Experiment for validation of fluid-structure interaction models and algorithms

Multi-Modal in Vitro Experiments Mimicking the Flow Through a Mitral Heart Valve Phantom

PURPOSE

Fluid-structure interaction (FSI) models are more commonly applied in medical research as computational power is increasing. However, understanding the accuracy of FSI models is crucial, especially in the context of heart valve disease in patient-specific models. Therefore, this study aimed to create a multi-modal benchmarking data set for cardiac-inspired FSI models, based on clinically important parameters, such as the pressure, velocity, and valve opening, with an in vitro phantom setup.

METHOD

An in vitro setup was developed with a 3D-printed phantom mimicking the left heart, including a deforming mitral valve. A range of pulsatile flows were created with a computer-controlled motor-and-pump setup. Catheter pressure measurements, magnetic resonance imaging (MRI), and echocardiography (Echo) imaging were used to measure pressure and velocity in the domain. Furthermore, the valve opening was quantified based on cine MRI and Echo images.

RESULT

The experimental setup, with 0.5% cycle-to-cycle variation, was successfully built and six different flow cases were investigated. Higher velocity through the mitral valve was observed for increased cardiac output. The pressure difference across the valve also followed this trend. The flow in the phantom was qualitatively assessed by the velocity profile in the ventricle and by streamlines obtained from 4D phase-contrast MRI.

CONCLUSION

A multi-modal set of data for validation of FSI models has been created, based on parameters relevant for diagnosis of heart valve disease. All data is publicly available for future development of computational heart valve models.

Validation of fluid-structure interaction simulations of the opening phase of phantom mitral heart valves under physiologically inspired conditions

BACKGROUND AND OBJECTIVE

Atrioventricular valve disease is a common cause of heart failure, and successful surgical or interventional outcomes are crucial. Patient-specific fluid-structure interaction (FSI) modeling may provide valuable insights into valve dynamics and guidance of valve repair strategies. However, lack of validation has kept FSI modeling from clinical implementation. Therefore, this study aims to validate FSI simulations against in vitro benchmarking data, based on clinically relevant parameters for evaluating heart valve disease.

METHODS

An FSI model that mimics the left heart was developed. The domain included a deformable mitral valve of different stiffnesses run with different inlet velocities. Five different cases were simulated and compared to in vitro data based on the pressure difference across the valve, the valve opening, and the velocity in the flow domain.

RESULTS

The simulations underestimate the pressure difference across the valve by 6.8-14 % compared to catheter measurements. Evaluation of the valve opening showed an underprediction of 5.4-7.3 % when compared to cine MRI, 2D Echo, and 3D Echo data. Additionally, the simulated velocity through the valve showed a 7.9-8.4 % underprediction in relation to Doppler Echo measurements. Qualitative assessment of the velocity profile in the ventricle and the streamlines of the flow in the domain showed good agreement of the flow behavior.

CONCLUSIONS

Parameters relevant to the diagnosis of heart valve disease estimated by FSI simulations showed good agreement when compared to in vitro benchmarking data, with differences small enough not to affect the grading of heart valve disease. The FSI model is thus deemed good enough for further development toward patient-specific cases.

A sharp interface Lagrangian-Eulerian method for flexible-body fluid-structure interaction

This paper introduces a sharp-interface approach to simulating fluid-structure interaction (FSI) involving flexible bodies described by general nonlinear material models and across a broad range of mass density ratios. This new flexible-body immersed Lagrangian-Eulerian (ILE) scheme extends our prior work on integrating partitioned and immersed approaches to rigid-body FSI. Our numerical approach incorporates the geometrical and domain solution flexibility of the immersed boundary (IB) method with an accuracy comparable to body-fitted approaches that sharply resolve flows and stresses up to the fluid-structure interface. Unlike many IB methods, our ILE formulation uses distinct momentum equations for the fluid and solid subregions with a Dirichlet-Neumann coupling strategy that connects fluid and solid subproblems through simple interface conditions. As in earlier work, we use approximate Lagrange multiplier forces to treat the kinematic interface conditions along the fluid-structure interface. This penalty approach simplifies the linear solvers needed by our formulation by introducing two representations of the fluid-structure interface, one that moves with the fluid and another that moves with the structure, that are connected by stiff springs. This approach also enables the use of multi-rate time stepping, which allows us to use different time step sizes for the fluid and structure subproblems. Our fluid solver relies on an immersed interface method (IIM) for discrete surfaces to impose stress jump conditions along complex interfaces while enabling the use of fast structured-grid solvers for the incompressible Navier-Stokes equations. The dynamics of the volumetric structural mesh are determined using a standard finite element approach to large-deformation nonlinear elasticity via a nearly incompressible solid mechanics formulation. This formulation also readily accommodates compressible structures with a constant total volume, and it can handle fully compressible solid structures for cases in which at least part of the solid boundary does not contact the incompressible fluid. Selected grid convergence studies demonstrate second-order convergence in volume conservation and in the pointwise discrepancies between corresponding positions of the two interface representations as well as between first and second-order convergence in the structural displacements. The time stepping scheme is also demonstrated to yield second-order convergence. To assess and validate the robustness and accuracy of the new algorithm, comparisons are made with computational and experimental FSI benchmarks. Test cases include both smooth and sharp geometries in various flow conditions. We also demonstrate the capabilities of this methodology by applying it to model the transport and capture of a geometrically realistic, deformable blood clot in an inferior vena cava filter.

