A Proportional-Derivative Endogenous Insulin Secretion model with an Adapted Gauss Newton Approach

Abstract

Endogenous insulin (UN) secreted by pancreatic β-cells plays a leading role in glucose homeostasis. Pathological changes in UN can enable early diagnosis of metabolic dysfunction before the emergence of type 2 diabetes. The dynamic insulin sensitivity and secretion test (DISST) is a dynamic test that is able to quantify participant-specific insulin sensitivity (SI) values and UN profiles. Like most studies, the DISST uses direct inversion of C-peptide concentration measurements to quantify a UN profile which relies on the assumption that insulin and C-peptide are equimolarly secreted from β-cells. This study develops a proportional-derivative (PD) control model that defines UN as a function of glucose concentration to provide further insight and modeling capability for this prediabetic state. Results show that individuals with normal glucose tolerance (NGT) tend to have higher gain ratio compared to individuals with impaired fasting glucose (IFG) with median values of 19.11 and 2.79 min, respectively. In particular, the main difference between the UN profiles of NGT and IFG group lies within the derivative gain (𝜙𝐷), specifically in first phase secretion (U1). A higher value of 𝜙𝐷 is needed in response to an abrupt increase in plasma glucose level. This proposed model offers model simplicity as well as a link between insulin secretion and glucose concentration that is able to provide more information in determining each participant’s glycemic condition.