Assessment of CFD Performance in Simulations of an Idealized Medical Device: Results of FDA’s First Computational Interlaboratory Study

Hemodynamics in arterial bypass graft anastomoses with varying cuff sizes and proximal flow paths: a fluid-structure interaction study

This article investigates the effect of the cuff size of arterial bypass grafts and the flow conditions on the hemodynamics in the anastomosis (connection) to the artery, using numerical simulations. We consider a fluid-structure interaction problem which is solved based on a partitioned scheme. Additionally, we employ computational fluid dynamics to investigate the effect of a rigid wall assumption. The work focuses on clinically relevant hemodynamic quantities associated with the development of intimal hyperplasia. We also include a model for the prediction of hemolysis into the simulation. The results show that even minor changes of the cuff size can result into significant differences in the corresponding quantities of interest. The importance of the inflow path is shown to be lower than that of the cuff size. The usually employed rigid wall assumption is found to be adequate to address wall shear stress oscillations but falls short on predicting maximum and minimum wall shear stress-related quantities of interest.

Incorporating Unresolved Stresses in Blood Damage Modeling: Energy Dissipation More Accurate Than Reynolds Stress Formulation

OBJECTIVE

Reynolds Averaged Navier Stokes (RANS) models are often used as the basis for modeling blood damage in turbulent flows. To predict blood damage by turbulence stresses that are not resolved in RANS, a stress formulation that represents the corresponding scales is required. Here, we compare two commonly employed stress formulations: a scalar stress representation that uses Reynolds stresses as a surrogate for unresolved fluid stresses, and an effective stress formulation based on energy dissipation.

METHODS

We conducted unsteady RANS simulations of the CentriMag blood pump with three different closure models and a Large Eddy Simulation (LES) for reference. We implemented both stress representations in all models and compared the resulting total stress distributions in Eulerian and Lagrangian frameworks.

RESULTS

The Reynolds-stress-based approach overestimated the contribution of unresolved stresses in RANS, with differences between closure models of up to several orders of magnitude. With the dissipation-based approach, the total stresses predicted with RANS deviated by about 50% from the LES reference, which was more accurate than only considering resolved stresses.

CONCLUSION

The Reynolds-stress-based formulation proved unreliable for estimating scalar stresses in our RANS simulations, while the dissipation-based approach provided an accuracy improvement over simply neglecting unresolved stresses.

SIGNIFICANCE

Our results suggest that dissipation-based inclusion of unresolved stresses should be the preferred choice for blood damage modeling in RANS.

Blood-contacting magnetic levitation bearing design using computational fluid dynamics for haemocompatibility

The Hemocompatibility Assessment Platform (HAP) is a testing rig that will allow for the evaluation of blood trauma caused by individual components of rotary blood pumps including the NeoVAD - a proposed paediatric Left Ventricular Assist Device (LVAD). It is important that the HAP itself is only minimally haemolytic such that the plasma free haemoglobin measured can be assumed to come from the test component. In this study, Computational Fluid Dynamics simulations have been carried out to inform the design of a magnetically levitated motor bearing gap. Simulations show that issues with the original design, namely stagnation regions and large recirculation zones can be mitigated with the introduction of a pipe that introduces blood-flow to the centre of the bearing and disrupts the secondary flow patterns that cause these issues.Clinical relevance- The consequent reduction in shear exposure time will reduce heamolsyis from the HAP. The redesign of the bearing will result in reduced baseline blood trauma from the HAP, thus allowing quantification of test component haemolysis and will therefore aid the design of future paediatric LVADs.

The Comparative Method Based on Coronary Computed Tomography Angiography for Assessing the Hemodynamic Significance of Coronary Artery Stenosis

PURPOSE

An important aspect in the prevention and treatment of coronary artery disease is the functional evaluation of narrowed blood vessels. Medical image-based Computational Fluid Dynamic methods are currently increasingly being used in the clinical setting for flow studies of cardio vascular system. The aim of our study was to confirm the feasibility and functionality of a non-invasive computational method providing information about hemodynamic significance of coronary stenosis.

METHODS

A comparative method was used to simulate the flow energy losses in real (stenotic) and reconstructed models without (reference) stenosis of the coronary arteries under stress test conditions, i.e. for maximum blood flow and minimal, constant vascular resistance. In addition to the absolute pressure drop in the stenotic arteries (FFRsten) and in the reconstructed arteries (FFRrec), a new energy flow reference index (EFR) was also defined, which expresses the total pressure changes caused by stenosis in relation to the pressure changes in normal coronary arteries, which also allows a separate assessment of the haemodynamic significance of the atherosclerotic lesion itself. The article presents the results obtained from flow simulations in coronary arteries, reconstructed on the basis of 3D segmentation of cardiac CT images of 25 patients from retrospective data collection, with different degrees of stenoses and different areas of their occurrence.

RESULTS

The greater the degree of narrowing of the vessel, the greater drop of flow energy. Each parameter introduces an additional diagnostic value. In contrast to FFRsten, the EFR indices that are calculated on the basis of a comparison of stenosed and reconstructed models, are associated directly with localization, shape and geometry of stenosis only. Both FFRsten and EFR showed very significant positive correlation (P < 0.0001) with coronary CT angiography-derived FFR, with a correlation coefficient of 0.8805 and 0.9011 respectively.

CONCLUSION

The study presented promising results of non-invasive, comparative test to support of prevention of coronary disease and functional evaluation of stenosed vessels.

Machine learning based on computational fluid dynamics enables geometric design optimisation of the NeoVAD blades

The NeoVAD is a proposed paediatric axial-flow Left Ventricular Assist Device (LVAD), small enough to be implanted in infants. The design of the impeller and diffuser blades is important for hydrodynamic performance and haemocompatibility of the pump. This study aimed to optimise the blades for pump efficiency using Computational Fluid Dynamics (CFD), machine learning and global optimisation. Meshing of each design typically included 6 million hexahedral elements and a Shear Stress Transport turbulence model was used to close the Reynolds Averaged Navier-Stokes equations. CFD models of 32 base geometries, operating at 8 flow rates between 0.5 and 4 L/min, were created to match experimental studies. These were validated by comparison of the pressure-flow and efficiency-flow curves with those experimentally measured for all base prototype pumps. A surrogate model was required to allow the optimisation routine to conduct an efficient search; a multi-linear regression, Gaussian Process Regression and a Bayesian Regularised Artificial Neural Network predicted the optimisation objective at design points not explicitly simulated. A Genetic Algorithm was used to search for an optimal design. The optimised design offered a 5.51% increase in efficiency at design point (a 20.9% performance increase) as compared to the best performing pump from the 32 base designs. An optimisation method for the blade design of LVADs has been shown to work for a single objective function and future work will consider multi-objective optimisation.

