A discrete Single Delay Model for the Intra-Venous Glucose Tolerance Test.

Area of Science:

• Physiology
• Mathematical Modeling
• Endocrinology

Background:

• Identifying insulin resistance is crucial for patient health.
• Existing mathematical models for glucose-insulin dynamics can be complex.
• A need exists for a simple yet reliable model to assess insulin sensitivity.

Purpose of the Study:

• To introduce a new, discrete Single Delay Model (SDM) for glucose-insulin system analysis.
• To evaluate the SDM's ability to estimate insulin sensitivity accurately.
• To compare the SDM with the established Minimal Model (MM).

Main Methods:

• Developed a discrete Single Delay Model (SDM) for glucose-insulin dynamics.
• Applied the SDM to Intra-Venous Glucose Tolerance Tests (IVGTTs).
• Simultaneously fitted the model to glucose and insulin data, estimating the KxgI parameter for insulin sensitivity.

Main Results:

• The SDM demonstrated stable dynamics and positive bounded solutions.
• Insulin sensitivity (KxgI) was identifiable in all 40 subjects using the SDM, compared to 20/40 with the MM.
• KxgI from the SDM correlated well with the inverse of the HOMA-IR index.

Conclusions:

• The Single Delay Model (SDM) is theoretically sound and practically robust for determining insulin sensitivity.
• The SDM provides a reliable method for routine insulin sensitivity assessment from IVGTTs.
• Free software is available for estimating SDM parameters, facilitating its widespread adoption.