Laminar, Turbulent, and Transitional Simulations in Benchmark Cases with Cardiovascular Device Features

Simulation of the FDA nozzle benchmark: A lattice Boltzmann study

BACKGROUND AND OBJECTIVE

Contrary to flows in small intracranial vessels, many blood flow configurations such as those found in aortic vessels and aneurysms involve larger Reynolds numbers and, therefore, transitional or turbulent conditions. Dealing with such systems require both robust and efficient numerical methods.

METHODS

We assess here the performance of a lattice Boltzmann solver with full Hermite expansion of the equilibrium and central Hermite moments collision operator at higher Reynolds numbers, especially for under-resolved simulations. To that end the food and drug administration's benchmark nozzle is considered at three different Reynolds numbers covering all regimes: (1) laminar at a Reynolds number of 500, (2) transitional at a Reynolds number of 3500, and (3) low-level turbulence at a Reynolds number of 6500.

RESULTS

The lattice Boltzmann results are compared with previously published inter-laboratory experimental data obtained by particle image velocimetry. Our results show good agreement with the experimental measurements throughout the nozzle, demonstrating the good performance of the solver even in under-resolved simulations.

CONCLUSION

In this manner, fast but sufficiently accurate numerical predictions can be achieved for flow configurations of practical interest regarding medical applications.

Computational Prediction of Thrombosis in Food and Drug Administration's Benchmark Nozzle

Thrombosis seriously threatens human cardiovascular health and the safe operation of medical devices. The Food and Drug Administration’s (FDA) benchmark nozzle model was designed to include the typical structure of medical devices. However, the thrombosis in the FDA nozzle has yet not been investigated. The objective of this study is to predict the thrombus formation process in the idealized medical device by coupling computational fluid dynamics and a macroscopic hemodynamic-based thrombus model. We developed the hemodynamic-based thrombus model by considering the effect of platelet consumption. The thrombus model was quantitatively validated by referring to the latest thrombosis experiment, which was performed in a backward-facing step with human blood flow. The same setup was applied in the FDA nozzle to simulate the thrombus formation process. The thrombus shaped like a ring was firstly observed in the FDA benchmark nozzle. Subsequently, the accuracy of the shear-stress transport turbulence model was confirmed in different turbulent flow conditions. Five scenarios with different Reynolds numbers were carried out. We found that turbulence could change the shape of centrosymmetric thrombus to axisymmetric and high Reynolds number blood flow would delay or even prevent thrombosis. Overall, the present study reports the thrombosis process in the FDA benchmark nozzle using the numerical simulation method, and the primary findings may shed light on the effect of turbulence on thrombosis.

The effect of turbulence modelling on the assessment of platelet activation

Pathological platelet activation by abnormal shear stresses is regarded as a main clinical complication in recipients of cardiovascular mechanical devices. In order to improve their performance computational fluid dynamics (CFD) are used to evaluate flow fields and related shear stresses. CFD models are coupled with mathematical models that describe the relation between fluid dynamics variables, and in particular shear stresses, and the platelet activation state (PAS). These models typically use a Lagrangian approach to compute the shear stresses along possible platelet trajectories. However, in the case of turbulent flow, the choice of the proper turbulence closure is still debated for both concerning its effect on shear stress calculation and Lagrangian statistics. In this study different numerical simulations of the flow through a mechanical heart valve were performed and then compared in terms of Eulerian and Lagrangian quantities: a direct numerical simulation (DNS), a large eddy simulation (LES), two Reynolds-averaged Navier-Stokes (RANS) simulations (SST k-ω and RSM) and a "laminar" (no turbulence modelling) simulation. Results exhibit a large variability in the PAS assessment depending on the turbulence model adopted. "Laminar" and RSM estimates of platelet activation are about 60% below DNS, while LES is 16% less. Surprisingly, PAS estimated from the SST k- ω velocity field is only 8% less than from DNS data. This appears more artificial than physical as can be inferred after comparing frequency distributions of PAS and of the different Lagrangian variables of the mechano-biological model of platelet activation. Our study indicates how much turbulence closures may affect platelet activation estimates, in comparison to an accurate DNS, when assessing blood damage in blood contacting devices.

The effects of non-Newtonian blood modeling and pulsatility on hemodynamics in the food and drug administration's benchmark nozzle model

BACKGROUND

Computational fluid dynamics (CFD) is an important tool for predicting cardiovascular device performance. The FDA developed a benchmark nozzle model in which experimental and CFD data were compared, however, the studies were limited by steady flows and Newtonian models.

