Calculating all multiple parameter solutions of ODE models to avoid biological misinterpretations.

Biological system's dynamics are increasingly studied with nonlinear ordinary differential equations, whose parameters are estimated from input/output experimental data. Structural identifiability analysis addresses the theoretical question whether the inverse problem of recovering the unknown parameters from noise-free data is uniquely solvable (global), or if there is a finite (local), or an infinite number (non identifiable) of parameter values that generate identical input/output trajectories. In contrast, practical identifiability analysis aims to assess whether the experimental data provide information on the parameter estimates in terms of precision and accuracy. A main difference between the two identifiability approaches is that the former is mostly carried out analytically and provides exact results at a cost of increased computational complexity, while the latter is usually numerically tested by calculating statistical confidence regions and relies on decision thresholds. Here we focus on local identifiability, a critical issue in biological modeling. This is the case when a model has multiple parameter solutions which equivalently describe the input/output data, but predict different behaviours of the unmeasured variables, often those of major interest. We present theoretical background and applications to locally identifiable ODE models described by rational functions. We show how structural identifiability analysis completes the practical identifiability results. In particular we propose an algorithmic approach, implemented with our software DAISY, to calculate all numerical parameter solutions and to predict the corresponding behaviour of the unmeasured variables, which otherwise would remain hidden. A case study of a locally identifiable HIV model shows that one should be aware of the presence of multiple parameter solutions to comprehensively describe the biological system and avoid biological misinterpretation of the results.

Long-Acting GLP-1 Receptor Agonist Exenatide Influence on the Autonomic Cardiac Sympatho-Vagal Balance.

Long-acting glucagon-like peptide 1 receptor agonists are increasingly used to treat type 2 diabetes. An increase of heart rate (HR) has been observed with their use. To elucidate the role of the cardiac sympatho-vagal balance as a possible mediator of the reported increase in HR, we performed power spectral analysis of HR variability (HRV) in patients receiving exenatide extended-release (ER). Twenty-eight ambulatory patients with type 2 diabetes underwent evaluation at initiation of exenatide-ER and thereafter at 3 and at 6 months. To obtain spectral analyses of HRV, a computerized acquisition of 10 minutes of RR electrocardiogram intervals (mean values of ~700 RR intervals) were recorded both in lying and in standing positions. All patients showed a substantial increase of HR both in lying and in standing positions. Systolic blood pressure, body weight, and glycated hemoglobin A1c significantly decreased both at 3 and 6 months compared with basal levels. The low-frequency/high-frequency ratio varied from 3.05 ± 0.4 to 1.64 ± 0.2 (P < 0.001) after 3 months and to 1.57 ± 0.3 (P < 0.001) after 6 months in a lying position and from 4.56 ± 0.8 to 2.24 ± 0.3 (P < 0.001) after 3 months and to 2.38 ± 0.4 (P < 0.001) after 6 months in a standing position compared with basal values, respectively. HR variations, induced by exenatide-ER treatment, do not appear to be related to sympathetic autonomic tone. Of note, we observed a relative increase of vagal influence on the heart.

Modeling Pathological Hemodynamic Responses to the Valsalva Maneuver.

The Valsalva maneuver (VM) consisting in a forced expiration against closed airways is one of the most popular clinical tests of the autonomic nervous system function. When properly performed by a healthy subject, it features four characteristic phases of arterial blood pressure (BP) and heart rate (HR) variations, based on the magnitude of which the autonomic function may be assessed qualitatively and quantitatively. In patients with some disorders or in healthy patients subject to specific conditions, the pattern of BP and HR changes during the execution of the Valsalva maneuver may, however, differ from the typical sinusoidal-like pattern. Several types of such abnormal responses are well known and correspond to specific physiological conditions. In this paper, we use our earlier mathematical model of the cardiovascular response to the Valsalva maneuver to show that such pathological responses may be simulated by changing individual model parameters with a clear physiological meaning. The simulation results confirm the adaptability of our model and its usefulness for diagnostic or educational purposes.

