The inverse Womersley problem for pulsatile flow in straight rigid tubes

Area of Science:

• Fluid dynamics
• Biomedical engineering
• Computational mechanics

Background:

• Pulsatile flow in arteries is complex.
• Existing solutions like Womersley's often assume a known pressure gradient.
• Understanding blood flow dynamics is crucial for diagnosing vascular diseases.

Purpose of the Study:

• To develop and describe a numerical solution for pulsating flow in rigid tubes.
• To provide a method where the flow rate waveform is the known input.
• To calculate pressure gradient, wall shear stress, and velocity profiles.

Main Methods:

• A novel numerical solution was developed.
• The method was applied to rigid tube models.
• Input was the known flow rate waveform.

Main Results:

• The numerical solution successfully provided pressure gradient and wall shear stress waveforms.
• Instantaneous velocity profiles were accurately determined.
• The method's applicability to large artery blood flow was demonstrated.

Conclusions:

• The developed numerical method offers a valuable tool for analyzing pulsatile blood flow.
• It complements existing methods by utilizing flow rate as the primary input.
• This approach can enhance the study of blood flow characteristics in major arteries.