A strategy based on integer programming for optimal dosing and timing of preventive hypoglycemic treatments in type 1 diabetes management.

BACKGROUND AND OBJECTIVES: One of the major problems related to type 1 diabetes (T1D) management is hypoglycemia, a condition characterized by low blood glucose levels and responsible for reduced quality of life and increased mortality. Fast-acting carbohydrates, also known as hypoglycemic treatments (HT), can counteract this event. In the literature, dosage and timing of HT are usually based on heuristic rules. In the present work, we propose an algorithm for mitigating hypoglycemia by suggesting preventive HT consumption, with dosages and timing determined by solving an optimization problem. METHODS: By leveraging integer programming and linear inequality constraints, the algorithm can bind the amount of suggested carbohydrates to standardized quantities (i.e., those available in "off-the-shelf" HT) and the minimal distance between consecutive suggestions (to reduce the nuisance for patients). RESULTS: The proposed method was tested in silico and compared with competitor algorithms using the UVa/Padova T1D simulator. At the cost of a slight increase of HT consumed per day, the proposed algorithm produces the lowest median and interquartile range of the time spent in hypoglycemia, with a statistically significant improvement over most competitor algorithms. Also, the average number of hypoglycemic events per day is reduced to 0 in median. CONCLUSIONS: Thanks to its positive performances and reduced computational burden, the proposed algorithm could be a candidate tool for integration in a DSS aimed at improving T1D management.

Generation of post-meal insulin correction boluses in type 1 diabetes simulation models for in-silico clinical trials: More realistic scenarios obtained using a decision tree approach.

BACKGROUND AND OBJECTIVE: In type 1 diabetes (T1D) research, in-silico clinical trials (ISCTs) notably facilitate the design/testing of new therapies. Published simulation tools embed mathematical models of blood glucose (BG) and insulin dynamics, continuous glucose monitoring (CGM) sensors, and insulin treatments, but lack a realistic description of some aspects of patient lifestyle impacting on glucose control. Specifically, to effectively simulate insulin correction boluses, required to treat post-meal hyperglycemia (BG > 180 mg/dL), the timing of the bolus may be influenced by subjects' behavioral attitudes. In this work, we develop an easily interpretable model of the variability of correction bolus timing observed in real data, and embed it into a popular simulation tool for ISCTs. METHODS: Using data collected in 196 adults with T1D monitored in free-living conditions, we trained a decision tree (DT) model to classify whether a correction bolus is injected in a future time window, based on predictors collected back in time, related to CGM data, previous insulin boluses and subject's characteristics. The performance was compared to that of a logistic regression classifier with LASSO regularization (LC), trained on the same dataset. After validation, the DT was embedded within a popular T1D simulation tool and an ISCT was performed to compare the simulated correction boluses against those observed in a subset of data not used for model training. RESULTS: The DT provided better classification performance (accuracy: 0.792, sensitivity: 0.430, specificity: 0.878, precision: 0.455) than the LC and presented good interpretability. The most predictive features were related to CGM (and its temporal variations), time since the last insulin bolus, and time of the day. The correction boluses simulated by the DT, after implementation in the simulation tool, showed a good agreement with real-world data. CONCLUSIONS: The DT developed in this work represents a simple set of rules to mimic the same timing of correction boluses observed on real data. The inclusion of the model in simulation tools allows investigators to perform ISCTs that more realistically represent the patient behavior in taking correction boluses and the post-prandial BG response. In the future, more complex models can be investigated.

Super-twisting-based meal detector for type 1 diabetes management: Improvement and assessment in a real-life scenario.

