Shape optimization of pulsatile ventricular assist devices using FSI to minimize thrombotic risk

In this paper we perform shape optimization of a pediatric pulsatile ventricular assist device (PVAD). The device simulation is carried out using fluid–structure interaction (FSI) modeling techniques within a computational framework that combines FEM for fluid mechanics and isogeometric analysis for structural mechanics modeling. The PVAD FSI simulations are performed under realistic conditions (i.e., flow speeds, pressure levels, boundary conditions, etc.), and account for the interaction of air, blood, and a thin structural membrane separating the two fluid subdomains. The shape optimization study is designed to reduce thrombotic risk, a major clinical problem in PVADs. Thrombotic risk is quantified in terms of particle residence time in the device blood chamber. Methods to compute particle residence time in the context of moving spatial domains are presented in a companion paper published in the same issue (Comput Mech, doi:10.1007/s00466-013-0931-y, 2013). The surrogate management framework, a derivative-free pattern search optimization method that relies on surrogates for increased efficiency, is employed in this work. For the optimization study shown here, particle residence time is used to define a suitable cost or objective function, while four adjustable design optimization parameters are used to define the device geometry. The FSI-based optimization framework is implemented in a parallel computing environment, and deployed with minimal user intervention. Using five SEARCH/POLL steps the optimization scheme identifies a PVAD design with significantly better throughput efficiency than the original device.     

A combined fluid–structure interaction and multi–field scalar transport model for simulating mass transport in biomechanics

Mass transport processes are known to play an important role in many fields of biomechanics such as respiratory, cardiovascular, and biofilm mechanics. In this paper, we present a novel computational model considering the effect of local solid deformation and fluid flow on mass transport. As the transport processes are assumed to influence neither structure deformation nor fluid flow, a sequential one‐way coupling of a fluid–structure interaction (FSI) and a multi‐field scalar transport model is realized. In each time step, first the non‐linear monolithic FSI problem is solved to determine current local deformations and velocities. Using this information, the mass transport equations can then be formulated on the deformed fluid and solid domains. At the interface, concentrations are related depending on the interfacial permeability. First numerical examples demonstrate that the proposed approach is suitable for simulating convective and diffusive scalar transport on coupled, deformable fluid and solid domains. Copyright © 2014 John Wiley & Sons, Ltd.     

Immersed smoothed finite element method for fluid–structure interaction simulation of aortic valves

This paper presents a novel numerical method for simulating the fluid?Cstructure interaction (FSI) problems when blood flows over aortic valves. The method uses the immersed boundary/element method and the smoothed finite element method and hence it is termed as IS-FEM. The IS-FEM is a partitioned approach and does not need a body-fitted mesh for FSI simulations. It consists of three main modules: the fluid solver, the solid solver and the FSI force solver. In this work, the blood is modeled as incompressible viscous flow and solved using the characteristic-based-split scheme with FEM for spacial discretization. The leaflets of the aortic valve are modeled as Mooney-Rivlin hyperelastic materials and solved using smoothed finite element method (or S-FEM). The FSI force is calculated on the Lagrangian fictitious fluid mesh that is identical to the moving solid mesh. The octree search and neighbor-to-neighbor schemes are used to detect efficiently the FSI pairs of fluid and solid cells. As an example, a 3D idealized model of aortic valve is modeled, and the opening process of the valve is simulated using the proposed IS-FEM. Numerical results indicate that the IS-FEM can serve as an efficient tool in the study of aortic valve dynamics to reveal the details of stresses in the aortic valves, the flow velocities in the blood, and the shear forces on the interfaces. This tool can also be applied to animal models studying disease processes and may ultimately translate to a new adaptive methods working with magnetic resonance images, leading to improvements on diagnostic and prognostic paradigms, as well as surgical planning, in the care of patients.     