Influence of Inlet Boundary Conditions on the Prediction of Flow Field and Hemolysis in Blood Pumps Using Large-Eddy Simulation

Inlet boundary conditions (BC) are one of the uncertainties which may influence the prediction of flow field and hemolysis in blood pumps. This study investigated the influence of inlet BC, including the length of inlet pipe, type of inlet BC (mass flow rate or experimental velocity profile) and turbulent intensity (no perturbation, 5%, 10%, 20%) on the prediction of flow field and hemolysis of a benchmark centrifugal blood pump (the FDA blood pump) and a commercial axial blood pump (Heartmate II), using large-eddy simulation. The results show that the influence of boundary conditions on integral pump performance metrics, including pressure head and hemolysis, is negligible. The influence on local flow structures, such as velocity distributions, mainly existed in the inlet. For the centrifugal FDA blood pump, the influence of type of inlet BC and inlet position on velocity distributions can also be observed at the diffuser. Overall, the effects of position of inlet and type of inlet BC need to be considered if local flow structures are the focus, while the influence of turbulent intensity is negligible and need not be accounted for during numerical simulations of blood pumps.

Results of the Interlaboratory Computational Fluid Dynamics Study of the FDA Benchmark Blood Pump

Computational fluid dynamics (CFD) is widely used to simulate blood-contacting medical devices. To be relied upon to inform high-risk decision making, however, model credibility should be demonstrated through validation. To provide robust data sets for validation, researchers at the FDA and collaborators developed two benchmark medical device flow models: a nozzle and a centrifugal blood pump. Experimental measurements of the flow fields and hemolysis were acquired using each model. Concurrently, separate open interlaboratory CFD studies were performed in which participants from around the world, who were blinded to the measurements, submitted CFD predictions of each benchmark model. In this study, we report the results of the interlaboratory CFD study of the FDA benchmark blood pump. We analyze the results of 24 CFD submissions using a wide range of different flow solvers, methods, and modeling parameters. To assess the accuracy of the CFD predictions, we compare the results with experimental measurements of three quantities of interest (pressure head, velocity field, and hemolysis) at different pump operating conditions. We also investigate the influence of different CFD methods and modeling choices used by the participants. Our analyses reveal that, while a number of CFD submissions accurately predicted the pump performance for individual cases, no single participant was able to accurately predict all quantities of interest across all conditions. Several participants accurately predicted the pressure head at all conditions and the velocity field in all but one or two cases. Only one of the eight participants who submitted hemolysis results accurately predicted absolute plasma free hemoglobin levels at a majority of the conditions, though most participants were successful at predicting relative hemolysis levels between conditions. Overall, this study highlights the need to validate CFD modeling of rotary blood pumps across the entire range of operating conditions and for all quantities of interest, as some operating conditions and regions (e.g., the pump diffuser) are more challenging to accurately predict than others. All quantities of interest should be validated because, as shown here, it is possible to accurately predict hemolysis despite having relatively inaccurate predictions of the flow field.

Examining the universality of the hemolysis power law model from simulations of the FDA nozzle using calibrated model coefficients

Computational fluid dynamics (CFD) is widely used to predict mechanical hemolysis in medical devices. The most popular hemolysis model is the stress-based power law model that is based on an empirical correlation between hemoglobin release from red blood cells (RBCs) and the magnitude of flow-induced stress and exposure time. Empirical coefficients are traditionally calibrated using data from experiments in simplified Couette-type blood-shearing devices with uniform-shear laminar flow and well-defined exposure times. Use of such idealized coefficients in simulations of real medical devices with complex hemodynamics is thought to be a primary reason for the historical inaccuracy of absolute hemolysis predictions using the power law model. Craven et al. (Biomech Model Mechanobiol 18:1005-1030, 2019) recently developed a CFD-based Kriging surrogate modeling approach for calibrating empirical coefficients in real devices that could potentially be used to more accurately predict absolute hemolysis. In this study, we use the FDA benchmark nozzle to investigate whether utilizing such calibrated coefficients improves the predictive accuracy of the standard Eulerian power law model. We first demonstrate the credibility of our CFD flow simulations by comparing with particle image velocimetry measurements. We then perform hemolysis simulations and compare the results with in vitro experiments. Importantly, the simulations use coefficients calibrated for the flow of a suspension of bovine RBCs through a small capillary tube, which is relatively comparable to the flow of bovine blood through the FDA nozzle. The results show that the CFD predictions of relative hemolysis in the FDA nozzle are reasonably accurate. The absolute predictions are, however, highly inaccurate with modified index of hemolysis values from CFD in error by roughly three orders of magnitude compared with the experiments, despite using calibrated model coefficients from a relatively similar geometry. We rigorously examine the reasons for the inaccuracy that include differences in the flow conditions in the hemolytic regions of each device and the lack of universality of the hemolysis power law model that is entirely empirical. Thus, while the capability to predict relative hemolysis is valuable for product development, further improvements are needed before the power law model can be relied upon to accurately predict the absolute hemolytic potential of a medical device.

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 influence of non-conformal grid interfaces on the results of large eddy simulation of centrifugal blood pumps

BACKGROUND

Computational fluid dynamics has been widely used to assist the design and evaluation of blood pumps. Discretization errors associated with computational grid may influence the credibility of numerical simulations. Non-conformal grid interfaces commonly exist in rotary machines, including rotary blood pumps. Should grid size across the interface differ greatly, large errors may occur.

METHODS

This study explored the effects of non-conformal grid interface on the prediction of the flow field and hemolysis in blood pumps using large eddy simulation (LES). Two benchmarks, a nozzle model and a centrifugal blood pump were chosen as test cases.

