Annals of Biomedical Engineering

, Volume 40, Issue 8, pp 1760–1775 | Cite as

In Vitro Characterization of Bicuspid Aortic Valve Hemodynamics Using Particle Image Velocimetry

  • Neelakantan Saikrishnan
  • Choon-Hwai Yap
  • Nicole C. Milligan
  • Nikolay V. Vasilyev
  • Ajit P. Yoganathan


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.


Turbulent 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.


Valve Models

Three valve models—two BAV and one TAV were constructed for this study from fresh trileaflet aortic valves extracted from porcine hearts obtained from a local abattoir (Fig. 1). The BAV models consisted of the valve annulus, cusps as well as the sinus geometry within a rigid acrylic aortic section. The TAV model consisted of the aortic annulus and the three cusps as excised from the porcine heart. The BAV model was created from the normal trileaflet valve by surgically modifying the leaflets. Triangular portions of two of the aortic valve leaflets were excised, and the same two leaflets were then sutured together to form the fused leaflet of the BAV. While resecting and suturing the tissue, care was taken that the resultant fused leaflet was mobile, and also to prevent creating stenosis. The BAV model had one normal leaflet and one fused leaflet, where the fused BAV leaflet was constructed by suturing the left and right coronary leaflets together to simulate the most common clinically observed morphology of BAVs (Type 1 BAVs).34 The suturing line between the two leaflets simulated the stiff fibrous raphe commonly observed in BAV patients.9,30,34
Figure 1

Valve models used for experiments

The valve models were sutured at the annulus onto 21 mm inner diameter plastic holder rings and the commissures were sutured onto vertical stents to maintain physiological valve geometry—two stents for the BAVs and three stents for the TAV. The native valve sizes were carefully chosen such that there was minimal stretching/crimping on the valve upon suturing to the 21 mm holder ring. The valves were fixed in 0.1% glutaraldehyde to preserve the valves during lengthy experiments and were inserted into transparent idealized acrylic aortic chambers for optical access (Fig. 2a). These chambers had idealized axisymmetric aortic sections and two sinuses for the BAVs and three sinuses for the TAV (Fig. 2b). In the BAV models, the sinus next to the non-fused leaflet is referred to as the “non-fused leaflet sinus,” and the other sinus is referred to as the “fused leaflet sinus.” Two BAV models were constructed for this study—BAV_ECC with an eccentric and stenotic orifice, while BAV_CEN with a central and less stenotic orifice. The variations in eccentricity and stenosis were controlled by carefully manipulating the suturing line while forming the fused leaflet of the BAV models.
Figure 2

(a) Side view of chamber showing planes of data acquisition (b) End on view of bi-lobed (BAV) and tri-lobed sinus (TAV) chambers, and planes of data acquisition (c) Representative PIV image showing the regions of the flow where results will be discussed. The coordinate system used in these studies is shown to the left of the image. (d) Time points of acquisition of PIV images. (a) ES; (b) PS; (c) LS; (d) D

The chambers were attached to the Georgia Tech Left Heart Simulator (Fig. 3), to simulate pulsatile physiological flow and pressure conditions in an in vitro setup.11,22,40, 41, 42 Compliance and resistance elements were adjusted to achieve desired flow and pressure conditions. The cardiac output, ventricular pressure and aortic pressure were measured at 500 Hz using a custom LabView program for 15 cycles, to obtain statistically converged ensemble averaged flow and pressure curves. All data in this study were obtained at physiological flow and pressure conditions [Mean Aortic Pressure (MAP) = 100 mmHg, cardiac output (CO) = 5 L/min, Heart Rate (HR) = 70 beats/min]. A solution of 36% glycerin by volume in water was used as the working fluid to mimic the kinematic viscosity of blood (ν = 3.5 cSt). The Reynolds number (Re = VpeakD/ν) of the flow through these valve models based on the peak bulk velocity at Peak Systole (PS) and aortic diameter was about 5960. The Womersley number \( \left( {Wn = R \sqrt {2\pi f/\nu } } \right) \) based on the radius of the aorta and the fundamental frequency of the pulsatile flow was about 18.
Figure 3

Schematic of flow loop used for pulsatile studies

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.