Immersed-boundary/soft-sphere method for particle–particle-fluid interaction in a viscous flow: An OpenFOAM solver

We developed a stable OpenFOAM solver for Immersed Boundary Method based on direct forcing and regularized delta function. The soft-sphere model and a lubrication model were implemented to consider particle–particle collision in a viscous flow. We proposed a fluid–structure interaction (FSI) coupling method to accurately calculate the fluid forcing term and particle velocity. Our solver was validated for fixed and moving bodies, including rotation. The accuracy of various FSI schemes was evaluated in predicting the solid and fluid flow behavior in a viscous flow. It was demonstrated that neglecting or simplifying the fluid momentum change affects the accuracy of the solid velocity and fluid flow dynamic; for higher solid-to-fluid density ratios, a larger deviation was predicted. Furthermore, the FSI schemes highly influenced the behavior of the formed vortices.The solver was validated to predict the effective restitution coefficient of particles in a viscous flow as a function of the Stokes number. We also thoroughly analyzed the dynamic flow behavior of colliding particles through the pressure and velocity field and fluid force. This analysis helped us accurately determine the rebound velocity of particles in case of high Stokes numbers when the effect of viscous force is significant.     

Unified fractional step method for Lagrangian analysis of quasi‐incompressible fluid and nonlinear structure interaction using the PFEM

The fractional step method (FSM) is an efficient solution technique for the particle finite element method, a Lagrangian‐based approach to simulate fluid–structure interaction (FSI). Despite various refinements, the applicability of the FSM has been limited to low viscosity flow and FSI simulations with a small number of equations along the fluid–structure interface. To overcome these limitations, while incorporating nonlinear response in the structural domain, an FSM that unifies structural and fluid response in the discrete governing equations is developed using the quasi‐incompressible formulation. With this approach, fluid and structural particles do not need to be treated separately, and both domains are unified in the same system of equations. Thus, the equations along the fluid–structure interface do not need to be segregated from the fluid and structural domains. Numerical examples compare the unified FSM with the non‐unified FSM and show that the computational cost of the proposed method overcomes the slow convergence of the non‐unified FSM for high values of viscosity. As opposed to the non‐unified FSM, the number of iterations required for convergence with the unified FSM becomes independent of viscosity and time step, and the simulation run time does not depend on the size of the FSI interface. Copyright © 2016 John Wiley & Sons, Ltd.     

Fluid–structure interaction simulation of pulsatile ventricular assist devices

In this paper we present a collection of fluid–structure interaction (FSI) computational techniques that enable realistic simulation of pulsatile Ventricular Assist Devices (VADs). The simulations involve dynamic interaction of air, blood, and a thin membrane separating the two fluids. The computational challenges addressed in this work include large, buckling motions of the membrane, the need for periodic remeshing of the fluid mechanics domain, and the necessity to employ tightly coupled FSI solution strategies due to the very strong added mass effect present in the problem. FSI simulation of a pulsatile VAD at realistic operating conditions is presented for the first time. The FSI methods prove to be robust, and may be employed in the assessment of current, and the development of future, pulsatile VAD designs.     

Absorbing boundary conditions for a 3D non-Newtonian fluid-structure interaction model for blood flow in arteries

Blood flow in arteries is characterized by pulse pressure waves due to the interaction with the vessel walls. A 3D fluid-structure interaction (FSI) model in a compliant vessel is used to represent the pressure wave propagation. The 3D fluid is described through a shear-thinning generalized Newtonian model and the structure by a nonlinear hyperelastic model. In order to cope with the spurious reflections due to the truncation of the computational domain, several absorbing boundary conditions are analyzed. First, a 1D hyperbolic model that effectively captures the wave propagation nature of blood flow in arteries is coupled with the 3D FSI model. Extending previous results, an energy estimate is derived for the 3D FSI-1D coupling in the case of generalized Newtonian models. Secondly, absorbing boundary conditions obtained from the 1D model are imposed directly on the outflow sections of the 3D FSI model, and numerical results comparing the different absorbing conditions in an idealized vessel are presented. Results in a human carotid bifurcation reconstructed from medical images are also provided in order to show that the proposed methodology can be applied to anatomically realistic geometries.     

FSI analysis of the blood flow and geometrical characteristics in the thoracic aorta

We present a fluid–structure interaction (FSI) analysis of the blood flow and geometrical characteristics in the thoracic aorta. The FSI is handled with the sequentially-coupled arterial FSI technique. The fluid mechanics equations are solved with the ST-VMS method, which is the variational multiscale version of the deforming-spatial-domain/stabilized space–time (DSD/SST) method. We focus on the relationship between the centerline geometry of the aorta and the flow field, which influences the wall shear stress distribution. The centerlines of the aorta models we use in our analysis are extracted from the CT scans, and we assume a constant diameter. Torsion-free model geometries are generated by projecting the original centerline to its averaged plane of curvature. The flow fields for the original and projected geometries are compared to examine the influence of the torsion.     

