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

Impact of left atrial wall motion assumptions in fluid simulations on proposed predictors of thrombus formation

Atrial fibrillation (AF) poses a significant risk of stroke due to thrombus formation, which primarily occurs in the left atrial appendage (LAA). Medical image-based computational fluid dynamics (CFD) simulations can provide valuable insight into patient-specific hemodynamics and could potentially enhance personalized assessment of thrombus risk. However, the importance of accurately representing the left atrial (LA) wall dynamics has not been fully resolved. In this study, we compared four modeling scenarios; rigid walls, a generic wall motion based on a reference motion, a semi-generic wall motion based on patient-specific motion, and patient-specific wall motion based on medical images. We considered a LA geometry acquired from 4D computed tomography during AF, systematically performed convergence tests to assess the numerical accuracy of our solution strategy, and quantified the differences between the four approaches. The results revealed that wall motion had no discernible impact on LA cavity hemodynamics, nor on the markers that indicate thrombus formation. However, the flow patterns within the LAA deviated significantly in the rigid model, indicating that the assumption of rigid walls may lead to errors in the estimated risk factors. In contrast, the generic, semi-generic, and patient-specific cases were qualitatively similar. The results highlight the crucial role of wall motion on hemodynamics and predictors of thrombus formation, and also demonstrate the potential of using a generic motion model as a surrogate for the more complex patient-specific motion. While the present study considered a single case, the employed CFD framework is entirely open-source and designed for adaptability, allowing for integration of additional models and generic motions.

On the importance of fundamental computational fluid dynamics toward a robust and reliable model of left atrial flows

Computational fluid dynamics (CFD) studies of left atrial flows have reached a sophisticated level, for example, revealing plausible relationships between hemodynamics and stresses with atrial fibrillation. However, little focus has been on fundamental fluid modeling of LA flows. The purpose of this study was to investigate the spatiotemporal convergence, along with the differences between high- (HR) versus normal-resolution/accuracy (NR) solution strategies, respectively. Rigid wall CFD simulations were conducted on 12 patient-specific left atrial geometries obtained from computed tomography scans, utilizing a second-order accurate and space/time-centered solver. The convergence studies showed an average variability of around 30% and 55% for time averaged wall shear stress (WSS), oscillatory shear index (OSI), relative residence time (RRT), and endothelial cell activation potential (ECAP), even between intermediate spatial and temporal resolutions, in the left atrium (LA) and left atrial appendage (LAA), respectively. The comparison between HR and NR simulations showed good correlation in the LA for WSS, RRT, and ECAP (R 2 > .9 ), but not for OSI (R 2 = .63 ). However, there were poor correlations in the LAA especially for OSI, RRT, and ECAP (R 2 = .55, .63, and .61, respectively), except for WSS (R 2 = .81 ). The errors are comparable to differences previously reported with disease correlations. To robustly predict atrial hemodynamics and stresses, numerical resolutions of 10 M elements (i.e., Δ x = ∼ .5 mm) and 10 k time-steps per cycle seem necessary (i.e., one order of magnitude higher than normally used in both space and time). In conclusion, attention to fundamental numerical aspects is essential toward establishing a plausible, robust, and reliable model of LA flows.

A 3D scaling law for supravalvular aortic stenosis suited for stethoscopic auscultations

In this study a frequency scaling law for 3D anatomically representative supravalvular aortic stenosis (SVAS) cases is proposed. The law is uncovered for stethoscopy's preferred auscultation range (70-120 Hz). LES simulations are performed on the CFD solver Fluent, leveraging Simulia's Living Heart Human Model (LHHM), modified to feature hourglass stenoses that range between 30 to 80 percent (mild to severe) in addition to the descending aorta. For physiological hemodynamic boundary conditions the Windkessel model is implemented via a UDF subroutine. The flow-generated acoustic signal is then extracted using the FW-H model and analyzed using FFT. A preferred receiver location that matches clinical practice is confirmed (right intercostal space) and a correlation between the degree of stenosis and a corresponding acoustic frequency is obtained. Five clinical auscultation signals are tested against the scaling law, with the findings interpreted in relation to the NHS classification of stenosis and to the assessments of experienced cardiologists. The scaling law is thus shown to succeed as a potential quantitative decision-support tool for clinicians, enabling them to reliably interpret stethoscopic auscultations for all degrees of stenosis, which is especially useful for moderate degrees of SVAS. Computational investigation of more complex stenotic cases would enhance the clinical relevance of this proposed scaling law, and will be explored in future research.

