A mathematical model for the control mechanism of free fatty acid-glucose metabolism in normal humans

Minimal and Maximal Models to Quantitate Glucose Metabolism: Tools to Measure, to Simulate and to Run in Silico Clinical Trials

Several models have been proposed to describe the glucose system at whole-body, organ/tissue and cellular level, designed to measure non-accessible parameters (minimal models), to simulate system behavior and run in silico clinical trials (maximal models). Here, we will review the authors' work, by putting it into a concise historical background. We will discuss first the parametric portrait provided by the oral minimal models-building on the classical intravenous glucose tolerance test minimal models-to measure otherwise non-accessible key parameters like insulin sensitivity and beta-cell responsivity from a physiological oral test, the mixed meal or the oral glucose tolerance tests, and what can be gained by adding a tracer to the oral glucose dose. These models were used in various pathophysiological studies, which we will briefly review. A deeper understanding of insulin sensitivity can be gained by measuring insulin action in the skeletal muscle. This requires the use of isotopic tracers: both the classical multiple-tracer dilution and the positron emission tomography techniques are discussed, which quantitate the effect of insulin on the individual steps of glucose metabolism, that is, bidirectional transport plasma-interstitium, and phosphorylation. Finally, we will present a cellular model of insulin secretion that, using a multiscale modeling approach, highlights the relations between minimal model indices and subcellular secretory events. In terms of maximal models, we will move from a parametric to a flux portrait of the system by discussing the triple tracer meal protocol implemented with the tracer-to-tracee clamp technique. This allows to arrive at quasi-model independent measurement of glucose rate of appearance (Ra), endogenous glucose production (EGP), and glucose rate of disappearance (Rd). Both the fast absorbing simple carbs and the slow absorbing complex carbs are discussed. This rich data base has allowed us to build the UVA/Padova Type 1 diabetes and the Padova Type 2 diabetes large scale simulators. In particular, the UVA/Padova Type 1 simulator proved to be a very useful tool to safely and effectively test in silico closed-loop control algorithms for an artificial pancreas (AP). This was the first and unique simulator of the glucose system accepted by the U.S. Food and Drug Administration as a substitute to animal trials for in silico testing AP algorithms. Recent uses of the simulator have looked at glucose sensors for non-adjunctive use and new insulin molecules.

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.

Estimation of parameters for plasma glucose regulation in type-2 diabetics in presence of meal

In this study, the authors propose a methodology for the estimation of glucose masses in stomach (both in solid and liquid forms), intestine, plasma and tissue; insulin masses in portal vein, liver, plasma and interstitial fluid using only plasma glucose measurement. The proposed methodology fuses glucose–insulin homoeostasis model (in the presence of meal intake) and plasma glucose measurement with a Bayesian non‐linear filter. Uncertainty of the model over individual variations has been incorporated by adding process noise to the homoeostasis model. The estimation is carried out over 24 h for the healthy people as well as a type II diabetes mellitus patients. In simulation, the estimator follows the truth accurately for both the cases. Moreover, the performances of two non‐linear filters, namely the unscented Kalman filter (KF) and cubature quadrature KF are compared in terms of root mean square error. The proposed methodology will be helpful in future to: (i) observe a patient's insulin–glucose profile, (ii) calculate drug dose for any hyperglycaemic patients and (iii) develop a closed‐loop controller for automated insulin delivery system.

In silico assessment of biomedical products: The conundrum of rare but not so rare events in two case studies

In silico clinical trials, defined as "The use of individualized computer simulation in the development or regulatory evaluation of a medicinal product, medical device, or medical intervention," have been proposed as a possible strategy to reduce the regulatory costs of innovation and the time to market for biomedical products. We review some of the the literature on this topic, focusing in particular on those applications where the current practice is recognized as inadequate, as for example, the detection of unexpected severe adverse events too rare to be detected in a clinical trial, but still likely enough to be of concern. We then describe with more details two case studies, two successful applications of in silico clinical trial approaches, one relative to the University of Virginia/Padova simulator that the Food and Drug Administration has accepted as possible replacement for animal testing in the preclinical assessment of artificial pancreas technologies, and the second, an investigation of the probability of cardiac lead fracture, where a Bayesian network was used to combine in vivo and in silico observations, suggesting a whole new strategy of in silico-augmented clinical trials, to be used to increase the numerosity where recruitment is impossible, or to explore patients' phenotypes that are unlikely to appear in the trial cohort, but are still frequent enough to be of concern.

Plant lipidomics at the crossroads: From technology to biology driven science

The identification and quantification of lipids from plant tissues have become commonplace and many researchers now incorporate lipidomics approaches into their experimental studies. Plant lipidomics research continues to involve technological developments such as those in mass spectrometry imaging, but in large part, lipidomics approaches have matured to the point of being accessible to the novice. Here we review some important considerations for those planning to apply plant lipidomics to their biological questions, and offer suggestions for appropriate tools and practices. This article is part of a Special Issue entitled: BBALIP_Lipidomics Opinion Articles edited by Sepp Kohlwein.

