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.

Full-field microscale strain measurements of a nitinol medical device using digital image correlation.

Computational modeling and simulation are commonly used during the development of cardiovascular implants to predict peak strains and strain amplitudes and to estimate the associated durability and fatigue life of these devices. However, simulation validation has historically relied on comparison with surrogate quantities like force and displacement due to barriers to direct strain measurement-most notably, the small spatial scale of these devices. We demonstrate the use of microscale two-dimensional digital image correlation (2D-DIC) to directly characterize full-field surface strains on a nitinol medical device coupon under emulated physiological and hyperphysiological loading. Experiments are performed using a digital optical microscope and a custom, temperature-controlled load frame. Following applicable recommendations from the International DIC Society, hardware and environmental heating studies, noise floor analyses, and in- and out-of-plane rigid body translation studies are first performed to characterize the microscale DIC setup. Uniaxial tension experiments are also performed using a polymeric test specimen to characterize the strain accuracy of the approach up to nominal stains of 5%. Sub-millimeter fields of view and sub-micron displacement accuracies (9nm mean error) are achieved, and systematic (mean) and random (standard deviation) errors in strain are each estimated to be approximately 1,000µÏµ. The system is then demonstrated by acquiring measurements at the root of a 300µm-wide nitinol medical device strut undergoing fixed-free cantilever bending motion. Lüders-like transformation bands are observed originating from the tensile side of the strut that spread toward the neutral axis at an angle of approximately 55°. Despite the inherent limitations of optical microscopy and 2D-DIC, simple and relatively economical setups like that demonstrated herein could provide a practical and accessible solution for characterizing cardiovascular implant micromechanics, validating computational model strain predictions, and guiding the development of next-generation material models for simulating superelastic nitinol.

A CFD-based Kriging surrogate modeling approach for predicting device-specific hemolysis power law coefficients in blood-contacting medical devices.

Most stress-based hemolysis models used in computational fluid dynamics (CFD) are based on an empirical power law correlation between hemolysis generation and the flow-induced stress and exposure time. Empirical model coefficients are typically determined by fitting global hemolysis measurements in simplified blood shearing devices under uniform shear conditions and with well-defined exposure times. CFD simulations using these idealized global empirical coefficients are then performed to predict hemolysis in a medical device with complex hemodynamics. The applicability, however, of this traditional approach of using idealized coefficients for a real device with varying exposure times and non-uniform shear is currently unknown. In this study, we propose a new approach for determining device- and species-specific hemolysis power law coefficients (C, a, and b). The approach consists of calculating multiple hemolysis solutions using different sets of coefficients to map the hemolysis response field in three-dimensional (C, a, b) parameter space. The resultant response field is then compared with experimental data in the same device to determine the coefficients that when incorporated into the locally defined power law model yield correct global hemolysis predictions. We first develop the generalized approach by deriving analytical solutions for simple uniform and non-uniform shear flows (planar Couette flow and circular Poiseuille flow, respectively) that allow us to continuously map the hemolysis solution in (C, a, b) parameter space. We then extend our approach to more practical cases relevant to blood-contacting medical devices by replacing the requirement for an analytical solution in our generalized approach with CFD and Kriging surrogate modeling. Finally, we apply our verified CFD-based Kriging surrogate modeling approach to predict the device- and species-specific power law coefficients for developing laminar flow in a small capillary tube. We show that the resultant coefficients are much different than traditional idealized coefficients obtained from simplified uniform shear experiments and that using such idealized coefficients yields a highly inaccurate prediction of hemolysis that is in error by more than 2000% compared to experiments. Our approach and surrogate modeling framework may be applied to more complex medical devices and readily extended to determine empirical coefficients for other continuum-based models of hemolysis and other forms of flow-induced blood damage (e.g., platelet activation and thrombosis).

Steady Flow in a Patient-Averaged Inferior Vena Cava-Part II: Computational Fluid Dynamics Verification and Validation.

