Influence of the distensibility of large arteries on the longitudinal impedance: application for the development of non-invasive techniques to the diagnosis of arterial diseases

Abstract

Background: This study shows that the arterial longitudinal impedance constitutes a hemodynamic parameter of interest for performance characterization of large arteries in normal condition as well as in pathological situations. For this purpose, we solved the Navier-Stokes equations for an incompressible flow using the finite element analysis method and the Arbitrary Lagrangian Eulerian (ALE) formulation. The mathematical model assumes a two-dimensional flow and takes into account the nonlinear terms in the equations of fluid motion that express the convective acceleration, as well as the nonlinear deformation of the arterial wall. Several numerical simulations of the blood flow in large vessels have been performed to study the propagation along an arterial vessel of a pressure gradient pulse and a rate flow pulse. These simulations include various deformations of the wall artery leading to parietal displacements ranging from 0 (rigid wall) to 15% (very elastic wall) in order to consider physiological and pathological cases. Results: The results show significant changes of the rate flow and the pressure gradient wave as a function of aosc, the relative variation in the radius of the artery over a cardiac cycle. These changes are notable beyond a critical value of aosc equal to 0.05. This critical value is also found in the evolution of the longitudinal impedance. So, above a variation of radius of 5%, the convective acceleration, created by the fluid-wall interactions, have an influence on the flow detectable on the longitudinal impedance. Conclusions: The interpretation of the evolution of the longitudinal impedance shows that it could be a mean to test the performance of large arteries and can contribute to the diagnosis of parietal lesions of large arteries. For a blood vessel with a wall displacement higher than 5% similar to those of large arteries like the aorta, the longitudinal impedance is substantially greater than that obtained in the absence of wall displacement. This study also explains the effects of convective acceleration, on the shape of the decline of the pressure gradient wave and shows that they should not be neglected when the variation in radius is greater than 5%.

The Impact of Spinal Cord Nerve Roots and Denticulate Ligaments on Cerebrospinal Fluid Dynamics in the Cervical Spine

“…ILI is defined in a way to quantify the viscous resistance in an unsteady flow field [61] . This parameter has been investigated to quantify the performance of arterial functions in normal and pathological conditions [62] and patency of vein grafts [43] . Similarly, the assessment of ILI, as a single parameter taking into account the impact of full three-dimensional geometry, may prove to be useful to quantify CSF flow blockage inside SSS and can be considered as a tool for diagnosing pathological conditions where CSF dynamics are thought to be an important factor.…”

Pulsatility Index as a Diagnostic Parameter of Reciprocating Wall Shear Stress Parameters in Physiological Pulsating Waveforms

“…It was shown in previous studies that the goodness of fit of the models may be affected by the geometry and boundary conditions [44], Sahtout and Ben Salah [45] have shown that Womersley linear theory is accurate enough for the long rigid vessel with no taper or distensibility. Yet, the present experimental case is neither rigid, nor a straight infinite pipe with a fixed inner diameter.…”

“…The inverse Womersley method is based on Womersley's simplified model of a straight, rigid and infinitely long tube. It was shown in previous studies that the goodness of fit of the models may be affected by the geometry and boundary conditions [45], Sahtout and Ben Salah [46] have shown that Womersley linear theory is accurate enough for the long rigid vessel with no taper or distensibility.…”