Fredrik Ståhl

Diabetes mellitus modeling and short-term prediction based on blood glucose measurements.

Insulin-Dependent Diabetes Mellitus (IDDM) is a chronic disease characterized by the inability of the pancreas to produce sufficient amounts of insulin. Daily compensation of the deficiency requires 4-6 insulin injections to be taken daily, the aim of this insulin therapy being to maintain normoglycemia - i.e., a blood glucose level between 4 and 7mmol/l. To determine the quantity and timing of these injections, various different approaches are used. Currently, mostly qualitative and semi-quantitative models and reasoning are used to design such a therapy. Here, an attempt is made to show how system identification and control may be used to estimate predictive quantitative models to be used in design of optimal insulin regimens. The system was divided into three subsystems, the insulin subsystem, the glucose subsystem and the insulin-glucose interaction. The insulin subsystem aims to describe the absorption of injected insulin from the subcutaneous depots and the glucose subsystem the absorption of glucose from the gut following a meal. These subsystems were modeled using compartment models and proposed models found in the literature. Several black-box models and grey-box models describing the insulin/glucose interaction were developed and analyzed. These models were fitted to real data monitored by an IDDM patient. Many difficulties were encountered, typical of biomedical systems: Non-uniform and scarce sampling, time-varying dynamics and severe nonlinearities were some of the difficulties encountered during the modeling. None of the proposed models were able to describe the system accurately in all aspects during all conditions. However, all the linear models shared some dynamics. Based on the estimated models, short-term blood glucose predictors for up to two-hour-ahead blood glucose prediction were designed. Furthermore, we explored the issues that arise when applying prediction theory and control to short-term blood glucose prediction.

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)

Short-term diabetes blood glucose prediction based on blood glucose measurements

Insulin Dependent Diabetes Mellitus (IDDM) is a chronic disease characterized by the inability of the pancreas to produce sufficient amounts of insulin. Daily compensation of the deficiency requires 4–6 insulin injections to be taken daily, the aim of this insulin therapy being to maintain normoglycemia— i.e., a blood glucose level between 4–7 mmol/L. To determine the quantity and timing of these injections, various different approaches are used. Currently, mostly qualitative and semi-quantitative models and reasoning are used to design such a therapy. Here, an attempt is made to show how system identification and control may be used to estimate predictive quantitative models to be used in design of optimal insulin regimens. The system was divided into three subsystems, the insulin subsystem, the glucose subsystem and the insulin-glucose interaction. The insulin subsystem aims to describe the absorbtion of injected insulin from the subcutaneous depots and the glucose subsystem the absorbtion of glucose from the gut following a meal. These subsystems were modeled using compartment models and proposed models found in the literature. Several black-box models and grey-box models describing the insulin/glucose interaction were developed and analysed. These models were fitted to real data monitored by a IDDM patient. Many difficulties were encountered, typical of biomedical systems: Non-uniform and scarce sampling, time-varying dynamics and severe nonlinearities were some of the difficulties encountered during the modeling. None of the proposed models were able to describe the system accurately in all aspects during all conditions. However, all the linear models shared some dynamics. Based on the estimated models, short-term blood glucose predictors for up to two-hour-ahead blood glucose prediction were investigated.

Post-prandial plasma glucose prediction in type I diabetes based on Impulse Response Models

In this paper the impact of different meals and rapid insulin were estimated as Finite Impulse Response Models from a data set of 18 patients. Based on these models short-term individualized predictors were tested for 20 and 60 minute prediction. The predictors were evaluated using Clarke Grid Analysis and had on average more than 94 % and 75 % in the A zone and less than 1 % and 3 % in the errorous C/D/E zones, which in comparison to other published results is competitive.

Bayesian combination of multiple plasma glucose predictors

This paper presents a novel on-line approach of merging multiple different predictors of plasma glucose into a single optimized prediction. Various different predictors are merged by recursive weighting into a single prediction using regularized optimization. The approach is evaluated on 12 data sets of type I diabetes data, using three parallel predictors. The performance of the combined prediction is better, or in par, with the best predictor for each evaluated data set. The results suggest that the outlined method could be a suitable way to improve prediction performance when using multiple predictors, or as a means to reduce the risk associated with definite a priori model selection.

Sensor calibration models for a non-invasive blood glucose measurement sensor

A calibration model was developed for a noninvasive blood glucose sensor, to determine how the blood glucose data measured by this sensor is related to blood glucose data measured with laboratory capillary finger sticks and to corrupting noise. The variability of calibration models for different patients was analyzed as well as the dynamics of the non-invasive blood glucose sensor according to reference blood glucose measurements and corrupting noise.

Ensemble Glucose Prediction in Insulin-Dependent Diabetes

Real-time prediction of glucose in type 1 Diabetes Mellitus has received a considerable amount of scientific and commercial interest over the last decade. Numerous different models have been suggested using both physiological and data-driven approaches. Insulin-dependent diabetic glucose dynamics are known to be subject to time-shifting dynamics. Considering this, as well as the vast number of models developed in the literature, it is unclear if a single model can be determined to be optimal under every possible situation. This raises the question whether it is more useful to use one of the models solely, or if it is possible to gain additional prediction accuracy by combining their outcomes. Here, a novel merging approach—combining elements from both switching and averaging techniques, forming a ‘soft’ switcher in a Bayesian framework—is presented for the glucose prediction application. The method is demonstrated on both simulated and empirical data sets.

Continuous-time model identification using non-uniformly sampled data

This contribution reviews theory, algorithms, and validation results for system identification of continuous-time state-space models from finite input-output sequences. The algorithms developed are autoregressive methods, methods of subspace-based model identification and stochastic realization adapted to the continuous-time context. The resulting model can be decomposed into an input-output model and a stochastic innovations model. Using the Riccati equation, we have designed a procedure to provide a reduced-order stochastic model that is minimal with respect to system order as well as the number of stochastic inputs, thereby avoiding several problems appearing in standard application of stochastic realization to the model validation problem. Next, theory, algorithms and validation results are presented for system identification of continuous-time state-space models from finite non-uniformly sampled input-output sequences. The algorithms developed are methods of model identification and stochastic realization adapted to the continuous-time model context using non-uniformly sampled input-output data.

Predicting Nocturnal Hypoglycemia Using a Non-parametric Insulin Action Model

Nocturnal hypoglycemia is a common and potentially very dangerous condition facing persons with insulin-treated diabetes. To reduce the risk of going low while sleeping, many patient wilfully elevate their glucose level before bedtime, thereby also eroding the conditions for a sound glucose control for the next day. Recent advances in sensor technology allow for real time frequent monitoring of the glucose level, and the road map towards an artificial pancreas involves combining an insulin pump with such sensors. The first steps towards a more autonomous insulin pump have been taken by allowing the pump to suspend the insulin supply when a hypoglycemic episode is imminent. This feature relies on algorithms for predicting the nocturnal event. In this paper, we present a novel model for this purpose. In comparison to previous methods, a better trade-off between sensitivity and false alarm rate was achieved, as well as improved warning time.

Receding horizon prediction by bayesian combination of multiple predictors

This paper presents a novel online approach of merging multiple different predictors of time-varying dynamics into a single optimized prediction. Different predictors are merged by recursive weighting into a single prediction using regularized optimization. The approach is evaluated on two different cases of data with shifting dynamics; one example of prediction using several approximate models of a linear system and one case of glucose prediction on a non-linear physiologically based simulated type I diabetes data using several parallel linear predictors. The performance of the combined prediction significantly reduced the total prediction error compared to each predictor in each example.