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.

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.

A computational model of the human glucose-insulin regulatory system

OBJECTIVE

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

METHODS

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

RESULTS

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

CONCLUSION

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

Diabetes: Models, Signals, and Control

The control of diabetes is an interdisciplinary endeavor, which includes a significant biomedical engineering component, with traditions of success beginning in the early 1960s. It began with modeling of the insulin-glucose system, and progressed to large-scale in silico experiments, and automated closed-loop control (artificial pancreas). Here, we follow these engineering efforts through the last, almost 50 years. We begin with the now classic minimal modeling approach and discuss a number of subsequent models, which have recently resulted in the first in silico simulation model accepted as substitute to animal trials in the quest for optimal diabetes control. We then review metabolic monitoring, with a particular emphasis on the new continuous glucose sensors, on the analyses of their time-series signals, and on the opportunities that they present for automation of diabetes control. Finally, we review control strategies that have been successfully employed in vivo or in silico, presenting a promise for the development of a future artificial pancreas and, in particular, discuss a modular architecture for building closed-loop control systems, including insulin delivery and patient safety supervision layers. We conclude with a brief discussion of the unique interactions between human physiology, behavioral events, engineering modeling and control relevant to diabetes.

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.

The next generation of artificial pancreas control algorithms

Creating a wearable artificial pancreas (AP) by closing the loop between a glucose sensor and an insulin infusion pump has the potential to significantly impact the complications associated with and improve the quality of life of diabetic individuals. Despite recent progress on glucose sensor and insulin infusion technologies, control algorithms built on the simple glucose value efferent and insulin dose afferent model are not efficient and reliable. Based on glucose regulatory mechanisms known to date, their impairment in the diabetic state, and fundamental principles of control theory, some corrections to the present course of research are proposed to facilitate the removal of this barrier. A greater emphasis on model predictive controllers or controllers that exploit a mathematical representation, or model, of the patient's own physiology is proposed. Whole-body physiologically based pharmacokinetics-pharmacodynamics-type models hold the best odds for enabling a successful closed-loop AP. However, two major improvements to the diabetes modeling state of the art are required to make them practical for daily care: integrating hypothalamus-pituitary-adrenal axis and gastrointestinal tract submodels. Although there are simple representations of these in current existence, large concerted efforts between experimentalists and modelers will be required to enhance their accuracy. Finally, changes in hardware that complements controller performance are suggested. For instance, the development of dual control inputs of insulin and glucagon could relax tolerances on controller accuracy.

Meal simulation model of the glucose-insulin system

A simulation model of the glucose-insulin system in the postprandial state can be useful in several circumstances, including testing of glucose sensors, insulin infusion algorithms and decision support systems for diabetes. Here, we present a new simulation model in normal humans that describes the physiological events that occur after a meal, by employing the quantitative knowledge that has become available in recent years. Model parameters were set to fit the mean data of a large normal subject database that underwent a triple tracer meal protocol which provided quasi-model-independent estimates of major glucose and insulin fluxes, e.g., meal rate of appearance, endogenous glucose production, utilization of glucose, insulin secretion. By decomposing the system into subsystems, we have developed parametric models of each subsystem by using a forcing function strategy. Model results are shown in describing both a single meal and normal daily life (breakfast, lunch, dinner) in normal. The same strategy is also applied on a smaller database for extending the model to type 2 diabetes.

GIM, simulation software of meal glucose-insulin model

BACKGROUND

A simulation model of the glucose-insulin system in normal life conditions can be very useful in diabetes research, e.g., testing insulin infusion algorithms and decision support systems and assessing glucose sensor performance and patient and student training. A new meal simulation model has been proposed that incorporates state-of-the-art quantitative knowledge on glucose metabolism and its control by insulin at both organ/tissue and whole-body levels. This article presents the interactive simulation software GIM (glucose insulin model), which implements this model.

METHODS

The model is implemented in MATLAB, version 7.0.1, and is designed with a windows interface that allows the user to easily simulate a 24-hour daily life of a normal, type 2, or type 1 diabetic subject. A Simulink version is also available. Three meals a day are considered. Both open- and closed-loop controls are available for simulating a type 1 diabetic subject.

RESULTS

Software options are described in detail. Case studies are presented to illustrate the potential of the software, e.g., compare a normal subject vs an insulin-resistant subject or open-loop vs closed-loop insulin infusion in type 1 diabetes treatment.

CONCLUSIONS

User-friendly software that implements a state-of-the-art physiological model of the glucose-insulin system during a meal has been presented. The GIM graphical interface makes its use extremely easy for investigators without specific expertise in modeling.