Mathematical modelling of cardiovascular response to the Valsalva manoeuvre.

The Valsalva manoeuvre (VM) used for clinical autonomic testing results in a complex cardiovascular response with a concomitant action of several regulatory mechanisms whose nonlinear interactions are difficult to analyse without the aid of a mathematical model. The article presents a new non-pulsatile compartmental model of the human cardiovascular system with a variable intrathoracic pressure enabling the simulation of the haemodynamic response to the VM. The model is based on physiological data and includes three baroreflex mechanisms acting on heart rate, systemic resistance and venous unstressed volume. New nonlinear functions have been proposed to model cardiac output dependence on preload and afterload. Following the individual fitting of some parameters with a clear physiological meaning, the model is able to fit clinical data from patients with both typical and abnormal haemodynamic response to the VM. The sensitivity analysis showed that the model is most sensitive to the parameters describing the vascular pressure-volume relationships (the maximal volume of systemic veins and the relative level of vascular compliance). The use of nonlinear pressure-volume relationships for systemic veins proved crucial for the accurate modelling of the VM. On the contrary, the introduction of aroreflex time delays did not change significantly the haemodynamic response to the manoeuvre. The model can be a useful tool for aiding the interpretation of patient's response to the VM and provides a framework for analysing the interactions between the cardiovascular system and autonomic regulatory mechanisms.

Prevalence of Cardiovascular Autonomic Neuropathy in a Cohort of Patients With Newly Diagnosed Type 2 Diabetes: The Verona Newly Diagnosed Type 2 Diabetes Study (VNDS).

OBJECTIVE: Cardiovascular autonomic diabetic neuropathy (CAN) is a serious complication of diabetes. No reliable data on the prevalence of CAN among patients with newly diagnosed type 2 diabetes are available. Therefore, the aim of this study was to estimate the prevalence of CAN among patients with newly diagnosed type 2 diabetes. RESEARCH DESIGN AND METHODS: A cohort of 557 patients with newly diagnosed type 2 diabetes with cardiovascular autonomic test results available was selected. Early and confirmed neuropathy were assessed using a standardized methodology and their prevalences determined. A multivariate logistic regression analysis was modeled to study the factors associated with CAN. RESULTS: In the entire cohort, the prevalence of confirmed CAN was 1.8%, whereas that of early CAN was 15.3%. Prevalence did not differ between men and women. In the multivariate analyses BMI results were independently and significantly associated with CAN after adjusting for age, sex, hemoglobin A1c, pulse pressure, triglyceride-to-HDL cholesterol ratio, kidney function parameters, and antihypertensive treatment. CONCLUSIONS: CAN could be detected very early in type 2 diabetes. This study may suggest the importance of performing standardized cardiovascular autonomic tests after diagnosis of type 2 diabetes.

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

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

A regional blood flow model for glucose and insulin kinetics during hemodialysis.

The distribution and elimination of a bolus of glucose injected during hemodialysis (HD) was examined using a distributed double-pool regional blood flow model. Intracorporeal glucose disposal was assumed as insulin-independent (λ) in the central high-flow compartment comprising blood, brain, and internal organs, including pancreatic insulin secretion (a, C1) and hepatic insulin clearance (α). Insulin-dependent (γ) glucose utilization was allocated to the low-flow system comprising muscle, skin, and bone. This model was compared with a compact single-pool model using the same model parameters except for the distribution volume (V). Six parameters (C1, a, α, λ, γ, and V) were identified from data obtained in seven nondiabetic patients (59-115 kg). The fraction Fd of glucose removed by HD significantly (p < 0.05) correlated with baseline glucose concentration Cg,0 (5.561 ± 0.646 mmol/L; r = 0.535), extracorporeal clearance Kg (0.137 ± 0.024 L/min; r = 0.537), a (0.278 ± 0.095 L/mmol, r = -0.586), and λ (0.099 ± 0.078 L/min, r = -0.587). V was much larger in the double-compartment (17.8 ± 5.1 L) than in the single-compartment model (10.0 ± 3.0 L). The modeled glucose compartment volumes could be of interest for fluid management in HD patients. The use of extracorporeal glucose disposal to detect impaired glucose utilization (a, λ) remains to be validated in diabetic HD patients.

