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Objective: Subcutaneous (sc) administration of long-acting insulin analogs is often employed in multiple daily injection (MDI) therapy of type 1 diabetes (T1D) to cover patient's basal insulin needs. Among these, insulin glargine 100 U/mL (Gla-100) and 300 U/mL (Gla-300) are formulations indicated for once daily sc administration in MDI therapy of T1D. A few semi-mechanistic models of sc absorption of insulin glargine have been proposed in the literature, but were not quantitatively assessed on a large dataset. The aim of this paper is to propose a model of sc absorption of insulin glargine able to describe the data and provide precise model parameters estimates with a clear physiological interpretation., Methods: Three candidate models were identified on a total of 47 and 77 insulin profiles of T1D subjects receiving a single or repeated sc administration of Gla-100 or Gla-300, respectively. Model comparison and selection were performed on the basis of their ability to describe the data and numerical identifiability., Results: The most parsimonious model is linear two-compartment and accounts for the insulin distribution between the two compartments after sc administration through parameter k. Between the two formulations, we report a lower fraction of insulin in the first versus second compartment (k = 86% versus 94% in Gla-100 versus Gla-300, p < 0.05), a lower dissolution rate from the first to the second compartment ([Formula: see text] versus 0.0008 min -1 in Gla-100 versus Gla-300, p << 0.001), and a similar rate of insulin absorption from the second compartment to plasma ([Formula: see text] versus 0.0016 min -1 in Gla-100 versus Gla-300, p = NS), in accordance with the mechanisms of insulin glargine protraction., Conclusions: The proposed model is able to both accurately describe plasma insulin data after sc administration and precisely estimate physiologically plausible parameters., Significance: The model can be incorporated in simulation platforms potentially usable for optimizing basal insulin treatment strategies.

Background: The objective of this research is to show the effectiveness of individualized hypoglycemia predictive alerts (IHPAs) based on patient-tailored glucose-insulin models (PTMs) for different subjects. Interpatient variability calls for PTMs that have been identified from data collected in free-living conditions during a one-month trial., Methods: A new impulse-response (IR) identification technique has been applied to free-living data in order to identify PTMs that are able to predict the future glucose trends and prevent hypoglycemia events. Impulse response has been applied to seven patients with type 1 diabetes (T1D) of the University of Amsterdam Medical Centre. Individualized hypoglycemia predictive alert has been designed for each patient thanks to the good prediction capabilities of PTMs., Results: The PTMs performance is evaluated in terms of index of fitting (FIT), coefficient of determination, and Pearson's correlation coefficient with a population FIT of 63.74%. The IHPAs are evaluated on seven patients with T1D with the aim of predicting in advance (between 45 and 10 minutes) the unavoidable hypoglycemia events; these systems show better performance in terms of sensitivity, precision, and accuracy with respect to previously published results., Conclusion: The proposed work shows the successful results obtained applying the IR to an entire set of patients, participants of a one-month trial. Individualized hypoglycemia predictive alerts are evaluated in terms of hypoglycemia prevention: the use of a PTM allows to detect 84.67% of the hypoglycemia events occurred during a one-month trial on average with less than 0.4% of false alarms. The promising prediction capabilities of PTMs can be a key ingredient for new generations of individualized model predictive control for artificial pancreas.

Objective: Subcutaneous (sc) administration of fast-acting insulin analogues is the key in conventional therapy of type 1 diabetes (T1D). A model of sc insulin absorption would be helpful for optimizing insulin therapy and test new open- and closed-loop treatment strategies in in silico platforms. Some models have been published in the literature, but none was assessed on a frequently-sampled large dataset of T1D subjects. The aim here is to propose a model of sc absorption of fast-acting insulin, which is able to describe the data and precisely estimate model parameters with a clear physiological interpretation., Methods: Three candidate models were identified on 116 T1D subjects, who underwent a single sc injection of fast-acting insulin and were compared on the basis of their ability to describe the data and their numerical identifiability., Results: A linear two-compartment model including a subject-specific delay in sc insulin absorption is proposed. On average, a delay of 7.6 min in insulin appearance in the first compartment is detected, then the insulin is slowly absorbed into plasma (in 23% of the subjects) with a rate of 0.0034 min-1, while the remaining diffuses into the second compartment, with a rate constant of 0.028 min-1, and then finally absorbed into plasma with a rate constant of 0.014 min-1., Conclusion: Among the three tested models, the one proposed here is the only one able to both accurately describe plasma insulin data after a single sc injection and precisely estimate physiologically plausible parameters. The model needs to be further tested in case of variable sc insulin delivery and/or multiple insulin doses., Significance: Results are expected to help the development of new open- and closed-loop insulin treatment strategies.

Objective: Contemporary and future outpatient long-term artificial pancreas (AP) studies need to cope with the well-known large intra- and interday glucose variability occurring in type 1 diabetic (T1D) subjects. Here, we propose an adaptive model predictive control (MPC) strategy to account for it and test it in silico., Methods: A run-to-run (R2R) approach adapts the subcutaneous basal insulin delivery during the night and the carbohydrate-to-insulin ratio (CR) during the day, based on some performance indices calculated from subcutaneous continuous glucose sensor data. In particular, R2R aims, first, to reduce the percentage of time in hypoglycemia and, secondarily, to improve the percentage of time in euglycemia and average glucose. In silico simulations are performed by using the University of Virginia/Padova T1D simulator enriched by incorporating three novel features: intra- and interday variability of insulin sensitivity, different distributions of CR at breakfast, lunch, and dinner, and dawn phenomenon., Results: After about two months, using the R2R approach with a scenario characterized by a random 30% variation of the nominal insulin sensitivity the time in range and the time in tight range are increased by 11.39% and 44.87%, respectively, and the time spent above 180 mg/dl is reduced by 48.74%., Conclusions: An adaptive MPC algorithm based on R2R shows in silico great potential to capture intra- and interday glucose variability by improving both overnight and postprandial glucose control without increasing hypoglycemia., Significance: Making an AP adaptive is key for long-term real-life outpatient studies. These good in silico results are very encouraging and worth testing in vivo.

Goal: Quantitative assessment of hepatic insulin extraction (HE) after an oral glucose challenge, e.g., a meal, is important to understand the regulation of carbohydrate metabolism. The aim of the current study is to develop a model of system for estimating HE., Methods: Nine different models, of increasing complexity, were tested on data of 204 normal subjects, who underwent a mixed meal tolerance test, with frequent measurement of plasma glucose, insulin, and C-peptide concentrations. All these models included a two-compartment model of C-peptide kinetics, an insulin secretion model, a compartmental model of insulin kinetics (with number of compartments ranging from one to three), and different HE descriptions, depending on plasma glucose and insulin. Model performances were compared on the basis of data fit, precision of parameter estimates, and parsimony criteria., Results: The three-compartment model of insulin kinetics, coupled with HE depending on glucose concentration, showed the best fit and a good ability to precisely estimate the parameters. In addition, the model calculates basal and total indices of HE ( HE b and HE tot , respectively), and provides an index of HE sensitivity to glucose ( S G HE )., Conclusion: A new physiologically based HE model has been developed, which allows an improved quantitative description of glucose regulation., Significance: The use of the new model provides an in-depth description of insulin kinetics, thus enabling a better understanding of a given subject's metabolic state.

