Giovanni Sparacino

Diabetes: Models, Signals, and Control

The control of diabetes is an interdisciplinary endeavor, which includes a significant biomedical engineering component, with traditions of success beginning in the early 1960s. It began with modeling of the insulin-glucose system, and progressed to large-scale in silico experiments, and automated closed-loop control (artificial pancreas). Here, we follow these engineering efforts through the last, almost 50 years. We begin with the now classic minimal modeling approach and discuss a number of subsequent models, which have recently resulted in the first in silico simulation model accepted as substitute to animal trials in the quest for optimal diabetes control. We then review metabolic monitoring, with a particular emphasis on the new continuous glucose sensors, on the analyses of their time-series signals, and on the opportunities that they present for automation of diabetes control. Finally, we review control strategies that have been successfully employed in vivo or in silico, presenting a promise for the development of a future artificial pancreas and, in particular, discuss a modular architecture for building closed-loop control systems, including insulin delivery and patient safety supervision layers. We conclude with a brief discussion of the unique interactions between human physiology, behavioral events, engineering modeling and control relevant to diabetes.

Glucose Concentration can be Predicted Ahead in Time From Continuous Glucose Monitoring Sensor Time-Series

A clinically important task in diabetes management is the prevention of hypo/hyperglycemic events. In this proof-of-concept paper, we assess the feasibility of approaching the problem with continuous glucose monitoring (CGM) devices. In particular, we study the possibility to predict ahead in time glucose levels by exploiting their recent history monitored every 3 min by a minimally invasive CGM system, the Glucoday, in 28 type 1 diabetic volunteers for 48 h. Simple prediction strategies, based on the description of past glucose data by either a first-order polynomial or a first-order autoregressive (AR) model, both with time-varying parameters determined by weighted least squares, are considered. Results demonstrate that, even by using these simple methods, glucose can be predicted ahead in time, e.g., with a prediction horizon of 30 min crossing of the hypoglycemic threshold can be predicted 20-25 min ahead in time, a sufficient margin to mitigate the event by sugar ingestion

Nonparametric input estimation in physiological systems: problems, methods, and case studies

Input estimation from output data is an important problem in the analysis of physiological systems, because many signals of interest are not directly accessible to measurement. When the system is time-invariant, this problem is often referred to as deconvolution. Three representative physiological problems, regarding hormone secretion, insulin dynamics, and hepatic glucose production, are used to illustrate the major challenges: ill-conditioning, confidence intervals assessment, infrequent and nonuniform sampling, nonnegativity constraints, and computational efficiency. The paper provides a critical overview of the existing techniques, focusing on regularization theory and Bayesian estimation. In order to overcome some inadequacies of the existing methods, some new results are derived. In particular, the connection between the maximum-likelihood estimate of the regularization parameter and the notion of equivalent degree of freedom is studied. Moreover, a fast SVD-based numerical algorithm is developed that includes the optimization of the regularization parameter, and the computation of confidence intervals. The proposed techniques are validated on a benchmark problem and are shown to provide effective solutions to the three physiological case studies.

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.

A stochastic deconvolution method to reconstruct insulin secretion rate after a glucose stimulus

Insulin secretion rate (ISR) is not directly measurable in man but it can be reconstructed from C-peptide (CP) concentration measurements by solving an input estimation problem by deconvolution. The major difficulties posed by the estimation of ISR after a glucose stimulus, e.g., during an intravenous glucose tolerance test (IVGTT), are the ill-conditioning of the problem, the nonstationary pattern of the secretion rate, and the nonuniform/infrequent sampling schedule. In this work, a nonparametric method based on the classic Phillips-Tikhonov regularization approach is presented. The problem of nonuniform/infrequent sampling is addressed by a novel formulation of the regularization method which allows the estimation of quasi time-continuous input profiles. The input estimation problem is stated into a Bayesian context, where the a priori known nonstationary characteristics of ISR after the glucose stimulus are described by a stochastic model. Deconvolution is tackled by linear minimum variance estimation, thus allowing the derivation of new statistically based regularization criteria. Finally, a Monte-Carlo strategy is implemented to assess the uncertainty of the estimated ISR arising from CP measurement error and impulse response parameters uncertainty.

Numerical non-identifiability regions of the minimal model of glucose kinetics : superiority of Bayesian estimation

The so-called minimal model (MM) of glucose kinetics is widely employed to estimate insulin sensitivity (S(I)) both in clinical and epidemiological studies. Usually, MM is numerically identified by resorting to Fisherian parameter estimation techniques, such as maximum likelihood (ML). However, unsatisfactory parameter estimates are sometimes obtained, e.g. S(I) estimates virtually zero or unrealistically high and affected by very large uncertainty, making the practical use of MM difficult. The first result of this paper concerns the mathematical demonstration that these estimation difficulties are inherent to MM structure which can expose S(I) estimation to the risk of numerical non-identifiability. The second result is based on simulation studies and shows that Bayesian parameter estimation techniques are less sensitive, in terms of both accuracy and precision, than the Fisherian ones with respect to these difficulties. In conclusion, Bayesian parameter estimation can successfully deal with difficulties of MM identification inherently due to its structure.

