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Transcatheter aortic valve implantation (TAVI) is a minimally invasive intervention for the treatment of severe aortic valve stenosis. The main cause of failure is the structural deterioration of the implanted prosthetic leaflets, possibly inducing a valvular re‐stenosis 5–10 years after the implantation. Based solely on pre‐implantation data, the aim of this work is to identify fluid‐dynamics and structural indices that may predict the possible valvular deterioration, in order to assist the clinicians in the decision‐making phase and in the intervention design. Patient‐specific, pre‐implantation geometries of the aortic root, the ascending aorta, and the native valvular calcifications were reconstructed from computed tomography images. The stent of the prosthesis was modeled as a hollow cylinder and virtually implanted in the reconstructed domain. The fluid‐structure interaction between the blood flow, the stent, and the residual native tissue surrounding the prosthesis was simulated by a computational solver with suitable boundary conditions. Hemodynamical and structural indicators were analyzed for five different patients that underwent TAVI – three with prosthetic valve degeneration and two without degeneration – and the comparison of the results showed a correlation between the leaflets' structural degeneration and the wall shear stress distribution on the proximal aortic wall. This investigation represents a first step towards computational predictive analysis of TAVI degeneration, based on pre‐implantation data and without requiring additional peri‐operative or follow‐up information. Indeed, being able to identify patients more likely to experience degeneration after TAVI may help to schedule a patient‐specific timing of follow‐up. [ABSTRACT FROM AUTHOR]

In the current work, we present a descriptive fluid-structure interaction computational study of the end-to-side radio-cephalic arteriovenous fistula. This allows us to account for the different thicknesses and elastic properties of the radial artery and cephalic vein. The core of the work consists in simulating different arteriovenous fistula configurations obtained by virtually varying the anastomosis angle, i.e. the angle between the end of the cephalic vein and the side of the radial artery. Since the aim of the work is to understand the blood dynamics in the very first days after the surgical intervention, the radial artery is considered stiffer and thicker than the cephalic vein. Our results demonstrate that both the diameter of the cephalic vein and the anastomosis angle play a crucial role to obtain a blood dynamics without re-circulation regions that could prevent fistula failure. When an anastomosis angle close to the perpendicular direction with respect to the radial artery is combined with a large diameter of the cephalic vein, the recirculation regions and the low Wall Shear Stress (WSS) zones are reduced. Conversely, from a structural point of view, a low anastomosis angle with a large diameter of the cephalic vein reduces the mechanical stress acting on the vessel walls. • Fluid-structure interaction analysis for different configurations of the arteriovenous fistula. • Mismatch of the arterial and venous Young's moduli and different vessel thicknesses. • Real reconstruction of the shape of the anastomosis region. • The diameter of the cephalic vein drastically influences the hemodynamics. [ABSTRACT FROM AUTHOR]

Atherosclerosis is a systemic disease that leads to accumulation of deposits, known as atherosclerotic plaques, within the walls of the carotids. In particular, three types of plaque can be distinguished: soft, fibrous, and calcific. Most of the computational studies who investigated the interplay between the plaque and the blood flow on patient-specific geometries used nonstandard medical images to directly delineate and segment the plaque and its components. However, these techniques are not so widely available in the clinical practice. In this context, the aim of our work was twofold: (i) to propose a new geometric tool that allowed to reconstruct a plausible plaque in the carotids from standard images and (ii) to perform three-dimensional (3D) fluid-structure interaction (FSI) simulations where we compared some fluid-dynamic and structural quantities among 15 patients characterized by different typologies of plaque. Our results highlighted that both the morphology and the mechanical properties of different plaque components play a crucial role in determining the vulnerability of the plaque. [ABSTRACT FROM AUTHOR]

We consider a loosely-coupled algorithm for fluid-structure interaction based on a Robin interface condition for the fluid problem (explicit Robin-Neumann scheme). We study the dependence of the stability of this method on the interface parameter in the Robin condition. In particular, for a model problem we find sufficient conditions for instability and stability of the method. In the latter case, we find a stability condition relating the time discretization parameter, the interface parameter, and the fluid and structure densities. Numerical experiments confirm the theoretical findings and highlight optimal choices of the interface parameter that guarantee accurate solutions. [ABSTRACT FROM AUTHOR]