Fasting hyperglycemia occurs when an excessive rate of endogenous glucose production (EGP) is not accompanied by an adequate compensatory increase in the rate of glucose disappearance (Rd). The situation following food ingestion is more complex as the amount of glucose that reaches the circulation for disposal is a function of the systemic rate of appearance of the ingested glucose (referred to as the rate of meal appearance [Rameal]), the pattern and degree of suppression of EGP, and the rapidity of stimulation of the Rd In an effort to measure these processes, Steele et al. proposed what has come to be referred to as the dual-tracer method in which the ingested glucose is labeled with one tracer while a second tracer is infused intravenously at a constant rate. Unfortunately, subsequent studies have shown that although this approach is technically simple, the marked changes in plasma specific activity or the tracer-to-tracee ratio, if stable tracers are used, introduce a substantial error in the calculation of Rameal, EGP, and Rd, thereby leading to incorrect and at times misleading results. This Perspective discusses the causes of these so-called "nonsteady-state" errors and how they can be avoided by the use of the triple-tracer approach., (© 2016 by the American Diabetes Association. Readers may use this article as long as the work is properly cited, the use is educational and not for profit, and the work is not altered.)

The nonlinear mixed effects models are commonly used modeling techniques in the pharmaceutical research as they enable the characterization of the individual profiles together with the population to which the individuals belong. To ensure a correct use of them is fundamental to provide powerful diagnostic tools that are able to evaluate the predictive performance of the models. The visual predictive check (VPC) is a commonly used tool that helps the user to check by visual inspection if the model is able to reproduce the variability and the main trend of the observed data. However, the simulation from the model is not always trivial, for example, when using models with time-varying input function (IF). In this class of models, there is a potential mismatch between each set of simulated parameters and the associated individual IF which can cause an incorrect profile simulation. We introduce a refinement of the VPC by taking in consideration a correlation term (the Mahalanobis or normalized Euclidean distance) that helps the association of the correct IF with the individual set of simulated parameters. We investigate and compare its performance with the standard VPC in models of the glucose and insulin system applied on real and simulated data and in a simulated pharmacokinetic/pharmacodynamic (PK/PD) example. The newly proposed VPC performance appears to be better with respect to the standard VPC especially for the models with big variability in the IF where the probability of simulating incorrect profiles is higher.

Recently, a model was proposed to assess hepatic insulin sensitivity during a meal, i.e., the ability of insulin to suppress glucose production (EGP), SI (P). The model was developed on EGP data obtained from a triple-tracer meal and the tracer-to-tracee clamp technique and validated against the euglycemic hyperinsulinemic clamp. The aim of this study was to assess whether SI (P) can be obtained from plasma concentrations measured after a single-tracer meal by incorporating the above EGP model into the oral glucose minimal model by describing both glucose production and disposal (OMM(PD)). Triple-tracer meal data of two databases (20 healthy and 60 healthy and prediabetic subjects) were used. Virtually model-independent EGP estimates were calculated. OMM(PD) was identified on exogenous and endogenous glucose concentrations, providing indices of SI (P), disposal insulin sensitivity (SI (D)), and EGP. The model fitted the data well, and SI (P) and SI (D) were estimated with precision in both databases (SI (P) = 5.48 ± 0.54 10(-4) dl·kg(-1)·min(-1) per μU/ml and SI (D) = 9.93 ± 2.18 10(-4) dl·kg(-1)·min(-1) per μU/ml in healthy; SI (P) = 5.41 ± 3.55 10(-4) dl·kg(-1)·min(-1) per μU/ml and SI (D) = 5.34 ± 6.17 10(-4) dl·kg(-1)·min(-1) per μU/ml, in healthy and prediabetic subjects). Estimated SI (P) and that derived from the triple-tracer EGP model were very similar on average. Moreover, the time course of EGP normalized to basal EGP (EGPb), and EGP/EGPb agreed with the results obtained using the triple-tracer method. In this study, we have demonstrated that SI (P), SI (D), and EGP/EGPb time course can be estimated reliably from a single-tracer meal protocol in both healthy and prediabetic subjects., (Copyright © 2015 the American Physiological Society.)

Mathematical modeling of physiological systems is a fundamental milestone of biomedical engineering. Models allow for the quantitative understanding of the intimate functions of a biological system, estimating parameters that are not accessible to direct measurement and performing in silico trials by simulating and tracking a physiological system in case its function has been deranged. Modeling has always been central in the Italian biomedical engineering community. Here, we review the progress in two areas: glucose and neurocomputational modeling with an emphasis on their clinical impact.

Parameter reproducibility is necessary to perform longitudinal studies where parameters are assessed to monitor disease progression or effect of therapy but are also useful in powering the study, i.e., to define how many subjects should be studied to observe a given effect. The assessment of parameter reproducibility is usually accomplished by methods that do not take into account the fact that these parameters are estimated with uncertainty. This is particularly relevant in physiological and clinical studies where usually reproducibility cannot be assessed by multiple testing and is usually assessed from a single replication of the test. Working in a suitable stochastic framework, here we propose a new index (S) to measure reproducibility that takes into account parameter uncertainty and is particularly suited to handle the normal testing conditions of physiological and clinical investigations. Simulation results prove that S, by properly taking into account parameter uncertainty, is more accurate and robust than the methods available in the literature. The new metric is applied to assess reproducibility of insulin sensitivity and β-cell responsivity of a mixed-meal tolerance test from data obtained in the same subjects retested 1 wk apart. Results show that the indices of insulin sensitivity and β-cell responsivity to glucose are well reproducible. We conclude that the oral minimal models provide useful indices that can be used safely in prospective studies or to assess the efficacy of a given therapy., (Copyright © 2015 the American Physiological Society.)

A new computational model, based on the thermodynamically constrained averaging theory, has been recently proposed to predict tumor initiation and proliferation. A similar mathematical approach is proposed here as an aid in diabetic ulcer prevention. The common aspects at the continuum level are the macroscopic balance equations governing the flow of the fluid phase, diffusion of chemical species, tissue mechanics, and some of the constitutive equations. The soft plantar tissue is modeled as a two-phase system: a solid phase consisting of the tissue cells and their extracellular matrix, and a fluid one (interstitial fluid and dissolved chemical species). The solid phase may become necrotic depending on the stress level and on the oxygen availability in the tissue. Actually, in diabetic patients, peripheral vascular disease impacts tissue necrosis; this is considered in the model via the introduction of an effective diffusion coefficient that governs transport of nutrients within the microvasculature. The governing equations of the mathematical model are discretized in space by the finite element method and in time domain using the θ-Wilson Method. While the full mathematical model is developed in this paper, the example is limited to the simulation of several gait cycles of a healthy foot., (Copyright © 2014 John Wiley & Sons, Ltd.)

The glucose story begins with Claude Bernard's discovery of glycogen and milieu interieur, continued with Banting's and Best's discovery of insulin and with Rudolf Schoenheimer's paradigm of dynamic body constituents. Tracers and compartmental models allowed moving to the first quantitative pictures of the system and stimulated important developments in terms of modeling methodology. Three classes of multiscale models, models to measure, models to simulate, and models to control the glucose system, are reviewed in their historical development with an eye to the future.

The simultaneous assessment of insulin action, secretion, and hepatic extraction is key to understanding postprandial glucose metabolism in nondiabetic and diabetic humans. We review the oral minimal method (i.e., models that allow the estimation of insulin sensitivity, β-cell responsivity, and hepatic insulin extraction from a mixed-meal or an oral glucose tolerance test). Both of these oral tests are more physiologic and simpler to administer than those based on an intravenous test (e.g., a glucose clamp or an intravenous glucose tolerance test). The focus of this review is on indices provided by physiological-based models and their validation against the glucose clamp technique. We discuss first the oral minimal model method rationale, data, and protocols. Then we present the three minimal models and the indices they provide. The disposition index paradigm, a widely used β-cell function metric, is revisited in the context of individual versus population modeling. Adding a glucose tracer to the oral dose significantly enhances the assessment of insulin action by segregating insulin sensitivity into its glucose disposal and hepatic components. The oral minimal model method, by quantitatively portraying the complex relationships between the major players of glucose metabolism, is able to provide novel insights regarding the regulation of postprandial metabolism.