A CFD-FFT approach to hemoacoustics that enables degree of stenosis prediction from stethoscopic signals

In this paper, we identify a new (acoustic) frequency-stenosis relation whose frequencies lie within the recommended auscultation threshold of stethoscopy (< 120 Hz). We show that this relation can be used to extend the application of phonoangiography (quantifying the degree of stenosis from bruits) to widely accessible stethoscopes. The relation is successfully identified from an analysis restricted to the acoustic signature of the von Karman vortex street, which we automatically single out by means of a metric we propose that is based on an area-weighted average of the Q-criterion for the post-stenotic region. Specifically, we perform CFD simulations on internal flow geometries that represent stenotic blood vessels of different severities. We then extract their emitted acoustic signals using the Ffowcs Williams-Hawkings equation, which we subtract from a clean signal (stenosis free) at the same heart rate. Next, we transform this differential signal to the frequency domain and carefully classify its acoustic signatures per six (stenosis-)invariant flow phases of a cardiac cycle that are newly identified in this paper. We then automatically restrict our acoustic analysis to the sounds emitted by the von Karman vortex street (phase 4) by means of our Q-criterion-based metric. Our analysis of its acoustic signature reveals a strong linear relationship between the degree of stenosis and its dominant frequency, which differs considerably from the break frequency and the heart rate (known dominant frequencies in the literature). Applying our new relation to available stethoscopic data, we find that its predictions are consistent with clinical assessment. Our finding of this linear correlation is also unlike prevalent scaling laws in the literature, which feature a small exponent (i.e., low stenosis percentage sensitivity over much of the clinical range). They hence can only distinguish mild, moderate, and severe cases. Conversely, our linear law can identify variations in the degree of stenosis sensitively and accurately for the full clinical range, thus significantly improving the utility of the relevant scaling laws... Future research will investigate incorporating the vibroacoustic role of adjacent organs to expand the clinical applicability of our findings. Extending our approach to more complex 3D stenotic morphologies and including the vibroacoustic role of surrounding organs will be explored in future research to advance the clinical reach of our findings.

A verified and validated moving domain computational fluid dynamics solver with applications to cardiovascular flows

Computational fluid dynamics (CFD) in combination with patient-specific medical images has been used to correlate flow phenotypes with disease initiation, progression and outcome, in search of a prospective clinical tool. A large number of CFD software packages are available, but are typically based on rigid domains and low-order finite volume methods, and are often implemented in massive low-level C++ libraries. Furthermore, only a handful of solvers have been appropriately verified and validated for their intended use. Our goal was to develop, verify and validate an open-source CFD solver for moving domains, with applications to cardiovascular flows. The solver is an extension of the CFD solver Oasis, which is based on the finite element method and implemented using the FEniCS open source framework. The new solver, named OasisMove, extends Oasis by expressing the Navier-Stokes equations in the arbitrary Lagrangian-Eulerian formulation, which is suitable for handling moving domains. For code verification we used the method of manufactured solutions for a moving 2D vortex problem, and for validation we compared our results against existing high-resolution simulations and laboratory experiments for two moving domain problems of varying complexity. Verification results showed that the L 2 error followed the theoretical convergence rates. The temporal accuracy was second-order, while the spatial accuracy was second- and third-order using ℙ 1 / ℙ 1 and ℙ 2 / ℙ 1 finite elements, respectively. Validation results showed good agreement with existing benchmark results, by reproducing lift and drag coefficients with less than 1% error, and demonstrating the solver's ability to capture vortex patterns in transitional and turbulent-like flow regimes. In conclusion, we have shown that OasisMove is an open-source, accurate and reliable solver for cardiovascular flows in moving domains.

High-fidelity fluid structure interaction simulations of turbulent-like aneurysm flows reveals high-frequency narrowband wall vibrations: A stimulus of mechanobiological relevance?

