A circle of Willis simulation using distensible vessels and pulsatile flow.

Area of Science:

• Cardiovascular Physiology
• Biomedical Engineering
• Computational Fluid Dynamics

Background:

• The circle of Willis is a critical arterial network supplying blood to the brain.
• Understanding its hemodynamics is crucial for diagnosing and treating cerebrovascular diseases.

Purpose of the Study:

• To develop a one-dimensional numerical model of the circle of Willis arterial network.
• To simulate blood flow and pressure dynamics within this network.
• To investigate the circle of Willis' role in flow equalization and redistribution under normal and pathological conditions.

Main Methods:

• Developed a finite-difference numerical model based on Navier-Stokes and mass conservation equations for distensible vessels.
• Incorporated an elastic wall model with a logarithmic pressure-area relationship.
• Utilized a canine physiological pressure signature for afferent vessel input.
• Represented efferent arteries with single vessels containing resistance to ensure proper flow distribution.
• Determined resistance placement and wavelength based on input impedance analysis.

Main Results:

• Generated time histories of pressure and flow at various nodal points within the model.
• Simulated the effects of pathological conditions on pressure and flow distributions.
• Demonstrated the circle of Willis' capacity to equalize and redistribute blood flow in abnormal situations.

Conclusions:

• The developed numerical model effectively simulates the hemodynamics of the circle of Willis.
• The model highlights the circle of Willis' crucial role in maintaining cerebral blood flow stability.
• The simulation approach is effective for studying cerebrovascular diseases and testing therapeutic strategies.