In Vitro Characterization of Bicuspid Aortic Valve Hemodynamics Using Particle Image Velocimetry
- 1.1k Downloads
The congenital bicuspid aortic valve (BAV) is associated with increased leaflet calcification, ascending aortic dilatation, aortic stenosis (AS) and regurgitation (AR). Although underlying genetic factors have been primarily implicated for these complications, the altered mechanical environment of BAVs could potentially accelerate these pathologies. The objective of the current study is to characterize BAV hemodynamics in an in vitro system. Two BAV models of varying stenosis and jet eccentricity and a trileaflet AV (TAV) were constructed from excised porcine AVs. Particle Image Velocimetry (PIV) experiments were conducted at physiological flow and pressure conditions to characterize fluid velocity fields in the aorta and sinus regions, and ensemble averaged Reynolds shear stress and 2D turbulent kinetic energy were calculated for all models. The dynamics of the BAV and TAV models matched the characteristics of these valves which are observed clinically. The eccentric and stenotic BAV showed the strongest systolic jet (V = 4.2 m/s), which impinged on the aortic wall on the non-fused leaflet side, causing a strong vortex in the non-fused leaflet sinus. The magnitudes of TKE and Reynolds stresses in both BAV models were almost twice as large as comparable values for TAV, and these maximum values were primarily concentrated around the central jet through the valve orifice. The in vitro model described here enables detailed characterization of BAV flow characteristics, which is currently challenging in clinical practice. This model can prove to be useful in studying the effects of altered BAV geometry on fluid dynamics in the valve and ascending aorta. These altered flows can be potentially linked to increased calcific responses from the valve endothelium in stenotic and eccentric BAVs, independent of concomitant genetic factors.
KeywordsTurbulent kinetic energy Viscous shear stress Reynolds shear stress Calcification Fluid mechanics Fluid dynamics Jet eccentricity Stenosis
In about 1–2% of all live births, the human aortic valve only consists of two anomalous leaflets and is known as the bicuspid aortic valve (BAV). BAVs are the most common congenital cardiac anomaly, and are associated with significant valvular dysfunction, including calcific aortic stenosis (AS) and aortic regurgitation (AR), as well as aortic wall abnormalities including coarctation of the aorta, ascending aortic dilatation and aneurysms.9 Clinical studies have indicated that approximately 50% of adults with AS and 25% of adults with infective endocarditis have a bicuspid aortic valve,30,31,36 demonstrating a high correlation to valve pathology. Finally, BAV patients typically require surgery about two decades earlier than patients with a tricuspid AV.7
In spite of being a widespread congenital defect, the presence of a BAV does not imply complications for patients, since many people live with undiagnosed, normally functioning BAVs through their entire lifetime. This merits the question—what causes certain BAV patients to develop complications earlier than others? Multiple studies have hypothesized that complications in patients with BAV disease, specifically aortic dilatation, are caused by a common underlying genetic anomaly (‘genetic theory’).20,23,24 Other studies have identified mutations in the transcription regulator NOTCH-1, as well as suppressed expression of the endothelial nitric oxide synthase (eNOS) in BAV patients.1,13
However, the role of adverse hemodynamics in BAV patients in contributing to accelerated complications cannot be neglected, as indicated by other studies (‘hemodynamic theory’). Robicsek et al.32 noted excessive folding and creasing, and consequently increased leaflet stresses on BAV models. Although this work did not directly demonstrate turbulent flow downstream of BAVs using quantities such as turbulent kinetic energy (TKE), the authors suggested that BAVs are associated with increased levels of turbulent flow in the ascending aorta, based on simplified numerical simulations. PC-MRI studies of BAV patients display eccentric and helical flow in the ascending aorta, which was not observed in any normal volunteers, that can potentially be linked to accelerated disease in BAV patients.18 Recently, Girdauskas et al.15 pointed out the need to acknowledge the role of hemodynamics in the development of disease in BAV patients. Higher wall shear stresses as well as altered extracellular matrix (ECM) protein expression has been observed in the anterolateral wall of the ascending aortas of BAV patients, clearly demonstrating the adverse effect of an eccentric systolic jet.4,5,10 Recently, Weinberg et al.38 conducted a multiscale computational comparison of flow through bicuspid and tricuspid aortic valves, showing increased flexure in the bicuspid models, which can potentially be related to valve calcification.