The time spacing between the two PIV images Δt was optimized at all 20 points in the cardiac cycle, such that the average displacement of the particles between the two images was approximately 25% of the size of the interrogation window.19 Due to the large dynamic range of flow velocities expected in the aorta and sinus regions, two sets of data were acquired—small Δt to calculate aorta flow velocities, and large Δt to calculate sinus flow velocities. It was not possible to obtain these data simultaneously; hence the two fields could not be matched instantaneously. Using the large Δt, only the sinus flow could be resolved, whereas the small Δt was able to provide velocity vectors in both the aorta and sinus regions. A comparison of the ensemble averaged flow fields in the sinus regions from the large and small Δt experiments indicated that both choices of Δt captured the same ensemble averaged flow features in the sinus region. Consequently, it was decided to only report the small Δt measurements in this study. The values of Δt in this experiment varied between 50 μs at PS to 1000 μs at D in the small Δt experiments. The PIV processing protocol is schematically depicted in Fig. 4. Details of the processing protocol can be found in other studies.33
Figure 4

PIV processing protocol using DaVis 7.2 (Lavision, Germany)

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 XY 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:

Z vorticity (ωz): Vorticity (ω) is defined as the curl of the velocity vector and measures the solid-body like rotation of fluid elements rotating about an axis, and can indicates regions of high shear in the flow.3 In the context of the flows studied here, regions of high vorticity can indicate organized coherent swirling motion, which also plays into the energy dynamics of the flow through the aortic valve. The 2D PIV technique used here resolved the vorticity component perpendicular to the field of measurement (ωz). Although the flow fields in the aorta and sinus were three-dimensional in nature, the dominant vorticity component was expected to be perpendicular to the plane of measurement due to the orientation of the shear layer originating from the valve orifice. The Z vorticity is defined as:
$$ \omega_{\text{z}} = \frac{\partial V}{\partial x } - \frac{\partial U}{\partial y} $$
2D turbulent kinetic energy (TKE): The flow velocities can be decomposed into a mean \( \left( {\bar{U}} \right) \) and a fluctuating component \(({u^{\prime } } ) \) using a Reynolds decomposition methodology.3 The mean velocity field at each time point in the cardiac cycle was the average of 50 velocity fields acquired at that time point. The fluctuating component of the velocity field was obtained by subtracting the mean velocities from the instantaneous velocities. TKE refers to the mean kinetic energy per unit mass associated with eddies in turbulent flow. Physically, this quantity is characterized by measuring all three components of the root-mean-square (RMS) velocity fluctuations. In the current study, however, only 2D in-plane PIV measurements were available, so a 2D TKE was defined based on the normal Reynolds stresses in the flow.29 This quantity nonetheless provides information on the levels of kinetic energy associated with eddies in the flow, which is related to the level of fluctuations in the velocity field. The 2D TKE is defined as:
$$ {\text{TKE}} = \frac{1}{2}\left( {\overline{{u^{\prime 2} }} + \overline{{v^{\prime 2} }} } \right) $$
Principal Reynolds shear stress (RSS): The RSS is a mathematical artifact arising from the Reynolds decomposition of the Navier–Stokes equation. The principal RSS has been well-correlated to blood cell damage, and is used to predict potential regions of hemolysis.14 Although native valves are typically not associated with thromboembolic complications, high RSS values indicate regions of high fluctuating stresses, which could potentially trigger unsteady fluid–structure interaction with the leaflets and aortic walls, leading to adverse biological responses. The principal RSS is defined as:
$$ {\text{RSS}} = \rho \sqrt {\left( {\frac{{\overline{{u^{\prime } u^{\prime } }} - \overline{{v^{\prime } v^{\prime } }} }}{2}} \right)^{2} + \left( {\overline{{u^{\prime } v^{\prime } }} } \right)^{2} } $$
Viscous shear stress (VSS): VSS captures the effect of shearing between adjacent layers of fluid, which is a physical force exerted by the fluid on suspended blood cells. The in-plane VSS which can be calculated from the 2D PIV measurements is defined as:
$$ {\text{VSS}} = \mu \left( {\frac{\partial U}{\partial x } + \frac{\partial V}{\partial y}} \right) $$


