A robust and efficient valve model based on resistive immersed surfaces

Astorino, Matteo; Hamers, Jeroen; Shadden, Shawn C.; Gerbeau, Jean-Frédéric

doi:10.1002/cnm.2474

Cited by 61 publications

(76 citation statements)

References 49 publications

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“…In the FEM context, different approaches have been introduced aiming at controlling the approximation error induced by the discretization of the geometry; examples are the surface FEM [9,10], or geometrically consistent Adaptive FEM [11,12,13]. Other approaches are based on modeling the surfaces as immersed in the 3D domain or treated implicitly, as, for example, for level set formulations [3,14] or diffuse and resistive interface approaches [4,15].…”

Section: Introductionmentioning

confidence: 99%

Isogeometric Analysis of high order Partial Differential Equations on surfaces

Bartezzaghi

Dedè

Quarteroni

2015

Computer Methods in Applied Mechanics and Engineering

130

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We consider the numerical approximation of high order Partial Differential Equations (PDEs) defined on surfaces in the three dimensional space, with particular emphasis on closed surfaces. We consider computational domains that can be represented by B-splines or NURBS, as for example the sphere, and we spatially discretize the PDEs by means of NURBS-based Isogeometric Analysis in the framework of the standard Galerkin method. We numerically solve benchmark Laplace–Beltrami problems of the fourth and sixth order, as well as the corresponding eigenvalue problems, with the goal of analyzing the role of the continuity of the NURBS basis functions on closed surfaces. In this respect, we show that the use of globally high order continuous basis functions, as allowed by the construction of periodic NURBS, leads to the efficient solution of the high order PDEs. Finally, we consider the numerical solution of high order phase field problems on closed surfaces, namely the Cahn–Hilliard and crystal equations

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Section: Introductionmentioning

confidence: 99%

Isogeometric Analysis of high order Partial Differential Equations on surfaces

Bartezzaghi

Dedè

Quarteroni

2015

Computer Methods in Applied Mechanics and Engineering

130

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“…The pulmonary valve is modeled as a resistive immersed surface (RIS), 4 i.e., considering the valve as a thin porous interface which resistance to flow depends on the current flow and pressure conditions across the valve surface, varying between zero (when the valve is open) to a very high value (when the valve is closed).…”

Section: Valve Modelingmentioning

confidence: 99%

Blood Flow Simulations for the Design of Stented Valve Reducer in Enlarged Ventricular Outflow Tracts

Caiazzo

Guibert

Boudjemline

et al. 2015

Cardiovasc Eng Tech

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Tetralogy of Fallot is a congenital heart disease characterized over time, after the initial repair, by the absence of a functioning pulmonary valve, which causes regurgitation, and by progressive enlargement of the right ventricle outflow tract (RVOT). Due to this pathological anatomy, available transcatheter valves are usually too small to be deployed there. To avoid surgical valve replacement, an alternative consists in implanting a reducer prior to or in combination with the valve. It has been shown in animal experiments to be promising, but with some limitations. The effect of a percutaneous pulmonary valve reducer on hemodynamics in enlarged RVOT is thus studied by computational modeling. To this aim, blood flow in the RVOT is modeled with CFD coupled to a simplified valve model and 0D downstream models. Simulations are performed in an image-based geometry and boundary conditions tuned to reproduce the pathological flow without the device. Different device designs are built and compared with the initial device-free state, or with the reducer alone. Results suggest that pressure loss is higher for the reducer alone than for the full device, and that the latter successfully restores hemodynamics to a healthy state and induces a more symmetric flow in the pulmonary arteries. Moreover, pressure forces on the reducer and on the valve have the same magnitudes. Migration would occur towards the right ventricle rather than the pulmonary arteries. Results support the thesis that the reducer does not introduce clinically significant pressure gradients, as was found in animal experiments. Such study could help transfer to patients.

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“…FTLE/LCS has been computed for steady flow measured from PIV in a carotid artery showing the recirculating structures, and the increase in complexity of the structures with increase in Reynolds number [148]. LCS has been used in aortic valves to delineate the boundaries and area of the jet formed downstream of the valve [125, 8], used to quantify the severity of aortic stenosis. Xu et al [155] used LCS to study blood flow during clot formation and determined regions of blood that were delivered to the clot.…”

Section: Lagrangian Coherent Structures (Lcs)mentioning

confidence: 99%

Lagrangian Postprocessing of Computational Hemodynamics

Shadden

Arzani

2014

Ann Biomed Eng

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Recent advances in imaging, modeling and computing have rapidly expanded our capabilities to model hemodynamics in the large vessels (heart, arteries and veins). This data encodes a wealth of information that is often under-utilized. Modeling (and measuring) blood flow in the large vessels typically amounts to solving for the time-varying velocity field in a region of interest. Flow in the heart and larger arteries is often complex, and velocity field data provides a starting point for investigating the hemodynamics. This data can be used to perform Lagrangian particle tracking, and other Lagrangian-based postprocessing. As described herein, Lagrangian methods are necessary to understand inherently transient hemodynamic conditions from the fluid mechanics perspective, and to properly understand the biomechanical factors that lead to acute and gradual changes of vascular function and health. The goal of the present paper is to review Lagrangian methods that have been used in post-processing velocity data of cardiovascular flows.

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A robust and efficient valve model based on resistive immersed surfaces

Cited by 61 publications

References 49 publications

Isogeometric Analysis of high order Partial Differential Equations on surfaces

Isogeometric Analysis of high order Partial Differential Equations on surfaces

Blood Flow Simulations for the Design of Stented Valve Reducer in Enlarged Ventricular Outflow Tracts

Lagrangian Postprocessing of Computational Hemodynamics

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