(664f) Adaptation and Calibration for Accurate Inference of Blood Glucose Using Noninvasive Inputs

The importance of tight glucose control in reducing the complications associated with diabetes is widely recognized. 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. . The Wiener model takes the inputs and passes them through a series of linear dynamic block and a static nonlinear block with blood glucose as the predicted output. Each input xi is passed through a dynamic linear block to get intermediate variable vi's. The dynamic blocks use a second-order-plus-dead-time-plus-lead differential equation. The resulting vi's are then passed through a static nonlinear block, which is a quadratic regression model with interactions.

The models were developed under two different static structures that we call the ?Reduced Model? (RM) and the ?Full Model? (FM). The RM consists only of linear terms (i.e., the elimination of all second order terms) and the FM retains all the second-order terms in static gain function. The RM guards against severe accuracy reduction caused by either cross correlation of linear terms and their associated interaction terms (e.g., v1 and v1v2), or by extrapolation due to quadratic terms (e.g., v12), or by both. However, the drawback of the RM is reduced accuracy when these eliminated second order effects are significant. We train the models in two ways: supervised and unsupervised. Supervised training refers to use of validation data set to guide the parameter estimation using training data to guard against overfitting. Unsupervised training refers to parameter estimation based solely on the training data and without influence from test data. As we will show in this work, a RM trained on a 2006 data set fit a 2008 test data set quite well. The 2006 data set has 25 days and the 2008 data set has 16 days. In addition to using the full 16 days as a test set to evaluate the model longevity, this data set is used to assess model adaptation and calibration.

Model adaptation is when recently collected (i.e., ?on-line?) data are used to estimate, i.e., change, values of model parameters. By ?calibration,? we mean that on-line data, and more specifically, finger-stick or lancet data in the context, are used to adjust the values determined by the model. We evaluated model adaptation under frequent (e.g., CGMS sampling) and infrequent (e.g., lancet sampling) on-line data collection. Under frequent data collection we found that only a small number of days were needed to update model parameters and training was unsupervised. Thus, in this case, a validation set was not used and all the remaining 2008 data formed the test set. However, when using only four measurements per day for first seven days for model adaptation, we found it necessary to do supervised training on the remaining nine days due to the small number of samples.

All the calibration data is assumed to come from infrequent lancet data and that it is the only measured glucose data available. In this evaluation we used four values per day that came from the CGMS measurements that consisted of two high values and two low values spread out over the time that normal lancet measurements would be taken (e.g., not during sleep). Thus, we are assuming the use of a lancet meter that agrees perfectly with the CGMS for the purpose of evaluation. It is reasonable to do the evaluation this way since this study in all cases is evaluated based on the agreement of the model to the CGMS data. However, in practice, a lancet meter will be used and calibration will be relative to the lancet device used. The calibration scheme that we used consisted of two steps. The first step made an adjustment to correct for systematic bias under the assumption that previously determined deviations from measured values are random. The second correction is a local correction so that the model glucose is ?adjusted? to agree with the most recent measurement and as time passes it adjusts back to the value given by the model. We present the results of this for several data sets.