Micaela Morettini

Identification of an integrated mathematical model of standard oral glucose tolerance test for characterization of insulin potentiation in health

Two new formulations, respectively denominated INT_M1 and INT_M2, of an integrated mathematical model to describe the glycemic and insulinemic responses to a 75 g oral glucose tolerance test (OGTT) are proposed and compared. The INT_M1 assumes a single compartment for the intestine and the derivative of a power exponential function for the gastric emptying rate, while, in the INT_M2, a nonlinear three-compartment system model is adopted to produce a more realistic, multiphase gastric emptying rate. Both models were implemented in a Matlab-based, two-step procedure for estimation of seven adjustable coefficients characterizing the gastric emptying rate and the incretin, insulin and glucose kinetics. Model behaviour was tested vs. mean plasma glucagon-like peptide 1 (GLP-1), glucose-dependent insulinotropic polypeptide (GIP), glucose and insulin measurements from two different laboratories, where glycemic profiles observed during a 75 g OGTT were matched in healthy subjects (HC1- and HC2-group, respectively) by means of an isoglycemic intravenous glucose (I-IVG) infusion. Under the hypothesis of an additive effect of GLP-1 and GIP on insulin potentiation, our results demonstrated a substantial equivalence of the two models in matching the data. Model parameter estimates showed to be suitable markers of differences observed in the OGTT and matched I-IVG responses from the HC1-group compared to the HC2-group. Model implementation in our two-step parameter estimation procedure enhances the possibility of a prospective application for individualization of the incretin effect in a single subject, when his/her data are plugged in.

C-Peptide-based assessment of insulin secretion in the Zucker Fatty rat: a modelistic study.

A C-peptide-based assessment of β-cell function was performed here in the Zucker fatty rat, a suitable animal model of human metabolic syndrome. To this aim, a 90-min intravenous glucose tolerance test (IVGTT) was performed in seven Zucker fatty rats (ZFR), 7-to-9week-old, and seven age-matched Zucker lean rats (ZLR). The minimal model of C-peptide (CPMM), originally introduced for humans, was adapted to Zucker rats and then applied to interpret IVGTT data. For a comprehensive evaluation of glucose tolerance in ZFR, CPMM was applied in combination with the minimal model of glucose kinetics (GKMM). Our results showed that the present CPMM-based interpretation of data is able to: 1) provide a suitable fit of C-Peptide data; 2) achieve a satisfactory estimation of parameters of interest 3) quantify both insulin secretion by estimating the time course of pre-hepatic secretion rate, SR(t), and total insulin secretion, TIS, and pancreatic sensitivity by means of three specific indexes of β-cell responsiveness to glucose stimulus (first-phase, Ф1, second-phase, Ф2, and steady-state, Фss, never assessed in Zucker rats before; 4) detect the significant enhancement of insulin secretion in the ZFR, in face of a severe insulin-resistant state, previously observed only using a purely experimental approach. Thus, the methodology presented here represents a reliable tool to assess β-cell function in the Zucker rat, and opens new possibilities for the quantification of further processes involved in glucose homeostasis such as the hepatic insulin degradation.