Numerical simulations of cardiac blood pump systems are integral to the optimization of device design, hydraulic performance and hemocompatibility. In wave membrane blood pumps, blood propulsion arises from the wave propagation along an oscillating immersed membrane, which generates small pockets of fluid that are pushed towards the outlet against an adverse pressure gradient. We studied the Fluid–Structure Interaction between the oscillating membrane and the blood flow via three‐dimensional simulations using the Extended Finite Element Method (XFEM), an unfitted numerical technique that avoids remeshing by using a fluid fixed mesh. Our three‐dimensional numerical simulations in a realistic pump geometry highlighted, for the first time in this field of application, that XFEM is a reliable strategy to handle complex industrial problems. Moreover, they showed the role of the membrane deformation in promoting a blood flow towards the outlet despite an adverse pressure gradient. We also simulated the pump system at different pressure conditions and we validated the numerical results against in‐vitro experimental data. [ABSTRACT FROM AUTHOR]

We propose a surrogate model for the fluid–structure interaction (FSI) problem for the study of blood dynamics in carotid arteries in presence of plaque. This is based on the integration of a numerical model with subject‐specific data and clinical imaging. We propose to model the plaque as part of the tissues surrounding the vessel wall through the application of an elastic support boundary condition. In order to characterize the plaque and other surrounding tissues, such as the close‐by jugular vein, the elastic parameters of the boundary condition were spatially differentiated and their values were estimated by minimizing the discrepancies between computed vessel displacements and reference values obtained from CINE Magnetic Resonance Imaging data. We applied the model to three subjects with a degree of stenosis greater than 70%. We found that accounting for both plaque and jugular vein in the estimation of the elastic parameters increases the accuracy. In particular, in all patients, mismatches between computed and in vivo measured wall displacements were one to two orders of magnitude lower than the spatial resolution of the original MRI data. These results confirmed the validity of the proposed surrogate plaque model. We also compared fluid‐dynamics results with those obtained in a fixed wall setting and in a full FSI model, used as gold standard, highlighting the better accordance of our results in comparison to the rigid ones. [ABSTRACT FROM AUTHOR]

In this work we consider the optimized Schwarz method designed for computational domains that feature spherical or almost spherical interfaces. In the first part, we consider the diffusion-reaction problem. We provide a convergence analysis of the generalized Schwarz method and, following [G. Gigante and C. Vergara, Numer. Math., 131 (2015), pp. 369{404], we discuss an optimization procedure for constant interface parameters leading to a Robin{Robin scheme. Finally, we present some numerical results both in spherical and in ellipsoidal domains. In the second part of the work, we address the uid-structure interaction problem. Again, we provide a convergence analysis and discuss optimized choices of constant interface parameters. Finally, we present three- dimensional numerical results inspired by hemodynamic applications, to validate the proposed choices in the presence of large added mass effect. In particular, we consider numerical experiments both in an ideal spherical domain and in a realistic abdominal aortic aneurysm. [ABSTRACT FROM AUTHOR]

A numerical procedure that combines an extended finite element formulation and a discontinuous Galerkin technique is presented, with the final aim of providing an effective tool for the simulation of three-dimensional (3D) fluid -structure interaction problems. In this work we consider a thick structure immersed in a fluid . We describe the numerical models and discuss the specific implementation issues arising in three dimensions. Finally, 3D numerical results are provided to show the effectiveness of the approach. [ABSTRACT FROM AUTHOR]

We propose a unified convergence analysis of the generalized Schwarz method applied to a linear elliptic problem for a general interface (flat, cylindrical or spherical) in any dimension. In particular, we provide the exact convergence set of the interface symbols related to the operators involved in the transmission conditions. We also provide a general procedure to obtain estimates of the optimized interface symbols within the constants. We apply such general results to a simple fluid-structure interaction model problem given by the interaction between an incompressible, inviscid fluid and the wave equation. Finally, we assess the effectiveness of the theoretical findings through three-dimensional numerical experiments in the haemodynamic context, obtained by solving the coupling between the Navier-Stokes equations and the linear infinitesimal elasticity. [ABSTRACT FROM AUTHOR]

