Three-Element Fractional-Order Viscoelastic Arterial Windkessel Model

Area of Science:

• Biomedical Engineering
• Cardiovascular Physiology
• Mathematical Modeling

Background:

• Arterial hemodynamic assessment is crucial for cardiovascular system (CVS) diagnosis.
• Windkessel (WK) models offer a convenient, cost-effective, and accurate non-invasive method for predicting arterial parameters.
• Existing WK models are typically elastic or viscoelastic, with recent interest in fractional-order models for improved arterial wall viscoelasticity representation.

Purpose of the Study:

• To introduce the first three-element fractional-order viscoelastic Windkessel model for arterial hemodynamics.
• To incorporate a fractional-order capacitor, mimicking arterial viscoelastic behavior, into the standard WK model.
• To provide a reliable, realistic, and reduced representation of arterial viscoelasticity.

Main Methods:

• Development of a novel three-element fractional-order viscoelastic Windkessel model.
• Substitution of the ideal capacitor in a standard WK model with a fractional-order capacitor.
• Analysis of the fractional differentiation order (α) to control resistive and capacitive properties.

Main Results:

• The proposed model successfully integrates fractional-order elements to represent arterial viscoelasticity.
• The fractional-order capacitor exhibits combined resistive and capacitive properties, reflecting non-ideal behavior.
• The model's fractional order (α) allows for tunable physiological description of arterial dynamics.

Conclusions:

• The presented fractional-order viscoelastic Windkessel model offers a significant advancement in arterial hemodynamic assessment.
• This model provides a more accurate and physiologically relevant description of arterial wall viscoelasticity compared to traditional models.
• The fractional-order approach enables a reduced yet reliable representation of complex arterial behavior.