Fluid–structure interaction simulation of aortic blood flow

Crosetto, Paolo; Reymond, Philippe; Deparis, Simone; Kontaxakis, Dimitrios; Stergiopulos, Nikolaos; Quarteroni, Alfio

doi:10.1016/j.compfluid.2010.11.032

Cited by 178 publications

(129 citation statements)

References 24 publications

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“…18,20,21,24,34 An accurate model for the arterial wall should take into account the effects of anisotropy due to the distribution of the collagen fibers, the three layers (intima, media, and adventitia) structure, the nonlinear behavior due to collagen activation, and the incompressibility constraint. Nevertheless, a linear elastic isotropic structure is still considered a reasonable approximation for the large healthy arteries, as demonstrated numerically in, e.g., Crosetto et al 10 , 11 , and validated experimentally in, e.g., Kanyanta et al 22 .…”

Section: Equationsmentioning

confidence: 98%

“…In this regard, it is essential to account for the correct boundary data on the the solid wall geometries. This problem has been already addressed by Crosetto et al 10 and Moireau et al 30 for the external surface of the arterial wall, where Robin boundary conditions have been successfully used to account for the elastic and viscoelastic responses of the external tissues. Nevertheless, the values of the empiric tissue parameters appearing at the boundaries is rather difficult to estimate, and neither calibration procedures nor sensitivity analysis to show the effect of the variation of the parameters on the main quantities of interest were provided.…”

Section: Introductionmentioning

confidence: 96%

“…25 At the present time, the modeling of the detailed multi-contact relations between the arteries and the other tissues is unfeasible. However, Crosetto et al 10 show that for 3-D FSI problems the elastic behavior of external tissues support on the outer arterial wall can be handled by enforcing a Robin boundary condition on Γ 0 S,ext . This approach has been further extended in Moireau et al 30 to include also the viscoelastic response of the tissues, such that the resulting Robin boundary condition for the 3-D FSI problem reads…”

Section: Robin Boundary Condition For the Solid External Wallmentioning

confidence: 99%

“…In both Crosetto et al 10 and Moireau et al 30 a range of orders of magnitude for the aorta is identified on the basis of qualitative considerations about the pulse wave velocity and the maximum admissible displacement of the vessel wall. However, neither further investigations nor sensitivity analyses that show the effect of the variation of the parameters on the main quantities of interest are provided.…”

Section: Robin Boundary Condition For the Solid External Wallmentioning

confidence: 99%

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Section: Equationsmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 96%

Section: Robin Boundary Condition For the Solid External Wallmentioning

confidence: 99%

Section: Robin Boundary Condition For the Solid External Wallmentioning

confidence: 99%

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Numerical simulation of left ventricular assist device implantations: Comparing the ascending and the descending aorta cannulations

Bonnemain

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et al. 2013

Medical Engineering & Physics

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“…The computational cost of this nonsingular method is much smaller when compared to tradi tional approximation procedures, and its accuracy is two to three orders of magnitude better than in the traditional isoparametric BEM when compared with the results presented in [43] for the same number of degrees of freedom. The im proved performance obtained thanks to isogeometric analysis makes IGA BEM a very promising tool for the solution of com plex fluid structure interaction problems arising in biophysics and bio medical applications [15,12]. In fact, our choice of Stokes flows as a model problem is motivated by our interest in modeling the flows induced by swimming bacteria and uni cellular organisms [1,4,3,2,6] and lipid bilayer membranes [5,38].…”

mentioning

confidence: 99%

Nonsingular isogeometric boundary element method for Stokes flows in 3D

Heltai

Arroyo

DeSimone

2014

Computer Methods in Applied Mechanics and Engineering

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While the finite element isogeometric analysis (FE IGA) has received most of the attention of the scientific community, only few results are available for boundary element methods (BEM) and boundary integral equations (BIE) in general. In 2D, there are some works on potential flows, such as [36,44], and on elastostatic analysis [40]. Three dimensional appli cations are of great interest in the maritime community, and there are some works on NURBS based panel methods to study, for example, marine propellers [25] or the wavemaking resistance problem [10]. Three dimensional IGA BEM linear elasticity has recently been studied in [20] while some work on shape optimization has been presented in [29]. Boundary element isogeometric analysis (IGA BEM) is very attractive for the solution of homogeneous elliptic PDEs, both in the interior and in the exterior cases, since it requires the solution of integral equations only on the boundary of the enclos ing (or enclosed) domain, which is typically the only information that is generated by standard CAGD tools. In contrast, FE IGA requires the extension of the computational domain inside (or outside) the enclosing CAGD surface, an outstand ing problem in IGA.While the dimensional reduction of the domain diminishes significantly both the number of degrees of freedom and the computational cost associated with the handling of the geometry, there are two main drawbacks which require special attention, and are common to all boundary integral discretizations: (i) the system matrices that are produced with a bound ary integral method are full, and (ii) the integrands contain ð1=rÞ singularities or worse (in three dimensions) around the source point, arising from the fundamental solutions in formulating the boundary integrals. Both issues have perhaps con tributed in keeping the IGA community away from boundary integral formulations.In the literature, the first issue is usually tackled by acceleration techniques such as the fast multipole method [39] (see [31] for a survey of this technique applied to BEM), which allow one to solve the system without assembling the full matri ces, and at the same time reduce the cost of the matrix vector multiplication from Oðn 2 Þ to OðnÞ (this technique has already been applied to Laplace problems in two dimensional IGA BEM in [44]). The second issue is more delicate and its solution depends highly on the degree of the discrete functional spaces and of the geometry description, remaining one of the most difficult aspects of the implementation of BEM. Different approaches are possible, (see, for example, [23]) but high order methods and curved geometries still remain challenging.Popular approaches to tackle singular integration involve a local change of variables for the quadrature rules, following the principle that the Jacobian of the transformation can be used to eliminate locally the kernel singularities. Examples of these methods are given by Lachat and Watson [28] and by Telles [45]. Both methods are elegant and produce accurate re sults, but t...

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GPU‐assisted real‐time coupling of blood flow and vessel wall

Guo

Yuan

Liao

et al. 2015

Computer Animation & Virtual

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The vessel wall and the blood flow interact and influence each other, and real-time coupling between them is of great importance to the virtual surgery as well as the research and diagnosis of vascular disease. On the basis of smoothed particle hydrodynamics (SPH), we present a new approach to solve non-Newtonian viscous force of blood and a parallel mixed particles-based coupling method for blood flow and vessel wall. Meanwhile, we also design a proxy particle-based vessel wall force visualization method. Our method is as follows. Firstly, we solve the non-Newtonian viscous forces of blood through the SPH method to discretize the Casson equation. Secondly, in each time step, we combine blood particles and sampling proxy particles on the blood vessel wall to form mixed particles and calculate the interaction forces through the SPH method between every pair of the neighboring mixed particles inside the graphics processing unit. Thirdly, the forces of the proxy particles will be mapped to the color display of the proxy particle. Experimental results demonstrate that our method is able to implement real-time sizeable coupling of blood flow and vessel wall while mainly ensuring physical authenticity and it can also provide real-time and obvious information about vessel wall force distribution.

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Fluid–structure interaction simulation of aortic blood flow

Cited by 178 publications

References 24 publications

Numerical simulation of left ventricular assist device implantations: Comparing the ascending and the descending aorta cannulations

Numerical simulation of left ventricular assist device implantations: Comparing the ascending and the descending aorta cannulations

Nonsingular isogeometric boundary element method for Stokes flows in 3D

GPU‐assisted real‐time coupling of blood flow and vessel wall

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