RESULTS

This study found that non-conformal grid interfaces with considerable change of grid sizes led to discontinuities of flow variables and brought errors to metrics such as pressure head (7%) and hemolysis (up to 14%).

CONCLUSIONS

The results on the full unstructured grid are more accurate with negligible changes of flow variables across the non-conformal grid interface. A full unstructured grid should be employed for centrifugal blood pumps to minimize the influence of non-conformal grid interfaces for LES simulations.

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.

The Effect of Blood Viscosity on Shear-Induced Hemolysis using a Magnetically Levitated Shearing Device

INTRODUCTION

Blood contacting medical devices, including rotary blood pumps, can cause shear-induced blood damage that may lead to adverse effects in patients. Due in part to an inadequate understanding of how cell-scale fluid mechanics impact red blood cell membrane deformation and damage, there is currently not a uniformly accepted engineering model for predicting blood damage caused by complex flow fields within ventricular assist devices (VADs).

METHODS

We empirically investigated hemolysis in a magnetically levitated axial Couette flow device typical of a rotary VAD. The device is able to accurately control the shear rate and exposure time experienced by blood and to minimize the effects of other uncharacterized stresses. Using this device, we explored the effects of both hematocrit and plasma viscosity on shear-induced hemolysis to characterize blood damage based on the viscosity-independent shear rate, rather than on shear stress.

RESULTS

Over a shear rate range of 20,000-80,000 1/s, the Index of Hemolysis (IH) was found to be dependent upon and well-predicted by shear rate alone. IH was independent of hematocrit, bulk viscosity, or the suspension media viscosity, and less correlated to shear stress (MSE=0.46-0.75) than to shear rate (MSE=0.06-0.09).

CONCLUSION

This study recommends that future investigations of shear-induced blood damage report findings with respect to the viscosity-neutral term of shear rate, in addition to the bulk whole blood viscosity measured at an appropriate shear rate relevant to the flow conditions of the device.

Distribution and history of extensional stresses on vWF surrogate molecules in turbulent flow

The configuration of proteins is critical for their biochemical behavior. Mechanical stresses that act on them can affect their behavior leading to the development of decease. The von Willebrand factor (vWF) protein circulating with the blood loses its efficacy when it undergoes non-physiological hemodynamic stresses. While often overlooked, extensional stresses can affect the structure of vWF at much lower stress levels than shear stresses. The statistical distribution of extensional stress as it applies on models of the vWF molecule within turbulent flow was examined here. The stress on the molecules of the protein was calculated with computations that utilized a Lagrangian approach for the determination of the molecule trajectories in the flow filed. The history of the stresses on the proteins was also calculated. Two different flow fields were considered as models of typical flows in cardiovascular mechanical devises, one was a Poiseuille flow and the other was a Poiseuille–Couette flow field. The data showed that the distribution of stresses is important for the design of blood flow devices because the average stress can be below the critical value for protein damage, but tails of the distribution can be outside the critical stress regime.

Development of a computational fluid dynamic model to investigate the hemodynamic impact of REBOA

Background: Resuscitative endovascular balloon occlusion of the aorta (REBOA) is a lifesaving intervention for major truncal hemorrhage. Balloon-tipped arterial catheters are inserted via the femoral artery to create a temporary occlusion of the aorta, which minimizes the rate of internal bleeding until definitive surgery can be conducted. There is growing concern over the resultant hypoperfusion and potential damage to tissues and organs downstream of REBOA. To better understand the acute hemodynamic changes imposed by REBOA, we developed a three-dimensional computational fluid dynamic (CFD) model under normal, hemorrhage, and aortic occlusion conditions. The goal was to characterize the acute hemodynamic changes and identify regions within the aortic vascular tree susceptible to abnormal flow and shear stress. Methods: Hemodynamic data from established porcine hemorrhage models were used to build a CFD model. Swine underwent 20% controlled hemorrhage and were randomized to receive a full or partial aortic occlusion. Using CT scans, we generated a pig-specific aortic geometry and imposed physiologically relevant inlet flow and outlet pressure boundary conditions to match in vivo data. By assuming non-Newtonian fluid properties, pressure, velocity, and shear stresses were quantified over a cardiac cycle. Results: We observed a significant rise in blood pressure (∼147 mmHg) proximal to REBOA, which resulted in increased flow and shear stress within the ascending aorta. Specifically, we observed high levels of shear stress within the subclavian arteries (22.75 Pa). Alternatively, at the site of full REBOA, wall shear stress was low (0.04 ± 9.07E-4 Pa), but flow oscillations were high (oscillatory shear index of 0.31). Comparatively, partial REBOA elevated shear levels to 84.14 ± 19.50 Pa and reduced flow oscillations. Our numerical simulations were congruent within 5% of averaged porcine experimental data over a cardiac cycle. Conclusion: This CFD model is the first to our knowledge to quantify the acute hemodynamic changes imposed by REBOA. We identified areas of low shear stress near the site of occlusion and high shear stress in the subclavian arteries. Future studies are needed to determine the optimal design parameters of endovascular hemorrhage control devices that can minimize flow perturbations and areas of high shear.

Bedsores Management: Efficiency Simulation of a New Mattress Design

Bedsores, also known as pressure ulcers, are wounds caused by the applied external force (pressure) on body segments, thereby preventing blood supply from delivering the required elements to the skin tissue. Missing elements hinder the skin’s ability to maintain its health. It poses a significant threat to patients that have limited mobility. A new patented mattress design and alternative suggested designs aimed to reduce pressure are investigated in this paper for their performance in decreasing pressure. A simulation using Ansys finite element analysis (FEA) is carried out for comparison. Three-dimensional models are designed and tested in the simulation for a mattress and human anthropometric segments (Torso and Hip). All designs are carried out in solidworks. Results show that the original design can redistribute the pressure and decrease it up to 17% less than the normal mattress. The original design shows better ability to decrease the absolute amount of pressure on the body. However, increasing the surface area of the movable parts results in less pressure applied to the body parts. Thus, this work suggests changing the surface area of the cubes from 25 to 100 cm².

