Validation of CFD simulations of cerebral aneurysms with implication of geometric variations

BACKGROUND: Computational fluid dynamics (CFD) simulations using medical-image-based anatomical vascular geometry are now gaining clinical relevance. This study aimed at validating the CFD methodology for studying cerebral aneurysms by using particle image velocimetry (PIV) measurements, with a focus on the effects of small geometric variations in aneurysm models on the flow dynamics obtained with CFD. METHOD OF APPROACH: An experimental phantom was fabricated out of silicone elastomer to best mimic a spherical aneurysm model. PIV measurements were obtained from the phantom and compared with the CFD results from an ideal spherical aneurysm model (S1). These measurements were also compared with CFD results, based on the geometry reconstructed from three-dimensional images of the experimental phantom. We further performed CFD analysis on two geometric variations, S2 and S3, of the phantom to investigate the effects of small geometric variations on the aneurysmal flow field. Results. We found poor agreement between the CFD results from the ideal spherical aneurysm model and the PIV measurements from the phantom, including inconsistent secondary flow patterns. The CFD results based on the actual phantom geometry, however, matched well with the PIV measurements. CFD of models S2 and S3 produced qualitatively similar flow fields to that of the phantom but quantitatively significant changes in key hemodynamic parameters such as vorticity, positive circulation, and wall shear stress. CONCLUSION: CFD simulation results can closely match experimental measurements as long as both are performed on the same model geometry. Small geometric variations on the aneurysm model can significantly alter the flow-field and key hemodynamic parameters. Since medical images are subjected to geometric uncertainties, image-based patient-specific CFD results must be carefully scrutinized before providing clinical feedback.     

PIV-measured versus CFD-predicted flow dynamics in anatomically realistic cerebral aneurysm models

Computational fluid dynamics (CFD) modeling of nominally patient-specific cerebral aneurysms is increasingly being used as a research tool to further understand the development, prognosis, and treatment of brain aneurysms. We have previously developed virtual angiography to indirectly validate CFD-predicted gross flow dynamics against the routinely acquired digital subtraction angiograms. Toward a more direct validation, here we compare detailed, CFD-predicted velocity fields against those measured using particle imaging velocimetry (PIV). Two anatomically realistic flow-through phantoms, one a giant internal carotid artery (ICA) aneurysm and the other a basilar artery (BA) tip aneurysm, were constructed of a clear silicone elastomer. The phantoms were placed within a computer-controlled flow loop, programed with representative flow rate waveforms. PIV images were collected on several anterior-posterior (AP) and lateral (LAT) planes. CFD simulations were then carried out using a well-validated, in-house solver, based on micro-CT reconstructions of the geometries of the flow-through phantoms and inlet/outlet boundary conditions derived from flow rates measured during the PIV experiments. PIV and CFD results from the central AP plane of the ICA aneurysm showed a large stable vortex throughout the cardiac cycle. Complex vortex dynamics, captured by PIV and CFD, persisted throughout the cardiac cycle on the central LAT plane. Velocity vector fields showed good overall agreement. For the BA, aneurysm agreement was more compelling, with both PIV and CFD similarly resolving the dynamics of counter-rotating vortices on both AP and LAT planes. Despite the imposition of periodic flow boundary conditions for the CFD simulations, cycle-to-cycle fluctuations were evident in the BA aneurysm simulations, which agreed well, in terms of both amplitudes and spatial distributions, with cycle-to-cycle fluctuations measured by PIV in the same geometry. The overall good agreement between PIV and CFD suggests that CFD can reliably predict the details of the intra-aneurysmal flow dynamics observed in anatomically realistic in vitro models. Nevertheless, given the various modeling assumptions, this does not prove that they are mimicking the actual in vivo hemodynamics, and so validations against in vivo data are encouraged whenever possible.     