BACKGROUND AND OBJECTIVE: Hybrid automated insulin delivery systems rely on carbohydrate counting to improve postprandial control in type 1 diabetes. However, this is an extra burden on subjects, and it introduces a source of potential errors that could impact control performances. In fact, carbohydrates estimation is challenging, prone to errors, and it is known that subjects sometimes struggle to adhere to this requirement, forgetting to perform this task. A possible solution is the use of automated meal detection algorithms. In this work, we extended a super-twisting-based meal detector suggested in the literature and assessed it on real-life data. METHODS: To reduce the false detections in the original meal detector, we implemented an implicit discretization of the super-twisting and replaced the Euler approximation of the glucose derivative with a Kalman filter. The modified meal detector is retrospectively evaluated in a challenging real-life dataset corresponding to a 2-week trial with 30 subjects using sensor-augmented pump control. The assessment includes an analysis of the nature and riskiness of false detections. RESULTS: The proposed algorithm achieved a recall of 70 [13] % (median [interquartile range]), a precision of 73 [26] %, and had 1.4 [1.4] false positives-per-day. False positives were related to rising glucose conditions, whereas false negatives occurred after calibrations, missing samples, or hypoglycemia treatments. CONCLUSIONS: The proposed algorithm achieves encouraging performance. Although false positives and false negatives were not avoided, they are related to situations with a low risk of hypoglycemia and hyperglycemia, respectively.

A Mathematical Formula to Determine the Minimum Continuous Glucose Monitoring Duration to Assess Time-in-ranges: Sensitivity Analysis Over the Parameters.

In diabetes management, the fraction of time spent with glucose concentration within the physiological range of [70-180] mg/dL, namely time in range (TIR) is often computed by clinicians to assess glycemic control using a continuous glucose monitoring sensor. However, a sufficiently long monitoring period is required to reliably estimate this index. A mathematical equation derived by our group provides the minimum trial duration granting a desired uncertainty around the estimated TIR. The equation involves two parameters, pr and α, related to the population under analysis, which should be set based on the clinician's experience. In this work, we evaluated the sensitivity of the formula to the parameters.Considering two independent datasets, we predicted the uncertainty of TIR estimate for a population, using the parameters of the formula estimated for a different population. We also stressed the robustness of the formula by testing wider ranges of parameters, thus assessing the impact of large errors in the parameters' estimates.Plausible errors on the α estimate impact very slightly on the prediction (relative discrepancy < 5%), thus we suggest using a fixed value for α independently on the population being analyzed. Instead, pr should be adjusted to the TIR expected in the population, considering that errors around 20% result in a relative discrepancy of ~10%.In conclusion, the proposed formula is sufficiently robust to parameters setting and can be used by investigators to determine a suitable duration of the study.

Nonlinear Machine Learning Models for Insulin Bolus Estimation in Type 1 Diabetes Therapy.

Type 1 diabetes (T1D) therapy requires multiple daily insulin injections to compensate the lack of endogenous insulin production due to ß-cells destruction. An empirical standard formula (SF) is commonly used for such a task. Unfortunately, SF does not include information on glucose dynamics, e.g. the glucose rate-of-change (ROC) provided by continuous glucose monitoring (CGM) sensor. Hence, SF can sometimes lead to under/overestimations that can cause critical hypo/hyperglycemic episodes during/after the meal. Recently, to overcome this limitation, we proposed new linear regression models, integrating ROC information and personalized features. Despite the first encouraging results, the nonlinear nature of the problem calls for the application of nonlinear models. In this work, random forest (RF) and gradient boosting tree (GBT), nonlinear machine learning methodologies, were investigated. A dataset of 100 virtual subjects, opportunely divided into training and testing sets, was used. For each individual, a single-meal scenario with different meal conditions (preprandial ROC, BG and meal amounts) was simulated. The assessment was performed both in terms of accuracy in estimating the optimal bolus and glycemic control. Results were compared to the best performing linear model previously developed. The two tree-based models proposed lead to a statistically significant improvement of glycemic control compared to the linear approach, reducing the time spent in hypoglycemia (from 32.49% to 27.57-25.20% for RF and GBT, respectively). These results represent a preliminary step to prove that nonlinear machine learning techniques can improve the estimation of insulin bolus in T1D therapy. Particularly, RF and GBT were shown to outperform the previously linear models proposed.Clinical Relevance- Insulin bolus estimation with nonlinear machine learning techniques reduces the risk of adverse events in T1D therapy.