Cats differ from other species in their cytokine and antioxidant enzyme response when developing obesity.

OBJECTIVES: Obese cats show many similarities to obese people, including insulin resistance and an increased diabetes risk. However, atherosclerosis and cardiovascular disease are not seen in cats. In people, they are associated with the development of an inflammatory response, which, we hypothesized, does not occur in cats. DESIGN AND METHODS: Twenty neutered cats of equal gender distribution were allowed to gain weight by offering food ad libitum and were examined before and at 10, 30, 60, and 100% weight gain. All cats reached 60% of weight gain, 12 cats gained 100% in 12 months. RESULTS: Fat was equally distributed between subcutaneous and visceral depots. Insulin-independent glucose uptake increased and insulin sensitivity decreased with increasing adiposity. However, baseline glucose concentrations were unchanged suggesting a decrease in EGP. Inflammatory cytokines (Il-1, IL-6, TNFa) and catalase, superoxide dismutase, glutathione peroxidase did not change. Insulin, proinsulin, and leptin were positively and adiponectin negatively correlated with adiposity. Heat production increased with obesity, but became less when body weight gain was > 60%. CONCLUSIONS: This indicates that metabolism adapts more appropriately to the higher intake of calories in the initial phase of obesity but slows at higher body fat content. This likely contributes to the difficulty to lose weight.

Evaluation of long-term glucose homeostasis in lean and obese cats by use of continuous glucose monitoring.

OBJECTIVE: To evaluate intraday and interday variations in glucose concentrations in cats and to test the utility of a continuous glucose monitoring system (CGMS). ANIMALS: 6 lean and 8 long-term (> 5 years) obese cats. PROCEDURES: Blood glucose concentrations were measured during the course of 156 hours by use of a laboratory hexokinase-based reference method and a handheld glucometer. Interstitial glucose concentrations were evaluated with a CGMS. RESULTS: Paired measures of glucose concentrations obtained with the CGMS typically were marginally higher than concentrations for the reference method and less biased than concentrations obtained with the glucometer. This was partially confirmed by the concordance correlation coefficients of the concentration for the CGMS or glucometer versus the concentration for the reference method, although the correlation coefficients were not significantly different. Mean ± SD area under the curve for the glucose concentration (AUCG) did not differ significantly between lean (14.0 ± 0.5 g/dL•h) and obese (15.2 + 0.5 g/dL•h) cats during the 156-hour period, but one of the obese cats had a much higher AUCG. Within-day glucose variability was small in both lean and obese cats. CONCLUSIONS AND CLINICAL RELEVANCE: Glucose homeostasis was maintained, even in long-term obese cats, and intraday glucose fluctuations were small. One obese cat might have been classified as prediabetic on the basis of the AUCG, which was approximately 25% higher than that of the other obese and lean cats. The CGMS can be useful in the evaluation of long-term effects of drugs or diet on glucose homeostasis in cats.

Insulinogenic index in non-diabetics during haemodialysis.

