(675d) Low-Order Linear Dynamic Models for Prediction of Blood Glucose Concentration

In this research, we investigate the reliability of simple linear models developed from frequently measured glucose data for prediction of future blood glucose concentration values in healthy and glucose intolerant subjects, and patients with type 2 diabetes. Such predicted values are very useful in adjusting the dose of manual or automated insulin infusion, and meal or physical activity planning. Results reported will include low-order autoregressive (AR), autoregressive moving average (ARMA), and subspace state space models with time-invariant parameters and linear models with time-varying parameters incorporated with a recursive algorithm and a forgetting factor. Two sources of data will be used: (1) real subject/patient blood glucose concentration data collected at high frequency (5 minute intervals); (2) simulation data on blood glucose concentration with additional information on food intake and other disturbances.

Diabetes is a disease characterized by no insulin secretion (type 1 diabetes) or degradation of insulin secretion accompanied with insulin resistance (type 2 diabetes) in the body. For people with type 1 diabetes, the current therapy includes 3-4 daily insulin injections or insulin infusion by a manual pump, with the insulin dose being tuned according to the diet and physical activity. Recently, there is also an increasing trend towards using the insulin therapy in patients with type 2 diabetes. Although the main objective of the insulin therapy is to keep the blood glucose levels within the normal range (70-180 mg/dl), this is usually not a trivial task for insulin users and occurrence of hypoglycemic/hyperglycemic episodes is common. Prediction of blood glucose levels will improve the calculation of insulin doses to be administered.

Various physiological models that describe the glucose-insulin interactions under certain conditions are available; including linear/nonlinear, compartmental/non-compartmental models. For the prediction of blood glucose levels, these models also incorporate submodels for carbohydrate absorption in the gastrointestinal track (for the case of meal consumption) and insulin absorption in the subcutaneous tissue (for the case of insulin injection/infusion). The main restriction of these models is the increased number of parameters to be identified. Too many parameters make it also difficult to isolate the effect of inter-individual variations in the model. Therefore, with the ongoing development of continuous glucose measurement devices, there is a growing need for predicting blood glucose levels with simple linear models based on patient's own glucose sensor data.

For this study, a total of 30 patient data (14 data sets for healthy, 10 for type 2 diabetic and 6 for glucose intolerant subjects) consisting of glucose measurements from continuous glucose monitoring system (CGMS® System Gold^TM, Medtronic MiniMed, Northridge, CA) are used. Data consist of glucose readings at 5 minute intervals up to 48 hour period, and venous blood measurements on a portable glucose monitor (30 min, 60 min, 120 min and 180 min after each meal and additional samples before and after the exercise) over a 24 hour period, for sedentary and exercise cases with predetermined diet.

In first part of this research, the data in the form of time series from CGMS® is used to develop simple linear models with time invariant parameters. The first half of the data is utilized for model development, while the second half is utilized for model validation (prediction of future glucose levels). The presentation will cover the comparison of AR, ARMA, and subspace state space models for predicting the glucose levels of healthy, type 2 diabetic and glucose intolerant subjects. Since the main concern is using the recent glucose history for prediction, only low-order models will be considered. Additionally, for a specified model and order, the parameter variations among subgroups (healthy, glucose intolerant and type 2 diabetic) will be shown. For example, for second order AR model, it will be demonstrated that parameters are higher for a model derived from data of patients with diabetes compared to a model from healthy subjects' data, implying the overweighed effect of past glucose levels in glucose prediction in the case of type 2 diabetes. Likewise, the effect of exercise on model parameters and prediction performance will be evaluated, and the effect of different prediction horizons will be illustrated.

We will also report whether a model derived from a specific patient data can be used in prediction of glucose levels of another patient belonging to the same subgroup. Although this approach shows promising results, this might be mainly due to the predetermined and fixed diet (e.g. fixed meal contents and timings for all patients). However, in real life, a person with diabetes usually confronts with larger and unexpected disturbances (e.g. overdose of meal content or unplanned exercise or meal timing). For the prediction of glucose in such cases, we believe that a linear model with time varying parameters is more appealing. Hence, in the second part of the presentation, we will present the prediction performance of a linear model with time-variant parameters based on 4 day data of a simulated subject. The GlucoSim (a web-based educational simulation package for glucose-insulin levels in human body) is used for data acquisition. The 4 day scenario for simulation includes predefined meal content and timing on day 1, overdosed meal on day 2, variation in meal timing on day 3, and both variation in meal timing and content on day 4. For this alternative approach, at each sampling time, the linear model is updated based on the available glucose data, and for the relative weights in the past data sequence, a constant forgetting factor is adopted. To account for the case of disturbances, error detection (error is defined as difference between the measured and the predicted glucose values) is incorporated in the model. For instance, in the case of large error detection, the past data (the data before the error detection) are excluded, and the model is developed based on the fresh data (the data after the error detection) only. The effects of large deviations in meals, values of forgetting factors, and model types on prediction accuracy will be discussed.