The aim of the present study is to create and validate an in vitro model of BAVs and obtain high resolution hemodynamic measurements using these models in order to quantitatively assess their altered fluid flow environment. The BAV models were constructed by surgically modifying normal excised porcine aortic valves, and were studied at physiological flow and pressure conditions using Particle Image Velocimetry (PIV). Two BAV models with varying levels of jet eccentricity and stenosis and a trileaflet AV (TAV) model are presented in this study and differences in fluid flow between these models are characterized. The results of this study can provide inputs to mechanobiology experiments where the biological effects of altered hemodynamics can be characterized. This can provide key insights into the role of hemodynamics in causing complications associated with BAVs.
Characterization of BAV Models
The valve dynamics of the models were characterized using high speed imaging and 3D echocardiography. Both these measurements were conducted in the same pulsatile flow loop, with a modified ventricular side that had two lateral inlets and an en face viewing window, for end-on visualization of the valve. The high speed imaging system consisted of a CMOS camera (model A504K, Basler Vision Technologies, PA; 1280 × 1024px) and a Nikon Micro-Nikkor lens (Nikon, Melville, NY; f = 105 mm). Images were acquired at 250 fps over four cardiac cycles and analyzed using a custom Matlab program. The program provides the maximum geometric orifice area (GOA) at PS, the ratio of leaflet areas at peak diastole (D) and the eccentricity of the systolic orifice. GOA of a valve is the area of the systolic orifice formed by the free edges of the leaflets, as measured from planimetry.16,26,27 The GOA is always greater than or equal to the effective orifice area (EOA) of the valve, and can be measured from end-on high speed imaging in in vitro studies, and using CT, MRI or echocardiography in clinical practice. The eccentricity of the systolic orifice is defined as the distance between the orifice center and the annulus center, divided by the annular diameter, measured at PS. Results are calculated as average values calculated over three cardiac cycles using 15 images each at systole and diastole (total of 45 images at each phase). Multiple cycles were sampled to remove effects of cycle-to-cycle variability, while 45 images were sufficient to obtain statistically converged GOA and leaflet area values. An echocardiographic system (iE33, Philips Inc., Andover, MA) was used for characterizing the systolic and diastolic geometries of the valve models, to qualitatively compare to clinically observed BAV morphologies.
Particle Image Velocimetry Experiments
Particle Image Velocimetry is an instantaneous, non-intrusive whole-field optical measurement technique, which has been successfully used to study flow through prosthetic valves in in vitro systems.11,22,29 The present PIV system consisted of a pair of pulsed Nd:YAG lasers (ESI Inc., Portland, OR; 17 mJ energy, 532 nm wavelength, 9 ns pulse duration) and a combination of spherical and cylindrical lenses to create a laser sheet. The flow was seeded with fluorescent polymethyl methacrylate (PMMA) particles (Dantec Dynamics, Denmark, D = 1–20 μm, labeled with Rhodium-B dye, emission at 580 nm). The particles were imaged by a PIV CCD camera (LaVision, Germany, Imager Pro, 1600 × 1200 px) using a Nikon Micro-Nikkor 60 mm lens with an orange filter. The CCD resolution was 16.6 μm/pixel with particle sizes of 2–3 pixels in the image. The field of view of measurement was 45 × 33.75 mm, which covered the aortic section and the visible sinuses for all valve models. Calibration was performed by placing a calibration target with dots in the same plane as the laser sheet. The refractive index of the working fluid was 1.38, which is not matched to the refractive index of the acrylic chamber (n = 1.49). In order to compensate for radial distortions introduced by this mismatch, a 3rd order polynomial fit of the calibration points was utilized, which corrects for the velocity vectors based on the distortion observed with the calibration target. The optics were mounted on a traversing system to enable accurate laser sheet positioning. In this study, three planes of data were acquired (Fig. 2a). Figure 2c shows a representative PIV image from the BAV model showing the various regions of the flow.
50 phase locked image pairs were obtained at 20 time points through the cardiac cycle, indicated by the symbols shown on the representative flow curve in Fig. 2d. It is expected that the ensemble average of these 50 vector fields will indicate the dominant flow features in the flow fields. Although 50 vector fields might not be sufficient to obtain statistically converged values of the derived quantities, qualitative comparisons between different valve models can still be conducted. This was confirmed by qualitative comparison of the ensemble averaged flow fields obtained from increasing number of vector fields.