一种基于压力泊松方程的流体结构紧耦合算法

从流固耦合系统的整体控制方程出发,推导出与流体控制方程一致的耦合等价方程,并得到基于耦合方程的压力泊松方程,通过求解耦合系统压力泊松方程和一致的等价方程就能获得耦合系统的解,而不需要直接求解整体耦合系统的控制方程,有利于降低求解自由度。预估-校正多步迭代格式用于耦合系统的时间推进,克服了传统迭代耦合方法由于时间不同步而产生较大数值误差的不足。应用该方法对附带局部突起的主动脉弓动脉瘤进行流固耦合分析,验证数值方法的可行性。     

Blast response simulation of an elastic structure: Evaluation of the fluid–structure interaction effect

Blast pressure wave interaction with an elastic structure is investigated using a numerical analysis approach, which considers fluid–structure interaction (FSI) within an Arbitrary Lagrange Euler (ALE) framework. Approximate numerical procedures for solving the Riemann problem associated with the shock are implemented within the Godunov finite volume scheme for the fluid domain. The structural displacement predicted by ignoring FSI is larger than the corresponding displacement considering FSI. The influence of the structural and blast pressure wave parameters on the importance of FSI is studied using an analysis of variables. Two non-dimensional parameters corresponding to the ratios of blast duration to the time period of the structure and the velocity of the structure to the particle velocity of the incident blast pressure wave are identified. It is shown that for a given blast pressure wave, the error in the maximum displacement predicted by ignoring FSI effect during structural motion is directly proportional to the ratio of the structure velocity to the particle velocity of the incident blast pressure wave. There is a continuous exchange of energy between the structure and air during the structural motion, which is significant when the structural velocity is significant compared to the particle velocity of incident blast pressure wave. FSI effect become insignificant when the ratio of velocities starts approaching zero.     

Immersed smoothed finite element method for two dimensional fluid–structure interaction problems

A novel method called immersed smoothed FEM using three‐node triangular element is proposed for two‐dimensional fluid–structure interaction (FSI) problems with largely deformable nonlinear solids placed within incompressible viscous fluid. The fluid flows are solved using the semi‐implicit characteristic‐based split method. Smoothed FEMs are employed to calculate the transient responses of solids based on explicit time integration. The fictitious fluid with two assumptions is introduced to achieve the continuous form of the FSI conditions. The discrete formulations to calculate the FSI forces are obtained in terms of the characteristic‐based split scheme, and the algorithm based on a set of fictitious fluid mesh is proposed for evaluating the FSI force exerted on the solid. The accuracy, stability, and convergence properties of immersed smoothed FEM are verified by numerical examples. Investigations on the mesh size ratio indicate that the stability is fairly independent of the wide range of the mesh size ratio. No additional volume correction is required to satisfy the incompressible constraints. Copyright © 2012 John Wiley & Sons, Ltd.     

流固耦合问题的PD-SPH建模与分析

针对涉及结构变形破坏的流固耦合(Fluid-structure interaction, FSI)问题,提出一种基于虚粒子和排斥力的近场动力学(Peridynamics, PD)-光滑粒子动力学(Smoothed particle hydrodynamics, SPH)耦合方法。结合PD方法求解不连续问题以及SPH方法在流体模拟方面的优势,分别采用PD方法与SPH方法求解固体域和流体域,并通过流体粒子-虚粒子接触算法处理流-固界面,既能利用粒子间排斥力有效防止粒子穿透现象发生,又能利用虚粒子修正流体粒子的边界缺陷,提高计算精度。采用PD-SPH耦合方法模拟静水压力作用下的铝板变形问题以及溃坝水流冲击弹性板问题,所得结果与解析解或其它数值结果吻合良好,验证了耦合方法的可行性和有效性。进一步应用耦合方法模拟了流体作用下的结构变形、破坏以及破坏后部分结构运动全过程,验证了PD-SPH耦合方法在流固耦合-结构破坏问题模拟方面的适用性。     