The onset of type 2 diabetes: Proposal for a multi-scale model

Background Type 2 diabetes mellitus (T2D) is a common age-related disease, and is a major health concern, particularly in developed countries where the population is aging, including Europe. The multi-scale immune system simulator for the onset of type 2 diabetes (MISSION-T2D) is a European Union-funded project that aims to develop and validate an integrated, multilevel, and patient-specific model, incorporating genetic, metabolic, and nutritional data for the simulation and prediction of metabolic and inflammatory processes in the onset and progression of T2D. The project will ultimately provide a tool for diagnosis and clinical decision making that can estimate the risk of developing T2D and predict its progression in response to possible therapies. Recent data showed that T2D and its complications, specifically in the heart, kidney, retina, and feet, should be considered a systemic disease that is sustained by a pervasive, metabolically-driven state of inflammation. Accordingly, there is an urgent need (1) to understand the complex mechanisms underpinning the onset of this disease, and (2) to identify early patient-specific diagnostic parameters and related inflammatory indicators. Objective We aim to accomplish this mission by setting up a multi-scale model to study the systemic interactions of the biological mechanisms involved in response to a variety of nutritional and metabolic stimuli and stressors. Methods Specifically, we will be studying the biological mechanisms of immunological/inflammatory processes, energy intake/expenditure ratio, and cell cycle rate. The overall architecture of the model will exploit an already established immune system simulator as well as several discrete and continuous mathematical methods for modeling of the processes critically involved in the onset and progression of T2D. We aim to validate the predictions of our models using actual biological and clinical data. Results This study was initiated in March 2013 and is expected to be completed by February 2016. Conclusions MISSION-T2D aims to pave the way for translating validated multilevel immune-metabolic models into the clinical setting of T2D. This approach will eventually generate predictive biomarkers for this disease from the integration of clinical data with metabolic, nutritional, immune/inflammatory, genetic, and gut microbiota profiles. Eventually, it should prove possible to translate these into cost-effective and mobile-based diagnostic tools.

MATLAB-implemented estimation procedure for model-based assessment of hepatic insulin degradation from standard intravenous glucose tolerance test data

Present study provides a novel MATLAB-based parameter estimation procedure for individual assessment of hepatic insulin degradation (HID) process from standard frequently-sampled intravenous glucose tolerance test (FSIGTT) data. Direct access to the source code, offered by MATLAB, enabled us to design an optimization procedure based on the alternating use of Gauss-Newtons and Levenberg-Marquardts algorithms, which assures the full convergence of the process and the containment of computational time. Reliability was tested by direct comparison with the application, in eighteen non-diabetic subjects, of well-known kinetic analysis software package SAAM II, and by application on different data. Agreement between MATLAB and SAAM II was warranted by intraclass correlation coefficients ≥0.73; no significant differences between corresponding mean parameter estimates and prediction of HID rate; and consistent residual analysis. Moreover, MATLAB optimization procedure resulted in a significant 51% reduction of CV% for the worst-estimated parameter by SAAM II and in maintaining all model-parameter CV% <20%. In conclusion, our MATLAB-based procedure was suggested as a suitable tool for the individual assessment of HID process.

Effects of walking on low-grade inflammation and their implications for Type 2 Diabetes

Objective Inflammatory cytokines released by hypertrophic adipocytes contribute to low-grade inflammation, a characteristic of Type 2 Diabetes. Skeletal muscle contraction during physical activity stimulates the secretion of anti-inflammatory cytokines able to counteract this inflammatory status. The aim of this study was to review the evidence of the effectiveness of walking as a physical activity intervention to reduce inflammation. The interplay between adipose tissue and skeletal muscle contributions was also investigated. Method A structured literature review of papers available up to December 2014 was carried out within the PubMed, Scopus and ISI Web of Science databases using the keywords “walking” and “inflammation” in order to identify the studies involving healthy subjects and subjects diagnosed with, or at increased risk of, Type 2 Diabetes. Results Thirty-two studies were reviewed, five investigating the acute effects of walking and twenty-seven its chronic effects (n = 21 interventional and n = 6 observational). Acute effects of walking bouts led to an increase of interleukin-6 in one study, although without any increase in the concentration of the anti-inflammatory marker interleukin-1 receptor antagonist. Eight interventional studies showed a significant reduction of inflammation. A reduction in tumour necrosis factor-α concentration was often associated with an adiposity reduction. The observational studies showed that individuals who walk more present a lower inflammatory status. Conclusion There is no consensus regarding the efficacy of walking in the reduction of low-grade systemic inflammation, even though a relationship cannot be excluded. In each walking bout, no anti-inflammatory effect due to the IL-6-stimulated myokine cascade can be demonstrated.

