Outflow boundary conditions for three-dimensional simulations of non-periodic blood flow and pressure fields in deformable arteries

Vignon-Clémentel, Irène; Figueroa, C. Alberto; Marsden, Alison L.; Feinstein, Jeffrey A.; Jansen, Kenneth E.; Taylor, Charles A.

doi:10.1016/s0021-9290(06)84756-1

Cited by 14 publications

(19 citation statements)

References 44 publications

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“…At the proximal veins and distal vessels, a stress-free condition is enforced; the pressure stress and normal viscous stress on the outflow boundary are balanced, and the tangential viscous stresses are zero. The pressure on all proximal veins and all distal vessels are prescribed by using two-element Windkessel, i.e., resistance-capacitance models [21] (one exception is the distal artery in patient 4 where an inflow is prescribed using a Womersley velocity profile). In vivo measurements of fistula outflow vein impedance show that it is well approximated by a single resistive element up to %10 Hz [22].…”

Section: Methodsmentioning

confidence: 99%

Incomplete Restoration of Homeostatic Shear Stress Within Arteriovenous Fistulae

McGah

Leotta

Beach³

et al. 2012

Journal of Biomechanical Engineering

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Arteriovenous fistulae are surgically created to provide adequate access for dialysis patients suffering from end-stage renal disease. It has long been hypothesized that the rapid blood vessel remodeling occurring after fistula creation is, in part, a process to restore the mechanical stresses to some preferred level, i.e., mechanical homeostasis. We present computational hemodynamic simulations in four patient-specific models of mature arteriovenous fistulae reconstructed from 3D ultrasound scans. Our results suggest that these mature fistulae have remodeled to return to ''normal'' shear stresses away from the anastomoses: about 1.0 Pa in the outflow veins and about 2.5 Pa in the inflow arteries. Large parts of the anastomoses were found to be under very high shear stresses > 15 Pa, over most of the cardiac cycle. These results suggest that the remodeling process works toward restoring mechanical homeostasis in the fistulae, but that the process is limited or incomplete, even in mature fistulae, as evidenced by the elevated shear at or near the anastomoses. Based on the long term clinical viability of these dialysis accesses, we hypothesize that the elevated nonhomeostatic shear stresses in some portions of the vessels were not detrimental to fistula patency.

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Section: Methodsmentioning

confidence: 99%

Incomplete Restoration of Homeostatic Shear Stress Within Arteriovenous Fistulae

McGah

Leotta

Beach³

et al. 2012

Journal of Biomechanical Engineering

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“…Furthermore, to represent the vascular bed downstream of the computational domain, the traction h at outlets can be calculated using a boundary condition based on prescribed traction, resistance, impedance, or a three-element Windkessel model [34,35]. As the Galerkin method is well known to be unstable for equal-order interpolation of the velocity and pressure, a stabilized semi-discrete finite element method [4,10,30,36] is utilized in this study.…”

Section: Methodsmentioning

confidence: 99%

“…4, along with the labels of sections where the velocity magnitude are reported. The figure also shows the inflow waveform and the three-element Windkessel model [34,35] assigned to each outlet. The geometric model consists of seventy eight arteries, starting from the root of the aorta and including major branch vessels and main branches of the upper-body and lower-body vasculature.…”

Section: "Whole" Body Simulationmentioning

confidence: 99%

“…A Womersley velocity profile [37] is applied at the inlet and both rigid or deformable walls are considered. At the outlets a threeelement Windkessel model [34,35] is applied. As stated above, this study is meant only to establish the feasibility of such simulations and therefore involves only 20 time steps.…”

Section: Scaling Study Of Aaa Model With Fsimentioning

confidence: 99%

“…To consider these interactions, more sophisticated boundary conditions have been developed. These boundary conditions use relationships between pressure and flow and assign weak pressure or flow rate boundary conditions as the boundary conditions [9,17,20,34]. Further, blood vessel walls are not rigid but deform in response to blood flow and pressure and models to represent these effects must be included to capture the altered flow and traction fields near the wall, as well as the overall pressure and flow wave propagation phenomena in the system [6][7][8]19,21,33].…”

Section: Introductionmentioning

confidence: 99%

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Cardiovascular flow simulation at extreme scale

et al. 2009

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As cardiovascular models grow more sophisticated in terms of the geometry considered, and more physiologically realistic boundary conditions are applied, and fluid flow is coupled to structural models, the computational complexity grows. Massively parallel adaptivity and flow solvers with extreme scalability enable cardiovascular simulations to reach an extreme scale while keeping the time-to-solution reasonable. In this paper, we discuss our efforts in this area and provide two demonstrations: one on an extremely large and complex geometry (including many of the major arteries below the neck) where the solution is efficiently captured with anisotropic adaptivity and another case (severe abdominal aorta aneurysm) where the transitional flow leads to extremely large meshes (O(10 9 )) and scalability to extremely large core counts (O(10 5 )) for both rigid and deforming wall simulations.

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Fluid–structure interaction simulations of the Fontan procedure using variable wall properties

Hsu

Bazilevs

et al. 2012

Numer Methods Biomed Eng

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Children born with single ventricle heart defects typically undergo a staged surgical procedure culminating in a total cavopulmonary connection (TCPC) or Fontan surgery. The goal of this work was to perform physiologic, patient-specific hemodynamic simulations of two post-operative TCPC patients by using fluid-structure interaction (FSI) simulations. Data from two patients are presented, and post-op anatomy is reconstructed from MRI data. Respiration rate, heart rate, and venous pressures are obtained from catheterization data, and inflow rates are obtained from phase contrast MRI data and are used together with a respiratory model. Lumped parameter (Windkessel) boundary conditions are used at the outlets. We perform FSI simulations by using an arbitrary Lagrangian-Eulerian finite element framework to account for motion of the blood vessel walls in the TCPC. This study is the first to introduce variable elastic properties for the different areas of the TCPC, including a Gore-Tex conduit. Quantities such as wall shear stresses and pressures at critical locations are extracted from the simulation and are compared with pressure tracings from clinical data as well as with rigid wall simulations. Hepatic flow distribution and energy efficiency are also calculated and compared for all cases. There is little effect of FSI on pressure tracings, hepatic flow distribution, and time-averaged energy efficiency. However, the effect of FSI on wall shear stress, instantaneous energy efficiency, and wall motion is significant and should be considered in future work, particularly for accurate prediction of thrombus formation.

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Outflow boundary conditions for three-dimensional simulations of non-periodic blood flow and pressure fields in deformable arteries

Cited by 14 publications

References 44 publications

Incomplete Restoration of Homeostatic Shear Stress Within Arteriovenous Fistulae

Incomplete Restoration of Homeostatic Shear Stress Within Arteriovenous Fistulae

Cardiovascular flow simulation at extreme scale

Fluid–structure interaction simulations of the Fontan procedure using variable wall properties

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