Computationally efficient finite element formulation for blood flow analysis in multi‐layered aorta modeled as viscoelastic material

Abstract

In the literature, blood flow study in an arterial segment/arterial network, using one-dimensional wave propagation model, has been carried out considering flat/parabolic/logarithmic/different degree polynomial velocity profile functions. However, such assumptions are not capable of capturing actual blood and arterial wall interaction occurring while the blood flows through the arteries. In this study, a computationally efficient axisymmetric-formulation of the Navier-Stokes equation is presented to eliminate the requirement of a priori assumed velocity profile function. Present formulation in terms of axial velocity (u), pressure (p), and domain radius (R) leads to the evolution of velocity profile as flow progresses with the time and space. We propose a multi-layered structural model of the arterial wall with each layer idealized using four-element Maxwell viscoelastic material model. Partial differential equations, mathematically representing the physical phenomena of blood flow in the complaint blood vessels, are discretized in the spatial domain by finite element method and in time domain by Galerkin time integration technique. A velocity boundary condition is prescribed at inlet and outlet boundary condition is prescribed in terms of three-parameter based Windkessel model. Results of flow characteristics are found to be in excellent agreement with the three-dimensional results available in the literature.

Multiscale constitutive framework of 1D blood flow modeling: Asymptotic limits and numerical methods

“…Even though mathematical models of blood circulation frequently neglect the viscous component of the vessel wall, it is well known that blood vessels (and living tissues in general) exhibit viscoelastic properties [45]. Viscoelastic effects are simulated in literature using different (more or less complex) rheological models, whether linear or not [1,22,9,43,19,21,23]. With a simple but still effective choice, we can close system (1) by considering a linear viscoelastic model as representative of the fluidstructure interaction mechanics of blood with the vessel wall.…”

Automated generation of 0D and 1D reduced‐order models of patient‐specific blood flow

“…Good agreement was found between 3D and 1D solutions, albeit in one case only after manually tuning vessel resistances 38 . Two further studies found good agreement between pressure and flow waveforms at multiple locations in several idealized compliant arterial models, single vessel, bifurcation, aortic arch, and aorta 40,41 . Several studies compared 1D solutions to a 3D whole arterial tree model 42–46 .…”

“…38 Two further studies found good agreement between pressure and flow waveforms at multiple locations in several idealized compliant arterial models, single vessel, bifurcation, aortic arch, and aorta. 40,41 Several studies compared 1D solutions to a 3D whole arterial tree model. [42][43][44][45][46] In summary, there was reasonable agreement in larger vessels and healthy scenarios but less in anatomical variations or abnormal hemodynamic conditions.…”

A brachial artery-based system for blood pressure pulse wave measurement and its signal filtering technique

“…Z Deng and F Liang constructed a numerical model to simulate stress distribution in the upper arm tissues under an inflatable cuff, and they have found the thickness of the upper arm tissues would significantly damped the transmission of cuff pressure [4]. Hasan et al proposed a novel computationally efficient axisymmetric formulation to simulate hemodynamics behavior accurately in the multi-layered elastic arterial model [5]. Other researchers tried to figure out the standardized calibration for the BP measurement devices.…”