Model-Based Insulin Sensitivity and Pharmacodynamic Surfaces

Abstract

Objective: The minimal model (MM) is widely used for model-based insulin sensitivity testing. A pharmacodynamic (PD) surface analysis shows how the MM can under-predict insulin sensitivity and its changes over time, particularly in high(er) insulin dose tests.

Methods: PD surfaces at steady state are fitted to N = 77 clinical results for: 1) the MM; 2) a receptor model for type 1 diabetes (RM); and 3) an MM-derived nonlinear metabolic control model (CM). The MM has no insulin effect saturation. The CM has insulin effect saturation and glucose removal saturation can be added. The RM model saturates the combined insulin and glucose removal effect. Errors are reported as: 1) RMS; 2) Mode of the Absolute Error (AME) distribution; and 3) Frequency of Errors Near Zero (FNZ) - over all 77 reported results.

Results: Results for the MM are: RMS = 4.77; AME = -0.05, FNZ = 3 (of 77). For the RM: RMS = 0.04; AME = -0.01, FNZ = 32. For the CM: RMS = 0.07; AME = -0.01, FNZ = 36. Adding glucose saturation effects to the CM yields: RMS = 0.06; AME = -0.01, FNZ = 39. CM and RM have small and tight error distributions.

Conclusions: The MM consistently under-predicts insulin saturation resulting in large errors due to the shape of its PD surface. The ability to fit a single or small group of data sets can yield large error for others, illustrating the value of using a large set of clinical results to test these models. The results show that insulin and/or glucose saturation dynamics are necessary to yield consistent model-based insulin sensitivity values.