Uncertainty Analysis of PIV Measurements
The PIV setup used in these experiments primarily suffers from two types of errors—random errors and bias errors. A common method to determine the total uncertainty in PIV is by imaging a known displacement and calculating the displacement using cross-correlation, with the uncertainty defined as the difference between the calculated and the actual measurement. For a plane PIV system similar to one used here, the reported uncertainty in velocity measurement is about 0.2%, which corresponds to an uncertainty of 0.008 m/s at the maximum velocity of 4.0 m/s.28 Using an error propagation analysis as described by Kline and McClintock,21 uncertainties in in-plane velocity gradients calculated using the PIV data can be shown to be proportional to the velocity uncertainty divided by the vector spacing used for gradient calculations. Using the maximum velocity uncertainty calculated above and the spacing between vectors, the maximum uncertainty in vorticity is equal to 11.5 s−1.
Definitions of Calculated Quantities
The reference system used in the current study is shown in Fig. 2c, where the plane of interest is in the X–Y plane, while Z is perpendicular to the interrogation plane. U, V and W are the instantaneous velocity components in the X, Y and Z directions, while u′, v′ and w′ are the instantaneous velocity fluctuations in the three directions.
The quantities relevant to cardiovascular flows which were calculated are:
Flow and pressure parameters of various valve models
Peak systolic transvalvular pressure gradient (mmHg)
Mean systolictransvalvular pressure gradient (mmHg)
Cardiac output (L/min)
Peak flow rate (L/min)
Characterization of Valve Models
Quantities calculated from analysis of high speed images
Ratio of leaflet areas (bicuspid: normal)
Eccentricity of systolic orifice (E) (%)
Velocity Vector Fields—Ascending Aorta
The highest velocities in all the models were seen at PS as expected. The maximum jet velocities for the valve models were: 4.2 m/s for BAV_ECC, 3.1 m/s for BAV_CEN and 2.3 m/s for TAV. BAV_ECC continued to have a strong eccentric jet, resulting in a strong vortex within the non-fused leaflet sinus. The vortex in the fused leaflet sinus appeared to be a secondary vortex, induced by the swirling fluid in the aorta from earlier in the cardiac cycle (ES). BAV_CEN displayed an elongated vortex structure in the aorta, as well as vortices in both the sinuses at PS. In contrast, TAV showed weaker vortex structures compared to the other models, predominantly at the shear region surrounding the central jet. At LS, velocity fields were very similar to those observed at PS, but with lower magnitudes for all models. During D, after the valve closed, the flow fields did not display any coherent structures for all models and the fluid velocities were close to zero across the entire flow field, through gradual dissipation of fluid momentum imparted during systole.
Velocity Vector Fields—Sinus Sections
In the non-fused leaflet sinus of BAV_CEN, the stenotic central jet initially causes entrainment of fluid at the sino-tubular junction, causing reversed velocities at the aortic walls during ES. This appeared to preempt formation of a clockwise vortex structure in the sinuses. High momentum reverse flow along the aortic walls entered the non-fused leaflet sinus close to the leaflet, thus setting up a counter-clockwise vortex in the fused leaflet sinus. This vortex was first seen at PS and remained stationary through the remainder of systole. At LS, the pressure drop in the ventricle forced the aortic valve to shut and fed additional energy into the existing counter-clockwise vortex, which results in the persistence of the same vortex structure into D. Finally, viscous dissipation led to the breakup of this vortex at t = 500 ms. In contrast, the flow in the fused leaflet sinus appeared to be more affected by the forward flow jet, leading to the formation of a counter-clockwise vortex at ES, caused by entrainment of fluid into the strong forward jet. This vortex remained close to the sinus walls until t = 300 ms. In LS, as the forward flow jet diminished in momentum, this vortex structure became unstable and convected away. At ES, no remnants of the vortex remained in the sinus, and there were no coherent structures observed through D.
For TAV, an initial strong counter-clockwise sinus vortex was set up due to the effect of the forward flow jet entraining fluid from the sinus region. This vortex died away rapidly, leaving very little vortex flow close to the sino-tubular junction in the sinus. At PS, no coherent structure was observed in the sinus. When the reverse flow close to the aortic walls was created due to the entrainment by the forward flow jet, a clockwise vortex was set up in the sinus, which was observed from t = 250 to t = 300 ms. This short lived vortex structure appeared to convect toward the leaflet before dissipating away.