Multilaboratory particle image velocimetry analysis of the FDA benchmark nozzle model to support validation of computational fluid dynamics simulations

This study is part of a FDA-sponsored project to evaluate the use and limitations of computational fluid dynamics (CFD) in assessing blood flow parameters related to medical device safety. In an interlaboratory study, fluid velocities and pressures were measured in a nozzle model to provide experimental validation for a companion round-robin CFD study. The simple benchmark nozzle model, which mimicked the flow fields in several medical devices, consisted of a gradual flow constriction, a narrow throat region, and a sudden expansion region where a fluid jet exited the center of the nozzle with recirculation zones near the model walls. Measurements of mean velocity and turbulent flow quantities were made in the benchmark device at three independent laboratories using particle image velocimetry (PIV). Flow measurements were performed over a range of nozzle throat Reynolds numbers (Re(throat)) from 500 to 6500, covering the laminar, transitional, and turbulent flow regimes. A standard operating procedure was developed for performing experiments under controlled temperature and flow conditions and for minimizing systematic errors during PIV image acquisition and processing. For laminar (Re(throat)=500) and turbulent flow conditions (Re(throat)≥3500), the velocities measured by the three laboratories were similar with an interlaboratory uncertainty of ～10% at most of the locations. However, for the transitional flow case (Re(throat)=2000), the uncertainty in the size and the velocity of the jet at the nozzle exit increased to ～60% and was very sensitive to the flow conditions. An error analysis showed that by minimizing the variability in the experimental parameters such as flow rate and fluid viscosity to less than 5% and by matching the inlet turbulence level between the laboratories, the uncertainties in the velocities of the transitional flow case could be reduced to ～15%. The experimental procedure and flow results from this interlaboratory study (available at http://fdacfd.nci.nih.gov) will be useful in validating CFD simulations of the benchmark nozzle model and in performing PIV studies on other medical device models.     

Quantitative comparison of CFD predicted and MRI measured velocity fields in a carotid bifurcation phantom

Steady flow of a blood mimicking fluid in a physiologically realistic model of the human carotid bifurcation was studied using both magnetic resonance imaging (MRI) and computational fluid dynamics (CFD) modelling techniques. Quantitative comparisons of the 3D velocity field in the bifurcation phantom were made between phase contrast MRI measurements and CFD predictions. The geometry for the CFD model was reconstructed from T(1) weighted MR imaging of the test phantom. It was found that the predicted velocity fields were in fair agreement with MR measured velocities. In both the internal and external carotid arteries, the agreement between CFD predictions and MRI measurements was better along the inner-outer wall axis with a correlation factor C>0.897 (average 0.939) where the velocity profiles were skewed, than along the anterior-posterior axis (average correlation factor 0.876) where the velocity profiles were in M-shape.     

Acinus-on-a-chip: A microfluidic platform for pulmonary acinar flows

Convective respiratory flows in the pulmonary acinus and their influence on the fate of inhaled particles are typically studied using computational fluid dynamics (CFD) or scaled-up experimental models. However, experiments that replicate several generations of the acinar tree while featuring cyclic wall motion have not yet been realized. Moreover, current experiments generally capture only flow dynamics, without inhaled particle dynamics, due to difficulties in simultaneously matching flow and particle dynamics. In an effort to overcome these limitations, we introduce a novel microfluidic device mimicking acinar flow characteristics directly at the alveolar scale. The model features an anatomically-inspired geometry that expands and contracts periodically with five dichotomously branching airway generations lined with alveolar-like cavities. We use micro-particle image velocimetry with a glycerol solution as the carrying fluid to quantitatively characterize detailed flow patterns within the device and reveal experimentally for the first time a gradual transition of alveolar flow patterns along the acinar tree from recirculating to radial streamlines, in support of hypothesized predictions from past CFD simulations. The current measurements show that our microfluidic system captures the underlying characteristics of the acinar flow environment, including Reynolds and Womersley numbers as well as cyclic wall displacements and alveolar flow patterns at a realistic length scale. With the use of air as the carrying fluid, our miniaturized platform is anticipated to capture both particle and flow dynamics and serve in the near future as a promising in vitro tool for investigating the mechanisms of particle deposition deep in the lung.     