Distributed model of human glucose metabolism and computer simulation study

Metabolism is the basic character of living activity. Through the research on the physiological process of carbohydrate metabolism, we have established the compartment model of organ glucose metabolism, which is incorporated into our multi-element non-linear cardiovascular model. The simulation of the incorporated model can reflect the status of carbohydrate metabolism under different situations. This will help to understand the mechanism of metabolism procedure and give advices on curing metabolism diseases.

The Särimner diabetes simulator--a look in the rear view mirror

BACKGROUND

At the end of the 1980s, the Department of Pediatrics at Linköping University, Linköping, Sweden developed a computerized diabetes simulator. The main purpose was to allow teenagers with Type 1 diabetes to experiment with food, exercise, and insulin without the risk of inconvenience. The aim of this paper is to discuss experiences from the previous work with teenagers on the Särimner diabetes simulator.

METHODS AND RESULTS

In 1991, shortly before Sweden became computerized, the impact of the simulator was evaluated in a study with 11 teenagers. Improvements were seen in a few individuals regarding locus of control, self-esteem, diabetes knowledge, and diabetes-related stress, but could not be shown on a group level. The simulator was used for longer periods at some clinics, also by individual health professionals and in a diabetes camp, but support for further development has been lacking. It was also used in modeling projects of Type 2 diabetes and obesity.

CONCLUSIONS

Proactive pedagogic measures may find it hard to compete with corrective technological measures since their effectiveness is more difficult to prove by scientific methods. Nevertheless, they are needed together with other methods to improve understanding and motivation in the treatment of Type 1 diabetes.

A critical review of mathematical models and data used in diabetology

The literature dealing with mathematical modelling for diabetes is abundant. During the last decades, a variety of models have been devoted to different aspects of diabetes, including glucose and insulin dynamics, management and complications prevention, cost and cost-effectiveness of strategies and epidemiology of diabetes in general. Several reviews are published regularly on mathematical models used for specific aspects of diabetes. In the present paper we propose a global overview of mathematical models dealing with many aspects of diabetes and using various tools. The review includes, side by side, models which are simple and/or comprehensive; deterministic and/or stochastic; continuous and/or discrete; using ordinary differential equations, partial differential equations, optimal control theory, integral equations, matrix analysis and computer algorithms.

Minimal model: perspective from 2005

The minimal model was proposed over 25 years ago. Despite (or because of) its simplicity it continues to be used today - both as a clinical tool and an approach to understanding the composite effects of insulin secretion and insulin sensitivity on glucose tolerance and risk for type 2 diabetes mellitus. The original assumptions of the model have led to an understanding of the kinetics of insulin in vivo, as well as the relative importance of beta-cell compensatory failure in the pathogenesis of diabetes. The disposition index (DI), a parameter emerging from the model, represents the ability of the pancreatic islets to compensate for insulin resistance. There is evidence that a locus on chromosome 11 codes for the DI, which has a significant heritability and can predict type 2 diabetes better than any known genetic locus. Even today, the model continues to be a subject of scientific discovery and discourse.

Särimner: a computer model of diabetes physiology for education of physicians and patients

Often diabetic patients have developed their skills by some trial-and-error-like training over a long period of time. To minimize this inconvenience we have made a mathematical model to facilitate diabetes education. The model consists of a number of blocks involved in diabetes physiology: digestion, blood (transport), pancreas, injected insulin absorption, liver, muscles, kidneys, metabolism and insulin sensitivity. The model serves as a demonstration object and the user can change meals, exercise and injections and see the resulting blood glucose level. A more experienced user can search for further explanations of different phenomena deeper in the physiology of the model. The model does not solve any problem for the user, but creates a learning situation in which the user, led by his own curiosity, successively increases his experience of diabetes physiology. Särimner is implemented as an easy-to-use menu driven computer program for IBM PC-clones with Hercules, EGA or VGA graphics.

Simulation of energy metabolism in the simple-stomached animal

1. A computer programme is described which simulates energy metabolism in the whole animal. Simulation was based on representation of the animal as a quasi-steady-state system. 2. Input for the programme consisted of the chemical composition of the diet and an estimate of either the maintenance energy requirement or an estimate of energy retention. 3. Simulation was performed by estimating the yield of adenosine triphosphate in the major metabolic pathways operative in simple-stomached animals, and on the utilization of adenosine triphosphate in major anabolic processes. 4. Results obtained from simulation were in close agreement with experimental observations reported by McCracken (1975).

A systems model of blood glucose control

A mathematical model for the short-term control of glucose is presented, focusing upon the role of the liver. Non-linear representation is provided, enabling complete system behaviour of the metabolic and endocrine processes to be analysed, including both basic auto-regulation and higher levels of control. The level of a priori knowledge incorporated in the formulation is maximised by including unit process dynamics, making direct use of known enzymological data. From simulation results, hypotheses concerning system structure are tested. Hormones are seen to be important in maintaining the biochemical environment, providing the coarse control. The dominant control of flux within the glucose metabolic pathways is intrinsic to the enzyme systems which can be looked upon as providing the fine tuning and auto regulatory effects.