The experimental protocol of the perfused rat pancreas is commonly used to evaluate β-cell function. In this context, mathematical models become useful tools through the determination of indexes that allow the assessment of β-cell function in different experimental groups and the quantification of the effects of antidiabetic drugs, secretagogues, or treatments. However, a minimal model applicable to the isolated perfused rat pancreas has so far been unavailable. In this work, we adapt the C-peptide minimal model applied previously to the intravenous glucose tolerance test to obtain a specific model for the experimental settings of the perfused pancreas. Using the model, it is possible to estimate indexes describing β-cell responsivity for first (ΦD) and second phase (ΦS, T) of insulin secretion. The model was initially applied to untreated pancreata and afterward used for the assessment of pharmacologically relevant agents (the gut hormone GLP-1, the potent GLP-1 receptor agonist lixisenatide, and a GPR40/FFAR1 agonist, SAR1) to quantify and differentiate their effect on insulin secretion. Model fit was satisfactory, and parameters were estimated with good precision for both untreated and treated pancreata. Model application showed that lixisenatide reaches improvement of β-cell function similarly to GLP-1 (11.7- vs. 13.1-fold increase in ΦD and 2.3- vs. 2.8-fold increase in ΦS) and demonstrated that SAR1 leads to an additional improvement of β-cell function in the presence of postprandial GLP-1 levels.

Background: The objective of this research is to develop a new artificial pancreas that takes into account the experience accumulated during more than 5000 h of closed-loop control in several clinical research centers. The main objective is to reduce the mean glucose value without exacerbating hypo phenomena. Controller design and in silico testing were performed on a new virtual population of the University of Virginia/Padova simulator., Methods: A new sensor model was developed based on the Comparison of Two Artificial Pancreas Systems for Closed-Loop Blood Glucose Control versus Open-Loop Control in Patients with Type 1 Diabetes trial AP@home data. The Kalman filter incorporated in the controller has been tuned using plasma and pump insulin as well as plasma and continuous glucose monitoring measures collected in clinical research centers. New constraints describing clinical knowledge not incorporated in the simulator but very critical in real patients (e.g., pump shutoff) have been introduced. The proposed model predictive control (MPC) is characterized by a low computational burden and memory requirements, and it is ready for an embedded implementation., Results: The new MPC was tested with an intensive simulation study on the University of Virginia/Padova simulator equipped with a new virtual population. It was also used in some preliminary outpatient pilot trials. The obtained results are very promising in terms of mean glucose and number of patients in the critical zone of the control variability grid analysis., Conclusions: The proposed MPC improves on the performance of a previous controller already tested in several experiments in the AP@home and JDRF projects. This algorithm complemented with a safety supervision module is a significant step toward deploying artificial pancreases into outpatient environments for extended periods of time., (© 2013 Diabetes Technology Society.)

Quantifying the effect size of acute exercise on insulin sensitivity (SI(exercise)) and simultaneous measurement of glucose disappearance (R(d)), endogenous glucose production (EGP), and meal glucose appearance in the postprandial state has not been developed in humans. To do so, we studied 12 healthy subjects [5 men, age 37.1 ± 3.1 yr, body mass index 24.1 ± 1.1 kg/m², fat-free mass (FFM) 50.9 ± 3.9 kg] during moderate exercise at 50% V(O₂max) for 75 min, 120-195 min after a triple-tracer mixed meal consumed at time 0. Tracer infusion rates were adjusted to achieve constant tracer-to-tracee ratio and minimize non-steady-state errors. Glucose turnover was estimated by accounting for the nonstationary kinetics introduced by exercise. Insulin sensitivity index was calculated in each subject both in the absence [time (t) = 0-120 min, SI(rest)] and presence (t = 0-360 min, SI(exercise)) of physical activity. EGP at t = 0 min (13.4 ± 1.1 μM·kg FFM⁻¹·min⁻¹) fell at t = 120 min (2.4 ± 0.4 μM·kg FFM⁻¹·min⁻¹) and then rapidly rose almost eightfold at t = 180 min (18.2 ± 2.6 μM·kg FFM⁻¹·min⁻¹) before gradually falling at t = 360 min (10.6 ± 0.9 μM·kg FFM⁻¹·min⁻¹). R(d) rapidly peaked at t = 120 min at the start of exercise (89.5 ± 11.6 μM·kg FFM⁻¹·min⁻¹) and then gradually declined at t = 195 min (26.4 ± 3.3 μM·kg FFM⁻¹·min⁻¹) before returning to baseline at t = 360 min. SI(exercise) was significantly higher than SI(rest) (21.6 ± 3.7 vs. 12.5 ± 2.0 10⁻⁴ dl·kg⁻¹·min⁻¹ per μU/ml, P < 0.0005). Glucose turnover was estimated for the first time during exercise with the triple-tracer technique. Our results, applying state-of-the-art techniques, show that moderate exercise almost doubles postprandial insulin sensitivity index in healthy subjects.

Carbohydrate metabolism in humans is regulated by insulin secretion from pancreatic β-cells and glucose disposal by insulin-sensitive tissues. Insulin facilitates glucose utilization in peripheral tissues and suppresses hepatic glucose production. Any defects in insulin action predispose an individual to glucose intolerance and Type 2 diabetes mellitus. Early detection of defects in insulin action could provide opportunities to prevent or delay progression of the disease state. There are different approaches to assess insulin action. Initial methods, such as peripheral insulin concentration and simple indices, have several limitations. Subsequently, researchers developed methodologies using intravenous glucose infusion to determine glucose fluxes. However, these methodologies are limited by being non-physiological. Newer, innovative techniques that have been developed are more sophisticated and physiological. By modelling glucose kinetics using isotope dilution techniques, several robust parameters can be obtained that are physiologically relevant and sound. This brief review summarizes most of the non-physiological and physiological methodologies used to measure the variables of insulin action., (© 2013 The Authors. Diabetic Medicine © 2013 Diabetes UK.)

Recently, we proposed a model describing the suppression of endogenous glucose production (EGP) during a meal. It assumes that EGP suppression depends on glucose concentration and its rate of change and on delayed insulin action. Hepatic insulin sensitivity (S(I)(Lmeal)) can be derived from EGP model parameters. This model was shown to adequately describe EGP profiles measured with multiple tracer techniques; however, S(I)(Lmeal) has never been compared directly with its euglycemic hyperinsulinemic clamp counterpart (S(I)(Lclamp)). To do so, 62 subjects with different degrees of glucose tolerance underwent a triple-tracer mixed meal. Fifty-seven subjects also underwent a labeled ([3-(3)H]glucose) euglycemic hyperinsulinemic clamp. From the triple-tracer meal data, virtually model-independent estimates of EGP were obtained using the tracer-to-tracee clamp technique, and the EGP model was identified in each subject. Model fit was satisfactory, and S(I)(Lmeal) was estimated with good precision. Correlation between S(I)(Lclamp) and S(I)(Lmeal) was good (r = 0.72, P < 0.001); however, S(I)(Lmeal) was lower than S(I)(Lclamp) (4.60 ± 0.64 vs. 8.73 ± 1.07 10(-4) dl·kg(-1)·min(-1) per μU/ml, P < 0.01). This difference may be due to different ranges of insulin explored during the two tests (ΔI(clamp) = 15.60 ± 1.61 vs. ΔI(meal)= 83.37 ± 10.71 μU/ml) as well as steady- vs. non-steady-state glucose and insulin profiles. In conclusion, the new EGP model provides an estimate of hepatic insulin sensitivity during a meal that is in good agreement with that derived in the same individuals with a hyperinsulinemic clamp. When used in conjunction with the minimal model, the approach potentially enables estimation of hepatic insulin sensitivity from a single-tracer labeled meal or oral glucose tolerance test.