Velocity Vector Fields—Variation with z Location
Z Vorticity and Viscous Shear Stress Fields
The VSS plots from the three valve models were very similar to the vorticity plots, where regions of highest viscous shear correlated with the edge of the systolic jet. This is as expected since the highest velocity gradients are expected near the edge of the jet for all models. Although both VSS and ωz are calculated using velocity gradients, their units are different because VSS also contains the dynamic viscosity. The overall trends from these two quantities were very similar. TAV did not display any regions of elevated VSS at any point in the cardiac cycle.
Turbulent Kinetic Energy and Reynolds Shear Stress Fields
The RSS plots resembled the TKE plots, showing that BAV_CEN had highest magnitudes of RSS, corresponding to higher levels of fluctuations in the flow surrounding the systolic jet. In BAV_ECC, the presence of the wall appeared to damp out the fluctuations in the flow field near the edge of the jet. In BAV_CEN, higher fluctuations were observed in the edge of the jet closer to the non-fused leaflet sinus, possibly due to the large vortex structure on that side, as demonstrated in Fig. 7. TAV did not display any regions of elevated RSS at any point in the cardiac cycle.
Validation of BAV Models
Clinically observed BAVs have wide morphological variations in terms of number of leaflets, orientation of fused leaflet, levels of stenosis and jet eccentricity among other factors.34 In an in vitro system, it is impossible to replicate all observed morphologies. In order to study the effects of pure geometric variations in the valve models, two types of BAVs were modeled in this study. This eliminates any other confounders such as genetic variations or concomitant ventricular dysfunction from the analysis, and purely focuses on the geometric influence of altered valve morphology. The two models utilized in this study represent the most commonly observed BAV morphology—fusion of the left and right coronary leaflets.34 The two models differ in stenosis degree and eccentricity of central jet, and we aim to demonstrate how two leaflets in the aortic position can generate differences in the flow fields. It must be noted that these models are not patient specific and represent two common morphologies of BAVs. In comparison to clinically observed BAVs, both BAV models displayed a characteristic “fish mouth” appearance and a reduced EOA at systole. In addition, BAV_ECC also displayed reduced leaflet mobility and an eccentric systolic orifice, as observed in some clinical BAVs.9,34 Further, the use of a bi-lobed sinus for the BAV models is based on clinical observations of excised BAVs.32 Hence, it is expected that these models reasonably model clinically observed BAVs.
Global Flow Characteristics of BAV and TAV Models
Characterization of the flow fields associated with the BAV and TAV models yielded many interesting insights into the fluid flow environment associated with these models. The study of normal AV fluid flow has been the subject of studies in the past.6,25 It is commonly accepted that the aortic sinuses are regions of intense vortex activity due to the entrainment of fluid into these regions, while blood fills the entire ascending aorta distal to the sino-tubular junction during systole. During diastole, a strong reverse pressure wave forces the valve shut, and viscous dissipation makes the flow quiescent later in diastole. In case of the BAV, the presence of only two sinuses as well as valve eccentricity and stenosis resulted in alterations in the entrainment of fluid into these regions. The flow fields associated with BAV_CEN and TAV are similar to those observed in Weinberg and Kaazempur Mofrad38 but the systolic jets in this computational study were symmetric due to assumptions made in modeling. The flow fields observed in BAV_ECC resemble results from PC-MRI measurements in humans, with eccentric systolic jets.12,18
The eccentricity and level of stenosis of the forward flow was a strong determinant of fluid flow in the sinus and ascending aorta, with the eccentricity playing a potentially larger role. As observed in BAV_ECC, the eccentric jet can directly enter the non-fused leaflet sinus due to impaired motion of the fused leaflet and normal motion of the non-fused leaflet, causing very strong vortex formation in this sinus, whereas the other sinus has a much weaker vortex, which only forms later during systole. In BAV_CEN, a more central systolic jet delays vortex formation in the sinuses due to the lack of direct fluid flow into the sinus. Further, since the two sinus geometries are different from each other, the fluid flow on either side of the jet is not symmetric. The fluid flow in the non-fused leaflet sinus shows vortex formation at ES, beyond which the stenosis of the valve model forces this vortex to convect away. The reverse flow close to the wall causes the formation of a vortex of opposite rotation in the sinus, as is the case with BAV_CEN. In this regard, BAV_CEN resembles TAV more than BAV_ECC.