BACKGROUND: The aim of this study was to analyse whether the insulin to glucose relationship following an intravenous glucose load in non-diabetic patients delivered during haemodialysis was affected by extracorporeal clearance and whether this relationship could be determined by an abridged sampling protocol. METHODS: Studies were done during routine haemodialysis following the infusion of 0.5 g glucose per kilogram body mass. Extracorporeal effects were measured by online clearance (K(OCM)) and insulin clearance (K(I)). The insulin to glucose relationship was examined for a period of 1 h following the infusion of glucose. The integral response measured as the insulinogenic index (I(G)) was compared to the relationship between insulin and glucose concentrations measured for the whole period (k(IG)) as well as from only two samples taken at baseline and after 10 min (k(10)). RESULTS: Eight non-diabetic haemodialysis patients (three females) with a dry body mass of 76.9 ± 18.2 kg completed the study. I(G) was 5.4 ± 4.4 U/mol and not different from normal reference values. A linear relationship providing characteristic slopes k(IG) was observed between arterial insulin and glucose levels. k(IG) was 6.1 ± 5.0 U/mol and not different from k(10) = 5.9 ± 4.8 U/mol measured after 10 min of glucose infusion and ongoing dialysis. I(G), k(IG) and k(10) were highly correlated (P < 0.0001), and k(10) showed substantial concordance (ρ(c) = 0.99) with I(G). Moreover, I(G), k(IG) and k(10) were independent of K(OCM) or K(I). CONCLUSIONS: The insulin to glucose relationship is measurable within 10 min of glucose administration and unaffected by extracorporeal clearance. This could be helpful to characterize the insulin response to a glucose stimulus during haemodialysis.

Intracorporeal glucose disposal during hemodialysis after a standardized glucose load.

The aim of this study was to quantify intracorporeal clearance and disposal of glucose after the administration of a standardized glucose load during regular hemodialysis done in stable and non-diabetic patients and to account for effects of extracorporeal clearance. A standardized load of glucose was administered approximately 30 min after starting hemodialysis with a constant dialysate glucose of 5.0 +/- 0.2 mmol/L. Glucose in the arterial line blood and in dialysate outflow was measured at baseline and in short intervals for a period of 1 h after the infusion. Tests were repeated within 1 week. Nine patients completed the study. Extracorporeal blood and dialysate flows were 304 +/- 34 and 500 mL/min, respectively. The intracorporeal clearance of glucose was 327 +/- 137 mL/min and 69.1 +/- 9.4% of total glucose clearance. Mass balance assessed from dialysate samples showed that 60.1 +/- 10.5% of glucose injected was disposed intracorporeally. The fraction of intracorporeal clearance and the fraction of intracorporeal glucose disposal were highly correlated (r = 0.94, p < 0.0001). The fraction of glucose disposed in hemodialysis patients can be determined from the amount of glucose injected and from the amount of glucose removed extracorporeally during hemodialysis without blood sampling. This measure could be of interest in surveillance of glucose control in hemodialysis patients.

Dissociated effects of glucose-dependent insulinotropic polypeptide vs glucagon-like peptide-1 on beta-cell secretion and insulin clearance in mice.

Glucagon-like peptide-1 (GLP-1) and glucose-dependent insulinotropic polypeptide (GIP) potently augment insulin response to glucose. It is less known what their effects are insulin clearance, which also contributes to peripheral hyperinsulinemia observed after administration of incretins together with glucose. The aims of this study were the quantification of C-peptide secretion and the evaluation of insulin clearance after administration of GIP with glucose. This allows the assessment of GIP's effects on hyperinsulinemia. In addition, GIP's effects were compared with those of GLP-1. Anesthetized female NMRI mice were injected intravenously with glucose alone (1 g/kg, n = 35) or glucose together with GIP (50 microg/kg, n = 12). Samples were taken through the following 50 minutes, and C-peptide and insulin concentrations were used to reconstruct C-peptide secretion rate and insulin clearance. In a previous study, GLP-1 (10 microg/kg) was used in 12 mice; and we used those GLP-1 results to compare GIP effects with those of GLP-1. C-peptide secretion rate peaked at 1 minute after glucose injection, and the immediate part of the insulin-releasing process was markedly augmented by both incretin hormones (1-minute suprabasal increment secretory rate was 20 +/- 2 pmol/min for GIP and 28 +/- 2 pmol/min for GLP-1, vs only 9 +/- 1 pmol/min for glucose alone; P < .001). Until 10 minutes after administration, C-peptide secretion remained higher with incretins (P < .0001), whereas starting from 20 minutes, the 3 patterns were undistinguishable (P > .2). Insulin clearance, previously shown to be abridged by 46% with GLP-1, was reduced only by a nonsignificant (P = .27) 21% with GIP. This study thus shows that the 2 incretins markedly augment glucose-stimulated insulin secretion in mice by a preferential action on the immediate response to glucose of insulin secretion. However, the action of GIP is less effective than that of GLP-1. Insulin clearance with GIP is not significantly reduced. We conclude that GIP is less potent than GLP-1 in inducing glucose-stimulated hyperinsulinemia in the mouse.

