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.

Implantable and transcutaneous continuous glucose monitoring system: a randomized cross over trial comparing accuracy, efficacy and acceptance.

AIM: To compare accuracy, efficacy and acceptance of implantable and transcutaneous continuous glucose monitoring (CGM) systems. METHODS: In a randomized crossover trial we compared 12 weeks with Eversense implantable sensor (EVS) and 12 weeks with Dexcom G5 transcutaneous sensor (DG5) in terms of accuracy, evaluated as Mean Absolute Relative Difference (MARD) vs capillary glucose (SMBG), time of CGM use, adverse events, efficacy (as HbA1c, time in range, time above and below range) and psychological outcomes evaluated with Diabetes Treatment Satisfaction Questionnaire (DTSQ), Glucose Monitoring Satisfaction Survey (GMSS), Hypoglycemia Fear Survey (HFS2), Diabetes Distress Scale (DDS). RESULTS: 16 subjects (13 males, 48.8 ± 10.1 years, HbA1c 55.8 ± 7.9 mmol/mol, mean ± SD) completed the study. DG5 was used more than EVS [percentage of use 95.7 ± 3.6% vs 93.5 ± 4.3% (p = 0.02)]. MARD was better with EVS (12.2 ± 11.5% vs. 13.1 ± 14.7%, p< 0.001). No differences were found in HbA1c. While using EVS time spent in range increased and time spent in hyperglycemia decreased, but these data were not confirmed by analysis of retrofitted data based on SMBG values. EVS reduced perceived distress, without significant changes in other psychological outcomes. CONCLUSIONS: CGM features may affect glycemic control and device acceptance.

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.

FreeStyle Libre and Dexcom G4 Platinum sensors: Accuracy comparisons during two weeks of home use and use during experimentally induced glucose excursions.

BACKGROUND AND AIMS: This study compared the accuracy of the FreeStyle Libre (Abbott, Alameda, CA) and Dexcom G4 Platinum (DG4P, Dexcom, San Diego, CA) CGM sensors. METHODS AND RESULTS: Twenty-two adults with type 1 diabetes wore the two sensors simultaneously for 2 weeks. Libre was used according to manufacturer-specified lifetime (MSL); DG4P was used 7 days beyond MSL. At a clinical research center (CRC), subjects were randomized to receive the same breakfast with standard insulin bolus (standard) or a delayed and increased (delayed & increased) bolus to induce large glucose swings during weeks 1 and 2; venous glucose was checked every 5-15 min for 6 h. Subjects performed ≥4 reference fingersticks/day at home. Accuracy was assessed by differences in mean absolute relative difference (%MARD) in glucose levels compared with fingerstick test (home use) and YSI reference (CRC). During home-stay the Libre MARD was 13.7 ± 3.6% and the DG4P MARD 12.9 ± 2.5% (difference not significant [NS]). With both systems MARD increased during hypoglycaemia and decreased during hyperglycaemia, without significant difference between sensors. In the euglycaemic range MARD was smaller with DG4P [12.0 ± 2.4% vs 14.0 ± 3.6%, p = 0.026]. MARD increased in both sensors following delayed & increased vs. standard bolus (Libre: 14.9 ± 5.5% vs. 10.9 ± 4.1%, p = 0.008; DG4P: 18.1 ± 8.1% vs. 13.1 ± 4.6%, p = 0.026); between-sensor differences were not significant (p = 0.062). Libre was more accurate during moderate and rapid glucose changes. CONCLUSIONS: DG4P and Libre performed similarly up to 7 days beyond DG4P MSL. Both sensors performed less well during hypoglycaemia but Libre was more accurate during glucose swings. TRIAL REGISTRATION: The study was registered in ClinicalTrials.gov (NCT02734745) April 12, 2016.

Switching from twice-daily glargine or detemir to once-daily degludec improves glucose control in type 1 diabetes. An observational study.