The temporal evolution of the sinus vortices is of potential significance since these vortices directly influence the flow field in the vicinity of the valve leaflets, which in turn modulates the shear stress experienced by the valve leaflet. Previous mechanobiological studies have shown the role of mechanical environment in contribution to calcification on the aortic surface of the aortic valve.2,35,39 It is possible that the temporal variations of shear stress on the aortic surface contribute toward calcific responses from the leaflets. Additionally, it has been clinically observed that the raphe of the fused leaflet experiences the highest amount of calcification in BAVs. The lack of a coherent and strong sinus vortex due to the eccentric central jet might significantly reduce the shear stresses on the fused leaflet, potentially contributing to accelerated disease processes.
The study of streamtraces provided information about the spatial extent of the vortex structures surrounding the systolic jet in the aorta and the sinuses. While the sinus vortices remained almost the same between Z = 0.0 mm and Z = 2.5 mm, the large vortex seen in the aorta of BAV_CEN at Z = 0.0 mm did not appear at Z = 2.5 mm, indicating a very elongated but narrow vortex structure. On the other hand, the long vortex in the aorta of TAV appeared at both Z = 0.0 mm and Z = 2.5 mm, indicating a long and wide vortex structure occupying a much larger region of the flow. These results indicate that the fluid mechanics in both the aorta and sinuses are very dependent on the three dimensional nature of the valve orifice, as well as the level of stenosis of the valve model.11,12,18
Effect of Velocity Gradients, Shear and Fluctuating Velocities in BAV and TAV Models
In this study, the levels of fluid shear and circulation were assessed using the vorticity and VSS as described earlier. Both these quantities were calculated using gradients of the streamwise and spanwise velocities within the plane of interest. An analysis of the individual velocity gradients revealed that ∂U/∂Y is about one order of magnitude larger than all other gradients, indicating that the most significant contributor to vorticity was due to the variation of the streamwise velocity across the edge of the systolic jet. The presence of high VSS suggested high levels of shear experienced by the blood cells in the flow. Although the quantities discussed here are ensemble averaged, the instantaneous plots also reflect the same dominant structures, indicating that the ensemble average faithfully captures the dynamics of the flow. The VSS represents the physical shear stress experienced, as opposed to the RSS which is a pseudo-force, which is purely derived due to the Reynolds decomposition methodology.
The intensity of fluctuations in the fluid flow environment is characterized using the TKE and RSS, which are both derived using fluctuating components of the velocities. These quantities characterize the level of fluctuations introduced by the flow through the valve as well as due to cycle to cycle variations in the fluid flow. The TKE is a sum of the normal fluctuating stresses, whereas the RSS represents the ensemble averaged correlation between the two in-plane velocity components. Although the RSS is more commonly used to correlate to hemolysis and blood damage in mechanical heart valves, it is instructive to study this quantity here since it represents the presence of simultaneous fluctuating velocity components in two orthogonal directions, which is not captured by the TKE. From the results, it was demonstrated that although BAV_ECC had the highest levels of vorticity and VSS, BAV_CEN had the highest levels of TKE and RSS at PS. This is a potential important observation since it implies that higher levels of stenosis do not necessarily correlate to the highest levels of velocity fluctuations in the aorta and sinus regions. In the models studied here, one edge of the systolic jet from BAV_ECC directly impinges on the aortic wall distal to the sino-tubular junction. It is possible that the presence of the aortic wall results in a reduction of the fluctuating intensity in the velocity jet in BAV_ECC. On the other hand, the jet from BAV_CEN does not impinge on the aortic wall directly, leading to sustenance of the velocity fluctuations in the fluid flow. This implied that morphologies similar to BAV_CEN might result in higher levels of fluctuations in the ascending aortic velocity, even though it does not have the most severe stenosis. In general, the BAV models have higher TKE and RSS compared to the TAV, suggesting larger fluctuations through the BAV model. This could be due to the lesser degree of stenosis as well as the presence of three sinuses of the TAV model which could act as a damping mechanism to the valve dynamics, resulting in lesser variation in cycle to cycle flow fields in TAV compared to BAV_ECC and BAV_CEN.
Overall, these results have demonstrated the significantly altered fluid mechanics associated with BAV models compared to TAVs. These altered fluid mechanics directly impact the mechanical forces imparted to both the aortic root as well as the aortic valve leaflets. At the level of the aortic root, higher impinging velocities as well as fluctuating components of velocity could result in progressive tissue alterations due to non-physiological loading. On the leaflets, the presence of shear stresses which are altered in magnitude, directionality and high frequency fluctuations may be related to adverse mechanobiological responses by the valve endothelium. Between the BAV models, the levels of TKE and RSS were not directly correlated to the level of stenosis of the valve model, which implies that valve stenosis might not be the only independent predictor of adverse mechanobiological response, and jet eccentricity might have a key role to play in disease progression. A detailed coupling of fluid mechanical characterization followed by mechanobiological studies can potentially elucidate unfavorable morphologies of BAVs, which might be more prone to disease progression.
