Analysis of thrombosis risk of commissural misaligned transcatheter aortic valve prostheses using particle image velocimetry

: Due to excellent clinical results, transcatheter aortic valve replacement (TAVR) has evolved to a treat-ment option for patients with low surgical risk, resulting in an increasing demand for durable heart valve prostheses. Durability of TAVR could be limited by leaﬂet thrombosis. Thrombus formation in the aortic root is mainly affected by the hemodynamic situation, which is dependent on the positioning of the implant. We investigated the ﬂow ﬁeld in the aortic root after TAVR implantation by means of particle image velocimetry. To quantify the inﬂuence of the implant-position with respect to an alignment or misalignment of the leaﬂet commissures on the thrombogenic potential, we used a transport equation for residence time (RT) to consider washout behavior. Furthermore, we introduced a shear effect criterion (SIE) to address platelet activation as a measure for a potential thrombus formation. Misaligned implantation of a TAVR resulted in a reversed direction of rotation of the occurring recirculation area. This led to ﬂuid ﬂow with comparable areas of increased relative blood RT (RT aligned : 97.6%, RT misaligned : 88.0%) and a smaller area of low shear load for the misaligned TAVR (SIE aligned : 57.7%, SIE misaligned : 3.70%) into the sinus region, indicating a higher potential for thrombus formation.


Introduction
Transcatheter aortic valve replacement was introduced as an alternative treatment for patients with severe aortic valve stenosis, who exhibit a too high risk for surgical aortic valve replacement (SAVR) [1].During the last years clinical studies reported noninferiority of transcatheter aortic valve replacement (TAVR) against SAVR in patients at intermediate surgical risk [2,3].These findings substantiate the implantation of TAVR as a valid treatment of severe aortic valve stenosis even in patients with a low-risk profile and younger patients.However, TAVR implantation in younger patient raised concerns regarding the durability of the implant because of a longer life expectancy of the patients [4].In this context, detailed investigation of leaflet thrombosis and the associated reduction of the leaflet motion as a potential risk for late adverse clinical effects are coming into focus of research [5].Regarding the Virchow's triad, hemodynamics in the aortic root, the target region for the implant, is found to be one key aspect for the thrombus formation among endothelial injury and hypercoagulation [6].
The hemodynamic situation in the aortic root is strongly influenced by the geometrical situation and the positioning of the TAVR [7].But although the position of the implant with respect to its implant height in the annulus is considered important, the orientation of the TAVR regarding the commissural alignment of the native aortic valve commissures is currently not in the focus of the physicians [8].In contrast, during the surgical procedure the bioprosthetic valve is aligned to the native aortic root anatomy by the surgeon.The long-term significance of shortcomings of the so-called commissural misalignments of TAVR is not fully understood due to the relative recency of this topic and the long-term follow-up data needed for its evaluation [9].
Recently, the relevant ISO standard for heart valve testing, has been revised, and the newly published version ISO 5840:1 includes experimental flow field assessment as part of the evaluation of the thrombogenic und hemolytic potential of TAVR [10].Various experimental studies addressing the thrombogenic potential has been investigated [11][12][13][14], but only few research groups address the hemodynamic alteration due to the misalignment of the TAVR and the native valve commissures.Salmonsmith et al. investigated the effect of an aligned and misaligned SAPIEN XT valve (Edwards Lifescience, Irvine, CA, USA) on the hemodynamic situation by means of monoscope particle image velocimetry (mono PIV) [15].Even though global hemodynamic parameters were found to be similar, local vortex structures differ and may influence the washout behavior.A specific washout criterion was not used in this study.Hatoum et al. published 2018 an experimental study regarding to the impact of implantation depth and rotational orientation on Valve-in-Valve sinus flow [16].The risk of thrombosis was assessed by means of shear rates and the sinus particle washout.In this experiment, a TAVR was implanted in a bioprosthetic surgical aortic valve, and the effect of rotation orientation was studied.It was found that a commissural alignment had a better washout than a 60 • misaligned TAVR.
Since, a poor washout is associated with the development of thrombosis, hemodynamic criterion describing the washout are often used to quantify thrombogenic potential.The most common criterion is the number of remaining particles in the sinus after one or more cardiac cycles [16].To the authors' knowledge, this approach in the context of TAVR was first proposed by the working group with Hatoum et al. in 2018 [16].
A similar criterion has also been published, determining the number of cycles required until all particles have been washed out of the sinus [13,[17][18][19][20].However, both metrics refer to the approach of seeding a finite number of particles at a defined time into the sinus region and calculating the trajectories of the particles based on the velocity field.A large number of particles is required to obtain a statistically independent result.In addition, the position and timing of seeding could influence the washout result.
An alternative approach to assess the thrombogenic potential of TAVR has been proposed by our working group using a convection-diffusion equation to evaluate washout based on experimentally evaluated flow field [21].This approach has already been used in silico models and calculates the blood residence time as a passive scalar transport of time [22,23].An advantage of this approach is the calculation of a passive scalar that is used to calculate a surrogate parameter for the washout or the activation level of platelets in the entire measured flow field, independent of particle positioning or seeding time.
The purpose of our experimental study is, to assess the flow field in the vicinity of a TAVR by means of PIV and to quantify the influence of alignment and misalignment on the thrombogenic potential of TAVR.We used a transport equation for residence time as post-processing routine to consider the washout behavior [21].Furthermore, we extended the post-processing routine with a shear effect criterion to account for platelet activation in the thrombosis assessment model as well.