Bayesian Model Selection Framework to Improve Calibration of Continuous Glucose Monitoring Sensors for Diabetes Management.

Minimally-invasive continuous glucose monitoring (CGM) sensors have revolutionized perspectives in the treatment of type 1 diabetes (T1D). Their accuracy relies on an internal calibration function that transforms the raw, physically measured, electrical data into blood glucose concentration values. Usually, a unique, pre-determined, calibration functional is adopted, with parameters periodically updated in individual patients by using "gold standard" references suitably collected by finger prick devices. However, retrospective analysis of CGM data suggests that variability of sensor-subject characteristics is often inefficiently coped with. In the present study, we propose a conceptual Bayesian model- selection framework aimed at guaranteeing wide margins of flexibility for both the determination of the most appropriate calibration functional and the numerical values of its unknown parameters. The calibration model is determined among a finite specified set of candidates, each one depending on a set of unknown model parameters, for which a priori statistical expectations are available. Model selection is based on predictive distributions carrying out asymptotic calculations through Monte Carlo integration methods. Performance of the proposed approach is assessed on synthetic data generated by a well-established T1D simulation model.

Non-Invasive Continuous-Time Blood Pressure Estimation from a Single Channel PPG Signal using Regularized ARX Models.

Continuous blood pressure (BP) monitoring can help in preventing hypertension and other cardiovascular diseases. In principle, an indirect non-invasive continuous-time measurement of BP is possible by exploiting the photoplethysmography (PPG) signal, which can be obtained through wearable optical sensor devices. However, a model of the PPG-to-BP dynamical system is needed. In this study, we investigate if autoregressive with exogenous input (ARX) models with kernel-based regularization are suited for the scope. We analyzed 10 PPG time-series acquired on different individuals by a wearable optical sensor and correspondent BP reference values to evaluate feasibility of continuous BP estimation from a single PPG source. This first proof-of-concept study shows promising results in continuous BP estimation during resting states.

Automated analysis of local field potentials evoked by mechanical whisker stimulation in rat barrel cortex.

Local field potentials (LFPs) recorded in the barrel cortex in rats and mice are important to investigate somatosensory systems, the final aim being to start to understand mechanisms of brain representation of sensory stimuli in humans. Parameters extracted from LFP of particular interest include spike timing and transmembrane current flow. Recent improvements in microelectrodes technology have enabled neuroscientists to acquire a great amount of LFP signals during the same experimental session, calling for the development of algorithms for their quantitative automatic analysis. In the present work, an algorithm based on Phillips-Tikhonov regularization is presented to automatically detect the main features (in terms of amplitude and latency) of LFP waveforms recorded after whisker stimulation in rat. The accuracy of the algorithm is first assessed in a Monte Carlo simulation mimicking the acquisition of LFP in three different conditions of SNR. Then, the algorithm is tested by analyzing a set of 100 LFP recorded in the primary somatosensory (S1) cortex, i.e., the region involved in the cortical representation of touch in mammals.

Accuracy of devices for self-monitoring of blood glucose: A stochastic error model.

Self-monitoring of blood glucose (SMBG) devices are portable systems that allow measuring glucose concentration in a small drop of blood obtained via finger-prick. SMBG measurements are key in type 1 diabetes (T1D) management, e.g. for tuning insulin dosing. A reliable model of SMBG accuracy would be important in several applications, e.g. in in silico design and optimization of insulin therapy. In the literature, the most used model to describe SMBG error is the Gaussian distribution, which however is simplistic to properly account for the observed variability. Here, a methodology to derive a stochastic model of SMBG accuracy is presented. The method consists in dividing the glucose range into zones in which absolute/relative error presents constant standard deviation (SD) and, then, fitting by maximum-likelihood a skew-normal distribution model to absolute/relative error distribution in each zone. The method was tested on a database of SMBG measurements collected by the One Touch Ultra 2 (Lifescan Inc., Milpitas, CA). In particular, two zones were identified: zone 1 (BG≤75 mg/dl) with constant-SD absolute error and zone 2 (BG>75mg/dl) with constant-SD relative error. Mean and SD of the identified skew-normal distributions are, respectively, 2.03 and 6.51 in zone 1, 4.78% and 10.09% in zone 2. Visual predictive check validation showed that the derived two-zone model accurately reproduces SMBG measurement error distribution, performing significantly better than the single-zone Gaussian model used previously in the literature. This stochastic model allows a more realistic SMBG scenario for in silico design and optimization of T1D insulin therapy.

