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Updated: Jun 4, 2025

Hyperinsulinemic-euglycemic Clamps in Conscious, Unrestrained Mice
Published on: November 16, 2011
Dynamic modeling of the Insulin-Glucose-Glucocorticoid impulsive control system
Yuntao Liu1, Changtong Li2, Xiaozhou Feng1
1School of Science, Xi'an Technological University, Xi'an, 710021, PR China.
This study presents a mathematical model for diabetes treatment, analyzing insulin, glucose, and glucocorticoid interactions. Findings suggest optimized therapeutic strategies by integrating hormonal effects with medication doses for better clinical outcomes.
Area of Science:
- Mathematical biology
- Endocrinology
- Pharmacology
Background:
- Diabetes mellitus (DM) management requires understanding complex hormonal interactions.
- Glucocorticoids significantly impact glucose metabolism and insulin sensitivity.
- Impulsive dynamical systems offer a framework for modeling time-dependent biological processes.
Purpose of the Study:
- To develop and analyze an insulin-glucose-glucocorticoid impulsive system for diabetes treatment.
- To investigate the existence, uniqueness, and stability of solutions in type 1 diabetes mellitus (T1DM).
- To confirm the system's permanence in type 2 diabetes mellitus (T2DM).
Main Methods:
- Utilized a [Formula: see text] function to establish the existence and uniqueness of positive periodic solutions for T1DM.
- Applied Floquet multiplier theory and comparison principles to demonstrate global asymptotic stability.
- Employed the comparison theorem to confirm system permanence in T2DM.
Main Results:
- Confirmed the existence, uniqueness, and global asymptotic stability of positive periodic solutions for T1DM.
- Established the permanence of the impulsive system for T2DM.
- Numerical simulations validated theoretical findings.
Conclusions:
- The developed mathematical model provides insights into the dynamics of diabetes under hormonal influences.
- Integrating exogenous insulin and glucocorticoid therapy, considering hormonal interactions, leads to more effective clinical strategies.
- This approach offers a basis for personalized diabetes treatment plans.
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