A Nodal Immersed Finite Element-Finite Difference Method

The immersed finite element-finite difference (IFED) method is a computational approach to modeling interactions between a fluid and an immersed structure. The IFED method uses a finite element (FE) method to approximate the stresses, forces, and structural deformations on a structural mesh and a finite difference (FD) method to approximate the momentum and enforce incompressibility of the entire fluid-structure system on a Cartesian grid. The fundamental approach used by this method follows the immersed boundary framework for modeling fluid-structure interaction (FSI), in which a force spreading operator prolongs structural forces to a Cartesian grid, and a velocity interpolation operator restricts a velocity field defined on that grid back onto the structural mesh. With an FE structural mechanics framework, force spreading first requires that the force itself be projected onto the finite element space. Similarly, velocity interpolation requires projecting velocity data onto the FE basis functions. Consequently, evaluating either coupling operator requires solving a matrix equation at every time step. Mass lumping, in which the projection matrices are replaced by diagonal approximations, has the potential to accelerate this method considerably. This paper provides both numerical and computational analyses of the effects of this replacement for evaluating the force projection and for the IFED coupling operators. Constructing the coupling operators also requires determining the locations on the structure mesh where the forces and velocities are sampled. Here we show that sampling the forces and velocities at the nodes of the structural mesh is equivalent to using lumped mass matrices in the IFED coupling operators. A key theoretical result of our analysis is that if both of these approaches are used together, the IFED method permits the use of lumped mass matrices derived from nodal quadrature rules for any standard interpolatory element. This is different from standard FE methods, which require specialized treatments to accommodate mass lumping with higher-order shape functions. Our theoretical results are confirmed by numerical benchmarks, including standard solid mechanics tests and examination of a dynamic model of a bioprosthetic heart valve.

Application of Dynamic Mode Decomposition to Study Temporal Flow Behavior in a Saccular Aneurysm

Aneurysms are abnormal expansion of weakened blood vessels which can cause mortality or long-term disability upon rupture. Several studies have shown that inflow conditions spatially and temporally influence aneurysm flow behavior. The objective of this investigation is to identify impact of inflow conditions on spatio-temporal flow behavior in an aneurysm using dynamic mode decomposition (DMD). For this purpose, low-frame rate velocity field measurements are performed in an idealized aneurysm model using particle image velocimetry (PIV). The inflow conditions are precisely controlled using a ViVitro SuperPump system where nondimensional fluid parameters such as peak Reynolds number (Rep) and Womersely number (α) are varied from 50-270 and 2-5, respectively. The results show the ability of DMD to identify the spatial flow structures and their frequency content. Furthermore, DMD captured the impact of inflow conditions, and change in mode shapes, amplitudes, frequency, and growth rate information is observed. The DMD low-order flow reconstruction also showed the complex interplay of flow features for each inflow scenario. Furthermore, the low-order reconstruction results provided a mathematical description of the flow behavior in the aneurysm which captured the vortex formation, evolution, and convection in detail. These results indicated that the vortical structure behavior varied with the change in α while its strength and presence of secondary structures are influenced by the change in Rep.

Application of Proper Orthogonal Decomposition to Study Coherent Flow Structures in a Saccular Aneurysm

Aneurysms are localized expansions of weakened blood vessels that can be debilitating or fatal upon rupture. Previous studies have shown that flow in an aneurysm exhibits complex flow structures that are correlated with its inflow conditions. Therefore, the objective of this study was to demonstrate the application of proper orthogonal decomposition (POD) to study the impact of different inflow conditions on energetic flow structures and their temporal behavior in an aneurysm. To achieve this objective, experiments were performed on an idealized rigid sidewall aneurysm model. A piston pump system was used for precise inflow control, i.e., peak Reynolds number (Rep) and Womersley number (α) were varied from 50 to 270 and 2 to 5, respectively. The velocity flow field measurements at the midplane location of the idealized aneurysm model were performed using particle image velocimetry (PIV). The results demonstrate the efficacy of POD in decomposing complex data, and POD was able to capture the energetic flow structures unique to each studied inflow condition. Furthermore, the time-varying coefficient results highlighted the interplay between the coefficients and their corresponding POD modes, which in turn helped explain how POD modes impact certain flow features. The low-order reconstruction results were able to capture the flow evolution and provide information on complex flow in an aneurysm. The POD and low-order reconstruction results also indicated that vortex formation, evolution, and convection varied with an increase in α, while vortex strength and formation of secondary structures were correlated with an increase in Rep.