Patient decision-making of CGM sensor driven insulin therapies in type 1 diabetes: In silico assessment.

In type 1 diabetes (T1D) therapy, continuous glucose monitoring (CGM) sensors, which provide glucose concentration in the subcutis every 1-5 min for 7 consecutive days, should allow in principle a more efficient insulin dosing than that based on the conventional 3-4 self-monitoring of blood glucose (SMBG) measurements per day. However, CGM, at variance with SMBG, is still not approved for insulin dosing in T1D management because regulatory agencies, e.g. FDA, are looking for more factual evidence on its safety. An in silico assessment of SMBG- vs CGM-driven insulin therapy can be a first step. Here we present a simulation model of T1D patient decision-making obtained by interconnecting models of glucose-insulin dynamics, SMBG and CGM measurement errors, carbohydrates-counting errors, insulin boluses time variability and forgetfulness, and subcutaneous insulin pump delivery. Inter- and intra- patient variability of model parameters are considered. The T1D patient decision-making model allows to run realistic multi-day simulations scenarios in a population of virtual subjects. We present the first results of simulations run in 20 virtual subjects over a 7-day period, which demonstrates that additional information brought by CGM (trend and hypo/hyperglycemic warnings) with respect to SMBG produces a statistically significant increment (about of 9%) of time spent by the patient in the euglycemic range (70-180 mg/dl).

Decrease of EEG Coherence during hypoglycemia in type 1 diabetic subjects.

Hypoglycemic events have been proven to be associated with measurable EEG changes. Several works in the literature have evaluated these changes by considering approaches at the single EEG channel level, but multivariate analyses have been scarcely investigated in Type 1 diabetes (T1D) subjects. The aim of the present work is to assess if and how hypoglycemia affects EEG coherence in a subset of EEG channels acquired in a hospital setting where eye- and muscle activation-induced artifacts are virtually absent. In particular, EEG multichannel data, acquired in 19 T1D hospitalized subjects undertaken to an insulin-induced hypoglycemia experiment, are considered. Computation of Partial Directed Coherence (PDC) through multivariate autoregressive models of P3-A1A2, P4-A1A2, C3-A1A2 and C4-A1A2 EEG channels shows that a decrease in the value of coherence, most likely related to the progressive loss of cognitive function and altered cerebral activity, occurs when passing from eu- to hypoglycemia, in both theta ([4, 8] Hz) and alpha ([8, 13] Hz) bands.

An EEGLAB plugin to analyze individual EEG alpha rhythms using the "channel reactivity-based method".

A recent paper [1] proposed a new technique, termed the channel reactivity-based method (CRB), for characterizing EEG alpha rhythms using individual (IAFs) and channel (CAFs) alpha frequencies. These frequencies were obtained by identifying the frequencies at which the power of the alpha rhythms decreases. In the present study, we present a graphical interactive toolbox that can be plugged into the popular open source environment EEGLAB, making it easy to use CRB. In particular, we illustrate the major functionalities of the software and discuss the advantages of this toolbox for common EEG investigations. The CRB analysis plugin, along with extended documentation and the sample dataset utilized in this study, is freely available on the web at http://bio.dei.unipd.it/crb/.

Jump neural network for online short-time prediction of blood glucose from continuous monitoring sensors and meal information.