Model-based assessment of insulin sensitivity of glucose disposal and endogenous glucose production from double-tracer oral glucose tolerance test.

A new mathematical model of short-term glucose regulation by insulin is proposed to exploit the oral glucose tolerance test (OGTT), which is commonly used for clinical diagnosis of glucose intolerance and diabetes. Contributions of endogenous and exogenous sources to measured plasma glucose concentrations have been separated by means of additional oral administration and constant intravenous infusion of glucose labeled with two different tracers. Twelve type 2 diabetic patients (7 males and 5 females) and 10 control subjects (5 males and 5 females) with normal glucose tolerance and matched body mass index (BMI) participated in this study. Blood samples for measurement of concentrations/activity of unlabeled and double-tracer glucose and insulin were collected every 15 min for 3 h following the oral glucose load. A minimal model combined with non-linear mixed-effects population parameter estimation has been devised to characterize group-average and between-patient variability of: (i) gastrointestinal glucose absorption; (ii) endogenous glucose production (EGP), and (iii) glucose disposal rate. Results indicate that insulin-independent glucose clearance does not vary significantly with gender or diabetic state and that the latter strongly affects, as expected, insulin-dependent clearance (insulin sensitivity). Inhibition of EGP, interpreted in terms of variations from basal of insulin concentrations, does not appear to be affected by diabetes but rather by BMI, i.e. by the degree of obesity. This study supports the utility of a minimal modelling approach, combined with population parameter estimation, to characterize glucose absorption, production and disposition during double-tracer OGTT experiments. The model provides a means for planning further experiments to validate the new hypothesis on the influence of individual factors, such as BMI and diabetes, on glucose appearance and disappearance, and for designing new simplified clinical tests.

Importance of glycemic control on the course of glomerular filtration rate in type 2 diabetes with hypertension and microalbuminuria under tight blood pressure control.

BACKGROUND AND AIMS: To evaluate the role of glycemic control on the evolution of glomerular filtration rate (GFR) in type 2 diabetes (T2DM) with mild-moderate hypertension under tight blood pressure control, and to address the current controversy whether diabetic nephropathy worsens, independently of blood pressure, proportionally to HbA1c at any physiological level or only when HbA1c is above a 7.5-8% threshold. METHODS AND RESULTS: T2DM (N=127) during early stage diabetic nephropathy characterized by microalbuminuria were followed during a 2 year multicenter study. Individual GFR profiles were accurately obtained by (51)Cr - EDTA bolus injections and analyzed with linear statistical mixed-effects models. GFR at baseline was significantly negatively correlated with age and plasma creatinine concentration (P

A new equation for estimating renal function using age, body weight and serum creatinine.