To correctly evaluate the glucose control system, it is crucial to account for both insulin sensitivity and secretion. The disposition index (DI) is the most widely accepted method to do so. The original paradigm (hyperbolic law) consists of the multiplicative product of indices related to insulin sensitivity and secretion, but more recently, an alternative formula has been proposed with the exponent α (power function law). Traditionally, curve-fitting approaches have been used to evaluate the DI in a population: the algorithmic implementations often introduce some critical issues, such as the assumption that one of the two indices is error free or the effects of the log transformation on the measurement errors. In this work, we review the commonly used approaches and show that they provide biased estimates. Then we propose a novel nonlinear total least square (NLTLS) approach, which does not need to use the approximations built in the previously proposed alternatives, and show its superiority. All of the traditional fit procedures, including NLTLS, account only for uncertainty affecting insulin sensitivity and secretion indices when they are estimated from noisy data. Thus, they fail when part of the observed variability is due to inherent differences in DI values between individuals. To handle this inevitable source of variability, we propose a nonlinear mixed-effects approach that describes the DI using population hyperparameters such as the population typical values and covariance matrix. On simulated data, this novel technique is much more reliable than the curve-fitting approaches, and it proves robust even when no or small population variability is present in the DI values. Applying this new approach to the analysis of real IVGTT data suggests a value of α significantly smaller than 1, supporting the importance of testing the power function law as an alternative to the simpler hyperbolic law.

Diabetes mellitus is one of the most common chronic diseases, and a clinically important task in its management is the prevention of hypo/hyperglycemic events. This can be achieved by exploiting continuous glucose monitoring (CGM) devices and suitable short-term prediction algorithms able to infer future glycemia in real time. In the literature, several methods for short-time glucose prediction have been proposed, most of which do not exploit information on meals, and use past CGM readings only. In this paper, we propose an algorithm for short-time glucose prediction using past CGM sensor readings and information on carbohydrate intake. The predictor combines a neural network (NN) model and a first-order polynomial extrapolation algorithm, used in parallel to describe, respectively, the nonlinear and the linear components of glucose dynamics. Information on the glucose rate of appearance after a meal is described by a previously published physiological model. The method is assessed on 20 simulated datasets and on 9 real Abbott FreeStyle Navigator datasets, and its performance is successfully compared with that of a recently proposed NN glucose predictor. Results suggest that exploiting meal information improves the accuracy of short-time glucose prediction.

Minimally invasive continuous glucose monitoring (CGM) sensors can greatly help diabetes management. Most of these sensors consist of a needle electrode, placed in the subcutaneous tissue, which measures an electrical current exploiting the glucose-oxidase principle. This current is then transformed to glucose levels after calibrating the sensor on the basis of one, or more, self-monitoring blood glucose (SMBG) samples. In this study, we design and test a real-time signal-enhancement module that, cascaded to the CGM device, improves the quality of its output by a proper postprocessing of the CGM signal. In fact, CGM sensors measure glucose in the interstitium rather than in the blood compartment. We show that this distortion can be compensated by means of a regularized deconvolution procedure relying on a linear regression model that can be updated whenever a pair of suitably sampled SMBG references is collected. Tests performed both on simulated and real data demonstrate a significant accuracy improvement of the CGM signal. Simulation studies also demonstrate the robustness of the method against departures from nominal conditions, such as temporal misplacement of the SMBG samples and uncertainty in the blood-to-interstitium glucose kinetic model. Thanks to its online capabilities, the proposed signal-enhancement algorithm can be used to improve the performance of CGM-based real-time systems such as the hypo/hyper glycemic alert generators or the artificial pancreas.

In diabetes, the mean square error (MSE) metric is extensively used for assessing glucose prediction methods and identifying glucose models. One limitation of this metric is that, by equally treating errors in hypo-, eu-, and hyperglycemia, it is not able to weight the different clinical impact of errors in these three situations. In this paper, we propose a new cost function, which overcomes this limitation and can be used in place of MSE for several scopes, in particular for assessing the quality of glucose predictors and identifying glucose models. The new metric called glucose-specific MSE (gMSE) modifies MSE with a Clark error grid inspired penalty function, which penalizes overestimation in hypoglycemia and underestimation in hyperglycemia, i.e., the most harmful conditions on a clinical perspective. From a mathematical point of view, gMSE retains sensitivity of MSE and inherits some of its important mathematical features, in particular it has no local minima, simplifying the optimization. This makes it suitable for model identification purposes also. First, the goodness of it is demonstrated by means of three experiments, designed ad hoc to evidence its sensitivity to accuracy, precision, and distortion in glucose predictions. Second, a prediction assessment problem is presented, in which two real prediction profiles are compared. Results show that the MSE chooses the worst clinical situation, while gMSE correctly selects the situation with less clinical risk. Finally, we also demonstrate that models identified minimizing gMSE are more accurate in potentially harmful situations (hypo- and hyperglycemia) than those obtained by MSE.

Insulin secretion from pancreatic beta cells is a fundamental physiological process, and its impairment plays a pivotal role in the development of diabetes. Mathematical modeling of insulin secretion has a long history, both on the level of the entire body and on the cellular and subcellular scale. However, little direct communication between these disparate scales has been included in mathematical models so far. Recently, we have proposed a minimal model for the incretin effect by which the gut hormone glucagon-like peptide 1 (GLP-1) enhances insulin secretion. To understand how this model couples to cellular events, we use a previously published mechanistic model of insulin secretion, and show mathematically that induction of glucose competence in beta cells by GLP-1 can underlie derivative control by GLP-1.

The use of arteriovenous (AV) concentration differences to measure the production of a substance at organ/tissue level by Fick principle is limited to steady state. Out of steady state, there is the need, as originally proposed by Zierler, to account for the nonnegligible transit time of the substance through the system. Based on this theory, we propose a modeling approach that adopts a parametric description for production and transit time. Once the unknown parameters are estimated on AV data, the transition time of the substance can be assessed and production can be reconstructed. As a case study, we discuss the estimation of pancreatic insulin secretion during a meal from C-peptide concentrations measured in femoral artery and hepatic vein in 12 subjects. Results support the importance of accounting for nonnegligible transit times, even if C-peptide mean transit time across the splanchnic bed is rather limited (3.3 ± 1.3 min), it affects the estimation of pancreatic insulin secretion which shows a significantly different profile in the early portion of the postprandial period when estimated either with the novel modeling approach or with the simplified steady state equation., (© 2011 IEEE)

Background: Continuous glucose monitoring (CGM) data can be exploited to prevent hypo-/hyperglycemic events in real time by forecasting future glucose levels. In the last few years, several glucose prediction algorithms have been proposed, but how to compare them (e.g., methods based on polynomial rather than autoregressive time-series models) and even how to determine the optimal parameter set for a given method (e.g., prediction horizon and forgetting) are open problems., Methods: A new index, J, is proposed to optimally design a prediction algorithm by taking into account two key components: the regularity of the predicted profile and the time gained thanks to prediction. Effectiveness of J is compared with previously proposed criteria such as the root mean square error (RMSE) and continuous glucose-error grid analysis (CG-EGA) on 20 Menarini (Florence, Italy) Glucoday® CGM data sets., Results: For a given prediction algorithm, the new index J is able to suggest a more consistent and better parameter set (e.g., prediction horizon and forgetting factor of choice) than RMSE and CG-EGA. In addition, the minimization of J can reliably be used as a selection criterion in comparing different prediction methods., Conclusions: The new index can be used to compare different prediction strategies and to optimally design their parameters.