Image-based computational fluid dynamics for estimating pressure drop and fractional flow reserve across iliac artery stenosis: A comparison with in-vivo measurements

Computational Fluid Dynamics (CFD) and time-resolved phase-contrast magnetic resonance imaging (PC-MRI) are potential non-invasive methods for the assessment of the severity of arterial stenoses. Fractional flow reserve (FFR) is the current "gold standard" for determining stenosis severity in the coronary arteries but is an invasive method requiring insertion of a pressure wire. CFD derived FFR (vFFR) is an alternative to traditional catheter derived FFR now available commercially for coronary artery assessment, however, it can potentially be applied to a wider range of vulnerable vessels such as the iliac arteries. In this study CFD simulations are used to assess the ability of vFFR in predicting the stenosis severity in a patient with a stenosis of 77% area reduction (>50% diameter reduction) in the right iliac artery. Variations of vFFR, overall pressure drop and flow split between the vessels were observed by using different boundary conditions. Correlations between boundary condition parameters and resulting flow variables are presented. The study concludes that vFFR has good potential to characterise iliac artery stenotic disease.

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.

Large eddy simulation as a fast and accurate engineering approach for the simulation of rotary blood pumps

An accurate representation of the flow field in blood pumps is important for the design and optimization of blood pumps. The primary turbulence modeling methods applied to blood pumps have been the Reynolds-averaged Navier-Stokes (RANS) or URANS (unsteady RANS) method. Large eddy simulation (LES) method has been introduced to simulate blood pumps. Nonetheless, LES has not been widely used to assist in the design and optimization of blood pumps to date due to its formidable computational cost. The purpose of this study is to explore the potential of the LES technique as a fast and accurate engineering approach for the simulation of rotary blood pumps. The performance of "Light LES" (using the same time and spatial resolutions as the URANS) and LES in two rotary blood pumps was evaluated by comparing the results with the URANS and extensive experimental results. This study showed that the results of both "Light LES" and LES are superior to URANS, in terms of both performance curves and key flow features. URANS could not predict the flow separation and recirculation in diffusers for both pumps. In contrast, LES is superior to URANS in capturing these flows, performing well for both design and off-design conditions. The differences between the "Light LES" and LES results were relatively small. This study shows that with less computational cost than URANS, "Light LES" can be considered as a cost-effective engineering approach to assist in the design and optimization of rotary blood pumps.

Video-based valve motion combined with computational fluid dynamics gives stable and accurate simulations of blood flow in the Realheart total artificial heart

BACKGROUND

Patients with end-stage, biventricular heart failure, and for whom heart transplantation is not an option, may be given a Total Artificial Heart (TAH). The Realheart® is a novel TAH which pumps blood by mimicking the native heart with translation of an atrioventricular plane. The aim of this work was to create a strategy for using Computational Fluid Dynamics (CFD) to simulate haemodynamics in the Realheart®, including motion of the atrioventricular plane and valves.

METHODS

The accuracies of four different computational methods for simulating fluid-structure interaction of the prosthetic valves were assessed by comparison of chamber pressures and flow rates with experimental measurements. The four strategies were: prescribed motion of valves opening and closing at the atrioventricular plane extrema; simulation of fluid-structure interaction of both valves; prescribed motion of the mitral valve with simulation of fluid-structure interaction of the aortic valve; motion of both valves prescribed from video analysis of experiments.

RESULTS

The most accurate strategy (error in ventricular pressure of 6%, error in flow rate of 5%) used video-prescribed motion. With the Realheart operating at 80 bpm, the power consumption was 1.03 W, maximum shear stress was 15 Pa, and washout of the ventricle chamber after 4 cycles was 87%.

CONCLUSIONS

This study, the first CFD analysis of this novel TAH, demonstrates that good agreement between computational and experimental data can be achieved. This method will therefore enable future optimisation of the geometry and motion of the Realheart®.

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.

Hemolysis estimation in turbulent flow for the FDA critical path initiative centrifugal blood pump

Hemolysis in medical devices and implants has been a primary concern over the past fifty years. Turbulent flow in particular can cause cell trauma and hemolysis in such devices. In this work, the effects of turbulence on red blood cell (RBC) damage are examined by simulating the flow field through a centrifugal blood pump that has been identified as a case study through the critical path initiative of the US Food and Drug Administration (FDA). In this study, a new model was employed to predict hemolysis in the turbulent flow environment in the pump selected for the FDA critical path initiative. The operating conditions for a centrifugal blood pump were specified by the FDA for rotational speeds of 2500 and 3500 rpm. The model is based on the analysis of the smaller eddies within the turbulent flow field, since it is assumed that turbulent flow eddies with sizes comparable to the dimensions of the RBCs lead to cell trauma. The Kolmogorov length scale of the velocity field is used to identify such small eddies. Using model parameters obtained in prior work through comparisons to capillary and jet flow, it is found that hemolysis for the 2500-rpm pump was predicted well, while hemolysis for the 3500-rpm pump was overpredicted. Results indicate refinement of the model and empirical constants with better experimental data is needed.

A computational model for predicting changes in infection dynamics due to leakage through N95 respirators

In the absence of fit-testing, leakage of aerosolized pathogens through the gaps between the face and N95 respirators could compromise the effectiveness of the device and increase the risk of infection for the exposed population. To address this issue, we have developed a model to estimate the increase in risk of infection resulting from aerosols leaking through gaps between the face and N95 respirators. The gaps between anthropometric face-geometry and N95 respirators were scanned using computed tomography. The gap profiles were subsequently input into CFD models. The amount of aerosol leakage was predicted by the CFD simulations. Leakage levels were validated using experimental data obtained using manikins. The computed amounts of aerosol transmitted to the respiratory system, with and without leaks, were then linked to a risk-assessment model to predict the infection risk for a sample population. An influenza outbreak in which 50% of the population deployed respirators was considered for risk assessment. Our results showed that the leakage predicted by the CFD model matched the experimental data within about 13%. Depending upon the fit between the headform and the respirator, the inward leakage for the aerosols ranged between 30 and 95%. In addition, the non-fit-tested respirator lowered the infection rate from 97% (for no protection) to between 42 and 80%, but not to the same level as the fit-tested respirators (12%). The CFD-based leakage model, combined with the risk-assessment model, can be useful in optimizing protection strategies for a given population exposed to a pathogenic aerosol.