Statistical baseline assessment in cardiotocography

Cardiotocography (CTG) is the most common non-invasive diagnostic technique to evaluate fetal well-being. It consists in the recording of fetal heart rate (FHR; bpm) and maternal uterine contractions. Among the main parameters characterizing FHR, baseline (BL) is fundamental to determine fetal hypoxia and distress. In computerized applications, BL is typically computed as mean FHR±ΔFHR, with ΔFHR=8 bpm or ΔFHR=10 bpm, both values being experimentally fixed. In this context, the present work aims: to propose a statistical procedure for ΔFHR assessment; to quantitatively determine ΔFHR value by applying such procedure to clinical data; and to compare the statistically-determined ΔFHR value against the experimentally-determined ΔFHR values. To these aims, the 552 recordings of the “CTU-UHB intrapartum CTG database” from Physionet were submitted to an automatic procedure, which consisted in a FHR preprocessing phase and a statistical BL assessment. During preprocessing, FHR time series were divided into 20-min sliding windows, in which missing data were removed by linear interpolation. Only windows with a correction rate lower than 10% were further processed for BL assessment, according to which ΔFHR was computed as FHR standard deviation. Total number of accepted windows was 1192 (38.5%) over 383 recordings (69.4%) with at least an accepted window. Statistically-determined ΔFHR value was 9.7 bpm. Such value was statistically different from 8 bpm (P<10−19) but not from 10 bpm (P=0.16). Thus, ΔFHR=10 bpm is preferable over 8 bpm because both experimentally and statistically validated.

IVGTT-based simple assessment of glucose tolerance in the Zucker fatty rat: Validation against minimal models

For the assessment of glucose tolerance from IVGTT data in Zucker rat, minimal model methodology is reliable but time- and money-consuming. This study aimed to validate for the first time in Zucker rat, simple surrogate indexes of insulin sensitivity and secretion against the glucose-minimal-model insulin sensitivity index (SI) and against first- (Φ1) and second-phase (Φ2) β-cell responsiveness indexes provided by C-peptide minimal model. Validation of the surrogate insulin sensitivity index (ISI) and of two sets of coupled insulin-based indexes for insulin secretion, differing from the cut-off point between phases (FPIR3-SPIR3, t = 3 min and FPIR5-SPIR5, t = 5 min), was carried out in a population of ten Zucker fatty rats (ZFR) and ten Zucker lean rats (ZLR). Considering the whole rat population (ZLR+ZFR), ISI showed a significant strong correlation with SI (Spearman’s correlation coefficient, r = 0.88; P<0.001). Both FPIR3 and FPIR5 showed a significant (P<0.001) strong correlation with Φ1 (r = 0.76 and r = 0.75, respectively). Both SPIR3 and SPIR5 showed a significant (P<0.001) strong correlation with Φ2 (r = 0.85 and r = 0.83, respectively). ISI is able to detect (P<0.001) the well-recognized reduction in insulin sensitivity in ZFRs, compared to ZLRs. The insulin-based indexes of insulin secretion are able to detect in ZFRs (P<0.001) the compensatory increase of first- and second-phase secretion, associated to the insulin-resistant state. The ability of the surrogate indexes in describing glucose tolerance in the ZFRs was confirmed by the Disposition Index analysis. The model-based validation performed in the present study supports the utilization of low-cost, insulin-based indexes for the assessment of glucose tolerance in Zucker rat, reliable animal model of human metabolic syndrome.

A system model of the effects of exercise on plasma Interleukin-6 dynamics in healthy individuals: Role of skeletal muscle and adipose tissue