Glucagon-like peptide-1 (GLP-1)-based therapies for diabetes have aroused interest because of their effects on insulin secretion and glycemic control. However, a mechanistic model enabling quantitation of pancreatic response to GLP-1 has never been developed. To develop such a model we studied 88 healthy individuals (age 26.3 +/- 0.6 yr, BMI 24.9 +/- 0.4 kg/m(2)) by use of a hyperglycemic clamp. A variable infusion maintained glucose concentrations at 150 mg/dl for 240 min. At 120 min, an intravenous infusion of GLP-1 was started (0.75 pmol kg(-1) min(-1) from 120-180 min, 1.5 pmol kg(-1) min(-1) from 181-240 min). Consequently, plasma C-peptide concentration rose from 1,852.0 +/- 62.8 pmol/l at 120 min to 4,272.2 +/- 176.4 pmol/l at 180 min and to 6,995.8 +/- 323.5 pmol/l at 240 min. Four models of GLP-1 action on insulin secretion were considered. All models share the common assumption that insulin secretion is made up of two components, one proportional to glucose rate of change through dynamic responsivity, Phi(d), and one proportional to glucose through static responsivity, Phi(s), but differing by modality of GLP-1 control. The model that best fit C-peptide data assumes that above-basal insulin secretion depends linearly on GLP-1 concentration and its rate of change. An index (Pi) measuring the percentage increase of secretion due to GLP-1 is derived. Before GLP-1 infusion, Phi(d) = 245.7 +/- 15.6 10(-9) and Phi(s) = 25.2 +/- 1.4 10(-9) min(-1). Under GLP-1 stimulus, Pi = 12.6 +/- 0.71% per pmol/l, meaning that an increase of 5 pmol/l in peripheral GLP-1 concentrations induces an approximately 60% increase in over-basal insulin secretion.

Population approaches, traditionally employed in pharmacokinetic-pharmacodynamic studies, have shown value also in the context of glucose-insulin metabolism models by providing more accurate individual parameters estimates and a compelling statistical framework for the analysis of between-subject variability (BSV). In this work, the advantages of population techniques are further explored by proposing integration of covariates in the intravenous glucose tolerance test (IVGTT) glucose minimal model analysis. A previously published dataset of 204 healthy subjects, who underwent insulin-modified IVGTTs, was analyzed in NONMEM, and relevant demographic information about each subject was employed to explain part of the BSV observed in parameter values. Demographic data included height, weight, sex, and age, but also basal glycemia and insulinemia, and information about amount and distribution of body fat. On the basis of nonlinear mixed-effects modeling, age, visceral abdominal fat, and basal insulinemia were significant predictors for SI (insulin sensitivity), whereas only age and basal insulinemia were significant for P2 (insulin action). The volume of distribution correlated with sex, age, percentage of total body fat, and basal glycemia, whereas no significant covariate was detected to explain variability in SG (glucose effectiveness). The introduction of covariates resulted in a significant shrinking of the unexplained BSV, especially for SI and P2 and considerably improved the model fit. These results offer a starting point for speculation about the physiological meaning of the relationships detected and pave the way for the design of less invasive and less expensive protocols for epidemiological studies of glucose-insulin metabolism.

The oral glucose tolerance test and meal tolerance test are common clinical tests of the glucose-insulin system. Several mathematical models have been suggested as means to extract information about beta-cell function from data from oral tolerance tests. Any such model needs to be fairly simple but should at the same time be linked to the underlying biology of the insulin-secreting beta-cells. The scope of the present work is to present a way to make such a connection using a recent model describing intracellular mechanisms. We show how the three main components of oral minimal secretion models, derivative control, proportional control, and delay, are related to subcellular events, thus providing mechanistic underpinning of the assumptions of the minimal models.

Background: Diabetic sensorimotor polyneuropathy is a long-term diabetic complication. It is involved in the pathogenesis of the diabetic foot, which is a major cause of morbidity and mortality. The study aims to investigate the effects of diabetic polyneuropathy on gait and posture., Methods: Sixty seven subjects were enrolled: 21 diabetics without polyneuropathy, 26 with polyneuropathy, 20 controls (respectively, mean age 63.8 (SD 5.4), 63.2 (SD 5.6), 59.0 (SD 5.2) years, mean body mass index 26.3 (SD 2.5), 25.6 (SD 3), 24.0 (SD 2.9)). Postural and morphological evaluation and gait analysis were performed. Physical examination, together with a motion capture system synchronized with two force plates and two baropodometric systems were used. We evaluated lower limb mobility, foot deformities, trunk and pelvic posture, knee and heel position, plantar foot arch, three dimensional kinematics and kinetics during gait. The effect of peripheral vascular disease and microangiopathy on trunk and lower limb motion was also evaluated., Findings: Trunk and lower limb joint mobility (in static and dynamic states) were more reduced in diabetics either with or without polyneuropathy on each plane; however in diabetics with polyneuropathy significantly lower ranges of motion were registered. Furthermore, both groups showed significant reductions in each joint moment and velocity (P0.003) during gait. In presence of both vasculopathy and microangiopathy a further significant reduction (P0.001) was noticed., Interpretation: Altered gait and posture were found in diabetic patients irrespective of polyneuropathy. This approach may be relevant to predict the risk ulceration before clinically detectable neuropathy.

This study considered the problem of identifying and evaluating the factors of individual performance during race walking. In particular, the study explored the use of functional principal component analysis (f-PCA), a multivariate data analysis, for assessing and classifying the kinematics and kinetics of the knee joint in competitive race walkers. Seven race walkers of international and national level participated to the study. An optoelectronic system and a force platform were used to capture three-dimensional kinematics and kinetics of lower limbs during the race walking cycle. Functional principal component analysis was applied bilaterally to the sagittal knee angle and net moment data, because knee joint motion is fundamental to race walking technique. Scatterplots of principal component scores provided evidence of athletes' technical differences and asymmetries even when traditional analysis (mean +/- s curves) was not effective. Principal components provided indications for race walkers' classification and identified potentially important technical differences between higher and lower skilled athletes. Therefore, f-PCA might represent a future aid for the fine analysis of sports movements, if consistently applied to performance monitoring.

Intravenous glucose tolerance test (IVGTT) minimal model parameters are commonly estimated by weighted least squares (WLSs) on each subject data. Sometimes, with sparse data, individual parameters cannot be satisfactorily obtained. In such cases, a population approach could be preferable. These methods allow borrowing information across all subjects simultaneously, quantifying population features directly, and subsequently, deriving individual parameter estimates. In this paper, we assessed different estimation methods on simulated datasets. Besides the standard WLS approach, we applied iterative procedures (iterative two-stage (ITS) and global two-stage (GTS) methods) as well as nonlinear mixed-effects models (NLMEMs), where the likelihood is based on model linearization: first-order (FO), FO conditional estimation (FOCE), and Laplace (LAP) approximations. The synthetic dataset, initially very rich, was progressively reduced (by 50% and 75%) in order to assess the robustness of the results in sparsely sampled situations. Our results show that, even with intensive sampling, population approaches provide more reliable parameter estimates. Moreover, these estimates are remarkably more robust when the data become scarce. ITS and GTS encounter critical problems when single subjects have very poor sampling schedules, whereas the NLMEM (excluding FO) methods are more versatile and able to cope with such situations. FOCE appears as the most satisfactory approach.

