Abstract
In the present work, we propose an FFT-based method for solving blood flow equations in an arterial network with variable properties and geometrical changes. An essential advantage of this approach is in correctly accounting for the vessel skin friction through the use of Womersley solution. To incorporate nonlinear effects, a novel approximation method is proposed to enable calculation of nonlinear corrections. Unlike similar methods available in the literature, the set of algebraic equations required for every harmonic is constructed automatically. The result is a generalized, robust and fast method to accurately capture the increasing pulse wave velocity downstream as well as steepening of the pulse front. The proposed method is shown to be appropriate for incorporating correct convection and diffusion coefficients. We show that the proposed method is fast and accurate and it can be an effective tool for 1D modelling of blood flow in human arterial networks.
Highlights
Mathematical and numerical modelling of blood flow in a human arterial network allows researchers to understand various flow related phenomena and disorders
It is obvious that several different values of viscosity coefficient are employed by currently used models
The nonlinear convection term used in the mathematical models in the past is not rigorous for a pulsating flow
Summary
Mathematical and numerical modelling of blood flow in a human arterial network allows researchers to understand various flow related phenomena and disorders. An alternative to space–time method is proposed in Flores et al (2016), which is based on linearization of the 1D equations and expanding the solution using the Fourier series In this approach, the problem of wave propagation in an arterial network is solved analytically in the frequency domain, separately for every harmonic component. The pressure and flow rate waveforms are calculated at any point of the network by numerically computing the inverse Fourier transform to the analytical solution obtained In this approach, the skin friction can be accurately incorporated via the Womersley solution. 6, a method for computing the second-order nonlinear corrections is presented for a single tapering vessel, for the boundary conditions and for full solution in an arterial network. Generalization of the Womersley solution for flow in a flexible pipe (“Appendix 1”)
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