OBJECTIVE

Newtonian and non-Newtonian blood models will be compared under steady and pulsatile flows to evaluate their influence on hemodynamics in the FDA nozzle.

METHODS

CFD simulations were validated against the FDA data for steady flow with a Newtonian model. Further simulations were performed using Newtonian and non-Newtonian models under both steady and pulsatile flows.

RESULTS

CFD results were within the experimental standard deviations at nearly all locations and Reynolds numbers. The model differences were most evident at Re = 500, in the recirculation regions, and during diastole. The non-Newtonian model predicted blunter upstream velocity profiles, higher velocities in the throat, and differences in the recirculation flow patterns. The non-Newtonian model also predicted a greater pressure drop at Re = 500 with minimal differences observed at higher Reynolds numbers.

CONCLUSIONS

An improved modeling framework and validation procedure were used to further investigate hemodynamics in geometries relevant to cardiovascular devices and found that accounting for blood's non-Newtonian and pulsatile behavior can lead to large differences in predictions in hemodynamic parameters.

Flow Structures on a Planar Food and Drug Administration (FDA) Nozzle at Low and Intermediate Reynolds Number

In this paper, we present a general description of the flow structures inside a two-dimensional Food and Drug Administration (FDA) nozzle. To this aim, we have performed numerical simulations using the numerical code Nek5000. The topology patters of the solution obtained, identify four different flow regimes when the flow is steady, where the symmetry of the flow breaks down. An additional case has been studied at higher Reynolds number, when the flow is unsteady, finding a vortex street distributed along the expansion pipe of the geometry. Linear stability analysis identifies the evolution of two steady and two unsteady modes. The results obtained have been connected with the changes in the topology of the flow. Finally, higher-order dynamic mode decomposition has been applied to identify the main flow structures in the unsteady flow inside the FDA nozzle. The highest-amplitude dynamic mode decomposition (DMD) modes identified by the method model the vortex street in the expansion of the geometry.

Modern discontinuous Galerkin methods for the simulation of transitional and turbulent flows in biomedical engineering: A comprehensive LES study of the FDA benchmark nozzle model

This work uses high-order discontinuous Galerkin discretization techniques to simulate transitional and turbulent flows through medical devices. Flows through medical devices are characterized by moderate Reynolds numbers and typically involve different flow regimes such as laminar, transitional, and turbulent flows. Previous studies for the FDA benchmark nozzle model revealed limitations of Reynolds-averaged Navier-Stokes turbulence models when applied to more complex flow scenarios. Recent works based on large-eddy simulation approaches indicate that these limitations can be overcome but also highlight potential limitations due to a high sensitivity with respect to numerical parameters. The methodology presented in this work introduces two novel ingredients compared with previous studies. Firstly, we use high-order discontinuous Galerkin methods for discretization in space. The inherent dissipation and dispersion properties of high-order discontinuous Galerkin discretizations are expected to render this approach well suited for transitional and turbulent flow simulations. Secondly, to mimic blinded CFD studies, we propose to use a precursor simulation approach in order to predict the inflow boundary condition for laminar, transitional, and turbulent flow regimes instead of prescribing analytical velocity profiles at the inflow. We investigate the whole range of Reynolds numbers as suggested by the FDA benchmark nozzle problem and compare the numerical results to experimental data obtained by particle image velocimetry in order to critically assess the predictive capabilities of the solver on the one hand and the suitability of the FDA nozzle problem as a benchmark in computational fluid dynamics on the other hand.

The FDA nozzle benchmark: "In theory there is no difference between theory and practice, but in practice there is"

The utility of flow simulations relies on the robustness of computational fluid dynamics (CFD) solvers and reproducibility of results. The aim of this study was to validate the Oasis CFD solver against in vitro experimental measurements of jet breakdown location from the FDA nozzle benchmark at Reynolds number 3500, which is in the particularly challenging transitional regime. Simulations were performed on meshes consisting of 5, 10, 17, and 28 million (M) tetrahedra, with Δt  =  10^-5 seconds. The 5M and 10M simulation jets broke down in reasonable agreement with the experiments. However, the 17M and 28M simulation jets broke down further downstream. But which of our simulations are "correct"? From a theoretical point of view, they are all wrong because the jet should not break down in the absence of disturbances. The geometry is axisymmetric with no geometrical features that can generate angular velocities. A stable flow was supported by linear stability analysis. From a physical point of view, a finite amount of "noise" will always be present in experiments, which lowers transition point. To replicate noise numerically, we prescribed minor random angular velocities (approximately 0.31%), much smaller than the reported flow asymmetry (approximately 3%) and model accuracy (approximately 1%), at the inlet of the 17M simulation, which shifted the jet breakdown location closer to the measurements. Hence, the high-resolution simulations and "noise" experiment can potentially explain discrepancies in transition between sometimes "sterile" CFD and inherently noisy "ground truth" experiments. Thus, we have shown that numerical simulations can agree with experiments, but for the wrong reasons.