PURPOSE: The embolus trapping performance of inferior vena cava (IVC) filters critically depends on how emboli flow through the IVC and, thereby, on the underlying hemodynamics. Most previous studies of IVC hemodynamics have used computational fluid dynamics (CFD), but few have validated their results by comparing with quantitative experimental measurements of the flow field and none have validated in an anatomical model of the IVC that includes the primary morphological features that influence the hemodynamics (iliac veins, infrarenal curvature, and non-circular vessel cross-section). In this study, we perform verification and validation of CFD simulations in a patient-averaged anatomical model of the IVC. METHODS: Because we are most interested in the fluid dynamics that influence embolus transport and IVC filter embolus trapping, we focus our analyses on the velocity distribution and the amount of swirl and mixing in the infrarenal IVC. A rigorous mesh refinement study is first conducted at the highest flow rate condition to verify the computed solutions. To validate the CFD predictions of the flow patterns, we then compare with particle image velocimetry (PIV) data acquired in the same model in two planes (coronal and sagittal) within the infrarenal IVC at two flow rates corresponding to rest and exercise conditions. RESULTS: Using unstructured hexahedral meshes ranging in size from 800,000 to 102.5 million computational cells, we demonstrate that a coarse mesh may be used to resolve the gross flow patterns and velocity distribution in the IVC. A finer mesh is, however, required to obtain asymptotic mesh convergence of swirl and mixing in the IVC, as quantified by the local normalized helicity, LNH, and the volume-averaged helicity intensity, [Formula: see text]. Based on the results of the mesh refinement study, we use a moderately fine mesh containing approximately 26 million cells for comparison with experimental data. The validation study demonstrates excellent qualitative agreement between CFD predictions and PIV measurements of the velocity field at both conditions. Quantitatively, we show that the global relative comparison error, E, between CFD and PIV ranges from 3 to 11%. By performing sensitivity studies, we demonstrate that the quantitative discrepancy is attributable to a combination of uncertainty in the inlet flow rates and uncertainty associated with precisely aligning the PIV data with the CFD geometry. CONCLUSIONS: Overall, the study demonstrates mesh-convergent CFD simulations that predict IVC flow patterns that agree reasonably well with PIV data, even at exercise conditions where the flow in the IVC is extremely complex.

Steady Flow in a Patient-Averaged Inferior Vena Cava-Part I: Particle Image Velocimetry Measurements at Rest and Exercise Conditions.

PURPOSE: Although many previous computational fluid dynamics (CFD) studies have investigated the hemodynamics in the inferior vena cava (IVC), few studies have compared computational predictions to experimental data, and only qualitative comparisons have been made. Herein, we provide particle image velocimetry (PIV) measurements of flow in a patient-averaged IVC geometry under idealized conditions typical of those used in the preclinical evaluation of IVC filters. METHODS: Measurements are acquired under rest and exercise flow rate conditions in an optically transparent model fabricated using 3D printing. To ensure that boundary conditions are well-defined and to make follow-on CFD validation studies more convenient, fully-developed flow is provided at the inlets (i.e., the iliac veins) by extending them with straight rigid tubing longer than the estimated entrance lengths. Velocity measurements are then obtained at the downstream end of the tubing to confirm Poiseuille inflow boundary conditions. RESULTS: Measurements in the infrarenal IVC reveal that flow profiles are blunter in the sagittal plane (minor axis) than in the coronal plane (major axis). Peak in-plane velocity magnitudes are 4.9 cm/s and 27 cm/s under the rest and exercise conditions, respectively. Flow profiles are less parabolic and exhibit more inflection points at the higher flow rate. Bimodal velocity peaks are also observed in the sagittal plane at the elevated flow condition. CONCLUSIONS: The IVC geometry, boundary conditions, and infrarenal velocity measurements are provided for download on a free and publicly accessible repository at https://doi.org/10.6084/m9.figshare.7198703 . These data will facilitate future CFD validation studies of idealized, in vitro IVC hemodynamics and of similar laminar flows in vascular geometries.

Inter-Laboratory Characterization of the Velocity Field in the FDA Blood Pump Model Using Particle Image Velocimetry (PIV).