Hemodynamic Results

The flow and pressure curves obtained from the three valve models are shown in Fig. 5, while the key hemodynamic parameters obtained are listed in Table 1. The pulsatile flow loop was tuned such that the cardiac output and aortic pressure trace of the three valve models was almost identical. Table 1 documents the EOA values for all three valve models. The EOA refers to the area of the vena contracta of the systolic jet originating from a valve, and is commonly used to assess the level of stenosis of a valve. The EOA is a function of both the flow through the valve, as well as the pressure drop across the valve. EOA values from Table 1 indicate that BAV_ECC was severely stenotic, BAV_CEN was moderately stenotic, while TAV had almost no stenosis, based on clinically established thresholds.8,37 BAV_ECC also had the highest mean and peak transvalvular pressure gradients compared to the other two models.
Figure 5

Flow and pressure waveforms from (a) BAV_ECC, (b) BAV_CEN and (c) TAV models. The duration of systole is indicated by the vertical dashed lines

Table 1

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)




EOA (cm2)




Characterization of Valve Models

The various parts of the cardiac cycle are classified as: Early Systole (ES) (100–250 ms), Peak Systole (PS) (250 ms), Late Systole (LS) (250–400 ms) and Diastole (D) (400–860, 0–100 ms). Figure 6 shows representative images from the echocardiographic analysis of the valve models at time points PS and D. BAV_ECC showed restricted motion of the fused leaflet at PS and normal motion of the non-fused leaflet, resulting in an eccentric stenotic orifice with increased transvalvular gradients as seen in table 1. On the other hand, BAV_CEN had normal opening characteristics and lesser stenosis than BAV_ECC, similar to that shown by TAV. All valve models demonstrated adequate coaptation at D, without any noticeable regurgitant jets.
Figure 6

2D echocardiographic images of the three valve models. In the BAV models, the green dashed line indicates the fused leaflet, and the red dashed line indicates the non-fused leaflet

The results of processing the high speed images are presented in Table 2. BAV_ECC had the smallest GOA at PS, caused by the reduced mobility of the fused leaflet. BAV_CEN had larger GOA, with TAV having the highest GOA. Although GOA does not directly relate to the level of valve stenosis, it is a direct representation of leaflet mobility. Both BAVs had a fused to non-fused leaflet area ratio of about 60:40 at D, similar to clinical observations.
Table 2

Quantities calculated from analysis of high speed images





GOA (mm2)




Ratio of leaflet areas (bicuspid: normal)



Eccentricity of systolic orifice (E) (%)




Velocity Vector Fields—Ascending Aorta

Ensemble averaged flow patterns are shown at four representative time points in the cardiac cycle in the central plane in Fig. 7. At ES, BAV_ECC showed an eccentric jet, directed toward the non-fused leaflet, due to the impaired mobility of the fused leaflet. This eccentric jet also caused the formation of a vortex within the non-fused leaflet sinus, as well as in the proximal ascending aorta adjoining the high-speed jet of fluid. In BAV_CEN, the jet was more centrally located in the ascending aorta and no vortex structures were observed in the non-fused leaflet sinus, while a very weak vortex was seen in the fused leaflet sinus. The lower momentum of the central jet due to the lesser stenosis did not induce any vortex structures in the aorta for BAV_CEN. At the same time point for TAV, a starting jet emanating from the valve orifice was observed. This jet immediately induced vortex type structures on either side of its edge. In a three dimensional sense, this is characteristic of a 3-D vortex ring formed by the jet ejection into quiescent fluid in the aorta.17 It must be noted, however, that such a vortex ring is expected to be formed in all valve models, and the ring is captured exactly at ES for TAV, while it occurs slightly earlier for BAV_ECC and BAV_CEN.
Figure 7