Interleukin-6 (IL-6) has been recently shown to play a central role in glucose homeostasis, since it stimulates the production and secretion of Glucagon-like Peptide-1 (GLP-1) from intestinal L-cells and pancreas, leading to an enhanced insulin response. In resting conditions, IL-6 is mainly produced by the adipose tissue whereas, during exercise, skeletal muscle contractions stimulate a marked IL-6 secretion as well. Available mathematical models describing the effects of exercise on glucose homeostasis, however, do not account for this IL-6 contribution. This study aimed at developing and validating a system model of exercise’s effects on plasma IL-6 dynamics in healthy humans, combining the contributions of both adipose tissue and skeletal muscle. A two-compartment description was adopted to model plasma IL-6 changes in response to oxygen uptake’s variation during an exercise bout. The free parameters of the model were estimated by means of a cross-validation procedure performed on four different datasets. A low coefficient of variation (<10%) was found for each parameter and the physiologically meaningful parameters were all consistent with literature data. Moreover, plasma IL-6 dynamics during exercise and post-exercise were consistent with literature data from exercise protocols differing in intensity, duration and modality. The model successfully emulated the physiological effects of exercise on plasma IL-6 levels and provided a reliable description of the role of skeletal muscle and adipose tissue on the dynamics of plasma IL-6. The system model here proposed is suitable to simulate IL-6 response to different exercise modalities. Its future integration with existing models of GLP-1-induced insulin secretion might provide a more reliable description of exercise’s effects on glucose homeostasis and hence support the definition of more tailored interventions for the treatment of type 2 diabetes.

Separation of Superimposed Electrocardiographic and Electromyographic Signals

Electrocardiography (ECG) and surface electromyography (SEMG) are two non-invasive tests to evaluate cardiac and muscular functionality, respectively. They are both acquired by placing electrodes on the body surface so they become one the interference of the other. Typically, linear filters are used for ECG and SEMG separation: high-pass filters with cutoff at 20 Hz to attenuate ECG interference in SEMG, and low-pass filters with cut-off at 50 Hz to attenuate SEMG interference in ECG. In spite of that, linear filtering is not adequate due to the presence of a 20-50 Hz frequency-band in which the two signal spectra overlap. The aim of the present study was to evaluate the ability of the Segmented-Beat Modulation Method (SBMM) for ECG and SEMG separation and by accurately maintaining signals characteristics. SBMM is a template-based technique for ECG denoising: under the hypothesis of ECG and SEMG linearly superimposed, it first provides an ECG estimation, and then an SEMG estimation by subtraction. In order to test the method under several conditions, SBMM was applied to simulated as well as clinical recordings with superimposed ECG and SEMG. SBMM was able to accurately estimate both ECG and SEMG in all cases. Indeed, ECG and SEMG were estimated by maintain their features such as amplitude (estimation errors <6%), heart rate and heart-rate variability. Moreover, estimated ECG was always characterized by a spectrum mostly (76.4-100.0%) included in the 0-50 Hz frequency-band, whereas estimated SEMG was always characterized by a spectrum mostly (80.9-95.6%) included in the 20-450 Hz frequency-band. Such results confirm the existence of a 20-50 Hz frequency-band in which ECG and SEMG spectral components are overlapped. Thus, SBMM is a robust filtering procedure to separate superimposed ECG and SEMG.

Estimation of second-phase insulin secretion in the Zucker fatty rat

The purpose of the present study was to test the efficacy of the empiric index SPIR (Second-phase Insulin Release) in the quantification of second-phase insulin secretion in the Zucker Fatty Rat. SPIR index is defined as the area under the curve of insulin between 8 and 90 min after an Intravenous Glucose Tolerance Test (IVGTT). The validation of such index was performed against the second-phase β-cell responsiveness index (Φ 2 ) provided by C-peptide minimal model. To this aim, Φ 2 and SPIR were simultaneously computed from IVGTT data, measured in six Zucker fatty rats (ZFR), 7-to-9week-old, and seven age-matched Zucker lean rats (ZLR). SPIR index showed a significant linear correlation with Φ 2 (Pearsons correlation coefficient, r = 0.91, R-square = 0.82, P 2 (P 2 , in the evaluation of the second-phase insulin secretion and of its alteration in Zucker Fatty Rats. Thus, the study proposes the SPIR, as a suitable index for a simple, reliable and low-cost quantification of the second-phase insulin secretion in ZFR.