Several real-time short-term prediction methods, based on time-series modeling of past continuous glucose monitoring (CGM) sensor data have been proposed with the aim of allowing the patient, on the basis of predicted glucose concentration, to anticipate therapeutic decisions and improve therapy of type 1 diabetes. In this field, neural network (NN) approaches could improve prediction performance handling in their inputs additional information. In this contribution we propose a jump NN prediction algorithm (horizon 30 min) that exploits not only past CGM data but also ingested carbohydrates information. The NN is tuned on data of 10 type 1 diabetics and then assessed on 10 different subjects. Results show that predictions of glucose concentration are accurate and comparable to those obtained by a recently proposed NN approach (Zecchin et al. (2012) [26]) having higher structural and algorithmical complexity and requiring the patient to announce the meals. This strengthen the potential practical usefulness of the new jump NN approach.

Insight into the relationship between brain/behavioral speed and variability in patients with minimal hepatic encephalopathy.

OBJECTIVE: Intra-individual variability (IIV) of response reaction times (RTs) and psychomotor slowing were proposed as markers of brain dysfunction in patients with minimal hepatic encephalopathy (MHE), a subclinical disorder of the central nervous system frequently detectable in patients with liver cirrhosis. However, behavioral measures alone do not enable investigations into the neural correlates of these phenomena. The aim of this study was to investigate the electrophysiological correlates of psychomotor slowing and increased IIV of RTs in patients with MHE. METHODS: Event-related potentials (ERPs), evoked by a stimulus-response (S-R) conflict task, were recorded from a sample of patients with liver cirrhosis, with and without MHE, and a group of healthy controls. A recently presented Bayesian approach was used to estimate single-trial P300 parameters. RESULTS: Patients with MHE, with both psychomotor slowing and higher IIV of RTs, showed higher P300 latency jittering and lower single-trial P300 amplitude compared to healthy controls. In healthy controls, distribution analysis revealed that single-trial P300 latency increased and amplitude decreased as RTs became longer; however, in patients with MHE the linkage between P300 and RTs was weaker or even absent. CONCLUSIONS: These findings suggest that in patients with MHE, the loss of the relationship between P300 parameters and RTs is related to both higher IIV of RTs and psychomotor slowing. SIGNIFICANCE: This study highlights the utility of investigating the relationship between single-trial ERPs parameters along with RT distributions to explore brain functioning in normal or pathological conditions.

Sparse Principal Component Analysis for the parsimonious description of glucose variability in diabetes.

Abnormal glucose variability (GV) is considered to be a risk factor for the development of diabetes complications. For its quantification from continuous glucose monitoring (CGM) data, tens of different indices have been proposed in the literature, but the information carried by them is highly redundant. In the present work, the Sparse Principal Component Analysis (SPCA) technique is used to select, from a wide pool of GV metrics, a smaller subset of indices that preserves the majority of the total original variance, providing a parsimonious but still comprehensive description of GV. In detail, SPCA is applied to a set of 25 literature GV indices evaluated on CGM time-series collected in 17 type 1 (T1D) and 13 type 2 (T2D) diabetic subjects. Results show that the 10 GV indices selected by SPCA preserve more than the 75% of the variance of the original set of 25 indices, both in T1D and T2D. Moreover, 6 indices of the parsimonious set are shared by T1D and T2D.

A novel method for the determination of the EEG individual alpha frequency.

The individual alpha frequency (IAF) is one of the most common tools used to study the variability of EEG rhythms among subjects. Several approaches have been proposed in the literature for IAF determination, including the popular peak frequency (PF) method, the extended band (EB) method, and the transition frequency (TF) method. However, literature techniques for IAF determination are over-reliant on the presence of peaks in the EEG spectrum and are based on qualitative criteria that require visual inspection of every individual EEG spectrum, a task that can be time consuming and difficult to reproduce. In this paper a novel channel reactivity based (CRB) method is proposed for IAF computation. The CRB method is based on quantitative indexes and criteria and relies on task-specific alpha reactivity patterns rather than on the presence of peaks in the EEG spectrum. Application of the technique to EEG signals recorded from 19 subjects during a cognitive task demonstrates the effectiveness of the CRB method and its capability to overcome the limits of PF, EB, and TF approaches.

A methodology to improve estimation of stimulus-evoked hemodynamic response from fNIRS measurements.