The primary limitation of the current study is the in vitro nature of the valve models and experimental setup. These limitations include—lack of compliance in the aorta and valve annulus sections, deviation from in vivo flow and pressure waveforms and idealized valve models. Secondly, the BAV models used in the current study are only representative of a specific morphology of bicuspid valves—fusion of left and right coronary leaflets. The wide variation of valve morphology in patients cannot be captured in the present study. Next, glutaraldehyde fixation is unavoidable due to long experimental time necessary for these studies. High speed imaging of the valves before and after fixation showed little change in leaflet dynamics due to the fixation. It is expected that future studies will use flexible aortic sections to represent more physiologic compliance of the arterial sections. Additionally, coronary flow is not modeled in the current study. The sinus and aortic sections used in this study are idealized and not matched one to one with the leaflet morphologies. Also, the current experimental methodology only provides the in plane velocity components, whereas the flow through the aortic valve is expected to be three-dimensional. However, based on the valve leaflet morphology, it is expected that the planes investigated in this study capture the most important components of the fluid flow environment. The current in vitro studies only capture the isolated effects of geometric changes of the leaflets on levels of fluctuations in the valve models, and do not incorporate any effects of genetic variations across patients. Also, it was difficult to experimentally reproduce the entire range of BAV morphologies due to challenges in making BAV models with minimum stenosis. Finally, other variations in BAV and TAV morphologies might display different flow characteristics, and a detailed statistical study is necessary for generalize these results for other BAV morphologies.
The current study characterizes the variation in hemodynamics across bicuspid aortic valve and trileaflet aortic valve models. It is demonstrated the hemodynamics in the aorta and sinus regions are strongly dependent on the valve morphology, which influence the jet eccentricity and stenosis level. Increased stenosis is observed to correlate with higher VSSs and vorticity. However, level of stenosis is not directly correlated to increased fluctuations in the velocity field, characterized using the TKE and RSS. Such variations in the hemodynamic fields associated with BAVs can potentially influence disease processes associated with this congenital anomaly, in addition to genetic factors.
The authors would like to acknowledge Holifield Farms, Covington, GA and Town & Country Packing Company, Thomson, GA for providing porcine hearts. This study was funded by the American Heart Association Postdoctoral Fellowship Number 10POST3050054 and the Petit Undergraduate Research Scholars Program.
- 3.Batchelor, G. K. An Introduction to Fluid Dynamics. Cambridge Mathematical Library: Cambridge, UK, 1967, p. 660.Google Scholar
- 8.Bonow, R. O., et al. ACC/AHA 2006 guidelines for the management of patients with valvular heart disease: a report of the American College of Cardiology/American Heart Association Task Force on Practice Guidelines (writing committee to revise the 1998 Guidelines for the Management of Patients With Valvular Heart Disease): developed in collaboration with the Society of Cardiovascular Anesthesiologists: endorsed by the Society for Cardiovascular Angiography and Interventions and the Society of Thoracic Surgeons. Circulation 114(5):e84–e231, 2006.PubMedCrossRefGoogle Scholar
- 21.Kline, S. J., and F. A. McClintock. Describing uncertainties in single-sample experiments. Mech. Eng. 75:3–8, 1953.Google Scholar
- 33.Saikrishnan, N. Studies in wall turbulence using dual plane particle image velocimetry and direct numerical simulation data. In: Aerospace Engineering & Mechanics. Minneapolis, MN: University of Minnesota, 2010, p. 224.Google Scholar
- 37.Warnes, C. A., et al. ACC/AHA 2008 guidelines for the management of adults with congenital heart disease: a report of the American College of Cardiology/American Heart Association Task Force on Practice Guidelines (Writing Committee to Develop Guidelines on the Management of Adults With Congenital Heart Disease). Developed in Collaboration with the American Society of Echocardiography, Heart Rhythm Society, International Society for Adult Congenital Heart Disease, Society for Cardiovascular Angiography and Interventions, and Society of Thoracic Surgeons. J. Am. Coll. Cardiol. 52(23):e1–e121, 2008.CrossRefGoogle Scholar