Flow field analysis in a compliant acinus replica model using particle image velocimetry (PIV)

Inhaled particles reaching the alveolar walls have the potential to cross the blood–gas barrier and enter the blood stream. Experimental evidence of pulmonary dosimetry, however, cannot be explained by current whole lung dosimetry models. Numerical and experimental studies shed some light on the mechanisms of particle transport, but realistic geometries have not been investigated. In this study, a three dimensional expanding model including two generations of respiratory bronchioles and five terminal alveolar sacs was created from a replica human lung cast. Flow visualization techniques were employed to quantify the fluid flow while utilizing streamlines to evaluate recirculation. Pathlines were plotted to track the fluid motion and estimate penetration depth of inhaled air. This study provides evidence that the two generations immediately proximal to the terminal alveolar sacs do not have recirculating eddies, even for intense breathing. Results of Peclet number calculations indicate that substantial convective motion is present in vivo for the case of deep breathing, which significantly increases particle penetration into the alveoli. However, particle diffusion remains the dominant mechanism of particle transport over convection, even for intense breathing because inhaled particles do not reach the alveolar wall in a single breath by convection alone. Examination of the velocity fields revealed significant uneven ventilation of the alveoli during a single breath, likely due to variations in size and location. This flow field data, obtained from replica model geometry with realistic breathing conditions, provides information to better understand fluid and particle behavior in the acinus region of the lung.     

Design of a side-view particle imaging velocimetry flow system for cell-substrate adhesion studies

Experimental models that mimic the flow conditions in microcapillaries have suggested that the local shear stresses and shear rates can mediate tumor cell and leukocyte arrest on the endothelium and subsequent sustained adhesion. However, further investigation has been limited by the lack of experimental models that allow quantitative measurement of the hydrodynamic environment over adherent cells. The purpose of this study was to develop a system capable of acquiring quantitative flow profiles over adherent cells. By combining the techniques of side-view imaging and particle image velocimetry (PIV), an in vitro model was constructed that is capable of obtaining quantitative flow data over cells adhering to the endothelium. The velocity over an adherent leukocyte was measured and the shear rate was calculated under low and high upstream wall shear. The microcapillary channel was modeled using computational fluid dynamics (CFD) and the calculated velocity profiles over cells under the low and high shear rates were compared to experimental results. The drag force applied to each cell by the fluid was then computed. This system provides a means for future study of the forces underlying adhesion by permitting characterization of the local hydrodynamic conditions over adherent cells.     

Lung structure parameters estimated from modeling aerosol deposition in isolated dog lungs

A three-compartment model predicting the recovery of aerosol boli (i.e., the ratio of the number of particles expired to the number inspired) as a function of breath-holding time and bolus penetration was fitted to experimental data measured in nine isolated dog lungs. For each lung, the diameters of alveoli and alveolar ducts, as well as the volume fractions of alveoli, alveolar ducts, and airways, were determined as parameters providing the best fit. Parameter values were alveolar diameter = 0.116 +/- 0.007 (SE) mm, alveolar duct diameter = 0.284 +/- 0.015 mm, total alveolar volume/total lung capacity (TLC) = 0.68 +/- 0.02, total alveolar duct volume/TLC = 0.24 +/- 0.02, and total airway volume/TLC = 0.09 +/- 0.01. These values agreed with published values for linear dimensions and volumetric fractions in the canine lung. The mean alveolar diameter determined by the model in the nine lungs agreed closely with a mean value of 0.115 +/- 0.002 mm determined by morphometric analysis of photographs of the subpleural alveoli in the same lungs. The procedure of fitting the model to experimental data appears to have promise as a noninvasive probe of the lung periphery. However, aerosol-derived dimensions were more variable than morphometric ones, possibly because of interlung differences in aerosol distribution not accounted for in the model.     

Validation of a fluid–structure interaction numerical model for predicting flow transients in arteries

Fluid–structure interaction (FSI) numerical models are now widely used in predicting blood flow transients. This is because of the importance of the interaction between the flowing blood and the deforming arterial wall to blood flow behaviour. Unfortunately, most of these FSI models lack rigorous validation and, thus, cannot guarantee the accuracy of their predictions. This paper presents the comprehensive validation of a two-way coupled FSI numerical model, developed to predict flow transients in compliant conduits such as arteries. The model is validated using analytical solutions and experiments conducted on polyurethane mock artery. Flow parameters such as pressure and axial stress (and precursor) wave speeds, wall deformations and oscillating frequency, fluid velocity and Poisson coupling effects, were used as the basis of this validation. Results show very good comparison between numerical predictions, analytical solutions and experimental data. The agreement between the three approaches is generally over 95%. The model also shows accurate prediction of Poisson coupling effects in unsteady flows through flexible pipes, which up to this stage have only being predicted analytically. Therefore, this numerical model can accurately predict flow transients in compliant vessels such as arteries.     

