Computational modelling of 1D blood flow with variable mechanical properties and its application to the simulation of wave propagation in the human arterial system

Sherwin, Spencer J.; Formaggia, Luca; Peiró, Joaquim; Franke, V.

doi:10.1002/fld.543

Cited by 274 publications

(407 citation statements)

References 20 publications

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“…A high-order discontinuous Galerkin approximation is considered in [177,178], allowing to propagate waves of different frequencies without suffering from excessive dispersion and diffusion errors, so to reliably capture the reflection at the junctions induced by tapering. Alternatively, a high-order finite volume scheme is presented in [129] and a space-time finite element method is proposed in [204].…”

Section: Numerical Discretizationmentioning

confidence: 99%

Geometric multiscale modeling of the cardiovascular system, between theory and practice

Quarteroni

Veneziani

Vergara

2016

Computer Methods in Applied Mechanics and Engineering

166

157

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This review paper addresses the so called geometric multiscale approach for the numerical simulation of blood flow problems, from its origin (that we can collocate in the second half of '90s) to our days. By this approach the blood fluid-dynamics in the whole circulatory system is described mathematically by means of heterogeneous featuring different degree of detail and different geometric dimension that interact together through appropriate interface coupling conditions.Our review starts with the introduction of the stand-alone problems, namely the 3D fluidstructure interaction problem, its reduced representation by means of 1D models, and the so-called lumped parameters (aka 0D) models, where only the dependence on time survives. We then address specific methods for stand-alone 3D models when the available boundary data are not enough to ensure the mathematical well posedness. These so-called "defective problems" naturally arise in practical applications of clinical relevance but also because of the interface coupling of heterogeneous problems that are generated by the geometric multiscale process. We also describe specific issues related to the boundary treatment of reduced models, particularly relevant to the geometric multiscale coupling. Next, we detail the most popular numerical algorithms for the solution of the coupled problems. Finally, we review some of the most representative works -from different research groups -which addressed the geometric multiscale approach in the past years.A proper treatment of the different scales relevant to the hemodynamics and their interplay is essential for the accuracy of numerical simulations and eventually for their clinical impact. This paper aims at providing a state-of-the-art picture of these topics, where the gap between theory and practice demands rigorous mathematical models to be reliably filled.

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Section: Numerical Discretizationmentioning

confidence: 99%

Geometric multiscale modeling of the cardiovascular system, between theory and practice

Quarteroni

Veneziani

Vergara

2016

Computer Methods in Applied Mechanics and Engineering

166

157

View full text Add to dashboard Cite

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“…Clearly if all artificial sections are interfaced with the 1D model, we can apply directly estimate (39). In this case, an extra positive term, depending on the boundary data of the 1D model, will appear on the right hand side of (39), as in (36) (see Lem.…”

Section: Remark 52mentioning

confidence: 99%

“…This motivates the adoption of simplified models, like for instance 1D models, originally proposed by Euler [10] and widely used nowadays [32,39]. These models are described by hyperbolic systems of partial differential equations and, despite having a lower level of accuracy compared to the fully 3D model, they capture effectively the pulse waves at a much lower computational cost.…”

mentioning

confidence: 99%

On the stability of the coupling of 3D and 1D fluid-structure interaction models for blood flow simulations

Formaggia¹,

Moura²,

Nobile³

2007

ESAIM: M2AN

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Abstract.We consider the coupling between three-dimensional (3D) and one-dimensional (1D) fluidstructure interaction (FSI) models describing blood flow inside compliant vessels. The 1D model is a hyperbolic system of partial differential equations. The 3D model consists of the Navier-Stokes equations for incompressible Newtonian fluids coupled with a model for the vessel wall dynamics. A non standard formulation for the Navier-Stokes equations is adopted to have suitable boundary conditions for the coupling of the models. With this we derive an energy estimate for the fully 3D-1D FSI coupling. We consider several possible models for the mechanics of the vessel wall in the 3D problem and show how the 3D-1D coupling depends on them. Several comparative numerical tests illustrating the coupling are presented.Mathematics Subject Classification. 65M12, 65M60, 92C50, 74F10, 76Z05.

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“…At the periphery of the arterial tree we typically prescribe a reflection condition [10,18], where the incoming characteristic is set to be equal to the outgoing characteristic value scaled by the reflection coefficient. More details are found in Sherwin et al [9,10].…”

Section: Boundary Conditionsmentioning

confidence: 99%

“…The physiological properties of blood flow in arterial networks can be reasonably approximated by a onedimensional model, where the blood velocity, pressure and vessel wall properties are assumed to be constant across a section [6,9,10]. The fundamental equations of conservation of mass and momentum lead to a hyperbolic conservation law describing the propagation of waves within the networks.…”

Section: Introductionmentioning

confidence: 99%

Time domain computational modelling of 1D arterial networks in monochorionic placentas

Franke¹,

Parker

Wee

et al. 2003

ESAIM: M2AN

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Abstract. In this paper we outline the hyperbolic system of governing equations describing onedimensional blood flow in arterial networks. This system is numerically discretised using a discontinuous Galerkin formulation with a spectral/hp element spatial approximation. We apply the numerical model to arterial networks in the placenta. Starting with a single placenta we investigate the velocity waveform in the umbilical artery and its relationship with the distal bifurcation geometry and the terminal resistance. We then present results for the waveform patterns and the volume fluxes throughout a simplified model of the arterial placental network in a monochorionic twin pregnancy with an arterio-arterial anastomosis and an arterio-venous anastomosis. The effects of varying the time period of the two fetus' heart beats, increasing the input flux of one fetus and the role of terminal resistance in the network are investigated and discussed. The results show that the main features of the in vivo, physiological waves are captured by the computational model and demonstrate the applicability of the methods to the simulation of flows in arterial networks.Mathematics Subject Classification. 92C35, 76Z05.

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Computational modelling of 1D blood flow with variable mechanical properties and its application to the simulation of wave propagation in the human arterial system

Cited by 274 publications

References 20 publications

Geometric multiscale modeling of the cardiovascular system, between theory and practice

Geometric multiscale modeling of the cardiovascular system, between theory and practice

On the stability of the coupling of 3D and 1D fluid-structure interaction models for blood flow simulations

Time domain computational modelling of 1D arterial networks in monochorionic placentas

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