Ensemble averaged velocity fields acquired from PIV at points in the cardiac cycle for the three valve models. Red arrows show bulk flow direction. Representative flow curves with the red dots indicate the time point at which the velocity fields were obtained. The black lines indicate streamtraces of velocity indicating the direction of flow

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 order to directly assess the fluid flow environment experienced by the aortic surface of the valve leaflet through the entire cardiac cycle, the flow fields within the sinus regions of the various valve models were investigated. For the two BAVs, fluid flows within the non-fused leaflet sinus and fused leaflet sinus were studied, while only fluid flow within the normal sinus of TAV was analyzed. In TAV, it must be noted that only one side of the image is within the sinus, while the other side is at the commissure of the remaining two leaflets (Fig. 2b). Due to the lack of coronary flow in the present valve model, the fluid flow in the three TAV sinuses is expected to be identical from symmetry considerations. Figure 8 shows representative sinus flow images from the three valve models at PS. In BAV_ECC, the flow within the non-fused leaflet sinus was mainly dictated by the strong eccentric systolic jet, since a part of the forward jet directly enters this sinus. Through the entire duration of systole, a strong, stationary, clockwise vortex was observed in the non-fused leaflet sinus of BAV_ECC. On the other hand, the fused leaflet sinus had lower velocities and weaker vortex dynamics. A clockwise vortex first formed at about t = 200 ms, convected toward the leaflet until t = 325 ms and remained near the leaflet surface until t = 400 ms. In D, the fluid motion in both sinuses was disorganized and did not demonstrate any coherent structures.
Figure 8

Velocity fields in the non-fused leaflet sinus and fused leaflet sinus regions for the two BAV models. For the TAV, only the normal sinus data are shown. The curved arrows show the direction of rotation of the overall flow in the sinus regions. Only every alternate vector is shown for clarity of presentation, and all vectors have uniform length

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

Figure 9 shows the velocity vector fields at PS for the three valve models at three planes, as depicted in Fig. 2b (Z = 0.0 mm, Z = 2.5 mm, Z = 5.0 mm). These flow fields provide a sense of the three dimensional extent of the systolic jet through the various models. In BAV_ECC, the strong eccentric systolic jet seen at Z = 0.0 mm was also observed at Z = 2.5 mm, but with a lower velocity magnitude. The jet characteristics were much weaker at Z = 5.0 mm, indicating that this location was outside the core of the eccentric jet. Although the radius of the geometric orifice was larger than 5.0 mm in Fig. 6, these results indicated that due to flow convergence, Z = 5.0 mm lies outside the central core of the systolic jet. The sinus vortex structures weakened upon moving away from the central plane, with very little coherent fluid motion at Z = 5.0 mm. In BAV_CEN, the width of the flow jet appeared to slightly increase from Z = 0.0 to Z = 2.5 mm, with a reduction in the velocity as observed with BAV_ECC. At Z = 5.0 mm, the flow appeared to widen and move more toward the fused leaflet side. This might be a characteristic of this specific valve model, where there was a slight impairment in the motion of the non-fused leaflet close to the commissural attachments, resulting in a slightly eccentric jet toward the fused leaflet side. Both sinuses displayed weak vortex structures even at Z = 5.0 mm due to the slightly eccentric jet. In TAV, the systolic jet widened from Z = 0.0 to Z = 2.5 mm, with a noticeable decrease in the velocity magnitudes at Z = 5.0 mm. At Z = 5.0 mm, no vortex structure was observed in the normal sinus, indicating that this plane was outside the span of the sinus vortex. Thus, the characteristics at Z = 2.5 mm appear similar to the observations from the central plane, while the plane at Z = 5.0 mm appeared to be outside the span of the vortex structure for all valve models.
Figure 9

Ensemble averaged velocity fields for the three valve models at PS across three planes

