A fractional-order model for MINMOD Millennium.

Area of Science:

• Biomedical Engineering
• Mathematical Modeling
• Endocrinology

Background:

• The MINMOD Millennium model is a standard for estimating insulin sensitivity (SI) in glucose-insulin dynamics.
• Understanding glucose-insulin dynamics is crucial for managing metabolic disorders like type 2 diabetes.
• Rheological behavior in glucose-insulin systems requires advanced modeling approaches.

Purpose of the Study:

• To modify the MINMOD Millennium model using fractional-order differentiation to better explain glucose-insulin dynamics.
• To analyze the impact of fractional calculus on model stability and solution properties.
• To investigate insulin sensitivity and glucose tolerance in normal and type 2 diabetic subjects using the enhanced model.

Main Methods:

• Incorporation of fractional-order differentiation (order α ∈ (0, 1]) into the MINMOD Millennium model.
• Application of nonlinear weighted least-squares and the Levenberg-Marquardt algorithm for parameter estimation.
• Utilizing the fractional Adams-Bashforth-Moulton method for numerical simulations.
• Testing the model on data from normal subjects and type 2 diabetic patients.

Main Results:

• The modified model demonstrates non-negative, bounded solutions and a stable equilibrium point.
• Quasi-optimal fractional orders and parameters were successfully estimated.
• Numerical results confirmed significantly lower insulin sensitivity (SI) in type 2 diabetic patients compared to normal subjects.
• A novel factor, τ(1 - α), was identified as crucial for determining glucose tolerance and its relation to SI.

Conclusions:

• Fractional-order modeling offers a robust approach to analyzing glucose-insulin dynamics.
• The enhanced model provides deeper insights into the physiological differences in insulin sensitivity between diabetics and non-diabetics.
• The newly identified factor τ(1 - α) offers a new perspective on glucose tolerance mechanisms.