Given the increase in the incidence of insulin resistance, obesity, and type 2 diabetes in children and adolescents, it would be of paramount importance to assess quantitative indices of insulin secretion and action during a physiological perturbation, such as a meal or an oral glucose-tolerance test (OGTT). A minimal model method is proposed to measure quantitative indices of insulin secretion and action in adolescents from an oral test. A 7 h, 21-sample OGTT was performed in 11 adolescents. The C-peptide minimal model was identified on C-peptide and glucose data to quantify indices of beta-cell function: static phi(s) and dynamic phi(d) responsivity to glucose from which total responsivity phi was also measured. The glucose minimal model was identified on glucose and insulin data to estimate insulin sensitivity, S(I), which was compared to a reference measure, S(I)(ref), provided by a tracer method. Disposition indices, which adjust insulin secretion for insulin action, were then calculated. Indices of beta-cell function were phi(s) = 51.35 +/- 8.89 x 10(-9)min(-1), phi(d) = 1,392 +/- 258 x 10(-9), and phi = 82.09 +/- 17.70 x 10(-9)min(-1). Insulin sensitivity was S(I) = 14.19 +/- 2.73 x 10(-4), not significantly different from S(I)(ref) = 14.96 +/- 3.04 x 10(-4) dl/kg.min per microU/ml, and well correlated: r = 0.98, P < 0.0001, thus indicating that S(I) can be accurately measured from an oral test. Disposition indices were DI(s) = 1,040 +/- 201 x 10(-14) dl/kg/min(2) per pmol/l, DI(d) = 33,178 +/- 10,720 x 10(-14) dl/kg/min per pmol/l, DI = 1,844 +/- 522 x 10(-14) dl/kg/min(2) per pmol/l. Virtually the same minimal model assessment was obtained with a reduced 3 h, 9-sample protocol. OGTT interpreted with C-peptide and glucose minimal model has the potential to provide novel insight regarding the regulation of glucose metabolism in adolescents, and to evaluate the effect of obesity and interventions such as diet and exercise.

Introduction: A simulation model of a glucose-insulin system accounting for physical activity is needed to reliably simulate normal life conditions, thus accelerating the development of an artificial pancreas. In fact, exercise causes a transient increase of insulin action and may lead to hypoglycemia. However, physical activity is difficult to model. In the past, it was described indirectly as a rise in insulin. Recently, a new parsimonious model of exercise effect on glucose homeostasis has been proposed that links the change in insulin action and glucose effectiveness to heart rate (HR). The aim of this study was to plug this exercise model into our recently proposed large-scale simulation model of glucose metabolism in type 1 diabetes to better describe normal life conditions., Methods: The exercise model describes changes in glucose-insulin dynamics in two phases: a rapid on-and-off change in insulin-independent glucose clearance and a rapid-on/slow-off change in insulin sensitivity. Three candidate models of glucose effectiveness and insulin sensitivity as a function of HR have been considered, both during exercise and recovery after exercise. By incorporating these three models into the type 1 diabetes model, we simulated different levels (from mild to moderate) and duration of exercise (15 and 30 minutes), both in steady-state (e.g., during euglycemic-hyperinsulinemic clamp) and in nonsteady state (e.g., after a meal) conditions., Results: One candidate exercise model was selected as the most reliable., Conclusions: A type 1 diabetes model also describing physical activity is proposed. The model represents a step forward to accurately describe glucose homeostasis in normal life conditions; however, further studies are needed to validate it against data., (© Diabetes Technology Society)

The ability to accurately quantify indexes of the individual role of glucose (GE(L)) and insulin (S(I)(L)) in the suppression of endogenous glucose production (EGP) would improve the understanding of liver metabolism. Measuring these indexes during an IVGTT by minimal modeling of tracer labeled and unlabeled glucose data is often unreliable, possibly due to an inadequate description of EGP included in the Minimal Model. Moreover, a validation of the assumptions of the Minimal Model on EGP data has never been done. Recently, Krudys et al. (Krudys KM, Dodds MG, Nissen SM, Vicini P. Am J Physiol Endocrinol Metab 288: E1038-E1046, 2005) have proposed a PK/PD (pharmacokinetic/pharmacodynamic) model of the EGP profile that occurs during an intravenous glucose tolerance test (IVGTT); however, this model has also not been validated. The aim of this study was thus to test the Minimal Model, the PK/PD model, and six alternative EGP descriptions on recent model-independent EGP data of 20 subjects obtained with a triple-tracer meal protocol. Model performance was compared in terms of data fit, precision of the estimated parameters, and physiological plausibility. Neither the PK/PD nor the traditional Minimal Model were able to accurately describe EGP data or provide reliable estimates of the indexes. In contrast, one of the new models performed best by showing a good fit and providing accurate and precise estimates of hepatic sensitivity indexes: GE(L) = 0.013 +/- 0.001 dl x kg(-1) x min(-1); S(I)(L) = 5.34 +/- 0.47 10(-4) dl x kg(-1) x min(-1) per microU/ml (42 and 34%, respectively, of total sensitivity indexes GE(TOT) and S(I)(TOT)). Although this model requires further validation, it has the potential to improve our understanding of the role of the liver in pathophysiological states.

Population kinetic modeling approaches, implemented as nonlinear mixed effects models, are attracting growing interest in many fields of biomedicine thanks to their value in estimating population features from sparsely sampled data. However, their application often entails approximations of the original model function, whose effect is difficult to gauge in general. We apply negative log-likelihood profiling to assess the effect of model approximation on the glucose-insulin Minimal Model, and compare nonlinear mixed-effects approximate methods to two-stage methods. Our preliminary findings suggest that nonlinear mixed effects models provide accurate parameter estimates, but also point out that the reliability of such estimates may be affected by large population variability and small sample size.

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.

Background: Microarray time series studies are essential to understand the dynamics of molecular events. In order to limit the analysis to those genes that change expression over time, a first necessary step is to select differentially expressed transcripts. A variety of methods have been proposed to this purpose; however, these methods are seldom applicable in practice since they require a large number of replicates, often available only for a limited number of samples. In this data-poor context, we evaluate the performance of three selection methods, using synthetic data, over a range of experimental conditions. Application to real data is also discussed., Results: Three methods are considered, to assess differentially expressed genes in data-poor conditions. Method 1 uses a threshold on individual samples based on a model of the experimental error. Method 2 calculates the area of the region bounded by the time series expression profiles, and considers the gene differentially expressed if the area exceeds a threshold based on a model of the experimental error. These two methods are compared to Method 3, recently proposed in the literature, which exploits splines fit to compare time series profiles. Application of the three methods to synthetic data indicates that Method 2 outperforms the other two both in Precision and Recall when short time series are analyzed, while Method 3 outperforms the other two for long time series., Conclusion: These results help to address the choice of the algorithm to be used in data-poor time series expression study, depending on the length of the time series.

Background: In patients with acute respiratory distress syndrome (ARDS), it is well known that only part of the lungs is aerated and surfactant function is impaired, but the extent of lung damage and changes in surfactant turnover remain unclear. The objective of the study was to evaluate surfactant disaturated-phosphatidylcholine turnover in patients with ARDS using stable isotopes., Methods: We studied 12 patients with ARDS and 7 subjects with normal lungs. After the tracheal instillation of a trace dose of 13C-dipalmitoyl-phosphatidylcholine, we measured the 13C enrichment over time of palmitate residues of disaturated-phosphatidylcholine isolated from tracheal aspirates. Data were interpreted using a model with two compartments, alveoli and lung tissue, and kinetic parameters were derived assuming that, in controls, alveolar macrophages may degrade between 5 and 50% of disaturated-phosphatidylcholine, the rest being lost from tissue. In ARDS we assumed that 5-100% of disaturated-phosphatidylcholine is degraded in the alveolar space, due to release of hydrolytic enzymes. Some of the kinetic parameters were uniquely determined, while others were identified as lower and upper bounds., Results: In ARDS, the alveolar pool of disaturated-phosphatidylcholine was significantly lower than in controls (0.16 +/- 0.04 vs. 1.31 +/- 0.40 mg/kg, p < 0.05). Fluxes between tissue and alveoli and de novo synthesis of disaturated-phosphatidylcholine were also significantly lower, while mean resident time in lung tissue was significantly higher in ARDS than in controls. Recycling was 16.2 +/- 3.5 in ARDS and 31.9 +/- 7.3 in controls (p = 0.08)., Conclusion: In ARDS the alveolar pool of surfactant is reduced and disaturated-phosphatidylcholine turnover is altered.