Z Vorticity and Viscous Shear Stress Fields

Figure 10 shows the Z vorticity (ωz) and VSS fields at PS at Z = 0.0 mm for all three valve models. In the vorticity plots, regions of red indicate regions of counter-clockwise rotation, while blue regions correspond to clockwise rotation. In the ωz and VSS plots, the highest magnitudes were correlated to the edge of the systolic jet from the valve models. In BAV_ECC, the edge of the jet close to the aortic wall displayed clockwise (negative) vorticity, while the other edge of the jet displayed counter-clockwise (positive) vorticity. This is as expected from the velocity plots shown in Fig. 7. The negative vorticity also fed into the non-fused leaflet sinus region. BAV_CEN also displayed similar characteristics, but with a smaller magnitude of vorticity. TAV showed the lowest magnitudes of vorticity among all valve models, with a smaller and stronger negative vorticity region near the stent attachment point at the top of the field of view.
Figure 10

(a) Out-of-plane vorticity and (b) VSS for all valve models

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

Figure 11 shows the TKE and RSS at PS at Z = 0.0 mm for all three valve models. In contrast to the vorticity and VSS plots, BAV_CEN displayed the highest magnitudes of TKE, while TAV had the least magnitude of TKE. This indicated that although BAV_CEN appeared to have a weaker systolic jet, the levels of velocity fluctuations in the edge of the systolic jet were higher than the stronger systolic jet from BAV_ECC. TAV had very few pockets of high TKE and did not have any coherent regions of large magnitudes of TKE.
Figure 11

(a) TKE and (b) RSS for all valve models

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.