Use of the FDA nozzle model to illustrate validation techniques in computational fluid dynamics (CFD) simulations

A "credible" computational fluid dynamics (CFD) model has the potential to provide a meaningful evaluation of safety in medical devices. One major challenge in establishing "model credibility" is to determine the required degree of similarity between the model and experimental results for the model to be considered sufficiently validated. This study proposes a "threshold-based" validation approach that provides a well-defined acceptance criteria, which is a function of how close the simulation and experimental results are to the safety threshold, for establishing the model validity. The validation criteria developed following the threshold approach is not only a function of Comparison Error, E (which is the difference between experiments and simulations) but also takes in to account the risk to patient safety because of E. The method is applicable for scenarios in which a safety threshold can be clearly defined (e.g., the viscous shear-stress threshold for hemolysis in blood contacting devices). The applicability of the new validation approach was tested on the FDA nozzle geometry. The context of use (COU) was to evaluate if the instantaneous viscous shear stress in the nozzle geometry at Reynolds numbers (Re) of 3500 and 6500 was below the commonly accepted threshold for hemolysis. The CFD results ("S") of velocity and viscous shear stress were compared with inter-laboratory experimental measurements ("D"). The uncertainties in the CFD and experimental results due to input parameter uncertainties were quantified following the ASME V&V 20 standard. The CFD models for both Re = 3500 and 6500 could not be sufficiently validated by performing a direct comparison between CFD and experimental results using the Student's t-test. However, following the threshold-based approach, a Student's t-test comparing |S-D| and |Threshold-S| showed that relative to the threshold, the CFD and experimental datasets for Re = 3500 were statistically similar and the model could be considered sufficiently validated for the COU. However, for Re = 6500, at certain locations where the shear stress is close the hemolysis threshold, the CFD model could not be considered sufficiently validated for the COU. Our analysis showed that the model could be sufficiently validated either by reducing the uncertainties in experiments, simulations, and the threshold or by increasing the sample size for the experiments and simulations. The threshold approach can be applied to all types of computational models and provides an objective way of determining model credibility and for evaluating medical devices.

About the numerical robustness of biomedical benchmark cases: Interlaboratory FDA's idealized medical device

The need for reliable approaches in numerical simulations stands out as a critical issue for the development and optimization of cardiovascular biomedical devices. This led the US Food and Drug Administration to undertake a programme of validation of computational fluid dynamics methods for transitional and turbulent flows. In the current investigation, large-eddy simulation is used to simulate the flow in the first benchmark medical device, and results are confronted to the existing laboratory experiments. This idealized medical device has the particularity to feature transition to turbulence after a sudden expansion. The effects of numerical parameters and low-level inlet perturbations are investigated. Results indicate a considerable impact of numerical aspects on the prediction of the location of the transition to turbulence. The study also demonstrates that injecting small perturbations at the inflow greatly improves the streamwise velocity estimation in the transition region and substantially contributes to the robustness of the flow statistical data. Copyright © 2016 John Wiley & Sons, Ltd.

Computational fluid dynamics in the microcirculation and microfluidics: what role can the lattice Boltzmann method play?

Patient-specific simulations, efficient parametric analyses, and the study of complex processes that are otherwise experimentally intractable are facilitated through the use of Computational Fluid Dynamics (CFD) to study biological flows. This review discusses various CFD methodologies that have been applied across different biological scales, from cell to organ level. Through this discussion the lattice Boltzmann method (LBM) is highlighted as an emerging technique capable of efficiently simulating fluid problems across the midrange of scales; providing a practical analytical tool compared to methods more attuned to the extremities of scale. Furthermore, the merits of the LBM are highlighted through examples of previous applications and suggestions for future research are made. The review focusses on applications in the midrange bracket, such as cell-cell interactions, the microcirculation, and microfluidic devices; wherein the inherent mesoscale nature of the LBM renders it well suited to the incorporation of fluid-structure interaction effects, molecular/particle interactions and interfacial dynamics. The review demonstrates that the LBM has the potential to become a valuable tool across a range of emerging areas in bio-CFD, such as understanding and predicting disease, designing lab-on-a-chip devices, and elucidating complex biological processes.