Tipless transseptal cannula concept combines improved hemodynamic properties and risk-reduced placement: An in silico proof-of-concept

As a leading cause of death worldwide, heart failure is a serious medical condition in which many critically ill patients require temporary mechanical circulatory support (MCS) as a bridge-to-recovery or bridge-to-decision. In many cases, the TandemHeart system is used to unload the left heart by draining blood from the left atrium (LA) to the femoral artery via a transseptal multistage cannula. However, even though the correct positioning of the cannula is crucial for a safe treatment, the long cannula tip currently used in transseptal cannulas complicates positioning, making the cannula vulnerable to displacement during MCS. To overcome these limitations, we propose the development of a new tipless transseptal cannula with improved hemodynamic properties. We discuss the tipless cannula concept by comparing it to the common multistage cannula concept using computational fluid dynamics simulations and assess the flow field in the LA, the wall shear stresses (WSS), and the pressure loss. Across the two distinct time points of end-systole and end-diastole and two drainage flow rates of 3.5 and 5.0 L/min, we find a more homogeneous inlet flow pattern for the tipless cannula concept, accompanied by a remarkably reduced area of platelet-activating WSS (up to 10-times smaller area compared to the multistage cannula). Moreover, pressure loss is up to 14.5% lower in the tipless cannula concept, confirming overall improved hemodynamic properties of the tipless cannula concept. Finally, a diameter-dependent study reveals that lower WSS and pressure losses can be further reduced by large-lumen designs for any simulation setting. Overall, our results suggest that a tipless cannula concept remedies the crucial disadvantages of a long-tip multistage cannula by reducing the risk of misplacement, and it furthermore promotes optimized hemodynamics. With this successful proof-of-concept, we underscore the potential for and encourage the realization of further experimental investigations regarding the development of a tipless transseptal cannula for MCS.

Validated Guidelines for Simulating Centrifugal Blood Pumps

PURPOSE

Rotary blood pumps (RBPs) employed as ventricular assist devices are developed to support the ventricles of patients suffering from heart failure. Computational Fluid Dynamics (CFD) is frequently used to predict the performance and haemocompatibility of these pumps during development, however different simulation techniques employed by various research groups result in inconsistent predictions. This inconsistency is further compounded by the lack of standardised model validation, thus it is difficult to determine which simulation techniques are accurate. To address these problems, the US Food and Drug Administration (FDA) proposed a simplified centrifugal RBP benchmark model. The aim of this paper was to determine simulation settings capable of producing accurate predictions using the published FDA results for validation.

METHODS

This paper considers several studies to investigate the impact of simulation options on the prediction of pressure and flow velocities. These included evaluation of the mesh density and interface position through steady simulations as well as time step size and turbulence models (k-ε realizable, k-ω SST, k-ω SST Intermittency, RSM ω-based, SAS and SBES) using a sliding mesh approach.

RESULTS

The most accurate steady simulation using the k-ω turbulence model predicted the pressure to within 5% of experimental results, however experienced issues with unphysical velocity fields. A more computationally expensive transient simulation that used the Stress-Blended Eddy Simulation (SBES) turbulence model provided a more accurate prediction of the velocity field and pressure rise to within experimental variation.

CONCLUSION

The findings of the study strongly suggest that SBES can be used to better predict RBP performance in the early development phase.

Equivalent Scalar Stress Formulation Taking into Account Non-Resolved Turbulent Scales

PURPOSE

Cardiovascular engineering includes flows with fluid-dynamical stresses as a parameter of interest. Mechanical stresses are high-risk factors for blood damage and can be assessed by computational fluid dynamics. By now, it is not described how to calculate an adequate scalar stress out of turbulent flow regimes when the whole share of turbulence is not resolved by the simulation method and how this impacts the stress calculation.

METHODS

We conducted direct numerical simulations (DNS) of test cases (a turbulent channel flow and the FDA nozzle) in order to access all scales of flow movement. After validation of both DNS with literature und experimental data using magnetic resonance imaging, the mechanical stress is calculated as a baseline. Afterwards, same flows are calculated using state-of-the-art turbulence models. The stresses are computed for every result using our definition of an equivalent scalar stress, which includes the influence from respective turbulence model, by using the parameter dissipation. Afterwards, the results are compared with the baseline data.

RESULTS

The results show a good agreement regarding the computed stress. Even when no turbulence is resolved by the simulation method, the results agree well with DNS data. When the influence of non-resolved motion is neglected in the stress calculation, it is underpredicted in all cases.

CONCLUSION

With the used scalar stress formulation, it is possible to include information about the turbulence of the flow into the mechanical stress calculation even when the used simulation method does not resolve any turbulence.

Fluid-Structure Interaction Analyses of Biological Systems Using Smoothed-Particle Hydrodynamics

Due to the inherent complexity of biological applications that more often than not include fluids and structures interacting together, the development of computational fluid-structure interaction models is necessary to achieve a quantitative understanding of their structure and function in both health and disease. The functions of biological structures usually include their interactions with the surrounding fluids. Hence, we contend that the use of fluid-structure interaction models in computational studies of biological systems is practical, if not necessary. The ultimate goal is to develop computational models to predict human biological processes. These models are meant to guide us through the multitude of possible diseases affecting our organs and lead to more effective methods for disease diagnosis, risk stratification, and therapy. This review paper summarizes computational models that use smoothed-particle hydrodynamics to simulate the fluid-structure interactions in complex biological systems.