  1. 1.
    Aicher, D., et al. Endothelial nitric oxide synthase in bicuspid aortic valve disease. Ann. Thorac. Surg. 83(4):1290–1294, 2007.PubMedCrossRefGoogle Scholar
  2. 2.
    Balachandran, K., et al. Elevated cyclic stretch alters matrix remodeling in aortic valve cusps: implications for degenerative aortic valve disease. Am. J. Physiol. Heart Circ. Physiol. 296(3):H756–H764, 2009.PubMedCrossRefGoogle Scholar
  3. 3.
    Batchelor, G. K. An Introduction to Fluid Dynamics. Cambridge Mathematical Library: Cambridge, UK, 1967, p. 660.Google Scholar
  4. 4.
    Bauer, M., et al. Configuration of the ascending aorta in patients with bicuspid and tricuspid aortic valve disease undergoing aortic valve replacement with or without reduction aortoplasty. J. Heart Valve Dis. 15(5):594–600, 2006.PubMedGoogle Scholar
  5. 5.
    Bauer, M., et al. Different hemodynamic stress of the ascending aorta wall in patients with bicuspid and tricuspid aortic valve. J. Card. Surg. 21(3):218–220, 2006.PubMedCrossRefGoogle Scholar
  6. 6.
    Bellhouse, B. J., and T. Talbot. The fluid mechanics of the aortic valve. J. Fluid Mech. 35(4):721–735, 1969.CrossRefGoogle Scholar
  7. 7.
    Beppu, S., et al. Rapidity of progression of aortic stenosis in patients with congenital bicuspid aortic valves. Am. J. Cardiol. 71(4):322–327, 1993.PubMedCrossRefGoogle Scholar
  8. 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
  9. 9.
    Braverman, A. C., et al. The bicuspid aortic valve. Curr. Probl. Cardiol. 30(9):470–522, 2005.PubMedCrossRefGoogle Scholar
  10. 10.
    Cotrufo, M., et al. Different patterns of extracellular matrix protein expression in the convexity and the concavity of the dilated aorta with bicuspid aortic valve: preliminary results. J. Thorac. Cardiovasc. Surg. 130(2):504–511, 2005.PubMedCrossRefGoogle Scholar
  11. 11.
    Dasi, L. P., et al. Vorticity dynamics of a bileaflet mechanical heart valve in an axisymmetric aorta. Phys. Fluids 19(6):067105(1)–067109(17), 2007.CrossRefGoogle Scholar
  12. 12.
    den Reijer, P. M., et al. Hemodynamic predictors of aortic dilatation in bicuspid aortic valve by velocity-encoded cardiovascular magnetic resonance. J. Cardiovasc. Magn. Reson. 12:4, 2010.CrossRefGoogle Scholar
  13. 13.
    Garg, V., et al. Mutations in NOTCH1 cause aortic valve disease. Nature 437(7056):270–274, 2005.PubMedCrossRefGoogle Scholar
  14. 14.
    Giersiepen, M., et al. Estimation of shear stress-related blood damage in heart valve prostheses—in vitro comparison of 25 aortic valves. Int. J. Artif. Organs 13(5):300–306, 1990.PubMedGoogle Scholar
  15. 15.
    Girdauskas, E., et al. Is aortopathy in bicuspid aortic valve disease a congenital defect or a result of abnormal hemodynamics? A critical reappraisal of a one-sided argument. Eur. J. Cardiothorac. Surg. 39(6):809–814, 2011.PubMedCrossRefGoogle Scholar
  16. 16.
    Goland, S., et al. Assessment of aortic stenosis by three-dimensional echocardiography: an accurate and novel approach. Heart 93(7):801–807, 2007.PubMedCrossRefGoogle Scholar
  17. 17.
    Hope, T. A., et al. Comparison of flow patterns in ascending aortic aneurysms and volunteers using four-dimensional magnetic resonance velocity mapping. J. Magn. Reson. Imaging 26:1471–1479, 2007.PubMedCrossRefGoogle Scholar
  18. 18.
    Hope, M. D., et al. Bicuspid aortic valve: four-dimensional MR evaluation of ascending aortic systolic flow patterns. Radiology 255(1):53–61, 2010.PubMedCrossRefGoogle Scholar
  19. 19.
    Keane, R. D., and R. J. Adrian. Optimization of particle image velocimeters. I. Double pulsed systems. Meas. Sci. Technol. 1(11):1202–1215, 1990.CrossRefGoogle Scholar
  20. 20.
    Keane, M. G., et al. Bicuspid aortic valves are associated with aortic dilatation out of proportion to coexistent valvular lesions. Circulation 102(19 Suppl 3):III35–III39, 2000.PubMedGoogle Scholar
  21. 21.
    Kline, S. J., and F. A. McClintock. Describing uncertainties in single-sample experiments. Mech. Eng. 75:3–8, 1953.Google Scholar
  22. 22.
    Leo, H. L., et al. Fluid dynamic assessment of three polymeric heart valves using particle image velocimetry. Ann. Biomed. Eng. 34(6):936–952, 2006.PubMedCrossRefGoogle Scholar
  23. 23.