PURPOSE: A credible computational fluid dynamics (CFD) model can play a meaningful role in evaluating the safety and performance of medical devices. A key step towards establishing model credibility is to first validate CFD models with benchmark experimental datasets to minimize model-form errors before applying the credibility assessment process to more complex medical devices. However, validation studies to establish benchmark datasets can be cost prohibitive and difficult to perform. The goal of this initiative sponsored by the U.S. Food and Drug Administration is to generate validation data for a simplified centrifugal pump that mimics blood flow characteristics commonly observed in ventricular assist devices. METHODS: The centrifugal blood pump model was made from clear acrylic and included an impeller, with four equally spaced, straight blades, supported by mechanical bearings. Particle Image Velocimetry (PIV) measurements were performed at several locations throughout the pump by three independent laboratories. A standard protocol was developed for the experiments to ensure that the flow conditions were comparable and to minimize systematic errors during PIV image acquisition and processing. Velocity fields were extracted at the pump entrance, blade passage area, back gap region, and at the outlet diffuser regions. A Newtonian blood analog fluid composed of sodium iodide, glycerin, and water was used as the working fluid. Velocity measurements were made for six different pump flow conditions, with the blood-equivalent flow rate ranging between 2.5 and 7 L/min for pump speeds of 2500 and 3500 rpm. RESULTS: Mean intra- and inter-laboratory variabilities in velocity were ~ 10% at the majority of the measurement locations inside the pump. However, the inter-laboratory variability increased to more than ~ 30% in the exit diffuser region. The variability between the three laboratories for the peak velocity magnitude in the diffuser region ranged from 5 to 25%. The bulk velocity field near the impeller changed proportionally with the rotational speed but was relatively unaffected by the pump flow rate. In contrast, flow in the exit diffuser region was sensitive to both the flow rate and the rotational speed. Specifically, at 3500 rpm, the exit jet tilted toward the inner wall of the diffuser at a flow rate of 2.5 L/min, but the jet tilted towards the outer wall when the flow rate was 7 L/min. CONCLUSIONS: Inter-laboratory experimental mean velocity data (and the corresponding variance) were obtained for the FDA pump model and are available for download at https://nciphub.org/wiki/FDA_CFD . Experimental datasets from the inter-laboratory characterization of benchmark flow models, including the blood pump model presented herein and our previous nozzle model, can be used for validating future CFD studies and to collaboratively develop guidelines on best practices for verification, validation, uncertainty quantification, and credibility assessment of CFD simulations in the evaluation of medical devices (e.g. ASME V&V 40 standards working group).

An experimental and computational study of the inferior vena cava hemodynamics under respiratory-induced collapse of the infrarenal IVC.

Inferior vena cava (IVC) filters have been used for over five decades as an alternative to anticoagulation therapy in the treatment of venous thromboembolic disease. However, complications associated with IVC filters remain common. Though many studies have investigated blood flow in the IVC, the effects of respiration-induced IVC collapse have not been evaluated. Our hypothesis is that IVC collapse may have an influence on IVC filter performance. Therefore, we herein investigate the hemodynamics in uncollapsed and collapsed IVC configurations using in vitro flow experiments and computational simulations. Particle image velocimetry (PIV) is used to measure the hemodynamics in an idealized, compliant model of the human IVC made of silicone rubber. Flow is studied under uncollapsed and collapsed scenarios, with the minor diameter of the IVC reduced by 30% in the collapsed state. Both rest and exercise flow conditions are investigated, corresponding to suprarenal flow rates of 2 lpm and 5.5 lpm, respectively. Finite element analysis simulations are carried out in a computational model of the undeformed, idealized IVC to reproduce the 30% collapse configuration and an additional 50% collapse configuration. Computational fluid dynamics (CFD) simulations are then performed to predict the flow in the uncollapsed and collapsed scenarios, and CFD results are compared to the experimental data. The results show that the collapsed states generate a higher velocity jet at the iliac junction that propagates farther into the lumen of the vena cava in comparison to the jet generated in the uncollapsed state. Moreover, 50% collapse of the IVC causes a shift of the jet away from the IVC wall and towards the center of the vena cava lumen. The area of maximum wall shear stress occurs where the jet impacts the wall and is larger in the collapsed scenarios. Secondary flow is also more complex in the collapsed scenarios. Interestingly, this study demonstrates that a small variation in the flow rate distribution between the right and left iliac veins induces significant variations in the flow characteristics. We speculate that asymmetries in the flow may generate unbalanced forces on the IVC wall and on placed IVC filters that could promote filter tilting and migration, although this requires further investigation. If unbalanced forces are present in vivo, the forces should be considered when determining the optimal placement positions and geometric features for IVC filters. Therefore, these findings motivate further investigation of the in vivo hemodynamics in the infrarenal IVC.

