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Waves in initially stressed fluid-filled thick tubes
1Marmara Research Centre, Department of Mathematics, Gebze-Kocaeli, Turkey.
Journal of Biomechanics
|March 1, 1997
Summary
This study models harmonic wave propagation in arteries, considering wall inertia and fluid dynamics. Results show wave dispersion due to inertial pressure effects, impacting blood flow dynamics.
Area of Science:
- Biomechanical Engineering
- Fluid Dynamics
- Materials Science
Background:
- Arteries are modeled as thick-walled cylindrical shells of incompressible, elastic, and isotropic material.
- Blood is treated as an incompressible, inviscid fluid.
- The inertia of the arterial wall is incorporated into the wave propagation model.
Purpose of the Study:
- To investigate the propagation of harmonic waves in an initially stressed, fluid-filled tube.
- To derive and analyze the dispersion relation for wave propagation in this system.
- To understand the influence of physical parameters on wave speed and dispersion.
Main Methods:
- Developed a model for a thick-walled cylindrical shell filled with inviscid fluid, including wall inertia.
- Utilized the inner-pressure-cross-sectional-area relation within the fluid's linear momentum and continuity equations.
- Solved incremental equations for small dynamical motions superimposed on large static deformations to obtain the dispersion relation.
Main Results:
- Derived two nonlinear equations governing axial velocity and tube cross-sectional area.
- Obtained a dispersion relation dependent on transmural pressure, axial stretch, thickness ratio, and wave number.
- Numerical evaluation and graphical representation of wave speed for various materials and dimensions revealed wave dispersion.
Conclusions:
- The inertial component of pressure is identified as the cause of wave dispersion in this arterial model.
- The derived formulation provides a comprehensive analysis of harmonic wave propagation in initially stressed, fluid-filled tubes.
- The results offer insights into the complex dynamics of blood flow and arterial wall interactions.
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