Measurement setup
The setup used for this measurement campaign essentially corresponds to the experimental setup already described in Borowski et al. [24].However, the setup components and acquisition properties used, as well as the approach to assess the risk of thrombosis, are described in more detail in the following chapter.To assess the velocity field in TAVR, both a hydraulic replication of the cardiovascular circulation for physiological flow conditions and a suitable PIV setup were required.Furthermore, the anatomical model of the implantation environment and the two TAVR implantation configurations with commissural alignment and misalignment, respectively, are described.

Hydraulic replication of the cardiovascular circulation
The experimental setup was configured according to anatomical and physiological conditions in the vicinity of the aortic valve.A commercially available pulse duplicator system (ViVitro Inc., Victoria, BC, Canada) was used to generate physiological flow and pressure conditions of the cardiovascular circulation, see Figure 1.The pulsatile flow was driven by a programmable piston pump (1) compressing a silicone membrane (2) in the ventricle chamber via a pump fluid.The silicone membrane mimicked the contraction of left ventricle to produce a pulsatile flow in the test circuit.During expansion of the ventricular membrane, test fluid from the atrial test fluid reservoir (3), which was opened to the atmosphere, passes through the mitral valve replacement (4) into the ventricle.Upon compression of the ventricular membrane by the pump fluid, the mitral valve replacement closed, and the test fluid was pumped into the PIV chamber containing the aortic root model with the implanted TAVR (5).The PIV chamber featured examination windows to provide optical access for the camera and the light source of the PIV setup.By connecting two Windkessel chambers (6) to the setup the compliance of the aorta was imitated.The crossflow heat exchanger (7) and a variable flow resistance (8) were used to adjust physiological temperature and pressure characteristics.The flow and the ventricular and aortic pressures were measured by an electromagnetic flow sensor with an analogue flowmeter (Carolina Medical Electronics, NC, USA) (9) and pressure sensors (Type 86A, TE Connectivity Corp., PA, USA) (10), (11) [25].
The tests were performed at a heartbeat of 70 beats per minute, with 35% of systolic duration of the whole cardiac cycle, a mean aortic pressure of 100 mmHg and a cardiac output of 5 l/min.
To measure the velocity field in the vicinity of the TAVR, we developed a generic aortic root model, based on patient specific CT-data of TAVR patients [26].The aortic root model consists of a tubular shaped inflow area proximal of the TAVR (D inflow = 24 mm), see Figure 1.The shape of the sinus valsalvae was defined based on the description of Reul et al. with an epitrochoidal form and was further modified [27].The height and sinusoidal expansion were also evaluated from the CT data analyses.The outflow region was also modeled with a tubular cross-section but adapted to the diameter of the sinutubular junction (D STJ = 30 mm).The native leaflets were modeled as a thin tube section (D R = 24 mm, h = 12 mm, d = 1 mm) according to ISO 5840:1 [10].
The aortic root model was made of a transparent silicone (Sylgard 184, The Dow Chemical Company, Midland, MI, USA) with a refractive index of 1.410 nD.The molds required for the silicone casting were manufactured additively by means of 3D printing (printer: Objet30, material: RGD 525, both Stratasys Ltd., Rechovot, Israel).
In order to obtain high accuracy of the flow field assessment by PIV, a suitable blood substitute fluid, that fulfills the requirements for kinematic viscosity on the one hand and optical characteristics on the other hand, is one key aspect.Numerous approaches to prepare blood substitute fluids can be found in literature depending on the aimed viscosity and refractive index, including saline solutions [28], water (or saline) glycerol mixtures [29], or more complex multicomponent mixtures [30,31].The ISO 5840:1 recommends a kinematic viscosity of  = 3.5 cSt for blood substitute fluids [10].
For this study, a mixture of a 0.9% saline solution (NaCl solution) and glycerol (mixing ratio m glycerol /m mixture = 0.506) with a density of  = 1.1 g/cm 3 and a kinematic viscosity of  = 3.5 cSt at a temperature  = 37 • C was used.A temperature regime of  = 37 • C ± 2 • C allowed to handle the TAVR at the recommended and physiological temperature.Details of the development of a suitable mixing ratio have been published before [32].To minimize optical refraction, the test fluid used in the test chamber is located both outside and inside the aortic root model (see (5) in Figure 1).