Computational predictions of the embolus-trapping performance of an IVC filter in patient-specific and idealized IVC geometries.

Embolus transport simulations are performed to investigate the dependence of inferior vena cava (IVC) filter embolus-trapping performance on IVC anatomy. Simulations are performed using a resolved two-way coupled computational fluid dynamics/six-degree-of-freedom approach. Three IVC geometries are studied: a straight-tube IVC, a patient-averaged IVC, and a patient-specific IVC reconstructed from medical imaging data. Additionally, two sizes of spherical emboli (3 and 5 mm in diameter) and two IVC orientations (supine and upright) are considered. The embolus-trapping efficiency of the IVC filter is quantified for each combination of IVC geometry, embolus size, and IVC orientation by performing 2560 individual simulations. The predicted embolus-trapping efficiencies of the IVC filter range from 10 to 100%, and IVC anatomy is found to have a significant influence on the efficiency results ([Formula: see text]). In the upright IVC orientation, greater secondary flow in the patient-specific IVC geometry decreases the filter embolus-trapping efficiency by 22-30 percentage points compared with the efficiencies predicted in the idealized straight-tube or patient-averaged IVCs. In a supine orientation, the embolus-trapping efficiency of the filter in the idealized IVCs decreases by 21-90 percentage points compared with the upright orientation. In contrast, the embolus-trapping efficiency is insensitive to IVC orientation in the patient-specific IVC. In summary, simulations predict that anatomical features of the IVC that are often neglected in the idealized models used for benchtop testing, such as iliac vein compression and anteroposterior curvature, generate secondary flow and mixing in the IVC and influence the embolus-trapping efficiency of IVC filters. Accordingly, inter-subject variability studies and additional embolus transport investigations that consider patient-specific IVC anatomy are recommended for future work.

FDA Benchmark Medical Device Flow Models for CFD Validation.

Computational fluid dynamics (CFD) is increasingly being used to develop blood-contacting medical devices. However, the lack of standardized methods for validating CFD simulations and blood damage predictions limits its use in the safety evaluation of devices. Through a U.S. Food and Drug Administration (FDA) initiative, two benchmark models of typical device flow geometries (nozzle and centrifugal blood pump) were tested in multiple laboratories to provide experimental velocities, pressures, and hemolysis data to support CFD validation. In addition, computational simulations were performed by more than 20 independent groups to assess current CFD techniques. The primary goal of this article is to summarize the FDA initiative and to report recent findings from the benchmark blood pump model study. Discrepancies between CFD predicted velocities and those measured using particle image velocimetry most often occurred in regions of flow separation (e.g., downstream of the nozzle throat, and in the pump exit diffuser). For the six pump test conditions, 57% of the CFD predictions of pressure head were within one standard deviation of the mean measured values. Notably, only 37% of all CFD submissions contained hemolysis predictions. This project aided in the development of an FDA Guidance Document on factors to consider when reporting computational studies in medical device regulatory submissions. There is an accompanying podcast available for this article. Please visit the journal's Web site (www.asaiojournal.com) to listen.

A resolved two-way coupled CFD/6-DOF approach for predicting embolus transport and the embolus-trapping efficiency of IVC filters.