Merging computational fluid dynamics and 4D Flow MRI using proper orthogonal decomposition and ridge regression

Time resolved phase-contrast magnetic resonance imaging 4D-PCMR (also called 4D Flow MRI) data while capable of non-invasively measuring blood velocities, can be affected by acquisition noise, flow artifacts, and resolution limits. In this paper, we present a novel method for merging 4D Flow MRI with computational fluid dynamics (CFD) to address these limitations and to reconstruct de-noised, divergence-free high-resolution flow-fields. Proper orthogonal decomposition (POD) is used to construct the orthonormal basis of the local sampling of the space of all possible solutions to the flow equations both at the low-resolution level of the 4D Flow MRI grid and the high-level resolution of the CFD mesh. Low-resolution, de-noised flow is obtained by projecting in vivo 4D Flow MRI data onto the low-resolution basis vectors. Ridge regression is then used to reconstruct high-resolution de-noised divergence-free solution. The effects of 4D Flow MRI grid resolution, and noise levels on the resulting velocity fields are further investigated. A numerical phantom of the flow through a cerebral aneurysm was used to compare the results obtained using the POD method with those obtained with the state-of-the-art de-noising methods. At the 4D Flow MRI grid resolution, the POD method was shown to preserve the small flow structures better than the other methods, while eliminating noise. Furthermore, the method was shown to successfully reconstruct details at the CFD mesh resolution not discernible at the 4D Flow MRI grid resolution. This method will improve the accuracy of the clinically relevant flow-derived parameters, such as pressure gradients and wall shear stresses, computed from in vivo 4D Flow MRI data.     

Validation of computational fluid dynamics methodology used for human upper airway flow simulations

An anatomically accurate human upper airway model was constructed from multiple magnetic resonance imaging axial scans. This model was used to conduct detailed Computational Fluid Dynamics (CFD) simulations during expiration, to investigate the fluid flow in the airway regions where obstruction could occur. An identical physical model of the same airway was built using stereo lithography. Pressure and velocity measurements were conducted in the physical model. Both simulations and experiments were performed at a peak expiratory flow rate of 200 L/min. Several different numerical approaches within the FLUENT commercial software framework were used in the simulations; unsteady Large Eddy Simulation (LES), steady Reynolds-Averaged Navier-Stokes (RANS) with two-equation turbulence models (i.e. k?ε, standard k?ω, and k?ω Shear Stress Transport (SST)) and with one-equation Spalart–Allmaras model. The CFD predictions of the average wall static pressures at different locations along the airway wall were favorably compared with the experimental data. Among all the approaches, standard k?ω turbulence model resulted in the best agreement with the static pressure measurements, with an average error of ～20% over all ports. The highest positive pressures were observed in the retroglossal regions below the epiglottis, while the lowest negative pressures were recorded in the retropalatal region. The latter is a result of the airflow acceleration in the narrow retropalatal region. The largest pressure drop was observed at the tip of the soft palate. This location has the smallest cross section of the airway. The good agreement between the computations and the experimental results suggest that CFD simulations can be used to accurately compute aerodynamic flow characteristics of the upper airway.     

LDA measurements and numerical prediction of pulsatile laminar flow in a plane 90-degree bifurcation

An experimental and numerical study of pulsatile laminar flow in a plane 90-degree bifurcation is presented. Detailed LDA velocity measurements of the oscillatory flow field have been carried out. The numerical predictions, which are based on an iterative, finite-difference numerical procedure using primitive dependent variables, are in good agreement with the measurements. The results show that one separation zone is established near the bottom wall of the main duct and another near the upstream wall of the branch. The location and size of the separation zones vary within the cycle and are influenced by the Reynolds number, the flow rate ratio, and the Stokes number.     