Smart Continuous Glucose Monitoring Sensors: On-Line Signal Processing Issues

The availability of continuous glucose monitoring (CGM) sensors allows development of new strategies for the treatment of diabetes. In particular, from an on-line perspective, CGM sensors can become “smart” by providing them with algorithms able to generate alerts when glucose concentration is predicted to exceed the normal range thresholds. To do so, at least four important aspects have to be considered and dealt with on-line. First, the CGM data must be accurately calibrated. Then, CGM data need to be filtered in order to enhance their signal-to-noise ratio (SNR). Thirdly, predictions of future glucose concentration should be generated with suitable modeling methodologies. Finally, generation of alerts should be done by minimizing the risk of detecting false and missing true events. For these four challenges, several techniques, with various degrees of sophistication, have been proposed in the literature and are critically reviewed in this paper.

Real-Time Improvement of Continuous Glucose Monitoring Accuracy The smart sensor concept

OBJECTIVE Reliability of continuous glucose monitoring (CGM) sensors is key in several applications. In this work we demonstrate that real-time algorithms can render CGM sensors smarter by reducing their uncertainty and inaccuracy and improving their ability to alert for hypo- and hyperglycemic events. RESEARCH DESIGN AND METHODS The smart CGM (sCGM) sensor concept consists of a commercial CGM sensor whose output enters three software modules, able to work in real time, for denoising, enhancement, and prediction. These three software modules were recently presented in the CGM literature, and here we apply them to the Dexcom SEVEN Plus continuous glucose monitor. We assessed the performance of the sCGM on data collected in two trials, each containing 12 patients with type 1 diabetes. RESULTS The denoising module improves the smoothness of the CGM time series by an average of ∼57%, the enhancement module reduces the mean absolute relative difference from 15.1 to 10.3%, increases by 12.6% the pairs of values falling in the A-zone of the Clarke error grid, and finally, the prediction module forecasts hypo- and hyperglycemic events an average of 14 min ahead of time. CONCLUSIONS We have introduced and implemented the sCGM sensor concept. Analysis of data from 24 patients demonstrates that incorporation of suitable real-time signal processing algorithms for denoising, enhancement, and prediction can significantly improve the performance of CGM applications. This can be of great clinical impact for hypo- and hyperglycemic alert generation as well in artificial pancreas devices.

Modeling the Error of Continuous Glucose Monitoring Sensor Data: Critical Aspects Discussed through Simulation Studies

Background: Knowing the statistical properties of continuous glucose monitoring (CGM) sensor errors can be important in several practical applications, e.g., in both open- and closed-loop control algorithms. Unfortunately, modeling the accuracy of CGM sensors is very difficult for both experimental and methodological reasons. It has been suggested that the time series of CGM sensor errors can be described as realization of the output of an autoregressive (AR) model of first order driven by a white noise process. The AR model was identified exploiting several reference blood glucose (BG) samples (collected frequently in parallel to the CGM signal), a procedure to recalibrate CGM data, and a linear time-invariant model of blood-to-interstitium glucose (BG-to-IG) kinetics. By resorting to simulation, this work shows that some assumptions made in the Breton and Kovatchev modeling approach may significantly affect the estimated sensor error and its statistical properties. Method: Three simulation studies were performed. The first simulation was devoted to assessing the influence of CGM data recalibration, whereas the second and third simulations examined the role of the BG-to-IG kinetic model. Analysis was performed by comparing the “original” (synthetically generated) time series of sensor errors vs its “reconstructed” version in both time and frequency domains. Results: Even small errors either in CGM data recalibration or in the description of BG-to-IG dynamics can severely affect the possibility of correctly reconstructing the statistical properties of sensor error. In particular, even if CGM sensor error is a white noise process, a spurious correlation among its samples originates from suboptimal recalibration or from imperfect knowledge of the BG-to-IG kinetics. Conclusions: Modeling the statistical properties of CGM sensor errors from data collected in vivo is difficult because it requires perfect calibration and perfect knowledge of BG-to-IG dynamics. Results suggest that correct characterization of CGM sensor error is still an open issue and requires further development upon the pioneering contribution of Breton and Kovatchev.

Modeling the Glucose Sensor Error

Continuous glucose monitoring (CGM) sensors are portable devices, employed in the treatment of diabetes, able to measure glucose concentration in the interstitium almost continuously for several days. However, CGM sensors are not as accurate as standard blood glucose (BG) meters. Studies comparing CGM versus BG demonstrated that CGM is affected by distortion due to diffusion processes and by time-varying systematic under/overestimations due to calibrations and sensor drifts. In addition, measurement noise is also present in CGM data. A reliable model of the different components of CGM inaccuracy with respect to BG (briefly, “sensor error”) is important in several applications, e.g., design of optimal digital filters for denoising of CGM data, real-time glucose prediction, insulin dosing, and artificial pancreas control algorithms. The aim of this paper is to propose an approach to describe CGM sensor error by exploiting n multiple simultaneous CGM recordings. The model of sensor error description includes a model of blood-to-interstitial glucose diffusion process, a linear time-varying model to account for calibration and sensor drift-in-time, and an autoregressive model to describe the additive measurement noise. Model orders and parameters are identified from the n simultaneous CGM sensor recordings and BG references. While the model is applicable to any CGM sensor, here, it is used on a database of 36 datasets of type 1 diabetic adults in which n = 4 Dexcom SEVEN Plus CGM time series and frequent BG references were available simultaneously. Results demonstrates that multiple simultaneous sensor data and proper modeling allow dissecting the sensor error into its different components, distinguishing those related to physiology from those related to technology.