Key result
A computationally efficient nonlinear axisymmetric formulation revealed that the axial velocity across the cross section of blood vessels exhibits neither flat nor parabolic profiles.
Why the study?
Most wave propagation models in blood vessels rely on assumed flat or parabolic velocity profiles, with few studies evaluating profile approximations using different functions.
A computationally efficient nonlinear axisymmetric formulation demonstrates that the axial velocity profile in deformable blood vessels is neither flat nor parabolic, challenging previous modeling assumptions.
Questions reliance on flat or parabolic profiles in vascular modeling; leaves open clinical relevance pending validation.
Wave propagation models in the time domain have been extensively used in the available literature to study the flow characteristics in blood vessels. Most of the wave propagation models have considered flat or parabolic velocity profile functions to estimate the nonlinear convection and diffusion terms present in the conservation of momentum equation. There are only a few works available on the wave propagation analysis in which the velocity profile is approximated using different polynomial functions. In this study, a computationally efficient nonlinear axisymmetric formulation is presented without a priori assumed velocity profile function across the cross section to model the blood flow. Such a formulation in terms of axial velocity (u), pressure (p), and domain radius (R) facilitates the evolution/development of axial velocity profile as the flow progresses with time. The arterial mechanical behavior is modeled using a linear elastic constitutive relation. Partial differential equations are discretized using the finite element method and the Galerkin time integration technique in space and time domains, respectively. This study finds a phase difference between the shear stress at the wall and the flow rate. The flow characteristics and the velocity profile function are found to be in good agreement with the three-dimensional computational results available in the literature. The detailed investigation of the axial velocity across the cross section reveals neither flat nor parabolic profiles, as previously assumed in the literature.
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Hasan et al. (2021) studied this question. Nonlinear axisymmetric formulation without a priori assumed velocity profile function vs. Flat or parabolic velocity profile functions was evaluated on Axial velocity profile and flow characteristics. A computationally efficient nonlinear axisymmetric formulation revealed that the axial velocity across the cross section of blood vessels exhibits neither flat nor parabolic profiles.
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