Enhanced discrete phase model for multiphase flow simulation of blood flow with high shear stress

Shear stress is often present in the blood flow within blood-contacting devices, which is the leading cause of hemolysis. However, the simulation method for blood flow with shear stress is still not perfect, especially the multiphase flow model and experimental verification. In this regard, this study proposes an enhanced discrete phase model for multiphase flow simulation of blood flow with shear stress. This simulation is based on the discrete phase model (DPM). According to the multiphase flow characteristics of blood, a virtual mass force model and a pressure gradient influence model are added to the calculation of cell particle motion. In the experimental verification, nozzle models were designed to simulate the flow with shear stress, varying the degree of shear stress through different nozzle sizes. The microscopic flow was measured by the Particle Image Velocimetry (PIV) experimental method. The comparison of the turbulence models and the verification of the simulation accuracy were carried out based on the experimental results. The result demonstrates that the simulation effect of the SST k-ω model is better than other standard turbulence models. Accuracy analysis proves that the simulation results are accurate and can capture the movement of cell-level particles in the flow with shear stress. The results of the research are conducive to obtaining accurate and comprehensive analysis results in the equipment development phase.

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.

Formation of Vortices in Idealised Branching Vessels: A CFD Benchmark Study

PURPOSE

Atherosclerosis preferentially occurs near the junction of branching vessels, where blood recirculation tends to occur (Malek et al. in J Am Med Assoc 282(21):2035-2042, 1999, https://doi.org/10.1001/jama.282.21.2035 ). For decades, CFD has been used to predict flow patterns such as separation and recirculation zones in hemodynamic models, but those predictions have rarely been validated with experimental data. In the context of verification and validation (V&V), we first conduct a CFD benchmark calculation that reproduces the vortex detection experiments of Karino and Goldsmith (1980) with idealised branching blood vessels (Karino and Goldsmith in Trans. Am. Soc. Artif. Internal Organs 26:500-506, 1980). The critical conditions for the formation of recirculation vortices, the so-called critical Reynolds numbers, are the main parameters for comparison with the experimental data to demonstrate the credibility of the CFD workflow. We then characterise the wall shear stresses and develop a surrogate model for the size of formed vortices.

METHODS

An automated parametric study generating more than 12,000 CFD simulations was performed, sweeping the geometries and flow conditions found in the experiments by Karino and Goldsmith. The flow conditions were restricted to steady-state laminar flow, with a range of inflow Reynolds numbers up to 350, with various flow ratios between the main branch outlet and side branch outlet. The side branch diameter was scaled relative to the main branch diameter, ranging from 1.05/3 to 3/3; and the branching angles ranged in size from [Formula: see text] to [Formula: see text]. Recirculation vortices were detected by the inversion of the velocity vector at certain locations, as well as by the inversion of the wall shear stress (WSS) vector.

RESULTS

The CFD simulations demonstrated good agreement with the experimental data on the critical Reynolds numbers. The spatial distributions of WSS on each branch were analysed to identify potential regions of disease. Once a vortex is formed, the size of the vortex increases by the square root of the Reynolds number. The CFD data was fitted to a surrogate model that accurately predicts the vortex size without the need to run computationally more expensive CFD simulations.

CONCLUSIONS

This benchmark study validates the CFD simulation of vortex detection in idealised branching vessels under comprehensive flow conditions. This work also proposes a surrogate model for the size of the vortex, which could reduce the computational requirements in the studies related to branching vessels and complex vascular systems.

Experimental Assessment of Two Non-Contrast MRI Sequences Used for Computational Fluid Dynamics: Investigation of Consistency Between Techniques

Purpose

Recent studies have noted a degree of variance between the geometries segmented by different groups from 3D medical images that are used in computational fluid dynamics (CFD) simulations of patient-specific cardiovascular systems. The aim of this study was to determine if the applied sequence of magnetic resonance imaging (MRI) also introduced observable variance in CFD results.

Methods

Using a series of phantoms MR images of vessels of known diameter were assessed for the time-of-flight and multi-echo data image combination sequences. Following this, patient images of arterio-venous fistulas were acquired using the same sequences. Comparisons of geometry were made using the phantom and patient images, and of wall shear stress quantities using the CFD results from the patient images.

Results

Phantom images showed deviations in diameter between 0 and 15% between the sequences, depending on vessel diameter. Patient images showed different geometrical features such as narrowings that were not present on both sequences. Distributions of wall shear stress (WSS) quantities differed from simulations between the geometries obtained from the sequences.

Conclusion

In conclusion, choosing different MRI sequences resulted in slightly different geometries of the same anatomy, which led to compounded errors in WSS quantities from CFD simulation.

Electronic supplementary material

The online version of this article (10.1007/s13239-020-00473-z) contains supplementary material, which is available to authorized users.

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

Large-Eddy Simulations of Flow in the FDA Benchmark Nozzle Geometry to Predict Hemolysis

PURPOSE

Modeling of hemolysis due to fluid stresses faces significant methodological challenges, particularly in geometries with turbulence or complex flow patterns. It is currently unclear how existing phenomenological blood-damage models based on laminar viscous stresses can be implemented into turbulent computational fluid dynamics simulations. The aim of this work is to generalize the existing laminar models to turbulent flows based on first principles, and validate this generalization with existing experimental data.

METHODS

A novel analytical and numerical framework for the simulation of flow-induced hemolysis based on the intermittency-corrected turbulent viscous shear stress (ICTVSS) is introduced. The proposed large-eddy simulation framework is able to seamlessly transition from laminar to turbulent conditions in a single flow domain by linking laminar shear stresses to dissipation of mechanical energy, accounting for intermittency in turbulent dissipation, and relying on existing power-law hemolysis models. Simulations are run to reproduce previously published hemolysis data with bovine blood in a benchmark geometry. Two sets of experimental data are relied upon to tune power-law parameters and justify that tuning. The first presents hemolysis measurements in a simple laminar flow, and the second is hemolysis in turbulent flow through the FDA benchmark nozzle. Validation is performed by simulation of blood injected into a turbulent jet of phosphate-buffered saline, with modifications made to account for the local concentration of blood.

RESULTS

Hemolysis predictions are found to be very sensitive to power-law parameters in the turbulent case, though a set of parameters is presented that both matches the turbulent data and is well-justified by the laminar data. The model is shown to be able to predict the general behavior of hemolysis in a second turbulent case. Results suggest that wall shear may play a dominant role in most cases.

CONCLUSION

The ICTVSS framework of generalizing laminar power-law models to turbulent flows shows promise, but would benefit from further numerical validation and carefully designed experiments.