Dynamic and fluid–structure interaction simulations of bioprosthetic heart valves using parametric design with T-splines and Fung-type material models

This paper builds on a recently developed immersogeometric fluid–structure interaction (FSI) methodology for bioprosthetic heart valve (BHV) modeling and simulation. It enhances the proposed framework in the areas of geometry design and constitutive modeling. With these enhancements, BHV FSI simulations may be performed with greater levels of automation, robustness and physical realism. In addition, the paper presents a comparison between FSI analysis and standalone structural dynamics simulation driven by prescribed transvalvular pressure, the latter being a more common modeling choice for this class of problems. The FSI computation achieved better physiological realism in predicting the valve leaflet deformation than its standalone structural dynamics counterpart.     

A computational approach for predicting the hydroelasticity of flexible structures based on the pressure Poisson equation

This work is concerned with the modeling of the interaction of fluid flow with flexible solid structures. The flow under consideration is governed by the Navier–Stokes equations for incompressible viscous fluids and modeled with low‐order velocity–pressure finite elements. The motion of the fluid domain is accounted for by the arbitrary Lagrangian–Eulerian formulation. The structure is represented by means of an appropriate standard finite element formulation. The spring smooth analogy is used to mesh control. The time integrating algorithm is based on the predictor–multi‐corrector algorithm. An important aspect of the present work is the introduction of a new monolithic approach based on the fluid pressure Poisson equation (PPE) to solve the hydroelasticity problem of an incompressible viscous fluid with an elastic body that is vibrating due to flow excitation. The PPE is derived to be consistent with the coupled system equation for the fluid–structure interaction (FSI). Based on this approach, an efficient monolithic method is adopted to simulate hydroelasticity between the flexible structure and the flow. The fluid pressure is implicitly derived to satisfy the incompressibility constraint, and the other unknown variables are explicitly derived. The coefficient matrix of the PPE for the FSI becomes symmetric and positive definite. To demonstrate the performance of the proposed approach, two working examples, a beam immersed in incompressible fluid and a guide vane of a Francis turbine passage, were used. The results show the validity of the proposed approach. Copyright © 2007 John Wiley & Sons, Ltd.     

径向基函数应用于流固耦合分析初探

该文在径向基函数(radial basis function, RBF)及其插值函数研究基础上,构建了基于RBF插值的流固耦合信息传递模型,进一步通过程序编制,在同济大学空间结构自动分析与设计软件—AADS系统中实现了对任一时间步上的流固交互作用分析,并得到与ADINA软件非常吻合的计算结果。算例分析表明:径向基函数可作为一种有效的界面信息传递方法应用于对三维流固耦合问题的研究。     

FSI modeling with the DSD/SST method for the fluid and finite difference method for the structure

We present a fluid–structure interaction (FSI) modeling method based on using the deforming-spatial-domain/stabilized space–time (DSD/SST) method for the fluid mechanics part and a finite difference (FD) method for the structural mechanics part. As the structural mechanics model, we focus on the thin-shell model. The fluid mechanics equations with moving boundaries are solved with the DSD/SST method and the thin-shell structural mechanics equation is solved with a FD method, with partitioned coupling between the two parts. The coupling of the DSD/SST and FD solvers makes sure that the boundary conditions on the fluid-structure interface at the end of each time step are matched between the fluid and the structure. A hanging plate in vacuum under gravitational force is performed to validate the structure solver. In addition, a pitching plate in a uniform flow is simulated to validate the FSI solver. The present results are in reasonable agreement with data predicted by other methods.     

Resolved CFD–DEM coupling simulation using Volume Penalisation method

A resolved CFD–DEM coupling model for the simulation of particulate flows is proposed in this work. The Volume Penalisation (VP) method, which is a family of the continuous forcing Immersed Boundary (IB) method, is employed to express the particle–fluid interaction. A smooth mask function is used to avoid sharp transition between the solid (particle) and fluid domains that may cause numerical oscillation with moving particles. Optimal permeability is employed to reduce the model error associated with the VP method. It is determined as a function of only the interface thickness and fluid kinematic viscosity. The proposed model is accurate, easy to implement with any discretisation scheme, and only requires small computational overhead for particle–fluid interaction. Several simulations are performed to test the validity of the proposed model in various systems, i.e. from dilute to relatively dense flows, and the results show good agreement with the exact solution or empirical correlation. It is found that the error can be scaled with the ratio between the gap and interface thickness. The proposed model is also applied to predict the relative viscosity of suspensions and the density segregation in fluidised beds.     

