In this work we present the results validating the efficacy and accuracy of a block-oriented modeling approach in modeling blood glucose of a real type 2 diabetic (T2D) subject using real data and its ability to predict over a period of almost two years. The model was developed (trained) from 3 weeks of data collected on a T2D subject in September –October 2006. The model was then tested on five days of data immediately after the training period (October 2006) and showed its excellent ability to model glucose over the test period using only non-invasive food and activity inputs. As a measure of evaluating performance, an average absolute error (AAE) (i.e., the average of the absolute values for the measured glucose minus modeled glucose) was used. The AAE in training was 12.0 mg/dL and 13.6 mg/dL in testing in 2006. While the ability of the model to predict well during testing in 2006, was itself noteworthy and indicative of its ability to give cause-and-effect, an additional testament to the model's capability is its ability to model the data collected on the same subject over a year later in September /October 2007 and then again (over year and a half later) in February/ March 2008 at similar level of accuracy. (For comparison consider that the glucose meter AAE for replicated measurements was 15.3 mg/dL).

The details of the study carried out in 2006 and then repeated in 2007 and 2008 are given 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 had115 parameters. The selected inputs for this study have nonlinear, highly interactive, and dynamic affects on blood glucose. A theoretical modeling approach is not practical due to inadequate first principle knowledge. An empirical approach is not likely to succeed because, by necessity, data collection is under free-living conditions, and therefore under high input correlation, and thus, inhibiting cause and effect modeling, a critical goal of this research. (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 chose 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.

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.