(111b) Extensive Noninvasive Exogenous Wiener Simulation Modeling of Glucose for Type 2 Diabetic Patients Under Free Living Conditions

In the United States, nearly 16 million people, or about 6% of the population, have diabetes. Type 2 diabetes is a chronic illness and accounts for nearly 95% of all cases, with significant morbidity and mortality. Most of the complications of type 2 diabetes can be prevented by tight glucose control ( Guthrie and Guthrie, 2004). However, type 2 diabetic (TTD) people have weakened or partially broken glucose control systems. In control vernacular, the control systems are said to have lost stability and performance, i.e., strength or robustness. In terms of glucose control, loss of ?strength? means that the body has loss ability to keep its glucose at healthy levels.

Our basic approach to tighten TTD glucose control is to develop an accurate understanding of factors affecting glucose response and use this information to improve glucose control, down to the individual level, if necessary. Our approach to obtain this understanding is noninvasive input modeling of blood glucose. Thus, this approach is not attempting to repair the glucose control system but seek to maximize its ability to control glucose in its weaken state and to minimize further damage by finding the conditions of minimal stress. Since no one has demonstrated the ability to effectively model TTD glucose response from noninvasive input variables over a prolonged period of time, a critical first step is the demonstration of this ability. Thus, this talk proposes a methodology that demonstrates this ability.

More specifically, this talk presents an accurate model of blood glucose concentration for a TTD subject with several unique attributes and accomplishments. First it is a simulation model (Nells, 2001) that depends only on exogenous variables. This means that it does not use previously measured glucose values to estimate or predict glucose responses and that it only depends on inputs. This is a critical attribute since our goal is to accurately explain (i.e., model) glucose behavior from variations in inputs. There are cases in the literature of k-steps-ahead prediction models for glucose concentration but our work appears to be the first development of a simulation models for TTD subjects. Secondly, the candidate set of input variables is extensive and all are noninvasive. Three inputs are food nutrient components, twenty are activity variables and one input represents the time of day (TOD) for a total of 24 candidates. Thirdly, we modeled the nonlinear static and nonlinear dynamic response of glucose using the Wiener modeling approached developed by Bhandari and Rollins (2003) and Rollins and Bhandari (2004), and developed input dynamic response models for each input. The strengths of the Wiener structure include a dynamic model for each input with phenomenological interpretation, the separation of dynamic and static model forms, and the modeling of nonlinear dynamic and nonlinear static behavior. Thus, this approach provides quantitative results for the dynamic properties. But not only this, from use of the Wiener structure, it also provides a periodic spectrum over time for each input that reveals correlations to low frequency and high frequency response behavior.

To obtain the fast sampling rate necessary for dynamic modeling we used the Medtronic MiniMed Continuous Glucose Monitor, MMT-7102® which measures glucose very accurately at five minute intervals. The activity measurements were obtained at the same sampling rate using the BodyMedia® body monitoring system. This is the first glucose modeling study to combine measurements from these two instruments. Fourthly, this study was challenged by developing the model under free living conditions and not under controlled clinic conditions where the input changes are organized over a well defined input space. We chose a free living study to determine if we could achieve accuracy under the conditions of normal living because future more extensive studies will be conducted under these conditions. Lastly, the criterion we set for model acceptability was accurate cross validation over an extended period of time. It is common in this type of study to fit the model to one data set (called the ?training data,?) and not test the model on a different data set (called the ?test data). The procedure to use a test data set is called ?cross validation? (Nells, 2001) and protects against ?over fitting? the model, i.e., significantly fitting the model to non-phenomenological anomalies. After using twenty days of data to build the model, we used the next five (5) days of five (5) minute sampled glucose data to cross validate our simulation model. The dynamic function for each input was second order, plus dead time, plus lead (SOPDTPL) with four parameters each. The nonlinear static function was a second order multiple linear regression function, including interaction terms, bringing the parameter total to 421 for the full Wiener model. However, the final reduced model has only 11 variables and 115 parameters. Given all the aforementioned constraints and challenges, we achieved training and testing fitted correlation coefficients (rfit) of 0.80 and 0.65, respectively; therefore, strongly supporting model efficacy.

This talk will also compare and contrast our modeling approach with another one for non-diabetic (i.e., ?normal?) subjects. The normal subject data come from Nuttall, et al. (1985) and were modeled by Holtschlag, et al. (1998). The proposed modeling approach was applied to this set of normal data and evaluated against their approach to further illustrate its strengths.

Literature Cited

1. Guthrie, R. A. and D. Guthrie. ?Pathophysiology of diabetes mellitus,? Critical Care Nursing Quarterly 27(13), 2004.

2. Nells, O. Nonlinear System Identification. Germany: Springer, 2001.

3. Bhandari, N. and D. K. Rollins, ?A Continuous-Time MIMO Wiener Modeling Method,? Industrial and Engineering Chemistry Research, 42(22), 5583-5595, 2003.

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

5. Nuttall, F. Q., M. C. Gannon, J. L. Wald, and M. Ahmed, ?Plasma glucose and insulin profiles in normal subjects ingesting diets of varying carbohydrate, fat, and protein content,? J. Am. Coll. Nutr. 4: 437?450, (1985).

6. Holtschlag, D. J., M. C. Gannon and F. Q. Nuttall. ?State-Space Models of Insulin and Glucose Response to Diets of Varying Nutrient Content in Men and Women,? Appl. Physiol. 85(3), 935-945, 1998.