BACKGROUND: Many formulas have been developed to estimate glomerular filtration rate (GFR). The aim of our study was to propose a new, more reliable equation. METHODS: The study considered 530 subjects (training sample) with M/F 280/250, age 57.1 +/- 17.4, creatinine clearance (CrCl) 55.2 +/- 38.2 (range 2.1-144.0) for the development the new equation. A linear model was used to describe Cr production using serum Cr (sCr), age, and body weight (BW) as variables: (CrCl + b(4)) . sCr = b(1) - (b(2) . age) + (b(3) . BW) subsequently estimating parameter values by linear least squares, with CrCl as the dependent variable, and 1/sCr, age/sCr, BW/sCr as independent variables. CrCl = {[69.4 - (0.59 . age) + (0.79 . BW)]/sCr} - 3.0 (males) and {[57.3 - (0.37 . age) + (0.51 . BW)]/sCr} - 2.9 (females). A 229-patient renal failure validation sample with M/F 166/63, age 53.0 +/- 14.8, GFR 32.0 +/- 14.3 (range 4.3-69.8), assessed using iohexol Cl, was considered to compare the Cockcroft-Gault (C-G) and MDRD formulas with the new equation for estimating GFR. RESULTS: The mean % error in GFR estimated by the new equation (+2.3 +/- 28.3%) was better than with the C-G and MDRD formulas (+5.2 +/- 30.1% and -11.4 +/- 25.9%, respectively, p < 0.0005 and p < 0.0001), and so was the mean absolute % error, bordering on statistical significance (19.8 +/- 20.3 vs. 21.1 +/- 22.0 and 22.4 +/- 17.3, p = 0.08 and p < 0.005). The precision was also better (RMSE = 7.89 vs. 8.02 and 9.13). The Bland-Altman test showed no GFR over or underestimation trend (measured +/- predicted GFR/2 vs. % error, R2 = 0.001). CONCLUSIONS: The new equation appears to be at least as accurate as the C-G and MDRD formulas for estimating GFR.

The role of endocrine counterregulation for estimating insulin sensitivity from intravenous glucose tolerance tests.

CONTEXT: During insulin-modified frequently sampled iv glucose tolerance tests (IM-FSIGT), which allow assessment of insulin action, plasma glucose can markedly decrease. OBJECTIVE: This study aimed to assess the counterregulatory impact of the insulin-induced fall of glucose on minimal model-derived indices of insulin sensitivity (S(I)) and glucose effectiveness. PARTICIPANTS: Thirteen nondiabetic volunteers (seven males, six females, aged 26 +/- 1 yr, body mass index 22.1 +/- 0.7 kg/m(2)) were studied. DESIGN: All participants were studied in random order during IM-FSIGT (0.3 g/kg glucose; 0.03 U/kg insulin at 20 min) and during identical conditions but with a variable glucose infusion preventing a decrease of plasma glucose concentration below euglycemia (IM-FSIGT-CLAMP). Five participants additionally underwent euglycemic-hyperinsulinemic (1 mU.kg(-1).min(-1)) clamp tests. RESULTS: Plasma glucose declined during IM-FSIGT to its nadir of 50 +/- 3 mg/dl at 60 min in parallel to a rise (P < 0.05 vs. basal) of plasma glucagon, cortisol, epinephrine, and GH. Glucose infusion rates of 4.6 +/- 0.5 mg.kg(-1).min(-1) between 30 and 180 min during IM-FSIGT-CLAMP prevented the decline of plasma glucose and the hypoglycemia counterregulatory hormone response. S(I) was approximately 68% lower during IM-FSIGT (3.40 +/- 0.36 vs. IM-FSIGT-CLAMP: 10.71 +/- 1.06 10(-4).min(-1) per microU/ml, P < 0.0001), whereas glucose effectiveness did not differ between both protocols (0.024 +/- 0.002 vs. 0.021 +/- 0.003 min(-1), P = NS). Compared with the euglycemic hyperinsulinemic clamp test, S(I) expressed in identical units from IM-FSIGT was approximately 66% (P < 0.001) lower but did not differ between the euglycemic hyperinsulinemic clamp test and the IM-FSIGT-CLAMP (P = NS). CONCLUSIONS: The transient fall of plasma glucose during IM-FSIGT results in lower estimates of S(I), which can be explained by hormonal response to hypoglycemia.

Local influence analysis when interfacing toxicokinetic and proportional hazard models.

We present a local influence analysis to assigned model quantities in the context of a dose-response analysis of cancer mortality in relation to estimated absorbed dose of dioxin. The risk estimation is performed using dioxin dose as a time-dependent explanatory variable in a proportional hazard model. The dioxin dose is computed using a toxicokinetic model, which depends on some factors, such as assigned constants and estimated parameters. We present a local influence analysis to assess the effects on final results of minor perturbations of toxicokinetic model factors. In the present context, there is no evidence of local influence in risk estimates. It is however possible to identify which factors are more influential.