Estimation of the stiffness of a biological soft tissue is useful for the detection of pathologies such as tumors or atherosclerotic plaques. Elastography is a method based on the comparison between two images before and after a forced deformation of the tissue of interest. An inverse elasticity problem is then solved for Young's modulus estimation. In the case of arteries. no forced deformation is required, since vessels naturally move under the action of blood. Young's modulus can therefore be estimated by solving a coupled inverse fluid-structure interaction problem. In this paper we locus on the mathematical properties of this problem and its numerical solution. We give some well posedness analysis and some preliminary results based on a synthetic data set, i.e., test cases where the exact Young's modulus is known and the displacement dataset is numerically generated by solving a forward fluid-structure interaction problem. We address the problem of the presence of the noise in the measured displacement and of the proper sampling frequency for obtaining reliable estimates. [ABSTRACT FROM AUTHOR]

In the solution of fluid-structure interaction (FSI) problems, partitioned procedures are modular algorithms that involve separate fluid and structure solvers that interact ill an iterative framework through the exchange of suitable transmission conditions at the FS interface. In this work we study, using Fourier analysis, the convergence of partitioned algorithms based on Robin transmission conditions. We derive, for different models of the fluid and the structure, a frequency-dependent reduction factor at each iteration of the partitioned algorithm, which is minimized by choosing optimal values of the coefficients in the Robin transmission conditions. Two-dimensional numerical results are also reported, which highlight the effectiveness of the optimization procedure. [ABSTRACT FROM AUTHOR]

Pulmonary valve replacement (PVR) consists of substituting a patient's original valve with a prosthetic one, primarily addressing pulmonary valve insufficiency, which is crucially relevant in Tetralogy of Fallot repairment. While extensive clinical and computational literature on aortic and mitral valve replacements is available, PVR's post‐procedural haemodynamics in the pulmonary artery and the impact of prosthetic valve dynamics remain significantly understudied. Addressing this gap, we introduce a reduced Fluid–Structure Interaction (rFSI) model, applied for the first time to the pulmonary valve. This model couples a three‐dimensional computational representation of pulmonary artery haemodynamics with a one‐degree‐of‐freedom model to account for valve structural mechanics. Through this approach, we analyse patient‐specific haemodynamics pre and post PVR. Patient‐specific geometries, reconstructed from CT scans, are virtually equipped with a template valve geometry. Boundary conditions for the model are established using a lumped‐parameter model, fine‐tuned based on clinical patient data. Our model accurately reproduces patient‐specific haemodynamic changes across different scenarios: pre‐PVR, six months post‐PVR, and a follow‐up condition after a decade. It effectively demonstrates the impact of valve implantation on sustaining the diastolic pressure gradient across the valve. The numerical results indicate that our valve model is able to reproduce overall physiological and/or pathological conditions, as preliminary assessed on two different patients. This promising approach provides insights into post‐PVR haemodynamics and prosthetic valve effects, shedding light on potential implications for patient‐specific outcomes. [ABSTRACT FROM AUTHOR]

We consider the two-dimensional numerical approximation of the fluid-structure interaction problem over unfitted fluid and structure meshes. In particular, we consider a method where the fluid mesh (on the background) is fixed, apart from the interface with the moving immersed structure, where general polygonal elements of arbitrary shape and changing in time are generated. The new idea of this work is to handle the discretization on such polygons by using the Discontinuous Galerkin method on polyhedral grids (PolyDG), which has been recently developed for different differential equations and here adapted for the first time to a heterogeneous problem. We prove a stability result of the proposed semi-discrete formulation and discuss how to deal with the partial or total covering of a fluid mesh element due to the structure movement. We finally present some numerical results with the aim of showing the effectiveness of the proposed method. • We present a new method based on the Discontinuous Galerkin method for polygonal elements for the interaction of a fluid with an immersed structure. • High order approximations are easily obtained by considering a modal basis functions directly in the physical frame configuration. • We provide a stability analysis of the discretized-in-space formulation. • We present several numerical results with the aim of assessing the validity of the proposed method. • These results show the ability of the method even with very small dimension of mesh elements and very anisotropic elements. [ABSTRACT FROM AUTHOR]

