# Analytical Basal-State Model of the Glucose, Insulin, and C-Peptide Systems for Type 2 Diabetes

## TL;DR

This paper introduces a new mathematical model to study type 2 diabetes by analyzing glucose, insulin, and C-peptide systems in a simplified analytical form.

## Contribution

The novel contribution is a computationally efficient analytical model for the basal state of type 2 diabetes.

## Key findings

- The model uses a quartic equation to express basal glucose concentration based on parameters.
- It enables accurate dynamic studies and avoids computational complexity.
- The model helps understand T2DM pathophysiology and improve treatment strategies.

## Abstract

We present a mechanistic mathematical model of the basal state for type 2 diabetes mellitus (T2DM) in an analytical form and illustrate its use for in silico basal-state and dynamic studies. At the core of the basal-state model is a quartic equation that expresses the basal plasma glucose concentration solely in terms of model parameters. This analytical model avoids a computationally intensive numerical solver and is illustrated by an investigation of how glucose-utilization parameters impact basal glucose, insulin, insulin-dependent utilization, and hepatic extraction, leveraging median parameter values of early-stage T2DM. Furthermore, the presented basal-state model ensures accurate execution of the corresponding dynamic model, which contains basal quantities within its derivative functions; erroneous, unintended dynamics in plasma glucose, insulin, and C-peptide are illustrated using an incorrect basal glucose value. The presented basal model enables efficient and accurate basal-state and dynamic studies, facilitating the understanding of T2DM pathophysiology and the development of T2DM diagnosis, treatment, and management strategies.