Recent high-fidelity/resolution computational fluid dynamics simulations of intracranial aneurysm hemodynamics have revealed turbulent-like flows. We hypothesized that the associated high-frequency pressure fluctuations could promote aneurysm wall vibrations. We performed fully coupled high-fidelity transient fluid structure interaction simulations between the blood flow and compliant aneurysm sac wall taking 5,000 time steps per second using a 3D patient-specific model previously shown to harbour turbulent-like flow. Our results show that the flow velocity contained fluctuations with a smooth and continuously decaying energy up to ∼160Hz, and fluctuating pressures with characteristic frequency peaks at approximately 30, 130 and 210Hz. There was a strong two-way coupling between the pressure and the wall deformation, for which the frequency spectrum showed similar characteristics, but with a narrow band peak at ∼120Hz with large regional differences in amplitude up to 80μm. The physics of the flow is broadly consistent with clinical reports of turbulent-like flows, while the physics of the wall is consistent with reports of spectral peaks in aneurysm patients. As many aneurysms are known to harbour turbulent-like flows, wall vibrations could be a widespread phenomenon. Finally, since aneurysms are vascular pathologies by definition and many/most aneurysms do not have endothelial cells but still display a focal remodeling, we hypothesize that vibrations and stresses within the wall itself might play a role in the mechanobiological processes of vessel wall pathology.

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.

Transition to Turbulence Downstream of a Stenosis for Whole Blood and a Newtonian Analog Under Steady Flow Conditions

Blood, a multiphase fluid comprised of plasma, blood cells, and platelets, is known to exhibit a shear-thinning behavior at low shear rates and near-Newtonian behavior at higher shear rates. However, less is known about the impact of its multiphase nature on the transition to turbulence. In this study, we experimentally determined the critical Reynolds number at which the flow began to transition to turbulence downstream of eccentric stenosis for whole porcine blood and a Newtonian blood analog (water-glycerin mixture). Velocity profiles for both fluids were measured under steady-state flow conditions using an ultrasound Doppler probe placed 12 diameters downstream of eccentric stenosis. Velocity was recorded at 21 locations along the diameter at 11 different flow rates. Normalized turbulent kinetic energy was used to determine the critical Reynolds number for each fluid. Blood rheology was measured before and after each experiment. Tests were conducted on five samples of each fluid inside a temperature-controlled in vitro flow system. The viscosity at a shear rate of 1000 s-1 was used to define the Reynolds number for each fluid. The mean critical Reynolds numbers for blood and water-glycerin were 470 ± 27.5 and 395 ± 10, respectively, indicating a ∼19% delay in transition to turbulence for whole blood compared to the Newtonian fluid. This finding is consistent with a previous report for steady flow in a straight pipe, suggesting some aspect of blood rheology may serve to suppress, or at least delay, the onset of turbulence in vivo.

Scale-Resolving Simulations of Steady and Pulsatile Flow Through Healthy and Stenotic Heart Valves

Blood-flow downstream of stenotic and healthy aortic valves exhibits intermittent random fluctuations in the velocity field which are associated with turbulence. Such flows warrant the use of computationally demanding scale-resolving models. The aim of this work was to compute and quantify this turbulent flow in healthy and stenotic heart valves for steady and pulsatile flow conditions. Large eddy simulations (LESs) and Reynolds-averaged Navier-Stokes (RANS) simulations were used to compute the flow field at inlet Reynolds numbers of 2700 and 5400 for valves with an opening area of 70 mm2 and 175 mm2 and their projected orifice-plate type counterparts. Power spectra and turbulent kinetic energy were quantified on the centerline. Projected geometries exhibited an increased pressure-drop (>90%) and elevated turbulent kinetic energy levels (>147%). Turbulence production was an order of magnitude higher in stenotic heart valves compared to healthy valves. Pulsatile flow stabilizes flow in the acceleration phase, whereas onset of deceleration triggered (healthy valve) or amplified (stenotic valve) turbulence. Simplification of the aortic valve by projecting the orifice area should be avoided in computational fluid dynamics (CFD). RANS simulations may be used to predict the transvalvular pressure-drop, but scale-resolving models are recommended when detailed information of the flow field is required.