Assessing Computational Model Credibility Using a Risk-Based Framework: Application to Hemolysis in Centrifugal Blood Pumps

Medical device manufacturers using computational modeling to support their device designs have traditionally been guided by internally developed modeling best practices. A lack of consensus on the evidentiary bar for model validation has hindered broader acceptance, particularly in regulatory areas. This has motivated the US Food and Drug Administration and the American Society of Mechanical Engineers (ASME), in partnership with medical device companies and software providers, to develop a structured approach for establishing the credibility of computational models for a specific use. Charged with this mission, the ASME V&V 40 Subcommittee on Verification and Validation (V&V) in Computational Modeling of Medical Devices developed a risk-informed credibility assessment framework; the main tenet of the framework is that the credibility requirements of a computational model should be commensurate with the risk associated with model use. This article provides an overview of the ASME V&V 40 standard and an example of the framework applied to a generic centrifugal blood pump, emphasizing how experimental evidence from in vitro testing can support computational modeling for device evaluation. Two different contexts of use for the same model are presented, which illustrate how model risk impacts the requirements on the V&V activities and outcomes.

Prediction of mechanical hemolysis in medical devices via a Lagrangian strain-based multiscale model

This work introduces a new Lagrangian strain-based model to predict the shear-induced hemolysis in biomedical devices. Current computational models for device-induced hemolysis usually utilize empirical fitting of the released free hemoglobin (Hb) in plasma from damaged red blood cells (RBCs). These empirical correlations contain parameters that depend on specific device and operating conditions, thus cannot be used to predict hemolysis in a general device. The proposed algorithm does not have any empirical parameters, thus can presumably be used for hemolysis prediction in various blood-wetting medical devices. In contrast to empirical correlations in which the Hb release is related to the shear stress and exposure time without considering the physical processes, the proposed model links flow-induced deformation of the RBC membrane to membrane permeabilization and Hb release. In this approach, once the steady-state numerical solution of blood flow in the device is obtained under a prescribed operating condition, sample path lines are traced from the inlet of the device to the outlet to calculate the history of the shear stress tensor. In solving the fluid flow, it is assumed that RBCs do not have any influence on the flow pattern. Along each path line, shear stress tensor will be input into a coarse-grained (CG) RBC model to calculate the RBC deformation. Then the correlations obtained from molecular dynamics (MD) simulations are applied to relate the local areal RBC deformation to the perforated area on the RBC membrane. Finally, Hb released out of transient pores is calculated over each path line via a diffusion equation considering the effects of the steric hindrance and increased hydrodynamic drag due to the size of the Hb molecule. The total index of hemolysis (IH) is calculated by integration of released Hb over all the path lines in the computational domain. Hemolysis generated in the Food and Drug Administration (FDA) nozzle and two blood pumps, that is, a CentriMag blood pump (a centrifugal pump) and HeartMate II (an axial pump), for different flow regimes including the laminar and turbulent flows are calculated via the proposed algorithm. In all the simulations, the numerical predicted IH is close to the range of experimental data. The results promisingly indicate that this multiscale approach can be used as a tool for predicting hemolysis and optimizing the hematologic design of other types of blood-wetting devices.

Computational modeling of the Food and Drug Administration's benchmark centrifugal blood pump

In order to simulate hemodynamics within centrifugal blood pumps and to predict pump hemolysis, CFD simulations must be thoroughly validated against experimental data. They must also account for and accurately model the specific working fluid in the pump, whether that is a blood-analog solution to match an experimental PIV study or animal blood in a hemolysis experiment. Therefore, the Food and Drug Administration (FDA) benchmark centrifugal blood pump and its database of experimental PIV and hemolysis data were used to thoroughly validate CFD simulations of the same blood pump. A Newtonian blood model was first used to compare to the PIV data with a blood analog fluid while hemolysis data were compared using a power-law hemolysis model fit to porcine blood data. A viscoelastic blood model was then incorporated into the CFD solver to investigate the importance of modeling blood's viscoelasticity in centrifugal pumps. The established computational framework, including a dynamic rotating mesh, animal blood-specific fluid properties and hemolysis modeling, and a k-ω SST turbulence model, was shown to more accurately predict pump pressure heads, velocity fields, and hemolysis compared to previously published CFD studies of the FDA centrifugal pump. The CFD simulations were able to match the FDA pressure and hemolysis data for multiple pump operating conditions, with the CFD results being within the standard deviations of the experimental results. While CFD radial velocity profiles between the impeller blades also compared well to the PIV velocity results, more work is still needed to address the large variability among both experimental and computational predictions of velocity in the diffuser outlet jet. Small differences were observed between the Newtonian and viscoelastic blood models in pressure head and hemolysis at the higher flow rate cases (FDA Conditions 4 and 5) but were more significant at lower flow rate and pump impeller speeds (FDA Condition 1). These results suggest that the importance of accounting for blood's viscoelasticity may be dependent on the specific blood pump operating conditions. This detailed computational framework with improved modeling techniques and an extensive validation procedure will be used in future CFD studies of centrifugal blood pumps to aid in device design and predictions of their biological responses.

Validation of numerically simulated ventricular flow patterns during left ventricular assist device support

Intraventricular flow patterns during left ventricular assist device support have been investigated via computational fluid dynamics by several groups. Based on such simulations, specific parameters for thrombus formation risk analysis have been developed. However, computational fluid dynamic simulations of complex flow configurations require proper validation by experiments. To meet this need, a ventricular model with a well-defined inflow section was analyzed by particle image velocimetry and replicated by transient computational fluid dynamic simulations. To cover the laminar, transitional, and turbulent flow regime, four numerical methods including the laminar, standard k-omega, shear-stress transport, and renormalized group k-epsilon were applied and compared to the particle image velocimetry results in 46 different planes in the whole left ventricle. The simulated flow patterns for all methods, except renormalized group k-epsilon, were comparable to the flow patterns measured using particle image velocimetry (absolute error over whole left ventricle: laminar: 10.5, standard k-omega: 11.3, shear–stress transport: 11.3, and renormalized group k-epsilon: 17.8 mm/s). Intraventricular flow fields were simulated using four numerical methods and validated with experimental particle image velocimetry results. In the given setting and for the chosen boundary conditions, the laminar, standard K-omega, and shear–stress transport methods showed acceptable similarity to experimental particle image velocimetry data, with the laminar model showing the best transient behavior.