A reliable model of glucose absorption after oral ingestion may facilitate simulation as well as pathophysiological studies. One of the difficulties for the development and quality assessment of such models has been the lack of gold standard data for their validation. Thus, while data on plasma concentrations of glucose are available, the rates of appearance in plasma of ingested glucose (Ra) were not available to develop such models. Here we utilize the recent availability of Ra data, estimated with a model-independent multiple tracer technique, to formulate a system model of intestinal glucose absorption. Two published and two new models are tested on this new data set. One of the two new models performed best: it is nonlinear, describes the Ra data well and its parameters are estimated with good precision. This model has important potential both in simulation contexts, e.g., it can be incorporated in whole-body models of the glucose regulatory system, as well as in physiological and clinical studies to quantitatively characterize possible impairment of glucose absorption in particular populations such as elderly and diabetic individuals.

Human motion capture is frequently used to study musculoskeletal biomechanics and clinical problems, as well as to provide realistic animation for the entertainment industry. The most popular technique for human motion capture uses markers placed on the skin, despite some important drawbacks including the impediment to the motion by the presence of skin markers and relative movement between the skin where the markers are placed and the underlying bone. The latter makes it difficult to estimate the motion of the underlying bone, which is the variable of interest for biomechanical and clinical applications. A model-based markerless motion capture system is presented in this study, which does not require the placement of any markers on the subject's body. The described method is based on visual hull reconstruction and an a priori model of the subject. A custom version of adapted fast simulated annealing has been developed to match the model to the visual hull. The tracking capability and a quantitative validation of the method were evaluated in a virtual environment for a complete gait cycle. The obtained mean errors, for an entire gait cycle, for knee and hip flexion are respectively 1.5 degrees (+/-3.9 degrees ) and 2.0 degrees (+/-3.0 degrees ), while for knee and hip adduction they are respectively 2.0 degrees (+/-2.3 degrees ) and 1.1 degrees (+/-1.7 degrees ). Results for the ankle and shoulder joints are also presented. Experimental results captured in a gait laboratory with a real subject are also shown to demonstrate the effectiveness and potential of the presented method in a clinical environment.

A simulation model of the glucose-insulin system in the postprandial state can be useful for studying the pathophysiology of diabetes. Here we present a new simulation model which describes the physiological events which occur after a meal, by employing the quantitative knowledge which has become available in recent years. Model parameters were set to fit data of 204 normal subjects which underwent a triple tracer meal protocol which provided quasi model-independent estimates of major glucose and insulin fluxes. Model results are shown in describing normal daily life (breakfast, lunch, dinner) both in normal and pathophysiological situations. The potential of the model for studying type 1 diabetes is illustrated by simulating both open- and closed-loop insulin infusion strategies.

The liver is the principal site of insulin degradation, and assessing its ability to extract insulin is important to understand several pathological states. Noninvasive quantification of hepatic extraction (HE) in an individual requires comparing the profiles of insulin secretion (ISR) and posthepatic insulin delivery rate (IDR). To do this, we propose here the combined use of the classical C-peptide minimal model with a new minimal model of insulin delivery and kinetics. The models were identified on insulin-modified intravenous glucose tolerance test (IM-IVGTT) data of 20 healthy subjects. C-peptide kinetics were fixed to standard population values, whereas insulin kinetics were assessed in each individual, along with IDR parameters, thanks to the presence of insulin decay data observed after exogenous insulin administration. From the two models, profiles of ISR and IDR were predicted, and ISR and IDR indexes of beta-cell responsivity to glucose in the basal state, as well as during first- and second-phase secretion, were estimated. HE profile, obtained by comparing ISR and IDR profiles, showed a rapid suppression immediately after the glucose administration. HE indexes, obtained by comparing ISR and IDR indexes, indicated that the liver is able to extract 70 +/- 9% of insulin passing through it in the basal state and 54 +/- 14% during IM-IVGTT. In conclusion, insulin secretion, kinetics, and hepatic extraction can be reliably assessed during an IM-IVGTT by using insulin and C-peptide minimal models.

The minimal model (MM) of glucose kinetics during an intravenous glucose tolerance test (IVGTT) is widely used in clinical studies to measure metabolic indexes such as glucose effectiveness (S(G)) and insulin sensitivity (S(I)). The standard (frequent) IVGTT sampling schedule (FSS) for MM identification consists of 30 points over 4 h. To facilitate clinical application of the MM, reduced sampling schedules (RSS) of 13-14 samples have also been derived for normal subjects. These RSS are especially appealing in large-scale studies. However, with RSS, the precision of S(G) and S(I) estimates deteriorates and, in certain cases, becomes unacceptably poor. To overcome this difficulty, population approaches such as the iterative two-stage (ITS) approach have been recently proposed, but, besides leaving some theoretical issues open, they appear to be oversized for the problem at hand. Here, we show that a Bayesian methodology operating at the single individual level allows an accurate determination of MM parameter estimates together with a credible measure of their precision. Results of 16 subjects show that, in passing from FSS to RSS, there are no significant changes of point estimates in nearly all of the subjects and that only a limited deterioration of parameter precision occurs. In addition, in contrast with the previously proposed ITS method, credible confidence intervals (e.g., excluding negative values) are obtained. They can be crucial for a subsequent use of the estimated MM parameters, such as in classification, clustering, regression, or risk analysis.

Measuring insulin sensitivity in the presence of physiological changes in glucose and insulin concentrations, e.g., during a meal or OGTT, is important to better understand insulin resistance in a variety of metabolic conditions. Recently, two oral minimal models have been proposed to measure overall insulin sensitivity (S(I)) and its selective effect on glucose disposal (S(I)*) from oral tests. S(I) and S(I)* have been successfully validated against multiple tracer meal estimates, but validation against euglycemic hyperinsulinemic clamp estimates is lacking. Here, we do so in 21 subjects who underwent both a multiple-tracer OGTT and a labeled euglycemic hyperinsulinemic clamp. Correlation between minimal-model S(I), S(I) and corresponding clamp estimates S(I)(*clamp), S(I)(*clamp) was satisfactory, respectively r = 0.81, P < 0.001, and r = 0.71, P < 0.001. S(I) was significantly lower than S(I)(clamp) (8.08 +/- 0.89 vs. 13.66 +/- 1.69 10(-4) dl.kg(-1).min(-1) per microU/ml, P = 0.0002), whereas S(I) and S(I)(*clamp) were very similar (8.17 +/- 1.59 vs. 8.84 +/- 1.39 10(-4) dl.kg(-1).min(-1) per microU/ml, P = 0.52). These results add credibility to the oral minimal-model method as a simple and reliable physiological tool to estimate S(I) and S(I)*, also in large-scale clinical trials.

