Physiological flow waveform in a rigid elliptical vessel

Area of Science:

• Biomedical Engineering
• Fluid Dynamics
• Computational Biology

Background:

• Physiological flow modeling is essential for understanding vascular diseases.
• Non-cylindrical vessel geometries, like elliptical cross-sections, are relevant for partially occluded or compressed arteries and veins.
• Accurate modeling of velocity and wall shear stress is critical for diagnosing and treating vascular conditions.

Purpose of the Study:

• To present a novel procedure for modeling velocity and wall shear stress in non-cylindrical vessels.
• To apply this procedure to simulate physiological flow in a slightly elliptical vessel, representing compressed or occluded arteries.
• To validate the model's accuracy against physiological flow data.

Main Methods:

• Developed a procedure to model fluid dynamics in elliptical cross-section vessels.
• Utilized Fourier analysis to represent physiological flow waveforms.
• Employed a series of harmonic terms and Mathieu functions to describe velocity and wall shear stress.
• Calculated Mathieu numbers and coefficients for harmonic and Nyquist frequencies.

Main Results:

• Successfully simulated physiological flow in a straight, rigid vessel with a slightly elliptical cross-section (ellipticity = 0.8).
• Achieved high accuracy in representing common carotid artery flow (Pearson correlation coefficient, r > 95%) using five harmonic terms.
• Demonstrated the ability to calculate overall flow properties by superposing individual harmonic contributions.

Conclusions:

• The presented procedure provides a robust method for modeling blood flow and wall shear stress in non-cylindrical vessels.
• The model accurately represents physiological flow in conditions mimicking compressed or partially occluded arteries.
• This approach offers valuable insights into hemodynamics relevant to vascular health and disease.