Energy Analysis of an Industrial Nozzle with Variable Outlet Conditions during Compressible and Transient Airflow

The nozzle which is applied in industrial pneumatic pulsators is studied. It is a part of the system for unclogging the drains and outlets of silos and hoppers for loose materials. The nozzle is required to achieve the lowest level of energy losses while directing the airflow, which impacts the loose material bed. The energy rate transferred into the bed depends on the temperature and pressure differences between the inlet and outlet of the nozzle. In this study, the available energy is determined assuming compressible and transient airflow through the nozzle, which is a part of the industrial pneumatic pulsator. Numerical simulations are performed using the OpenFOAM CFD toolbox. Energy analysis is carried out by using Reynolds Transport Theorem for specific energy for the variable temperature inside the silo on the basis of CFD results. In fact, the air parameters at the outlet of the nozzle are the ones inside the silo. The study showed that the design of the nozzle is not very sufficient from an energetic point of view.

Simulation of intracranial hemodynamics by an efficient and accurate immersed boundary scheme

We use computational fluid dynamics (CFD) to simulate blood flow in intracranial aneurysms (IAs). Despite ongoing improvements in the accuracy and efficiency of body-fitted CFD solvers, generation of a high quality mesh appears as the bottleneck of the flow simulation and strongly affects the accuracy of the numerical solution. To overcome this drawback, we use an immersed boundary method. The proposed approach solves the incompressible Navier-Stokes equations on a rectangular (box) domain discretized using uniform Cartesian grid using the finite element method. The immersed object is represented by a set of points (Lagrangian points) located on the surface of the object. Grid local refinement is applied using an automated algorithm. We verify and validate the proposed method by comparing our numerical findings with published experimental results and analytical solutions. We demonstrate the applicability of the proposed scheme on patient-specific blood flow simulations in IAs.

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.

On delayed transition to turbulence in an eccentric stenosis model for clean vs. noisy high-fidelity CFD

Recent comparisons between experiments and computational fluid dynamics (CFD) simulations of flow in the Food and Drug Administration (FDA) standardized nozzle geometry have highlighted the potential sensitivity of axisymmetric CFD models to small perturbations induced by mesh and inlet velocity, particularly for Reynolds numbers (Re) in the transitional regime. This evokes the classic experiment of Reynolds on transition to turbulence in a straight pipe, which can be delayed, apparently indefinitely, if special care is taken to control for external influences. Such idealized experiments are, however, extremely difficult to perform and, in the context of cardiovascular modeling, belie the "noise" inherent in typical experimental and physiological systems. Previous high-fidelity CFD of a canonical eccentric (i.e., non-axisymmetric) stenosis model showed transition occurring for steady flow at Re ~ 700-800, with modest delay caused by the introduction of shear-thinning rheology. On the other hand, recent experimental measurements of steady flowing blood and blood-mimicking fluids in this same stenosis model report transition for Re ~ 400-500. Taking a cue from the FDA nozzle controversy, the present study demonstrates that the addition of small-magnitude random noise at the inlet brings the eccentric-stenosis CFD results more in-line with experiments, and reveals a more gradual transition towards turbulence. This highlights that, even in non-axisymmetric idealized geometries, unnaturally "clean" high-fidelity CFD may impede not only good agreement with experiments, but also understanding of the onset and character of blood flow instabilities as they may exist, naturally, in the vasculature.

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.

The effect of turbulence on transitional flow in the FDA's benchmark nozzle model using large-eddy simulation

The Food and Drug Administration's (FDA) benchmark nozzle model has been studied extensively both experimentally and computationally. Although considerable efforts have been made on validations of a variety of numerical models against available experimental data, the transitional flow cases are still not fully resolved, especially with regards to detailed comparison of predicted turbulence quantities with experimental measurements. This study aims to fill this gap by conducting large-eddy simulations (LES) of flow through the FDA's benchmark model, at a transitional Reynolds number of 2000. Numerical results are compared to previous interlaboratory experimental results, with an emphasis on turbulence characteristics. Our results show that the LES methodology can accurately capture laminar quantities throughout the model. In the pre-jet breakdown region, predicted turbulence quantities are generally larger than high resolution experimental data acquired with laser Doppler velocimetry. In the jet breakdown regions, where maximum Reynolds stresses occur, Reynolds shear stresses show excellent agreement. Differences of up to 4% and 20% are observed near the jet core in the axial and radial normal Reynolds stresses, respectively. Comparisons between viscous and Reynolds shear stresses show that peak viscous shear stresses occur in the nozzle throat reaching a value of 18 Pa in the boundary layer, whilst peak Reynolds shear stresses occur in the jet breakdown region reaching a maximum value of 87 Pa. Our results highlight the importance in considering both laminar and turbulent contributions towards shear stresses and that neglecting the turbulence effect can significantly underestimate the total shear force exerted on the fluid.