In this paper we consider the numerical solution of the three-dimensional fluid-structure interaction problem in haemodynamics, in the case of real geometries, physiological data and finite elasticity vessel deformations. We study some new inexact schemes, obtained from semi-implicit approximations, which treat exactly the physical interface conditions while performing just one or few iterations for the management of the interface position and of the fluid and structure non-linearities. We show that such schemes allow to improve the efficiency while preserving the accuracy of the related exact (implicit) scheme. To do this we consider both a simple analytical test case and two real cases of clinical interest in haemodynamics. We also provide an error analysis for a simple differential model problem when a BDF method is considered for the time discretization and only few Newton iterations are performed at each temporal instant. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we consider the numerical solution of the interaction of an incompressible fluid and an elastic structure in a truncated computational domain. As well known, in this case there is the problem of prescribing realistic boundary data on the artificial sections, when only partial data are available. This problem has been investigated extensively for the rigid case. In this work we start considering the compliant case, by focusing on the flow rate conditions for the fluid. We propose three formulations of this problem, different algorithms for its numerical solution and carry out several 2D numerical simulations with the aim of comparing the performances of the different algorithms. [Copyright &y& Elsevier]

Abstract: In this work, we propose a Robin–Robin preconditioner combined with Krylov iterations for the solution of the interface system arising in fluid–structure interaction (FSI) problems. It can be seen as a partitioned FSI procedure and in this respect it generalizes the ideas introduced in [S. Badia, F. Nobile, C. Vergara, J. Comput. Phys. 227 (2008) 7027–7051]. We analyze the convergence of GMRES iterations with the Robin–Robin preconditioner on a model problem and compare its efficiency with some existing algorithms. The method is shown to be very efficient for many challenging fluid–structure interaction problems, such as those characterized by a large added-mass effect or by enclosed fluids. In particular, the possibility to solve balloon-type problems without any special treatment makes this algorithm very appealing compared to the computationally intensive existing approaches. [Copyright &y& Elsevier]

Abstract: In this article we design new partitioned procedures for fluid–structure interaction problems, based on Robin-type transmission conditions. The choice of the coefficient in the Robin conditions is justified via simplified models. The strategy is effective whenever an incompressible fluid interacts with a relatively thin membrane, as in hemodynamics applications. We analyze theoretically the new iterative procedures on a model problem, which represents a simplified blood-vessel system. In particular, the Robin–Neumann scheme exhibits enhanced convergence properties with respect to the existing partitioned procedures. The theoretical results are checked using numerical experimentation. [Copyright &y& Elsevier]

We present a loosely coupled scheme for the numerical simulation of the cardiac electro-fluid-structure interaction problem, whose solution is typically computationally intensive due to the need to suitably treat the coupling of the different submodels. Our scheme relies on a segregated treatment of the subproblems, in particular on an explicit Robin-Neumann algorithm for the fluid-structure interaction, aiming at reducing the computational burden of numerical simulations. The results, both in an ideal and a realistic cardiac setting, show that the proposed scheme is stable at the regimes typical of cardiac simulations. From a comparison with a scheme with implicit fluid-structure interaction, it emerges that, while conservation properties are not fully preserved, computational times significantly benefit from the explicit scheme. Overall, the explicit discretization represents a good trade-off between accuracy and cost, and is a valuable alternative to implicit schemes for fast large-scale simulations. • We present an explicit scheme for the simulation of cardiac electro-fluid-structure interaction. • The scheme uses Robin-Neumann fluid-structure interface conditions. • We analyze the stability, accuracy and efficiency of the explicit scheme. • The explicit scheme provides a compromise between accuracy and computational cost. [ABSTRACT FROM AUTHOR]