Multiscale sequentially-coupled arterial FSI technique

Multiscale versions of the Sequentially-Coupled Arterial Fluid–Structure Interaction (SCAFSI) technique are presented. The SCAFSI technique was introduced as an approximate FSI approach in arterial fluid mechanics. It is based on the assumption that the arterial deformation during a cardiac cycle is driven mostly by the blood pressure. First we compute a “reference” arterial deformation as a function of time, driven only by the blood pressure profile of the cardiac cycle. Then we compute a sequence of updates involving mesh motion, fluid dynamics calculations, and recomputing the arterial deformation. The SCAFSI technique was developed and tested in conjunction with the stabilized space–time FSI (SSTFSI) technique. Beyond providing a computationally more economical alternative to the fully coupled arterial FSI approach, the SCAFSI technique brings additional flexibility, such as being able to carry out the computations in a spatially or temporally multiscale fashion. In the test computations reported here for the spatially multiscale versions of the SCAFSI technique, we focus on a patient-specific middle cerebral artery segment with aneurysm, where the arterial geometry is based on computed tomography images. The arterial structure is modeled with the continuum element made of hyperelastic (Fung) material.     

An efficient parallel computation of unsteady incompressible viscous flow with elastic moving and compliant boundaries on unstructured grids

This paper presents the development and validation of a parallel unstructured‐grid fluid–structure interaction (FSI) solver for the simulation of unsteady incompressible viscous flow with long elastic moving and compliant boundaries. The Navier–Stokes solver on unstructured moving grid using the arbitrary Lagrangian Eulerian formulation is based on the artificial compressibility approach and a high‐order characteristics‐based finite‐volume scheme. Both unsteady flow and FSI are calculated with a matrix‐free implicit dual time‐stepping scheme. A membrane model has been formulated to study fluid flow in a channel with an elastic membrane wall and their interactions. This model can be employed to calculate arbitrary wall movement and variable tension along the membrane, together with a dynamic mesh method for large deformation of the flow field. The parallelization of the fluid–structure solver is achieved using the single program multiple data programming paradigm and message passing interface for communication of data. The parallel solver is used to simulate fluid flow in a two‐dimensional channel with and without moving membrane for validation and performance evaluation purposes. The speedups and parallel efficiencies obtained by this method are excellent, using up to 16 processors on a SGI Origin 2000 parallel computer. A maximum speedup of 23.14 could be achieved on 16 processors taking advantage of an improved handling of the membrane solver. The parallel results obtained are compared with those using serial code and they are found to be identical. Copyright © 2005 John Wiley & Sons, Ltd.     

Investigation of fluid–structure interactions using a velocity‐linked P2/P1 finite element method and the generalized‐ α method

A velocity‐linked algorithm for solving unsteady fluid–structure interaction (FSI) problems in a fully coupled manner is developed using the arbitrary Lagrangian–Eulerian method. The P2/P1 finite element is used to spatially discretize the incompressible Navier–Stokes equations and structural equations, and the generalized‐ α method is adopted for temporal discretization. Common velocity variables are employed at the fluid–structure interface for the strong coupling of both equations. Because of the velocity‐linked formulation, kinematic compatibility is automatically satisfied and forcing terms do not need to be calculated explicitly. Both the numerical stability and the convergence characteristics of an iterative solver for the coupled algorithm are investigated by solving the FSI problem of flexible tube flows. It is noteworthy that the generalized‐ α method with small damping is free from unstable velocity fields. However, the convergence characteristics of the coupled system deteriorate greatly for certain Poisson's ratios so that direct solvers are essential for these cases. Furthermore, the proposed method is shown to clearly display the advantage of considering FSI in the simulation of flexible tube flows, while enabling much larger time‐steps than those adopted in some previous studies. This is possible through the strong coupling of the fluid and structural equations by employing common primitive variables. Copyright © 2012 John Wiley & Sons, Ltd.