Diabetes is a disease that undermines the normal regulation of glucose levels in the blood. In people with diabetes, the body does not secrete insulin (Type 1 diabetes) or derangements occur in both insulin secretion and action (Type 2 diabetes). In
spite of the therapy, which is mainly based on controlled regimens of insulin and drug administration, diet, and physical exercise, tuned according to self-monitoring of blood glucose (SMBG) levels 3-4 times a day, blood glucose concentration often exceeds the normal range thresholds of 70-180 mg/dL. While hyperglycaemia mostly affects long-term complications (such as neuropathy, retinopathy, cardiovascular, and heart diseases), hypoglycaemia can be very dangerous in the short-term and, in the worst-case scenario, may bring the patient into hypoglycaemic coma. New scenarios in diabetes treatment have been opened in the last 15 years, when continuous glucose monitoring (CGM) sensors, able to monitor glucose concentration continuously (i.e. with a reading every 1 to 5 min) over several days, entered clinical research. CGM sensors can be used both retrospectively, e.g., to optimize the metabolic control, and in real-time applications, e.g., in the "smart" CGM sensors, able to generate alerts when glucose concentrations are predicted to exceed the normal range thresholds or in the so-called "artificial pancreas". Most CGM sensors exploit needles and are thus invasive, although minimally. In order to improve patients comfort, Non-Invasive Continuous Glucose Monitoring (NI-CGM) technologies have been widely investigated in the last years and their ability to monitor glucose changes in the human body has been demonstrated under highly controlled (e.g. in-clinic) conditions.
As soon as these conditions become less favourable (e.g. in daily-life use) several problems have been experienced that can be associated with physiological and environmental
perturbations. To tackle this issue, the multisensor concept received greater attention in the last few years. A multisensor consists in the embedding of sensors of different nature
within the same device, allowing the measurement of endogenous (glucose, skin perfusion, sweating, movement, etc.) as well as exogenous (temperature, humidity, etc.) factors.
The main glucose related signals and those measuring specific detrimental processes have to be combined through a suitable mathematical model with the final goal of estimating glucose non-invasively. White-box models, where differential equations are used to describe the internal behavior of the system, can be rarely considered to combine multisensor measurements because a physical/mechanistic model linking multisensor data
to glucose is not easily available. A more viable approach considers black-box models, which do not describe the internal mechanisms of the system under study, but rather depict how the inputs (channels from the non-invasive device) determine the output (estimated glucose values) through a transfer function (which we restrict to the class of multivariate linear models). Unfortunately, numerical problems usually arise in the
identication of model parameters, since the multisensor channels are highly correlated (especially for spectroscopy based devices) and for the potentially high dimension of the
measurement space.
The aim of the thesis is to investigate and evaluate different techniques usable for the identication of the multivariate linear regression models parameters linking multisensor data and glucose. In particular, the following methods are considered: Ordinary Least Squares (OLS); Partial Least Squares (PLS); the Least Absolute Shrinkage and Selection Operator (LASSO) based on l1 norm regularization; Ridge regression based on l2 norm regularization; Elastic Net (EN), based on the combination of the two previous norms. As a case study, we consider data from the Multisensor device mainly based on dielectric
and optical sensors developed by Solianis Monitoring AG (Zurich, Switzerland) which partially sponsored the PhD scholarship. Solianis Monitoring AG IP portfolio is now
held by Biovotion AG (Zurich, Switzerland). Forty-five recording sessions provided by Solianis Monitoring AG and collected in 6 diabetic human beings undertaken hypo and
hyperglycaemic protocols performed at the University Hospital Zurich are considered. The models identified with the aforementioned techniques using a data subset are then
assessed against an independent test data subset. Results show that methods controlling complexity outperform OLS during model test. In general, regularization techniques outperform PLS, especially those embedding the l1 norm (LASSO end EN), because they set many channel weights to zero thus resulting more robust to occasional spikes occurring in the Multisensor channels. In particular, the EN model results the best one,
sharing both the properties of sparseness and the grouping effect induced by the l1 and l2 norms respectively. In general, results indicate that, although the performance, in terms of overall accuracy, is not yet comparable with that of SMBG enzyme-based needle sensors, the Multisensor platform combined with the Elastic-Net (EN) models is a valid tool for the real-time monitoring of glycaemic trends. An effective application concerns the complement of sparse SMBG measures with glucose trend information within the recently developed concept of dynamic risk for the correct judgment of dangerous events such as hypoglycaemia.
The body of the thesis is organized into three main parts: Part I (including Chapters 1 to 4), first gives an introduction of the diabetes disease and of the current technologies for NI-CGM (including the Multisensor device by Solianis) and then states the aims of the thesis; Part II (which includes Chapters 5 to 9), first describes some of the issues to be faced in high dimensional regression problems, and then presents OLS, PLS, LASSO, Ridge and EN using a tutorial example to highlight their advantages and drawbacks; Finally, Part III (including Chapters 10-12), presents the case study with the data set and results. Some concluding remarks and possible future developments end the thesis. In particular, a Monte Carlo procedure to evaluate robustness of the calibration procedure for the Solianis Multisensor device is proposed, together with a new cost function to be used for identifying models
