Fitting a Multi-Timescale Mathematical Model to Longitudinal Data

Type 2 diabetes (T2D) is a chronic disorder of glucose homeostasis caused by dysfunction across multiple organs and tissues. A common pathophysiological feature of T2D is the inability of insulin-secreting pancreatic beta-cells to meet the body’s insulin demand, which is necessary to maintain normal blood glucose levels. For each patient’s diabetes intervention and therapy, accurately estimating an individual’s beta-cell secretory capacity is crucial for predicting T2D progression. Recently, a mathematical model of T2D has been developed to enhance our understanding of the disease's pathophysiology (Ha and Sherman, AJP, 2020). In this presentation, we aim to fit the model to longitudinal data to estimate a key metabolic parameter associated with beta-cell secretory capacity. Given that model operates on multiple timescales, incorporating both fast and slow dynamics, we divided the fitting process into two steps. In step 1, we treat the slow variables of the model as parameters and fit the resulting fast subsystem of the model to data collected at each time point to estimate the slow variables. Using these estimates, we then fit the full model to the entire longitudinal dataset to estimate the key metabolic parameter related to beta-cell secretory capacity.