In Vitro Clot Trapping Efficiency of the FDA Generic Inferior Vena Cava Filter in an Anatomical Model: An Experimental Fluid-Structure Interaction Benchmark

PURPOSE

Robust experimental data for performing validation of fluid-structure interaction (FSI) simulations of the transport of deformable solid bodies in internal flow are currently lacking. This in vitro experimental study characterizes the clot trapping efficiency of a new generic conical-type inferior vena cava (IVC) filter in a rigid anatomical model of the IVC with carefully characterized test conditions, fluid rheological properties, and clot mechanical properties.

METHODS

Various sizes of spherical and cylindrical clots made of synthetic materials (nylon and polyacrylamide gel) and bovine blood are serially injected into the anatomical IVC model under worst-case exercise flow conditions. Clot trapping efficiencies and their uncertainties are then quantified for each combination of clot shape, size, and material.

RESULTS

Experiments reveal the clot trapping efficiency increases with increasing clot diameter and length, with trapping efficiencies ranging from as low as approximately 42% for small 3.2 mm diameter spherical clots up to 100% for larger clot sizes. Because of the asymmetry of the anatomical IVC model, the data also reveal the iliac vein of clot origin influences the clot trapping efficiency, with the trapping efficiency for clots injected into the left iliac vein up to a factor of 7.5 times greater than that for clots injected into the right iliac (trapping efficiencies of approximately 10% versus 75%, respectively).

CONCLUSION

Overall, this data set provides a benchmark for validating simulations predicting IVC filter clot trapping efficiency and, more generally, low-Reynolds number FSI modeling.

Experiments on Flexible Filaments in Air Flow for Aeroelasticity and Fluid-Structure Interaction Models Validation

Several problems in science and engineering are characterized by the interaction between fluid flows and deformable structures. Due to their complex and multidisciplinary nature, these problems cannot normally be solved analytically and experiments are frequently of limited scope, so that numerical simulations represent the main analysis tool. Key to the advancement of numerical methods is the availability of experimental test cases for validation. This paper presents results of an experiment specifically designed for the validation of numerical methods for aeroelasticity and fluid-structure interaction problems. Flexible filaments of rectangular cross-section and various lengths were exposed to air flow of moderate Reynolds number, corresponding to laminar and mildly turbulent flow conditions. Experiments were conducted in a wind tunnel, and the flexible filaments dynamics was recorded via fast video imaging. The structural response of the filaments included static reconfiguration, small-amplitude vibration, large-amplitude limit-cycle periodic oscillation, and large-amplitude non-periodic motion. The present experimental setup was designed to incorporate a rich fluid-structure interaction physics within a relatively simple configuration without mimicking any specific structure, so that the results presented herein can be valuable for models validation in aeroelasticity and also fluid-structure interaction applications.

A class of analytic solutions for verification and convergence analysis of linear and nonlinear fluid-structure interaction algorithms

Fluid-structure interaction (FSI) problems are pervasive in the computational engineering community. The need to address challenging FSI problems has led to the development of a broad range of numerical methods addressing a variety of applicationspecific demands. While a range of numerical and experimental benchmarks are present in the literature, few solutions are available that enable both verification and spatiotemporal convergence analysis. In this paper, we introduce a class of analytic solutions to FSI problems involving shear in channels and pipes. Comprised of 16 separate analytic solutions, our approach is permuted to enable progressive verification and analysis of FSI methods and implementations, in two and three dimensions, for static and transient scenarios as well as for linear and hyperelastic solid materials. Results are shown for a range of analytic models exhibiting progressively complex behavior. The utility of these solutions for analysis of convergence behavior is further demonstrated using a previously published monolithic FSI technique. The resulting class of analytic solutions addresses a core challenge in the development of novel FSI algorithms and implementations, providing a progressive testbed for verification and detailed convergence analysis.

Validation of a non-conforming monolithic fluid-structure interaction method using phase-contrast MRI

This paper details the validation of a non-conforming arbitrary Lagrangian-Eulerian fluid-structure interaction technique using a recently developed experimental 3D fluid-structure interaction benchmark problem. Numerical experiments for steady and transient test cases of the benchmark were conducted employing an inf-sup stable and a general Galerkin scheme. The performance of both schemes is assessed. Spatial refinement with three mesh refinement levels and fluid domain truncation with two fluid domain lengths are studied as well as employing a sequence of increasing time step sizes for steady-state cases. How quickly an approximate steady-state or periodic steady-state is reached is investigated and quantified based on error norm computations. Comparison of numerical results with experimental phase-contrast magnetic resonance imaging data shows very good overall agreement including governing of flow patterns observed in the experiment.