Fluid mechanics of Windkessel effect

Area of Science:

• Biophysics
• Cardiovascular Physiology
• Fluid Dynamics

Background:

• The Windkessel phenomenon explains the dampening of pulsatile blood flow in the cardiovascular system.
• Existing models often use empirical electrical circuit analogies.
• A mechanistic understanding based on fluid-structure interactions is lacking.

Purpose of the Study:

• To develop a mechanistic theory of the Windkessel effect based on fluid-structure interactions.
• To derive explicit formulas for hemodynamic parameters.
• To theoretically validate the role of material and dimensional properties of blood vessels.

Main Methods:

• A one-dimensional model coupling wave motion in the elastic aorta with viscous flow in peripheral arteries.
• Derivation of explicit formulas based on fluid-structure interaction principles.
• Numerical simulations to analyze the effects of vessel dimensions and blood properties.

Main Results:

• Explicit formulas derived show the influence of blood density, viscosity, wall elasticity, and vessel dimensions.
• The two-element Windkessel model is shown to be a limiting case of the derived theory.
• Theoretical derivation of impedance coefficients, avoiding empirical parameters.

Conclusions:

• The developed mechanistic model accurately describes the Windkessel effect.
• The model highlights the critical role of blood and vessel properties in flow regulation.
• This approach provides a theoretically grounded alternative to empirical models in hemodynamics.