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.

Gluclas: A software for computer-aided modulation of glucose infusion in glucose clamp experiments

BACKGROUND AND OBJECTIVE

The glucose clamp (GC) is an experimental technique for assessing several aspects of glucose metabolism. In these experiments, investigators face the non-trivial challenge of accurately adjusting the rate of intravenous glucose infusion to drive subjects' blood glucose (BG) concentration towards a desired plateau level. In this work we present Gluclas, an open-source software to support researchers in the modulation of glucose infusion rate (GIR) during GC experiments.

METHODS

Gluclas uses a proportional-integrative-derivative controller to provide GIR suggestions based on BG measurements. The controller embeds an anti-wind-up scheme to account for actuator physical limits and suitable corrections of control action to accommodate for possible sampling jitter due to manual measurement and actuation. The software also provides a graphic user interface to increase its usability. A preliminary validation of the controller is performed for different clamp scenarios (hyperglycemic, euglycemic, hypoglycemic) on a simulator of glucose metabolism in healthy subjects, which also includes models of measurement error and sampling delay for increased realism. In silico trials are performed on 50 virtual subjects. We also report the results of the first in-vivo application of the software in three subjects undergoing a hypoglycemic clamp.

RESULTS

In silico, during the plateau period, the coefficient of variation (CV) is in median below 5% for every protocol, with 5% being considered the threshold for sufficient quality. In terms of median [5th percentile, 95th percentile], average BG level during the plateau period is 12.18 [11.58 - 12.53] mmol/l in the hyperglycemic clamp (target: 12.4 mmol/), 4.92 [4.51 - 5.14] mmol/l in the euglycemic clamp (target: 5.5 mmol/) and 2.38 [2.33 - 2.64] in the hypoglycemic clamp (target: 2.5 mmol/). Results in vivo are consistent with those obtained in silico during the plateau period: average BG levels are between 2.56 and 2.68 mmol/l (target: 2.5 mmol/l); CV is below 5% for all three experiments.

CONCLUSIONS

Gluclas offered satisfactory control for tested GC protocols. Although its safety and efficacy need to be further validated in vivo, this preliminary validation suggest that Gluclas offers a reliable and non-expensive solution for reducing investigator bias and improving the quality of GC experiments.

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.

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.

A PID Control Algorithm for a Post-Prandial Hypoglycemic Clamp Study

Post-prandial hypoglycemia occurs 2-5 hours after food intake, in not only insulin-treated patients with diabetes but also other metabolic disorders. For example, postprandial hypoglycemia is an increasingly recognized late metabolic complication of bariatric surgery (also known as PBH), particularly gastric bypass. Underlying mechanisms remain incompletely understood to date. Besides excessive insulin exposure, impaired counter-regulation may be a further pathophysiological feature. To test this hypothesis, we need standardized postprandial hypoglycemic clamp procedures in affected and unaffected individuals allowing to reach identical predefined postprandial hypoglycemic trajectories. Generally, in these experiments, clinical investigators manually adjust glucose infusion rate (GIR) to clamp blood glucose (BG) to a target hypoglycemic value. Nevertheless, reaching the desired target by manual adjustment may be challenging and possible glycemic undershoots when approaching hypoglycemia can be a safety concern for patients. In this study, we developed a PID algorithm to assist clinical investigators in adjusting GIR to reach the predefined trajectory and hypoglycemic target. The algorithm is developed in a manual mode to permit the clinical investigator to interfere. We test the controller in silico by simulating glucose-insulin dynamics in PBH and healthy nonsurgical individuals. Different scenarios are designed to test the robustness of the algorithm to different sources of variability and to errors, e.g. outliers in the BG measurements, sampling delays or missed measurements. The results prove that the PID algorithm is capable of accurately and safely reaching the target BG level, on both healthy and PBH subjects, with a median deviation from reference of 2.8% and 2.4% respectively.Clinical relevance- This control algorithm enables standardized, accurate and safe postprandial hypoglycemic clamps, as evidenced in silico in PBH patients and controls.

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, p_r 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, p_r 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 β-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.

Black-box Model Identification of Physical Activity in Type-l Diabetes Patients

In this paper we consider the problem of predicting future values of glucose in type-1 diabetes. In particular, we investigate the benefit of including physical activity, measured by an off-the-shelf wearable device, to other physiologic signals frequently used to predict blood-glucose concentration, namely injected insulin, carbohydrates intake, and past glucose samples measured by a Continuous Glucose Monitoring (CGM) sensor. Derivation of individualized predictors is crucial to cope with the wide inter- and intra-subject variability: learning and updating patient-specific models of the glucose-insulin system and using them to design personalized control actions has the potential to improve substantially patients' quality oflife. On data collected by 6 subjects for 5 days, we identify a black-box liner model that uses insulin and meal as inputs and glucose as output. Prediction Error Method (PEM) is used for parameter estimation. The personalized model is employed to derive patient-tailored predictors. This procedure is then repeated using a further physiological input, accounting for physical activity. The prediction accuracy of the two models, including or not physical activity, was compared on the basis of two metrics commonly used in system identification, namely Coefficient of Determination (COD) and Root Mean Squared Error. The models identified with physical activity have better performance, increasing the 3-hr prediction COD by mean ± standard deviation of 18.5% ± 30.1%.