Wall shear-rate estimation within the 50cc Penn State artificial heart using particle image velocimetry

Particle image velocimetry (PIV) has been gaining acceptance as a routine tool to evaluate the flow fields associated with fluid mechanical devices. We have developed algorithms to investigate the wall shear-rates within the 50cc Penn State artificial heart using low magnification, conventional particle image velocimetry (PIV). Wall shear has been implicated in clot formation, a major post-implant problem with artificial hearts. To address the issues of wall scattering and incomplete measurement volumes, associated with near wall measurements, we have introduced a zero masking and a fluid centroid shifting technique. Simulations using different velocity fields were conducted with the techniques to assess their viability. Subsequently, the techniques were applied to the experimental data collected. The results indicate that the size of the interrogation region should be chosen to be as small as possible to maximize resolution while large enough to ensure an adequate number of particles per region. In the current study, a 16 x 16 interrogation window performed well with good spatial resolution and particle density for the estimation of wall shear rate. The techniques developed with PIV allow wall shear-rate estimates to be obtained from a large number of sites at one time. Because a planar image of a flow field can be determined relatively rapidly, PIV may prove useful in any preliminary design procedure.     

MRI and CFD studies of pulsatile flow in healthy and stenosed carotid bifurcation models

Pulsatile flow was studied in physiologically realistic models of a normal and a moderately stenosed (30% diameter reduction) human carotid bifurcation. Time-resolved velocity measurements were made using magnetic resonance imaging, from which wall shear stress (WSS) vectors were calculated. Velocity measurements in the inflow and outflow regions were also used as boundary conditions for a computational fluid dynamics (CFD) model. Experimental flow patterns and derived WSS vectors were compared qualitatively with the corresponding CFD predictions. In the stenosed phantom, flow in the bulb region of the "internal carotid artery" was concentrated along the outer wall, with a region of low and recirculating flow near the inner wall. In the normal phantom, the converse was found, with a low flow region near the outer wall of the bulb. Time-averaged WSS and oscillatory shear index were also markedly different for the two phantoms.     

Stereoscopic particle image velocimetry analysis of healthy and emphysemic alveolar sac models

Emphysema is a progressive lung disease that involves permanent destruction of the alveolar walls. Fluid mechanics in the pulmonary region and how they are altered with the presence of emphysema are not well understood. Much of our understanding of the flow fields occurring in the healthy pulmonary region is based on idealized geometries, and little attention has been paid to emphysemic geometries. The goal of this research was to utilize actual replica lung geometries to gain a better understanding of the mechanisms that govern fluid motion and particle transport in the most distal regions of the lung and to compare the differences that exist between healthy and emphysematous lungs. Excised human healthy and emphysemic lungs were cast, scanned, graphically reconstructed, and used to fabricate clear, hollow, compliant models. Three dimensional flow fields were obtained experimentally using stereoscopic particle image velocimetry techniques for healthy and emphysematic breathing conditions. Measured alveolar velocities ranged over two orders of magnitude from the duct entrance to the wall in both models. Recirculating flow was not found in either the healthy or the emphysematic model, while the average flow rate was three times larger in emphysema as compared to healthy. Diffusion dominated particle flow, which is characteristic in the pulmonary region of the healthy lung, was not seen for emphysema, except for very small particle sizes. Flow speeds dissipated quickly in the healthy lung (60% reduction in 0.25 mm) but not in the emphysematic lung (only 8% reduction 0.25 mm). Alveolar ventilation per unit volume was 30% smaller in emphysema compared to healthy. Destruction of the alveolar walls in emphysema leads to significant differences in flow fields between the healthy and emphysemic lung. Models based on replica geometry provide a useful means to quantify these differences and could ultimately improve our understanding of disease progression.     