Inferior vena cava (IVC) filters are medical devices designed to provide a mechanical barrier to the passage of emboli from the deep veins of the legs to the heart and lungs. Despite decades of development and clinical use, IVC filters still fail to prevent the passage of all hazardous emboli. The objective of this study is to (1) develop a resolved two-way computational model of embolus transport, (2) provide verification and validation evidence for the model, and (3) demonstrate the ability of the model to predict the embolus-trapping efficiency of an IVC filter. Our model couples computational fluid dynamics simulations of blood flow to six-degree-of-freedom simulations of embolus transport and resolves the interactions between rigid, spherical emboli and the blood flow using an immersed boundary method. Following model development and numerical verification and validation of the computational approach against benchmark data from the literature, embolus transport simulations are performed in an idealized IVC geometry. Centered and tilted filter orientations are considered using a nonlinear finite element-based virtual filter placement procedure. A total of 2048 coupled CFD/6-DOF simulations are performed to predict the embolus-trapping statistics of the filter. The simulations predict that the embolus-trapping efficiency of the IVC filter increases with increasing embolus diameter and increasing embolus-to-blood density ratio. Tilted filter placement is found to decrease the embolus-trapping efficiency compared with centered filter placement. Multiple embolus-trapping locations are predicted for the IVC filter, and the trapping locations are predicted to shift upstream and toward the vessel wall with increasing embolus diameter. Simulations of the injection of successive emboli into the IVC are also performed and reveal that the embolus-trapping efficiency decreases with increasing thrombus load in the IVC filter. In future work, the computational tool could be used to investigate IVC filter design improvements, the effect of patient anatomy on embolus transport and IVC filter embolus-trapping efficiency, and, with further development and validation, optimal filter selection and placement on a patient-specific basis.

The Importance of Hemorheology and Patient Anatomy on the Hemodynamics in the Inferior Vena Cava.

Inferior vena cava (IVC) filters have been used for nearly half a century to prevent pulmonary embolism in at-risk patients. However, complications with IVC filters remain common. In this study, we investigate the importance of considering the hemorheological and morphological effects on IVC hemodynamics by simulating Newtonian and non-Newtonian blood flow in three IVC models with varying levels of geometric idealization. Partial occlusion by an IVC filter and a thrombus is also considered. More than 99% of the infrarenal IVC volume is found to contain flow in the nonlinear region of the shear rate-viscosity curve for blood (less than 100 s-1) in the unoccluded IVCs. Newtonian simulations performed using the asymptotic viscosity for blood over-predict the non-Newtonian Reynolds numbers by more than a factor of two and under-predict the mean wall shear stress (WSS) by 28-54%. Agreement with the non-Newtonian simulations is better using a characteristic viscosity, but local WSS errors are still large (up to 50%) in the partially occluded cases. Secondary flow patterns in the IVC also depend on the viscosity model and IVC morphological complexity. Non-Newtonian simulations required only a marginal increase in computational expense compared with the Newtonian simulations. We recommend that future studies of IVC hemodynamics consider the effects of hemorheology and IVC morphology when accurate predictions of WSS and secondary flow features are desired.

A computational method for predicting inferior vena cava filter performance on a patient-specific basis.

A computational methodology for simulating virtual inferior vena cava (IVC) filter placement and IVC hemodynamics was developed and demonstrated in two patient-specific IVC geometries: a left-sided IVC and an IVC with a retroaortic left renal vein. An inverse analysis was performed to obtain the approximate in vivo stress state for each patient vein using nonlinear finite element analysis (FEA). Contact modeling was then used to simulate IVC filter placement. Contact area, contact normal force, and maximum vein displacements were higher in the retroaortic IVC than in the left-sided IVC (144 mm(2), 0.47 N, and 1.49 mm versus 68 mm(2), 0.22 N, and 1.01 mm, respectively). Hemodynamics were simulated using computational fluid dynamics (CFD), with four cases for each patient-specific vein: (1) IVC only, (2) IVC with a placed filter, (3) IVC with a placed filter and model embolus, all at resting flow conditions, and (4) IVC with a placed filter and model embolus at exercise flow conditions. Significant hemodynamic differences were observed between the two patient IVCs, with the development of a right-sided jet, larger flow recirculation regions, and lower maximum flow velocities in the left-sided IVC. These results support further investigation of IVC filter placement and hemodynamics on a patient-specific basis.