Comparative quantification of primary mitral regurgitation by computer modeling and simulated echocardiography

Clinical investigations have demonstrated that mitral regurgitation (MR) quantification using echocardiography (echo) may significantly underestimate or overestimate the regurgitant volume, especially for two-dimensional (2D) echo. Computer modeling and simulated echo were conducted to evaluate the fundamental assumptions in the echo quantification of primary MR that is due to posterior mitral leaflet prolapse. The theoretical flaw of the proximal isovelocity surface area (PISA) method originates from the assumption that the MR flow rate is the product of the isovelocity surface area and aliasing velocity, which is only valid when the velocity vectors are perpendicular to the isovelocity surface. Other factors such as the Doppler angle effect, the view planes of 2D echo, and the single time instant of PISA were also analyzed. We find that the hemielliptic PISA method gives the smallest error for moderate and severe MR cases compared with other PISA methods. Compared with the PISA method, the volumetric technique (VT) is theoretically more robust. By considering correction factors that are caused by nonflat velocity profiles and the closing volume of the aortic valve, the accuracy of the VT method can be significantly improved. The corrected volumetric technique provides more accurate results compared with the PISA methods, especially for mild MR.NEW & NOTEWORTHY We evaluate the accuracy of common echocardiography techniques for the quantification of primary mitral regurgitations using computer modeling. The hemielliptic proximal isovelocity surface area (PISA) method gives the smallest error (within 15%) for moderate and severe mitral regurgitation cases compared with other PISA methods. The volumetric method is theoretically more robust than the PISA method. The accuracy of the volumetric method can be improved by a correction factor around 0.7 because of the nonflat velocity profiles and the closing volume of the aortic valve.

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 Turbulence in Abdominal Aortic Aneurysms

Computational fluid dynamics (CFD) is a powerful method to investigate aneurysms. The primary focus of most investigations has been to compute various hemodynamic parameters to assess the risk posed by an aneurysm. Despite the occurrence of transitional flow in aneurysms, turbulence has not received much attention. In this article, we investigate turbulence in the context of abdominal aortic aneurysms (AAA). Since the clinical practice is to diagnose an AAA on the basis of its size, hypothetical axisymmetric geometries of various sizes are constructed. In general, just after the peak systole, a vortex ring is shed from the expansion region of an AAA. As the ring advects downstream, an azimuthal instability sets in and grows in amplitude thereby destabilizing the ring. The eventual breakdown of the vortex ring into smaller vortices leads to turbulent fluctuations. A residence time study is also done to identify blood recirculation zones, as a recirculation region can lead to degradation of the arterial wall. In some of the geometries simulated, the enhanced local mixing due to turbulence does not allow a recirculation zone to form, whereas in other geometries, turbulence had no effect on them. The location and consequence of a recirculation zone suggest that it could develop into an intraluminal thrombus (ILT). Finally, the possible impact of turbulence on the oscillatory shear index (OSI), a hemodynamic parameter, is explored. To conclude, this study highlights how a small change in the geometric aspects of an AAA can lead to a vastly different flow field.

Grid-Induced Numerical Errors for Shear Stresses and Essential Flow Variables in a Ventricular Assist Device: Crucial for Blood Damage Prediction?

Adverse events due to flow-induced blood damage remain a serious problem for blood pumps as cardiac support systems. The numerical prediction of blood damage via computational fluid dynamics (CFD) is a helpful tool for the design and optimization of reliable pumps. Blood damage prediction models primarily are based on the acting shear stresses, which are calculated by solving the Navier–Stokes equations on computational grids. The purpose of this paper is to analyze the influence of the spatial discretization and the associated discretization error on the shear stress calculation in a blood pump in comparison to other important flow quantities like the pressure head of the pump. Therefore, CFD analysis using seven unsteady Reynolds-averaged Navier–Stokes (URANS) simulations was performed. Two simple stress calculation indicators were applied to estimate the influence of the discretization on the results using an approach to calculate numerical uncertainties, which indicates discretization errors. For the finest grid with 19 × 106 elements, numerical uncertainties up to 20% for shear stresses were determined, while the pressure heads show smaller uncertainties with a maximum of 4.8%. No grid-independent solution for velocity gradient-dependent variables could be obtained on a grid size that is comparable to mesh sizes in state-of-the-art blood pump studies. It can be concluded that the grid size has a major influence on the shear stress calculation, and therefore, the potential blood damage prediction, and that the quantification of this error should always be taken into account.

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.

Kinematic boundary conditions substantially impact in silico ventricular function

Computational cardiac mechanical models, individualized to the patient, have the potential to elucidate the fundamentals of cardiac (patho-)physiology, enable non-invasive quantification of clinically significant metrics (eg, stiffness, active contraction, work), and anticipate the potential efficacy of therapeutic cardiovascular intervention. In a clinical setting, however, the available imaging resolution is often limited, which limits cardiac models to focus on the ventricles, without including the atria, valves, and proximal arteries and veins. In such models, the absence of surrounding structures needs to be accounted for by imposing realistic kinematic boundary conditions, which, for prognostic purposes, are preferably generic and thus non-image derived. Unfortunately, the literature on cardiac models shows no consistent approach to kinematically constrain the myocardium. The impact of different approaches (eg, fully constrained base, constrained epi-ring) on the predictive capacity of cardiac mechanical models has not been thoroughly studied. For that reason, this study first gives an overview of current approaches to kinematically constrain (bi) ventricular models. Next, we developed a patient-specific in silico biventricular model that compares well with literature and in vivo recorded strains. Alternative constraints were introduced to assess the influence of commonly used mechanical boundary conditions on both the predicted global functional behavior of the in-silico heart (cavity volumes, stroke volume, ejection fraction) and local strain distributions. Meaningful differences in global functioning were found between different kinematic anchoring strategies, which brought forward the importance of selecting appropriate boundary conditions for biventricular models that, in the near future, may inform clinical intervention. However, whilst statistically significant differences were also found in local strain distributions, these differences were minor and mostly confined to the region close to the applied boundary conditions.