The importance of tight glucose control in reducing the complications associated with diabetes is widely recognized. The primary ways that glucose has been managed include diet and exercise, stress management, insulin injections, and different types of drugs. In most cases, control has been open loop requiring diabetics to use test strip meters to monitor glucose behavior from just a few readings per day, a method that is not only painful and inconvenient, but also unreliable due to the guess work involved. While, there have been recent technological advancements such as glucose monitors that measure as often as every five minutes, twenty four hours a day, such monitors are invasive, have sensors that need to be replaced frequently, and costly. Such monitors can be useful in providing dynamic and frequent glucose information in the short term, but their long-term use can be highly inconvenient and expensive. Therefore, there is a need for an adaptive methodology for inferring blood glucose from non invasive input variables like food and activity, which is the goal of this work.

The modeling methodology chosen for this work is semi-empirical, block-oriented modeling based on Wiener structure, using a set of noninvasive variables that provides adequate information to explain a sufficient amount of the variation in glucose to be useful. A theoretical modeling approach is not practical due to inadequate first principle knowledge. It is common knowledge that food consumption alone is not enough to meet this requirement. While nutrient components, especially carbohydrates have a significant effect on blood glucose, they do not account for major behaviors particularly during times of low food consumption such as during sleep. Furthermore, stress and activity can have as great an impact on glucose levels as eating. Hence, an adequate data set must not only contain frequent and accurate sampling of food but also variables that measure activity and stress levels. Thus, we chose a device that showed much promise in meeting this requirement (SenseWear® Pro3 body monitoring system from BodyMedia Inc., Pittsburgh, PA). This device utilizes pattern detection algorithms that employ physiologic signals from a unique combination of sensors. To adequately cover the response space that a subject experiences, the input space must adequately cover the changes experienced by the subject. Thus, data for the study were collected under free-living conditions and for a prolonged period of time (several weeks). An empirical approach is not likely to succeed because, by necessity, data collection is under free-living conditions, leading to high input correlation, and thus, inhibiting cause and effect modeling.

The details of the study carried out in 2006 for four weeks on a real subject and used to develop the inferential model for predicting blood glucose are given briefly below:

Subject: The subject was 50 years old, in good health (except type two diabetes) with a body mass index (BMI) of 27.9 kg/m2. He was not on diabetic medication or insulin.

Measures: To obtain the fast sampling rate necessary for dynamic modeling, the MiniMed Continuous Glucose Monitor, MMT-7102® (Medtronic, Minneapolis, Minnesota) was used to measure glucose at five minute intervals. The activity measurements were obtained using the SenseWear® Pro3 body monitoring system (BodyMedia Inc., Pittsburgh, PA). The glucose monitor requires the subcutaneous insertion of a sensor, typically in the torso, and assesses interstitial glucose at a reported rate of one sample every five minutes. The interstitial glucose measurements are used to infer blood glucose. The sensors were replaced weekly which resulted in one to two hours of no measurements for initialization. This monitor is self-calibrating but is referenced directly to measured blood glucose values obtained four times daily from a glucose meter. The subject in this study obtained these values from his personal One Touch Ultra® blood glucose meter (LifeScan, Inc., Milpitas, CA).

Protocol: Because this was a free-living study, no constraints were placed on diet or lifestyle. The subject recorded food ingested, the approximate serving sizes, and the eating times and durations in a food log. In addition, the subject also obtained at least four daily measurements of blood glucose using finger-stick measurement and entered that into the CGMS for calibration. Using nutrition tables the grams of carbohydrates, fats, and proteins ingested per meal or snack were determined and used in modeling

Model Development: The final Wiener model from this study consisted of the eleven variables and had 115 parameters. The selected inputs for this study have nonlinear, highly interactive, and dynamic affects on blood glucose. (By cause and effect modeling we mean model development that determines the independent and specific effect an input has on glucose response over the input space interest.) Therefore, given these limitations, we used a semi-empirical modeling approach. More specifically, the method was a unique and specific application of Wiener modeling that extends the method developed by Rollins and Bhandari [1] in a novel way to build accurate cause and effect models from free-living data.

The inferential model for glucose using non-invasive inputs only developed from this study has been made adaptive by using the glucose measurements obtained from the test-strip meter. On an average, the subject took four daily measurements from the test strip meter. (Note that the test strip meter is FDA-approved for monitoring blood glucose by diabetics at home). In this study 94 paired readings of monitor and meter were obtained in all (76 in training and 18 in test). These meter readings were used to improve the prediction accuracy of the inferential model by adaptively updating the model correction. The model correction term uses an exponentially-weighted value of the most current error (difference between the glucose meter and the monitor values). The optimum value of the weight was determined by minimizing the squared deviation between the monitor and the model values in training. This adaptive scheme was able to accurately infer blood glucose for several days of test data.

References:

1. D.K. Rollins, N. Bhandari Constrained MIMO Dynamic Discrete-Time Modeling Exploiting Optimal Experimental Design. Journal of Process Control: 14(6): 671-683, 2004.