Functional near-infrared spectroscopy (fNIRS) is a non-invasive optical neuroimaging method used to investigate functional activity of the cerebral cortex evoked by cognitive, visual, auditory and motor tasks, detecting regional changes of oxy- and deoxy-hemoglobin concentration. Accurate estimation of the stimulus-evoked hemodynamic response (HR) from fNIRS signals in order to quantitatively investigate cognitive functions requires to cope with several noise components. Some of them appear as random disturbances (typically tackled through averaging techniques), while others are due to physiological sources, such as heart beat, respiration, vasomotor waves, and are particularly challenging to be dealt with because they lie in the same frequency band of HR. In this work we present a new two-steps methodology for the HR estimation from fNIRS data. The first step is a pre-processing stage where physiological trends in fNIRS data are reduced by exploiting a mathematical model identified from the signal of a reference channel. In the second step, the pre-processed data of the other channels are filtered with a recently presented non-parametric Bayesian approach (Scarpa et al., Optics Express, 2010). The presented method for HR estimation is compared with widely used methods: conventional averaging, band-pass filtering and principal component analysis (PCA). Results on simulated data reveal the ability of the proposed method to improve the accuracy of the estimates of the functional hemodynamic response, as well as the estimate of peak amplitude and latency. Encouraging preliminary results in a representative real data set showing an improvement of contrast to noise ratio are also reported.

A new neural network approach for short-term glucose prediction using continuous glucose monitoring time-series and meal information.

In the last decade, improvements in diabetes daily management have become possible thanks to the development of minimally-invasive portable sensors which allow continuous glucose monitoring (CGM) for several days. In particular, hypo and hyperglycemia can be promptly detected when glucose exceeds the normal range thresholds, and even avoided through the use of on-line glucose prediction algorithms. Several algorithms with prediction horizon (PH) of 15-30-45 min have been proposed in the literature, e.g. including AR/ARMA time-series modeling and neural networks. Most of them are fed by CGM signals only. The purpose of this work is to develop a new short-term glucose prediction algorithm based on a neural network that, in addition to past CGM readings, also exploits information on carbohydrates intakes quantitatively described through a physiological model. Results on simulated data quantitatively show that the new method outperforms other published algorithms. Qualitative preliminary results on a real diabetic subject confirm the potentialities of the new approach.

Bayesian filtering of human brain hemodynamic activity elicited by visual short-term maintenance recorded through functional near-infrared spectroscopy (fNIRS).

Functional near-infrared spectroscopy (fNIRS) is a neuroimaging technique that measures changes in oxy-hemoglobin (ΔHbO) and deoxy-hemoglobin (ΔHbR) concentration associated with brain activity. The signal acquired with fNIRS is naturally affected by disturbances engendering from ongoing physiological activity (e.g., cardiac, respiratory, Mayer wave) and random measurement noise. Despite its several drawbacks, the so-called conventional averaging (CA) is still widely used to estimate the hemodynamic response function (HRF) from noisy signal. One such drawback is related to the number of trials necessary to derive stable HRF functions adopting the CA approach, which must be substantial (N >> 50). In this work, a pre-processing procedure to remove artifacts followed by the application of a non-parametric Bayesian approach is proposed that capitalizes on a priori available knowledge about HRF and noise. Results with the proposed Bayesian approach were compared with CA and with a straightforward band-pass filtering approach. On simulated data, a five times lower estimation error on HRF was obtained with respect to that obtained by CA, and 2.5 times lower than that obtained by band pass filtering. On real data, the improvement achieved by the present method was attested by an increase in the contrast to noise ratio (CNR) and by a reduced variability in single trial estimation. An application of the present Bayesian approach is illustrated that was optimized to monitor changes in hemodynamic activity reflecting variations in visual short-term memory load in humans, which are notoriously hard to detect using functional magnetic resonance imaging (fMRI). In particular, statistical analyses of HRFs recorded during a memory task established with high reliability the crucial role of the intraparietal sulcus and the intra-occipital sulcus in posterior areas of the human brain in visual short-term memory maintenance.