intravenous glucose tolerance test (IVGTT) in lactating dairy cows. The model was developed using data obtained from ten early-lactation, Holstein-Friesian cows given a standard IVGTT. The model described all of the major features of the NEFA response to an IVGTT; it was consistent with physiological processes and provided a number of parameters that can be used to quantify NEFA production and utilization. For all of the individual cows, all model parameters were well identified and usually had CV<10% of their estimated values. In the model, elevated plasma glucose concentrations cause an increase in the level of glucose in a remote compartment, which in turn suppresses the rate of entry of NEFA to the plasma compartment. The means (+/-sd) for the five adjustable parameters of the model were: rate of entry of NEFA to the plasma pool (SFFA) 183+/-71 [micromol l-1 min-1], rate of removal (oxidation, sequestration in adipose tissue and uptake by the mammary gland for milk production) of NEFA from the plasma pool (KFFA) 0.140+/-0.047 [min-1], a threshold parameter (gs) representing a plasma glucose concentration above which elevated levels of plasma glucose result in entry of glucose into a 'remote' or inaccessible glucose compartment, 3.30+/-0.52 [mmol/l], a rate constant (K) describing the movement of plasma glucose (above gs) into a remote compartment 0.063+/-0.033 [min-1] and a parameter Phi which is a Michaelis Menten type affinity constant which modulates the extent to which remote glucose inhibits the provision of NEFA to the plasma pool, 0.812+/-0.276 [mmol/l]. It is concluded that the model is suitable to describe NEFA kinetics in lactating dairy cows and it may have application in other species.

Recent progress in analytical instrumentation for glycemic control in diabetic and critically ill patients

Implementing strict glycemic control can reduce the risk of serious complications in both diabetic and critically ill patients. For this reason, many different analytical, mainly electrochemical and optical sensor approaches for glucose measurements have been developed. Self-monitoring of blood glucose (SMBG) has been recognised as being an indispensable tool for intensive diabetes therapy. Recent progress in analytical instrumentation, allowing submicroliter samples of blood, alternative site testing, reduced test time, autocalibration, and improved precision, is comprehensively described in this review. Continuous blood glucose monitoring techniques and insulin infusion strategies, developmental steps towards the realization of the dream of an artificial pancreas under closed loop control, are presented. Progress in glucose sensing and glycemic control for both patient groups is discussed by assessing recent published literature (up to 2006). The state-of-the-art and trends in analytical techniques (either episodic, intermittent or continuous, minimal-invasive, or noninvasive) detailed in this review will provide researchers, health professionals and the diabetic community with a comprehensive overview of the potential of next-generation instrumentation suited to either short- and long-term implantation or ex vivo measurement in combination with appropriate body interfaces such as microdialysis catheters.