Analytical solution for pulsatile axial flow velocity waveforms in curved elastic tubes.

Area of Science:

• Fluid dynamics
• Biomedical engineering
• Applied mathematics

Background:

• Pulsatile flow in elastic tubes is fundamental to cardiovascular dynamics.
• Curvature in blood vessels can alter flow patterns, impacting physiological measurements.
• Existing models often simplify vessel geometry, neglecting curvature effects.

Purpose of the Study:

• To develop an analytical solution for pulsatile axial flow velocity in curved elastic tubes.
• To investigate the impact of tube curvature on volumetric axial flow waveforms.
• To provide a tool for enhancing computational models of circulatory systems.

Main Methods:

• Exact solution of linearized Navier-Stokes and tube motion equations.
• Utilized a torroidal coordinate system for geometric accuracy.
• Applied Fourier analysis to separate flow into constant and oscillatory components.

Main Results:

• Curvature significantly affects the constant flow component (up to 60% variation at high Dean numbers).
• Oscillatory flow components show smaller relative changes (magnitude up to 1.2%, phase angle up to 0.15 rad).
• Effects are most pronounced on constant flow and low-frequency oscillatory components.

Conclusions:

• The developed analytical solution accurately models pulsatile flow in curved elastic tubes.
• Tube curvature has a substantial impact on flow characteristics, particularly the constant flow.
• This solution can be integrated into transmission-line analog models to improve simulations of mammalian circulatory systems.