Computed Poststenotic Flow Instabilities Correlate Phenotypically With Vibrations Measured Using Laser Doppler Vibrometry: Perspectives for a Promising In Vivo Device for Early Detection of Moderate and Severe Carotid Stenosis

Early detection of asymptomatic carotid stenosis is crucial for treatment planning in the prevention of ischemic stroke. Auscultation, the current first-line screening methodology, comes with severe limitations that create urge for novel and robust techniques. Laser Doppler vibrometer (LDV) is a promising tool for inferring carotid stenosis by measuring stenosis-induced vibrations. The goal of the current study was to evaluate the feasibility of LDV for carotid stenosis detection. LDV measurements on a carotid phantom were used to validate our previously verified high-resolution computational fluid dynamics methodology, which was used to evaluate the impact of flowrate, flow split, and stenosis severity on the poststenotic intensity of flow instabilities (IFI). We evaluated sensitivity, specificity, and accuracy of using IFI for stenoses detection. Linear regression analyses showed that computationally derived pressure fluctuations correlated (R2 = 0.98) with LDV measurements of stenosis-induced vibrations. The flowrate of stenosed vessels correlated (R2 = 0.90) with the presence of poststenotic instabilities. Receiver operating characteristic analyses of power spectra revealed that the most relevant frequency bands for the detection of moderate (56-76%) and severe (86-96%) stenoses were 80-200 Hz and 0-40 Hz, respectively. Moderate stenosis was identified with sensitivity and specificity of 90%; values decreased to 70% for severe stenosis. The use of LDV as screening tool for asymptomatic stenosis can potentially provide improved accuracy of current screening methodologies for early detection. The applicability of this promising device for mass screening is currently being evaluated clinically.

The nested block preconditioning technique for the incompressible Navier-Stokes equations with emphasis on hemodynamic simulations

We develop a novel iterative solution method for the incompressible Navier-Stokes equations with boundary conditions coupled with reduced models. The iterative algorithm is designed based on the variational multiscale formulation and the generalized-α scheme. The spatiotemporal discretization leads to a block structure of the resulting consistent tangent matrix in the Newton-Raphson procedure. As a generalization of the conventional block preconditioners, a three-level nested block preconditioner is introduced to attain a better representation of the Schur complement, which plays a key role in the overall algorithm robustness and efficiency. This approach provides a flexible, algorithmic way to handle the Schur complement for problems involving multiscale and multiphysics coupling. The solution method is implemented and benchmarked against experimental data from the nozzle challenge problem issued by the US Food and Drug Administration. The robustness, efficiency, and parallel scalability of the proposed technique are then examined in several settings, including moderately high Reynolds number flows and physiological flows with strong resistance effect due to coupled downstream vasculature models. Two patient-specific hemodynamic simulations, covering systemic and pulmonary flows, are performed to further corroborate the efficacy of the proposed methodology.

Efficacy of the FDA nozzle benchmark and the lattice Boltzmann method for the analysis of biomedical flows in transitional regime

Flows through medical devices as well as in anatomical vessels despite being at moderate Reynolds number may exhibit transitional or even turbulent character. In order to validate numerical methods and codes used for biomedical flow computations, the US Food and Drug Administration (FDA) established an experimental benchmark, which was a pipe with gradual contraction and sudden expansion representing a nozzle. The experimental results for various Reynolds numbers ranging from 500 to 6500 were publicly released. Previous and recent computational investigations of flow in the FDA nozzle found limitations in various CFD approaches and some even questioned the adequacy of the benchmark itself. This communication reports the results of a lattice Boltzmann method (LBM) – based direct numerical simulation (DNS) approach applied to the FDA nozzle benchmark for transitional cases of Reynolds numbers 2000 and 3500. The goal is to evaluate if a simple off the shelf LBM would predict the experimental results without the use of complex models or synthetic turbulence at the inflow. LBM computations with various spatial and temporal resolutions are performed—in the extremities of 45 million to 2.88 billion lattice cells—executed respectively on 32 CPU cores of a desktop to more than 300,000 cores of a modern supercomputer to explore and characterize miniscule flow details and quantify Kolmogorov scales. The LBM simulations transition to turbulence at a Reynolds number 2000 like the FDA’s experiments and acceptable agreement in jet breakdown locations, average velocity, shear stress, and pressure is found for both the Reynolds numbers.

