Marzia Cescon

Subspace-Based Model Identification of Diabetic Blood Glucose Dynamics

Diabetes Mellitus is a chronic desease characterized by the inability of the organism to autonomously regulate the blood glucose level due to insulin deficiency or resistance, thus leading to serious health damages. In order to keep tight glucose control treatment happens to be based essentially on insulin delivery. In common practice, a main limiting factor in adequate choice of insulin dosing is the lack of reliable predictions of blood glucose evolution. In this work, state-space models of various orders were investigated and evaluated for their capability of description of one diabetic subject blood glucose evolution over 24 hours. It turned out that models of low complexity are capable of detecting even abrupt changes in calibration data but they are not sufficient for validation data. Blood glucose levels could be predicted up to 30 minutes ahead on validation data. (Less)

Linear Modeling and Prediction in Diabetes Physiology

Diabetes Mellitus is a chronic disease characterized by the inability of the organism to autonomously regulate the blood glucose level due to insulin deficiency or resistance, leading to serious health damages. The therapy is essentially based on insulin injections and depends strongly on patient daily decisions, being mainly based upon empirical experience and rules of thumb. This chapter presents work on data-driven glucose metabolism modeling and short-term, that is, up to 120 min, blood-glucose prediction in Type 1 Diabetes Mellitus (T1DM) subjects. Low-order, individualized, data-driven, stable, physiologically relevant models were identified from a population of 9 datasets from T1DM patients. Model structures include: autoregressive moving average with exogenous inputs (ARMAX) models and state-space models. The performances of the model-based predictors were compared to those achieved by the zero-order hold (ZOH).

Glycemic trend prediction using empirical model identification

Using methods of system identification and prediction, we investigate near-future prediction of individual-specific T1DM blood glucose dynamics with the purpose of a decision-making tool development in diabetes treatment. Two strategies were approached: Firstly, Kalman estimators based on identified state-space models were designed; Secondly, direct identification of ARX- and ARMAX-based predictors was done. Predictions over 30 minutes look-ahead were capable to track glucose variation even in sensible ranges for estimation data, but not on validation data.

Identification of individualised empirical models of carbohydrate and insulin effects on T1DM blood glucose dynamics

One of the main limiting factors in improving glucose control for type 1 diabetes mellitus (T1DM) subjects is the lack of a precise description of meal and insulin intake effects on blood glucose. Knowing the magnitude and duration of such effects would be useful not only for patients and physicians, but also for the development of a controller targeting glycaemia regulation. Therefore, in this paper we focus on estimating low-complexity yet physiologically sound and individualised multi-input single-output (MISO) models of the glucose metabolism in T1DM able to reflect the basic dynamical features of the glucose–insulin metabolic system in response to a meal intake or an insulin injection. The models are continuous-time second-order transfer functions relating the amount of carbohydrate of a meal and the insulin units of the accordingly administered dose (inputs) to plasma glucose evolution (output) and consist of few parameters clinically relevant to be estimated. The estimation strategy is continuous-time data-driven system identification and exploits a database in which meals and insulin boluses are separated in time, allowing the unique identification of the model parameters.

Subspace-based identification of compliance dynamics of parallel kinematic manipulator

A high-bandwith robot-workpiece interaction requires a stiff robot without resonances in the frequency range of operation. In this article, the compliance dynamics of the Gantry-Tau parallel kinematic robot were identified using subspace-based identification and physical modeling. Measurements were performed both with a camera vision system developed and with a laser tracker. Although promising simulation results for another Gantry-Tau prototype exist, both vision and laser tracker experiments identified multiple resonances around 14 Hz, which can reduce force control performance.

Subspace-based linear multi-step predictors in type 1 diabetes mellitus

A major challenge for a person with diabetes is to adapt insulin dosage regimens and food intake to keep blood glucose within tolerable limits during daily life activities. The early knowledge about the effects of inputs on glycemia would provide the patients with invaluable information for appropriate on-the-spot decision making concerning the management of the disease. Against this background, in this paper we propose multi-step data-driven predictors to the purpose of predicting blood glucose multiple steps ahead in the future, supporting therefore the patients when deciding upon treatments. We formulate the predictors based on the state-space construction step in subspace identification methods for linear systems. Physiological models from the literature were used to filter the raw information on carbohydrate and insulin intakes in order to retrieve the input signals to the predictors. The clinical data of 14 type 1 diabetic patients collected in hospital during a 3-days long visit were used. Half of the data were employed for predictor development and the remaining half for validation. Mean population prediction error standard deviation on 30 min, 60 min, 90 min, 120 min ahead prediction on validation data resulted in, respectively, 19.17 mg/dL, 37.99 mg/dL, 50.62 mg/dL and 58.06 mg/dL

Multi-step-ahead multivariate predictors: A comparative analysis

The focus of this article is to undertake a comparative analysis of multi-step-ahead linear multivariate predictors. The approach considered for the estimation will be based on geometrically reliable linear algebra tools, resorting to subspace identification methods. A crucial issue is quantification of both bias error and variance affecting the estimate of the prediction for increasing values of the look ahead when only a small number of samples is available. No complete theory is available so far, nor sufficient numerical experience. Therefore, the analysis of this paper aims at shading some lights on the topic providing some insights and help to develop some intuitions.

Adaptive subspace-based prediction of T1DM glycemia

Blood glucose levels fluctuate widely in Type 1 diabetic patients expecially during stressful situations, intercurrent illness, exercise and changes in meal composition. Furthermore, inter- and intra-subject variability make the prediction of such fluctuations an even harder task. The paper deals with the application of online data-driven multi-step subspace-based patient-specific predictor models to T1DM glycemia prediction, exploiting the interplay between previously injected insulin, meal intake and eventually vital signs. When the unknown underlying model is changing over time we believe such an adaptive scheme may constitute a valuable step towards the development of an advisory tool capable of informing the patient at any time about the evolution of glycemia and possibly give advices on the most appropriate control action to take [1].

On Data-driven Multistep Subspace-based Linear Predictors

The focus of this contribution is the estimation of multi-step-ahead linear multivariate predictors of the output making use of finite input-output data sequences. Different strategies will be presented, the common factor being the exploitations of geometric operations on appropriate subspaces spanned by the data. In order to test the capabilities of the proposed methods in predicting new data, a real-life example, namely, the case of blood glucose prediction in Type 1 Diabetes patients, is provided.

Individualized empirical models of carbohydrate and insulin effects on T1DM blood glucose dynamics

One of the main limiting factors in improving glucose control for T1DM subjects is the lack of a precise description of meal and insulin intake effects on blood glucose. Knowing magnitude and duration of such effects would be useful not only for patients and physicians but also for the development of a controller targeting glycemia regulation. Therefore, in this paper we focus on estimating low-complexity yet physiologically sound and individualized MISO models of the glucose metabolism in T1DM able to reflect the basic dynamical features of the glucose-insulin metabolic system in response to a meal intake or an insulin injection. The models are continuous-time second-order transfer functions relating the amount of carbohydrate of a meal and the insulin units of the accordingly administered dose (inputs) to plasma glucose evolution (output) and consist of few parameters clinically relevant to be identified. The estimation strategy is data-driven and exploits a database in which meals and insulin boluses are separated in time, allowing the unique identification of the model parameters.