    Nistri, S., et al. Aortic root dilatation in young men with normally functioning bicuspid aortic valves. Heart 82(1):19–22, 1999.PubMedGoogle Scholar
  24. 24.
    Pachulski, R. T., A. L. Weinberg, and K. L. Chan. Aortic aneurysm in patients with functionally normal or minimally stenotic bicuspid aortic valve. Am. J. Cardiol. 67(8):781–782, 1991.PubMedCrossRefGoogle Scholar
  25. 25.
    Peskin, C. S. Numerical analysis of blood flow in the heart. J. Comput. Phys. 25(3):220–252, 1977.CrossRefGoogle Scholar
  26. 26.
    Pouleur, A. C., et al. Planimetric and continuity equation assessment of aortic valve area: Head to head comparison between cardiac magnetic resonance and echocardiography. J. Magn. Reson. Imaging 26(6):1436–1443, 2007.PubMedCrossRefGoogle Scholar
  27. 27.
    Pouleur, A. C., et al. Aortic valve area assessment: multidetector CT compared with cine MR imaging and transthoracic and transesophageal echocardiography. Radiology 244(3):745–754, 2007.PubMedCrossRefGoogle Scholar
  28. 28.
    Prasad, A. K., et al. Effect of resolution on the speed and accuracy of particle image velocimetry interrogation. Exp. Fluids 13(2–3):105–116, 1992.CrossRefGoogle Scholar
  29. 29.
    Querzoli, G., S. Fortini, and A. Cenedese. Effect of the prosthetic mitral valve on vortex dynamics and turbulence of the left ventricular flow. Phys. Fluids 22:041901, 2010.CrossRefGoogle Scholar
  30. 30.
    Roberts, W. C. The congenitally bicuspid aortic valve. A study of 85 autopsy cases. Am. J. Cardiol. 26(1):72–83, 1970.PubMedCrossRefGoogle Scholar
  31. 31.
    Roberts, W. C., and J. M. Ko. Frequency by decades of unicuspid, bicuspid, and tricuspid aortic valves in adults having isolated aortic valve replacement for aortic stenosis, with or without associated aortic regurgitation. Circulation 111(7):920–925, 2005.PubMedCrossRefGoogle Scholar
  32. 32.
    Robicsek, F., et al. The congenitally bicuspid aortic valve: how does it function? Why does it fail? Ann. Thorac. Surg. 77(1):177–185, 2004.PubMedCrossRefGoogle Scholar
  33. 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
  34. 34.
    Sievers, H. H., and C. Schmidtke. A classification system for the bicuspid aortic valve from 304 surgical specimens. J. Thorac. Cardiovasc. Surg. 133(5):1226–1233, 2007.PubMedCrossRefGoogle Scholar
  35. 35.
    Sucosky, P., et al. Altered shear stress stimulates upregulation of endothelial VCAM-1 and ICAM-1 in a BMP-4- and TGF-beta1-dependent pathway. Arterioscler. Thromb. Vasc. Biol. 29(2):254–260, 2009.PubMedCrossRefGoogle Scholar
  36. 36.
    Ward, C. Clinical significance of the bicuspid aortic valve. Heart 83(1):81–85, 2000.PubMedCrossRefGoogle Scholar
  37. 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
  38. 38.
    Weinberg, E. J., and M. R. Kaazempur Mofrad. A multiscale computational comparison of the bicuspid and tricuspid aortic valves in relation to calcific aortic stenosis. J. Biomech. 41(16):3482–3487, 2008.PubMedCrossRefGoogle Scholar
  39. 39.
    Xing, Y., et al. Cyclic pressure affects the biological properties of porcine aortic valve leaflets in a magnitude and frequency dependent manner. Ann. Biomed. Eng. 32(11):1461–1470, 2004.PubMedCrossRefGoogle Scholar
  40. 40.
    Yap, C. H., et al. Experimental measurement of dynamic fluid shear stress on the aortic surface of the aortic valve leaflet. Biomech. Model. Mechanobiol. 11:171–182, 2011.PubMedCrossRefGoogle Scholar
  41. 41.
    Yap, C. H., et al. Experimental technique of measuring dynamic fluid shear stress on the aortic surface of the aortic valve leaflet. J. Biomech. Eng. 133(6):15, 2011.CrossRefGoogle Scholar
  42. 42.
    Yap, C. H., et al. Experimental measurement of dynamic fluid shear stress on the ventricular surface of the aortic valve leaflet. Biomech. Model. Mechanobiol. 11:231–244, 2011.PubMedCrossRefGoogle Scholar

Copyright information

© Biomedical Engineering Society 2012

Authors and Affiliations

  • Neelakantan Saikrishnan
    • 1
  • Choon-Hwai Yap
    • 1
  • Nicole C. Milligan
    • 1
  • Nikolay V. Vasilyev
    • 2
  • Ajit P. Yoganathan
    • 1
  1. 1.Wallace H. Coulter Department of Biomedical EngineeringGeorgia Institute of Technology & Emory UniversityAtlantaUSA
  2. 2.Children’s Hospital BostonHarvard Medical SchoolBostonUSA

Personalised recommendations