Inlet boundary conditions for blood flow simulations in truncated arterial networks

Willemet, Marie; Lacroix, Valérie; Marchandise, Émilie

doi:10.1016/j.jbiomech.2010.11.036

Cited by 25 publications

(13 citation statements)

References 30 publications

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“…Since then, the pulsatile wave flow has been understood and is explained in classical books such as Lighthill [3] and Pedley [4]. More recently, much work has been done and many methods of resolution have been proposed to handle this set of equations, among them [1,[5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20], and we forgot many actors. Even if recent progress of fluid structure interaction in 3D have been performed ( [21,22], among others), those advances have not made the 1D modelization obsolete.…”

Section: Introductionmentioning

confidence: 99%

A ‘well‐balanced’ finite volume scheme for blood flow simulation

Delestre

Lagrée

2012

Numerical Methods in Fluids

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SUMMARYWe are interested in simulating blood flow in arteries with a one‐dimensional model. Thanks to recent developments in the analysis of hyperbolic system of conservation laws (in the Saint‐Venant shallow water equations context) we will perform a simple finite volume scheme. We focus on conservation properties of this scheme, which were not previously considered. To emphasize the necessity of this scheme, we present how a too simple numerical scheme may induce spurious flows when the basic static shape of the radius changes. On the contrary, the proposed scheme is ‘well‐balanced’: it preserves equilibria of Q = 0. Then examples of analytical or linearized solutions with and without viscous damping are presented to validate the calculations. The influence of abrupt change of basic radius is emphasized in the case of an aneurism. Copyright © 2012 John Wiley & Sons, Ltd.

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Section: Introductionmentioning

confidence: 99%

A ‘well‐balanced’ finite volume scheme for blood flow simulation

Delestre

Lagrée

2012

Numerical Methods in Fluids

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“…Taking case 5 in Table V as a representative case, the execution time of the viscoelastic flow rate for the PHCGCC/PGO algorithms is of 44.17 s, whereas for the SCO algorithm, it is of 376.49 s. Thus, the speed-up is of only 8.52 and not 243. 33 . In addition to the reasons enumerated earlier (because shared memory usage for this kernel is similar to the first kernel, occupancy is limited: only one thread block can be executed at a time on a streaming multiprocessor), also, the fact that the 17 .n T m T / C12m T log 2 m T operations cannot be executed in parallel plays an important role (the CR-PCR algorithm is executed on average in 2log 2 n T log 2 m T 1 D 8 sequential steps).…”

Section: Discussionmentioning

confidence: 99%

Graphics processing unit accelerated one‐dimensional blood flow computation in the human arterial tree

Itu

Sharma

Kamen

et al. 2013

Numer Methods Biomed Eng

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One-dimensional blood flow models have been used extensively for computing pressure and flow waveforms in the human arterial circulation. We propose an improved numerical implementation based on a graphics processing unit (GPU) for the acceleration of the execution time of one-dimensional model. A novel parallel hybrid CPU-GPU algorithm with compact copy operations (PHCGCC) and a parallel GPU only (PGO) algorithm are developed, which are compared against previously introduced PHCG versions, a single-threaded CPU only algorithm and a multi-threaded CPU only algorithm. Different second-order numerical schemes (Lax-Wendroff and Taylor series) are evaluated for the numerical solution of one-dimensional model, and the computational setups include physiologically motivated non-periodic (Windkessel) and periodic boundary conditions (BC) (structured tree) and elastic and viscoelastic wall laws. Both the PHCGCC and the PGO implementations improved the execution time significantly. The speed-up values over the single-threaded CPU only implementation range from 5.26 to 8.10 × , whereas the speed-up values over the multi-threaded CPU only implementation range from 1.84 to 4.02 × . The PHCGCC algorithm performs best for an elastic wall law with non-periodic BC and for viscoelastic wall laws, whereas the PGO algorithm performs best for an elastic wall law with periodic BC.

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“…The inlet volume flow rate during the whole cardiac cycle from which the inlet condition is extracted has been presented in Fig. There are several studies about the suitable outlet boundary condition in the vasculature (45,46). These data points are corresponding to a cardiac cycle of 800 ms that is a heart rate of 75 beats/min.…”

Section: Flow Solvermentioning

confidence: 99%

Non‐Newtonian Blood Flow Simulation of Diastolic Phase in Bileaflet Mechanical Heart Valve Implanted in a Realistic Aortic Root Containing Coronary Arteries

et al. 2016

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Coronary arteries, which are branched from the sinuses, have tangible effects on the hemodynamic performance of the bileaflet mechanical heart valve (BMHV), especially in the diastolic phase. To better understand this issue, a computer model of ascending aorta including realistic sinus shapes and coronary arteries has been generated in this study in order to investigate the BMHV performance during diastole. Three-dimensional transient numerical analysis is conducted to simulate the diastolic blood flow through the hinges and in coronary arteries under the assumption of non-Newtonian behavior. Results indicate that as blood flows to the coronary arteries mainly during diastole, leakage flow from the hinge and other gaps will change considering the influence of coronary arteries. In addition, BMHV in the case of aortic replacement will increase blood flow rate into the coronary arteries about 100% as the mechanical valve resistance is higher than a native heart valve. Also, it will change the wall shear stress (WSS) distribution and increase coronary artery disease (CAD) potential. It is found out that although less leakage flow reduces the velocity magnitudes through the gaps, the shear stress acting on blood elements with non-Newtonian assumption will be detrimental in the hinge corner at the ventricular side. High WSS of 1800 Pa is observed at beginning of diastole at this region.

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Inlet boundary conditions for blood flow simulations in truncated arterial networks

Cited by 25 publications

References 30 publications

A ‘well‐balanced’ finite volume scheme for blood flow simulation

A ‘well‐balanced’ finite volume scheme for blood flow simulation

Graphics processing unit accelerated one‐dimensional blood flow computation in the human arterial tree

Non‐Newtonian Blood Flow Simulation of Diastolic Phase in Bileaflet Mechanical Heart Valve Implanted in a Realistic Aortic Root Containing Coronary Arteries

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