Calibration of continuous glucose monitoring sensors by time-varying models and Bayesian estimation

Minimally invasive continuous glucose monitoring (CGM) sensors are wearable medical devices that provide frequent (e.g., 1-5 min sampling rate) real-time measurements of glucose concentration for several consecutive days. This can be of great help in the daily management of diabetes. Most of the CGM systems commercially available today have a wire-based electrochemical sensor, usually placed in the subcutaneous tissue, which measures a "raw" electrical current signal via a glucose-oxidase electrochemical reaction. Observations of the raw electrical signal are frequently revealed by the sensor on a fine, uniformly spaced, time grid. These samples of electrical nature are in real-time converted to interstitial glucose (IG) concentration levels through a calibration process by fitting a few blood glucose (BG) concentration measurements, sparsely collected by the patient through fingerprick. Usually, for coping with such a process, CGM sensor manufacturers employ linear calibration models to approximate, albeit in limited time-intervals, the nonlinear relationship between electrical signal and glucose concentration. Thus, on the one hand, frequent calibrations (e.g., two per day) are required to guarantee a good sensor accuracy. On the other, each calibration requires patients to add uncomfortable extra actions to the many already needed in the routine of diabetes management. The aim of this thesis is to develop new calibration algorithms for minimally invasive CGM sensors able to ensure good sensor accuracy with the minimum number of calibrations. In particular, we propose i) to replace the time-invariant gain and offset conventionally used by the linear calibration models with more sophisticated time-varying functions valid for multiple-day periods, with unknown model parameters for which an a priori statistical description is available from independent training sets; ii) to numerically estimate the calibration model parameters by means of a Bayesian estimation procedure that exploits the a priori information on model parameters in addition to some BG samples sparsely collected by the patient. The thesis is organized in 6 chapters. In Chapter 1, after a background introduction on CGM sensor technologies, the calibration problem is illustrated. Then, some state-of-art calibration techniques are briefly discussed with their open problems, which result in the aims of the thesis illustrated at the end of the chapter. In Chapter 2, the datasets used for the implementation of the calibration techniques are described, together with the performance metrics and the statistical analysis tools which will be employed to assess the quality of the results. In Chapter 3, we illustrate a recently proposed calibration algorithm (Vet- toretti et al., IEEE Trans Biomed Eng 2016), which represents the starting point of the study proposed in this thesis. In particular, we demonstrate that, thanks to the development of a time-varying day-specific Bayesian prior, the algorithm can become able to reduce the calibration frequency from two to one per day. However, the linear calibration model used by the algorithm has domain of validity limited to certain time intervals, not allowing to further reduce calibrations to less then one per day and calling for the development of a new calibration model valid for multiple-day periods like that developed in the remainder of this thesis. In Chapter 4, a novel Bayesian calibration algorithm working in a multi-day framework (referred to as Bayesian multi-day, BMD, calibration algorithm) is presented. It is based on a multiple-day model of sensor time-variability with second order statistical priors on its unknown parameters. In each patient-sensor realization, the numerical values of the calibration model parameters are determined by a Bayesian estimation procedure exploiting the BG samples sparsely collected by the patient. In addition, the distortion introduced by the BG-to-IG kinetics is compensated during parameter identification via non-parametric deconvolution. The BMD calibration algorithm is applied to two datasets acquired with the "present-generation" Dexcom (Dexcom Inc., San Diego, CA) G4 Platinum (DG4P) CGM sensor and a "next-generation" Dexcom CGM sensor prototype (NGD). In the DG4P dataset, results show that, despite the reduction of calibration frequency (on average from 2 per day to 0.25 per day), the BMD calibration algorithm significantly improves sensor accuracy compared to the manufacturer calibration algorithm. In the NGD dataset, performance is even better than that of present generation, allowing to further reduce calibrations toward zero. In Chapter 5, we analyze the potential margins for improvement of the BMD calibration algorithm and propose a further extension of the method. In particular, to cope with the inter-sensor and inter-subject variability, we propose a multi-model approach and a Bayesian model selection framework (referred to as multi-model Bayesian framework, MMBF) in which the most likely calibration model is chosen among a finite set of candidates. A preliminary assessment of the MMBF is conducted on synthetic data generated by a well-established type 1 diabetes simulation model. Results show a statistically significant accuracy improvement compared to the use of a unique calibration model. Finally, the major findings of the work carried out in this thesis, possible applications and margins for improvement are summarized in Chapter 6.