Modeling population kinetics of free fatty acids in isolated rat hepatocytes using Markov Chain Monte Carlo.

The aim of this study is the characterization, by means of mathematical models, of the activity of isolated hepatic rat cells as regards the conversion of free fatty acids (FFA) to ketone bodies (KB). A new physiologically based compartmental model of FFA metabolism is used within a context of population pharmacokinetics. This analysis is based on a hierarchical model, that differs from standard model formulations, to account for the fact that some data sets belong to the same animal but have been collected under different experimental conditions. The statistical inference problem has been addressed within a Bayesian context and solved by using Markov Chain Monte Carlo (MCMC) simulation. The results obtained in this study indicate that, although hormones epinephrine and insulin are important metabolic regulatory factors in vivo, the conversion of FFA to KB by isolated hepatic rat cells is not significantly affected by epinephrine and only little influenced by insulin. So we conclude that in vivo, the interaction of these two hormones with other compounds not considered in this study plays a fundamental role in ketogenesis. From this study it appears that mathematical models of metabolic processes can be successfully employed in population kinetic studies using MCMC methods.

Multidisciplinary modelling of biomedical systems.

This paper describes general principles and example results of a new software tool being developed for physiologically-based modelling of biomedical systems within a multidisciplinary framework. The aim is to overcome some limitations of currently available software designed either for general purpose or for highly specialised modelling applications. In fact, general purpose tools usually impose explicit coding of mathematical model equations or non-intuitive system representations, whereas specialised software use domain-specific notations that allow efficient and convenient model building only for special classes of systems. The aim of the present study is to pursue intuitive representation of various, possibly interacting, types of biological systems described as interconnected physical components, such as mass and energy storage elements, active and passive transport or biochemical transformations. The presented software generates automatically the mathematical model equations that can be coded in different formats. This allows interoperability with other existing software, e.g. for numerical simulation, symbolic analysis or text processing. A multi-domain structural language has been defined for an intuitive, hierarchical and self-explanatory specification of physiological models. The proposed strategies may become useful for dissemination and integration of multidisciplinary modelling knowledge.

Basal and dynamic proinsulin-insulin relationship to assess beta-cell function during OGTT in metabolic disorders.

The fasting proinsulin-to-insulin ratio is a currently used marker of beta-cell dysfunction. This ratio is calculated at the basal condition, but its behavior in dynamic conditions, i.e., during glucose stimulation, could be more informative. Given the different kinetics of the peptides, a mathematical model was necessary to analyze the oral glucose tolerance test (OGTT) data of insulin, C-peptide, and proinsulin in 55 healthy (NGT), 30 impaired glucose-tolerant (IGT), and 31 type 2 diabetic (T2DM) subjects. The model provided for secretion and disappearance of the peptides and an index of beta-cell function under dynamic conditions. Total proinsulin secretion during the OGTT was not different (P > 0.053) among NGT (0.17 +/- 0.01 mmol/l in 3 h), IGT (0.22 +/- 0.02), and T2DM (0.21 +/- 0.02) subjects. The proinsulin-to-insulin molar ratio measured from basal samples was higher (P < 0.0001) in T2DM (0.39 +/- 0.05) than in NGT (0.14 +/- 0.01) and IGT (0.13 +/- 0.02) subjects, and similar results (P < 0.003) were found by the dynamic index (0.27 +/- 0.04, 0.14 +/- 0.01, 0.15 +/- 0.01 in T2DM, NGT, IGT subjects, respectively). The basal ratio significantly correlated with the dynamic index, and the regression line slope was lower than 1 (0.43 +/- 0.08, 0.61 +/- 0.10, and 0.56 +/- 0.03 in NGT, IGT, and T2DM subjects, respectively, P < 0.0001). Impaired beta-cell function in T2DM could then be indicated by proinsulin-to-insulin indexes at both basal and dynamic phases.