Parental evaluation of a telemonitoring service for children with Type 1 Diabetes

Introduction In the past years, we developed a telemonitoring service for young patients affected by Type 1 Diabetes. The service provides data to the clinical staff and offers an important tool to the parents, that are able to oversee in real time their children. The aim of this work was to analyze the parents' perceived usefulness of the service. Methods The service was tested by the parents of 31 children enrolled in a seven-day clinical trial during a summer camp. To study the parents' perception we proposed and analyzed two questionnaires. A baseline questionnaire focused on the daily management and implications of their children's diabetes, while a post-study one measured the perceived benefits of telemonitoring. Questionnaires also included free text comment spaces. Results Analysis of the baseline questionnaires underlined the parents' suffering and fatigue: 51% of total responses showed a negative tendency and the mean value of the perceived quality of life was 64.13 in a 0-100 scale. In the post-study questionnaires about half of the parents believed in a possible improvement adopting telemonitoring. Moreover, the foreseen improvement in quality of life was significant, increasing from 64.13 to 78.39 ( p-value = 0.0001). The analysis of free text comments highlighted an improvement in mood, and parents' commitment was also proved by their willingness to pay for the service (median = 200 euro/year). Discussion A high number of parents appreciated the telemonitoring service and were confident that it could improve communication with physicians as well as the family's own peace of mind.

Multicenter outpatient dinner/overnight reduction of hypoglycemia and increased time of glucose in target with a wearable artificial pancreas using modular model predictive control in adults with type 1 diabetes

AIMS

To test in an outpatient setting the safety and efficacy of continuous subcutaneous insulin infusion (CSII) driven by a modular model predictive control (MMPC) algorithm informed by continuous glucose monitoring (CGM) measurement.

METHODS

13 patients affected by type 1 diabetes participated to a non-randomized outpatient 42-h experiment that included two evening meals and overnight periods (in short, dinner & night periods). CSII was patient-driven during dinner & night period 1 and MMPC-driven during dinner&night period 2. The study was conducted in hotels, where patients could move around freely. A CGM system (G4 Platinum; Dexcom Inc., San Diego, CA, USA) and insulin pump (AccuChek Combo; Roche Diagnostics, Mannheim, Germany) were connected wirelessly to a smartphone-based platform (DiAs, Diabetes Assistant; University of Virginia, Charlottesville, VA, USA) during both periods.

RESULTS

A significantly lower percentage of time spent with glucose levels <3.9 mmol/l was achieved in period 2 compared with period 1: 1.96 ± 4.56% vs 12.76 ± 15.84% (mean ± standard deviation, p < 0.01), together with a greater percentage of time spent in the 3.9-10 mmol/l target range: 83.56 ± 14.02% vs 62.43 ± 29.03% (p = 0.04). In addition, restricting the analysis to the overnight phases, a lower percentage of time spent with glucose levels <3.9 mmol/l (1.92 ± 4.89% vs 12.7 ± 19.75%; p = 0.03) was combined with a greater percentage of time spent in 3.9-10 mmol/l target range in period 2 compared with period 1 (92.16 ± 8.03% vs 63.97 ± 2.73%; p = 0.01). Average glucose levels were similar during both periods.

CONCLUSIONS

The results suggest that MMPC managed by a wearable system is safe and effective during evening meal and overnight. Its sustained use during this period is currently being tested in an ongoing randomized 2-month study.

Modular closed-loop control of diabetes

Modularity plays a key role in many engineering systems, allowing for plug-and-play integration of components, enhancing flexibility and adaptability, and facilitating standardization. In the control of diabetes, i.e., the so-called "artificial pancreas," modularity allows for the step-wise introduction of (and regulatory approval for) algorithmic components, starting with subsystems for assured patient safety and followed by higher layer components that serve to modify the patient's basal rate in real time. In this paper, we introduce a three-layer modular architecture for the control of diabetes, consisting in a sensor/pump interface module (IM), a continuous safety module (CSM), and a real-time control module (RTCM), which separates the functions of insulin recommendation (postmeal insulin for mitigating hyperglycemia) and safety (prevention of hypoglycemia). In addition, we provide details of instances of all three layers of the architecture: the APS© serving as the IM, the safety supervision module (SSM) serving as the CSM, and the range correction module (RCM) serving as the RTCM. We evaluate the performance of the integrated system via in silico preclinical trials, demonstrating 1) the ability of the SSM to reduce the incidence of hypoglycemia under nonideal operating conditions and 2) the ability of the RCM to reduce glycemic variability.