BACKGROUND AND AIMS: Degludec is an ultralong-acting insulin analogue with a flat and reproducible pharmacodynamic profile. As some patients with type 1 diabetes (T1D) fail to achieve 24-h coverage with glargine or detemir despite twice-daily injections, we studied the effect of switching T1D patients from twice-daily glargine or detemir to degludec. METHODS AND RESULTS: In this prospective observational study, T1D patients on twice-daily glargine or detemir were enrolled. At baseline and 12 weeks after switching to degludec, we recorded HbA1c, insulin dose, 30-day blood glucose self monitoring (SMBG) or 14-day continuous glucose monitoring (CGM), treatment satisfaction (DTSQ), fear of hypoglycemia (FHS). We included 29 patients (mean age 34 ± 11 years; diabetes duration 18 ± 10 years). After switching to degludec, HbA1c decreased from 7.9 ± 0.6% (63 ± 6 mmol/mol) to 7.7 ± 0.6% (61 ± 6 mmol/mol; p = 0.028). SMBG showed significant reductions in the percent and number of blood glucose values <70 mg/dl and in the low blood glucose index (LBGI) during nighttime. CGM showed a significant reduction of time spent in hypoglycemia, an increase in daytime spent in target 70-180 mg/dl, and a reduction in glucose variability. Total insulin dose declined by 17% (p < 0.001), with 24% reduction in basal and 10% reduction in prandial insulin. DTSQ and FHS significantly improved. CONCLUSION: Switching from twice-daily glargine or detemir to once daily degludec improved HbA1c, glucose profile, hypoglycemia risk and treatment satisfaction, while insulin doses decreased. ClinicalTrials.govNCT02360254.

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).

Carotid artery stenting: Influence of experience and cerebrovascular risk factors on outcome.

AIM: To evaluate technical success, complications and the influence of the learning curve on outcome in carotid artery stenting (CAS) performed in patients not suitable for surgery. PATIENTS AND METHODS: One hundred and nine procedures of protected carotid stenting in 103 high risk patients were performed. All patients presented at least one factor that potentially increased the surgical risk of carotid endoarterectomy (CEA), according to SAPPHIRE criteria. Neurologic complications were quantified by the National Institutes of Health Stroke Scale (NIHSS) and were evaluated by median Rankin Scale (mRS). To evaluate the influence of experience of the operator to perform CAS, we retrospectively analyzed periprocedural and neurological complications of the first 50 procedures compared with that of the following 59 interventions. RESULTS: Technical success rate was 98%. Neurological periprocedural complications were revealed in 4.5% of patients. In-hospital and 30-days neurological complications rate was 7.6 and 2.6% respectively. Periprocedural neurological complications rate was lower in the last procedures performed, according to a higher confidence of the operators. CONCLUSIONS: CAS may be performed as an alternative of CEA for the treatment of severe carotid obstructive disease in patients not suitable for surgery. The learning curve positively influence complications rate.

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.

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 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.

Artificial neural network algorithm for online glucose prediction from continuous glucose monitoring.

BACKGROUND AND AIMS: Continuous glucose monitoring (CGM) devices could be useful for real-time management of diabetes therapy. In particular, CGM information could be used in real time to predict future glucose levels in order to prevent hypo-/hyperglycemic events. This article proposes a new online method for predicting future glucose concentration levels from CGM data. METHODS: The predictor is implemented with an artificial neural network model (NNM). The inputs of the NNM are the values provided by the CGM sensor during the preceding 20 min, while the output is the prediction of glucose concentration at the chosen prediction horizon (PH) time. The method performance is assessed using datasets from two different CGM systems (nine subjects using the Medtronic [Northridge, CA] Guardian and six subjects using the Abbott [Abbott Park, IL] Navigator. Three different PHs are used: 15, 30, and 45 min. The NNM accuracy has been estimated by using the root mean square error (RMSE) and prediction delay. RESULTS: The RMSE is around 10, 18, and 27 mg/dL for 15, 30, and 45 min of PH, respectively. The prediction delay is around 4, 9, and 14 min for upward trends and 5, 15, and 26 min for downward trends, respectively. A comparison with a previously published technique, based on an autoregressive model (ARM), has been performed. The comparison shows that the proposed NNM is more accurate than the ARM, with no significant deterioration in the prediction delay. CONCLUSIONS: The proposed NNM is a reliable solution for the online prediction of future glucose concentrations from CGM data.