Individual Estimation of Parameters Describing the Glucose-Insulin Regulatory System: A Modeling Approach with Regularization for Reduced-Sampling Oral Glucose Tolerance Test Data

A recent modeling approach of the glucose-insulin regulatory system exploits a regularization procedure to allow estimation of model parameters from a 5-samples oral glucose tolerance test (OGTT). However, the complexity of the regularization procedure may limit its applicability; in addition, a considerable number of OGTT presents only 4 time samples rather than 5. Thus, leveraging such a glucose-insulin system model, the objective of the present work was to simplify the regularization procedure and to adapt the model approach to the case of 4-samples OGTT. Simplifying regularization involved minimizing the sum of squared residuals, in conjunction with applying appropriate weights (w1, w2) to the second derivatives of glucose and insulin vectors. Validation of the approach was conducted using both 5-samples and 4-samples OGTTs. In the case of the 4-sample OGTT, the available data did not provide sufficient information to estimate all 13 parameters, thus the number of parameters was reduced to 9. For the remaining four parameters, two sets of values were derived from 10 and 11-samples OGTTs. The selection between the two options was based on which one provided estimates closer to physiological values. Ultimately, the validation of the suggested approach was carried out for protocols with 4 and 5-samples OGTTs, employing appropriate weights, i.e., w1 = 2 and w2 = 0.0100, and w1 = 0.0680 and w2 = 0.0015, respectively. The obtained results yielded a root mean square error of 1.0258 and 1.3062, respectively.