Particle Imaging Velocimetry Evaluation of Intracranial Stents in Sidewall Aneurysm: Hemodynamic Transition Related to the Stent Design

We investigated the flow modifications induced by a large panel of commercial-off-the-shelf (COTS) intracranial stents in an idealized sidewall intracranial aneurysm (IA). Flow velocities in IA silicone model were assessed with and without stent implantation using particle imaging velocimetry (PIV). The use of the recently developed multi-time-lag method has allowed for uniform and precise measurements of both high and low velocities at IA neck and dome, respectively. Flow modification analysis of both regular (RSs) and flow diverter stents (FDSs) was subsequently correlated with relevant geometrical stent parameters. Flow reduction was found to be highly sensitive to stent porosity variations for regular stents RSs and moderately sensitive for FDSs. Consequently, two distinct IA flow change trends, with velocity reductions up to 50% and 90%, were identified for high-porosity RS and low-porosity FDS, respectively. The intermediate porosity (88%) regular braided stent provided the limit at which the transition in flow change trend occurred with a flow reduction of 84%. This transition occurred with decreasing stent porosity, as the driving force in IA neck changed from shear stress to differential pressure. Therefore, these results suggest that stents with intermediate porosities could possibly provide similar flow change patterns to FDS, favourable to curative thrombogenesis in IAs.     

Kinematically irreversible acinar flow: a departure from classical dispersive aerosol transport theories.

Current theories describe aerosol transport in the lung as a dispersive (diffusion-like) process, characterized by an effective diffusion coefficient in the context of reversible alveolar flow. Our recent experimental data, however, question the validity of these basic assumptions. In this study, we describe the behavior of fluid particles (or bolus) in a realistic, numerical, alveolated duct model with rhythmically expanding walls. We found acinar flow exhibiting multiple saddle points, characteristic of chaotic flow, resulting in substantial flow irreversibility. Computations of axial variance of bolus spreading indicate that the growth of the variance with respect to time is faster than linear, a finding inconsistent with dispersion theory. Lateral behavior of the bolus shows fine-scale, stretch-and-fold striations, exhibiting fractal-like patterns with a fractal dimension of 1.2, which compares well with the fractal dimension of 1.1 observed in our experimental studies performed with rat lungs. We conclude that kinematic irreversibility of acinar flow due to chaotic flow may be the dominant mechanism of aerosol transport deep in the lungs.     

Numerical simulation of blood flow in the left ventricle and aortic sinus using magnetic resonance imaging and computational fluid dynamics

Understanding cardiac blood flow patterns has many applications in analysing haemodynamics and for the clinical assessment of heart function. In this study, numerical simulations of blood flow in a patient-specific anatomical model of the left ventricle (LV) and the aortic sinus are presented. The realistic 3D geometry of both LV and aortic sinus is extracted from the processing of magnetic resonance imaging (MRI). Furthermore, motion of inner walls of LV and aortic sinus is obtained from cine-MR image analysis and is used as a constraint to a numerical computational fluid dynamics (CFD) model based on the moving boundary approach. Arbitrary Lagrangian–Eulerian finite element method formulation is used for the numerical solution of the transient dynamic equations of the fluid domain. Simulation results include detailed flow characteristics such as velocity, pressure and wall shear stress for the whole domain. The aortic outflow is compared with data obtained by phase-contrast MRI. Good agreement was found between simulation results and these measurements.     

Computational fluid dynamics analysis of cyclist aerodynamics: Performance of different turbulence-modelling and boundary-layer modelling approaches

This study aims at assessing the accuracy of computational fluid dynamics (CFD) for applications in sports aerodynamics, for example for drag predictions of swimmers, cyclists or skiers, by evaluating the applied numerical modelling techniques by means of detailed validation experiments. In this study, a wind-tunnel experiment on a scale model of a cyclist (scale 1:2) is presented. Apart from three-component forces and moments, also high-resolution surface pressure measurements on the scale model’s surface, i.e. at 115 locations, are performed to provide detailed information on the flow field. These data are used to compare the performance of different turbulence-modelling techniques, such as steady Reynolds-averaged Navier–Stokes (RANS), with several k–ε and k–ω turbulence models, and unsteady large-eddy simulation (LES), and also boundary-layer modelling techniques, namely wall functions and low-Reynolds number modelling (LRNM). The commercial CFD code Fluent 6.3 is used for the simulations. The RANS shear-stress transport (SST) k–ω model shows the best overall performance, followed by the more computationally expensive LES. Furthermore, LRNM is clearly preferred over wall functions to model the boundary layer. This study showed that there are more accurate alternatives for evaluating flow around bluff bodies with CFD than the standard k–ε model combined with wall functions, which is often used in CFD studies in sports.