The oral glucose minimal model (OMM) measures insulin sensitivity (S(I)) and the glucose rate of appearance (R(a)) of ingested glucose in the presence of physiological changes of insulin and glucose concentrations. However, S(I) of OMM measures the overall effect of insulin on glucose utilization and glucose production. In this study we show that, by adding a tracer to the oral dose, e.g., of a meal, and by using the labeled version of OMM, OMM* to interpret the data, one can measure the selective effect of insulin on glucose disposal, S(I)*. Eighty-eight individuals underwent both a triple-tracer meal with the tracer-to-tracee clamp technique, providing a model-independent reference of the R(a) of ingested glucose (R(a meal)(ref)) and an insulin-modified labeled intravenous glucose tolerance test (IVGTT*). We show that OMM* provides not only a reliable means of tracing the R(a) of ingested glucose (R(a meal)) but also accurately measures S(I)*. We do so by comparing OMM* R(a meal) with the model-independent R(a meal)(ref) provided by the tracer-to-tracee clamp technique, while OMM* S(I)* is compared with both S(I)(* ref), obtained by using as known input R(a meal)(ref), and with S(I)* measured during IVGTT*.

Highly informative yet simple protocols to assess insulin secretion and action would considerably enhance the quality of epidemiological and large-scale clinical trials. In an effort to develop such protocols, a 5-h, 11-sample oral glucose tolerance test (OGTT) was performed in 100 individuals and a 7-h, 21-sample meal in another 100. Plasma glucose, insulin, and C-peptide concentrations were measured. We show that virtually the same minimal model assessment of beta-cell responsivity (dynamic [Phi(d)] and static [Phi(s)]), insulin sensitivity (Si), and disposition index (DI) can be obtained with a reduced seven-sample 2-h protocol: Phi(d), reduced versus full: 871.50 vs. 873.32, r = 0.98 in OGTT and 494.88 vs. 477.99 10(-9), r = 0.91 in meal; Phi(s): 42.36 vs. 44.35, r = 0.88 in OGTT and 35.31 vs. 35.37 10(-9) min(-1), r = 0.90 in meal; Si: 24.33 vs. 22.77 10(-5) dl x kg(-1) x min(-1) per pmol/l, r = 0.89 in OGTT and 19.03 vs. 19.77 10(-5) dl x kg(-1) x min(-1) per pmol/l, r = 0.85 in meal; and DI: 1,282.26 vs. 1,273.23, r = 0.84 in OGTT and 726.92 vs. 776.97 10(-14) dl . kg(-1) x min(-2) per pmol/l, r = 0.84 in meal. This reduced protocol will facilitate the study of insulin secretion and action under physiological conditions in nondiabetic humans.

We previously found a shorter surfactant disaturated phosphatidylcholine palmitate (DSPC-PA) half-life in infants with bronchopulmonary dysplasia (BPD) by using a single stable isotope tracer and simple formulas based on a one-exponential fit of the final portion of the enrichment decay curve. The aim of this study was to apply noncompartmental and compartmental analysis on the entire enrichment decay curve of DSPC-PA and to compare the kinetic data with our previous results. We analyzed 10 preterm newborns with BPD (gestational age 26 +/- 0.6 wk, weight 777 +/- 199 g) and 6 controls (gestational age 26 +/- 1.4 wk, weight 787 +/- 259 g). All took part in our previous study. Endotracheal 13C-labeled dipalmitoyl phosphatidylcholine was administered, and the 13C-enrichment of surfactant DSPC-PA was measured from serial tracheal aspirates by gas chromatography-mass spectrometry. Noncompartmental and compartmental models were numerically identified from the tracer-to-tracee ratio and kinetic parameters related to the accessible (pool accessible to sampling, likely to be the lung alveolar pool) and to the nonaccessible pools (pools not accessible to samplings, likely to be the intracellular storage pool) were estimated in the two study groups. Comparison was performed by Mann-Whitney test. A two-compartment model provided the most reliable assessment of DSPC-PA kinetics. In BPD vs. controls, mean +/- SE residence time of DSPC-PA in the accessible was 17.5 +/- 2.6 vs. 32.2 +/- 6.4 h (P < 0.05), whereas it was 49.7 +/- 3.5 vs. 54.4 +/- 3.9 h (NS, not significant) in the nonaccessible pool; DSPC-PA recycling was 0.26 +/- 0.05 vs. 0.43 +/- 0.04% (NS), respectively. A two-compartment model of surfactant DSPC-PA kinetics allowed a thorough assessment of DSPC-PA kinetics, including masses, synthesis, and fluxes between pools. The most important findings of this study are that in BPD infants DSPC-PA loss from the alveolar pool was higher and recycling through the intracellular pool lower than in controls.

The identification of the insulin minimal model (MM) for the estimation of insulin secretion rate (ISR) and physiological indexes (e.g. beta-cell sensitivity) requires the knowledge of C-peptide (CP) kinetics. The four parameters of the two-compartment model of CP kinetics in a given individual can be derived either from an additional bolus experiment or, more frequently, from a population model. However, in both situations, the CP kinetics is uncertain and, in MM identification, it should be treated as such. This paper shows how to handle CP kinetics uncertainty by using a Bayesian methodology. In seven subjects, MM indexes and ISR were estimated together with their confidence intervals, using either the bolus data or the population model to assess CP kinetics. The two main results that arise from the application of the new methodology are: (i) the use of the population model in place of the bolus data to determine CP kinetics does not affect, on average, the point estimates of ISR profile and MM parameters but only the confidence intervals which becomes wider (less than 50%); (ii) in both the bolus and population situation neglecting the uncertainty of CP kinetics, as done in MM literature so far, introduces no bias, on average, on point estimates of MM indexes but only an underestimation of confidence intervals.

Kinetic modeling is used to indirectly measure physiological parameters from dynamic positron emission tomography (PET) data. Usually, the unknown parameters of the model are estimated, in any given region of interest (ROI), by least squares (LS). However, when the signal-to-noise ratio (SNR) of PET data is too low, LS does not allow reliable parameter estimation. To overcome this problem, we study in this paper the applicability of approaches originally developed in the pharmacokinetic/pharmacodynamic literature and referred to as "population approaches." In particular, we consider the iterative two stage (ITS) method, which, given a set of M ROIs drawn on PET images of a given individual, estimates the unknown model parameters of each ROI by exploiting the information contained in all the M ROIs. After having revised the theory behind ITS, we assess its performance versus LS by using Monte Carlo simulations which allow us to evaluate the bias of the two methods in a variety of situations. Then, we compare the performance of LS and ITS in two case studies on [18F]FDG kinetics in human skeletal muscle. Both simulated and real case studies results show that a population approach is of potential in modeling PET images since it allows to reliably estimate model parameters also in those ROIs where either a bad SNR or a poor sampling (e.g., infrequent scanning and/or short experiment duration) make the use of LS unsuccessful.

Models describing plasma glucose and insulin concentration of an intravenous glucose tolerance test (IVGTT) allow a noninvasive cost-effective approach to estimate important indexes characterizing the efficiency of glucose-insulin control system, i.e., glucose effectiveness (S(G)) and insulin sensitivity (S(I)). To overcome some limitations of the classic single compartment minimal model (1CMM) of glucose kinetics , a two-compartment Bayesian minimal model (2CBMM) has been recently proposed for the standard IVGTT. This study aims to assess 2CBMM ability to describe the insulin-modified IVGTT (IM-IVGTT) which is the protocol of choice since it allows to study insulinopenic states. Both a full-length IM-IVGTT (240 min) as well as a reduced version (90 min) of it are studied. Results of the maximum a posteriori identification of IM-IVGTT (240 min) in 13 normals agree with those of standard IVGTT, i.e., a 42% decrease (P < 0.002) of S(G) and a 13% increase (P < 0.006) of S(I) with respect to ICMM. When identified from IM-IVGTT (90 min), 2CBMM not only provides S(G) and S(I) estimates 46% lower (P < 0.002) and 41% higher (P < 0.002) than 1CMM ones respectively, but also seems to overcome some limitations of the 240 min-based identification that probably arise because the minimal model is unable to properly account for the hyperglycemic hormonal response taking place in the second half of IM-IVGTT.