Graphical Abstract

A framework for automated and objective modification of tubular structures: Application to the internal carotid artery

Patient-specific medical image-based computational fluid dynamics has been widely used to reveal fundamental insight into mechanisms of cardiovascular disease, for instance, correlating morphology to adverse vascular remodeling. However, segmentation of medical images is laborious, error-prone, and a bottleneck in the development of large databases that are needed to capture the natural variability in morphology. Instead, idealized models, where morphological features are parameterized, have been used to investigate the correlation with flow features, but at the cost of limited understanding of the complexity of cardiovascular flows. To combine the advantages of both approaches, we developed a tool that preserves the patient-specificness inherent in medical images while allowing for parametric alteration of the morphology. In our open-source framework morphMan we convert the segmented surface to a Voronoi diagram, modify the diagram to change the morphological features of interest, and then convert back to a new surface. In this paper, we present algorithms for modifying bifurcation angles, location of branches, cross-sectional area, vessel curvature, shape of bends, and surface roughness. We show qualitative and quantitative validation of the algorithms, performing with an accuracy exceeding 97% in general, and proof-of-concept on combining the tool with computational fluid dynamics. By combining morphMan with appropriate clinical measurements, one could explore the morphological parameter space and resulting hemodynamic response using only a handful of segmented surfaces, effectively minimizing the main bottleneck in image-based computational fluid dynamics.

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.

Numerical investigation of wall pressure fluctuations downstream of concentric and eccentric blunt stenosis models

Pressure fluctuations that cause acoustic radiation from vessel models with concentric and eccentric blunt stenoses are investigated. Large eddy simulations of non-pulsatile flow condition are performed using OpenFOAM. Calculated amplitude and spatial-spectral distribution of acoustic pressures at the post-stenotic region are compared with previous experimental and theoretical results. It is found that increasing the Reynolds number does not change the location of the maximum root mean square wall pressure, but causes a general increase in the spectrum level, although the change in the shape of the spectrum is not significant. On the contrary, compared to the concentric model at the same Reynolds number, eccentricity leads to an increase both at the distance of the location of the maximum root mean square wall pressure from the stenosis exit and the spectrum level. This effect becomes more distinct when radial eccentricity of the stenosis increases. Both the flow rate and the eccentricity of the stenosis shape are evaluated to be clinically important parameters in diagnosing stenosis.

High-Frequency Fluctuations in Post-stenotic Patient Specific Carotid Stenosis Fluid Dynamics: A Computational Fluid Dynamics Strategy Study

Purpose

Screening of asymptomatic carotid stenoses is performed by auscultation of the carotid bruit, but the sensitivity is poor. Instead, it has been suggested to detect carotid bruit as neck’s skin vibrations. We here take a first step towards a computational fluid dynamics proof-of-concept study, and investigate the robustness of our numerical approach for capturing high-frequent fluctuations in the post-stenotic flow. The aim was to find an ideal solution strategy from a pragmatic point of view, balancing accuracy with computational cost comparing an under-resolved direct numerical simulation (DNS) approach vs. three common large eddy simulation (LES) models (static/dynamic Smagorinsky and Sigma).

Method

We found a reference solution by performing a spatial and temporal refinement study of a stenosed carotid bifurcation with constant flow rate. The reference solution \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {\Delta x = 1.92 \times 10^{ - 4} \;{\text{m}},\; \Delta t = 5 \times 10^{ - 5} \;{\text{s}}} \right)$$\end{document}Δx=1.92×10-4m,Δt=5×10-5s was compared against LES for both a constant and pulsatile flow.

Results

Only the Sigma and Dynamic Smagorinsky models were able to replicate the flow field of the reference solution for a pulsatile simulation, however the computational cost of the Sigma model was lower. However, none of the sub-grid scale models were able to replicate the high-frequent flow in the peak-systolic constant flow rate simulations, which had a higher mean Reynolds number.

Conclusions

The Sigma model was the best combination between accuracy and cost for simulating the pulsatile post-stenotic flow field, whereas for the constant flow rate, the under-resolved DNS approach was better. These results can be used as a reference for future studies investigating high-frequent flow features.