Transcatheter aortic valve aligned and misaligned implantation configuration
A self-expanding TAVR prototype with a stent consisting of a nickel titanium alloy and porcine leaflets was used.The implantation of the TAVR was performed, according to the instructions for use of the device, with a dedicated catheter in a water bath at 37 • C. The TAVR was implanted intra-annular, meaning that the basal attachments of the prosthetic leaflets were positioned at the same height as the basal attachments of the native leaflets.
The effect of commissural misalignment on the thrombogenic potential was studied with two different implantation configurations.First, the velocity field was measured for a commissural aligned TAVR in which the commissures of the native aortic valve and the prosthetic aortic valve matched, see Figure 2 (left).In this configuration, the bulbus of the aortic sinus and the valve leaflets are also aligned and form a nearly spherical structure.
The measurements were repeated with a TAVR implanted exactly 60 • displaced to the commissures of the native aortic valve and the aortic sinus, see Figure 2 (right).

Particle image velocimetry setup
A PIV setup from Dantec Dynamics and the corresponding DynamicStudio 7.1 software (Dantec Dynamics, Skovlunde, Denmark) was utilized for flow field assessment.With an orthogonal orientation of the PIV camera to the laser light sheet, two velocity components (2C) of the flow could be measured in the two-dimensional measurement plane (2D).The arrangement of the pulse duplicator with the TAVR, the light sheet optic of the laser and the camera is shown in Figure 3

(left).
A double-pulsed Nd:YAG laser (Litron Laser Ltd., Rugby, UK) was used to illuminate the measurement plane.The laser beam was expanded to a 1 mm wide laser light plane using a light sheet optic.Fluorescent microparticles with a diameter of d p = 10 μm (micro particles GmbH, Berlin, Germany) were added to the test fluid.The particles absorbed the laser light ( laser = 532 nm) and emitted light with a wavelength of  = 607 nm.A CMOS camera (EoSens 12CXP+, Mikroton, Gilching, Germany) was used to acquire the particle displacement.In front of the camera lens, a suitable long-pass filter was mounted to absorb light with a wavelength below  filter = 590 nm.In this way, reflections of the TAVR stent or leaflets could be minimized.To determine the scalar factor in the measurement plane, a point target was used.
Particle images were acquired phase-averaged with an external trigger signal from the pulse duplicator system.
In this way, n = 100 particle images could be acquired for each time point.A previously performed sensitivity analysis showed that the number of images is sufficient for phase averaging (data not shown).Within the cardiac cycle 172 time points were recorded leading to a temporal resolution with a time step of Δt = 5 ms for the detection of the velocity field.Three different time delays (Δt = 100 μs, 1000 μs, 2000 μs) between the double images were used and all images were analyzed with each time delay.This resulted in a total of 51.600 double images for each TAVR configuration to detect the velocity field in the vicinity of the TAVR.
An acquired particle image with the TAVR in the aortic root model is shown in Figure 3.In particular, the region of interest (ROI) localized in the sinus is associated with the development of leaflet thrombosis and was therefore analyzed in more detail.
During post-processing, an averaged image was determined based on n = 100 images at each time point and for each time delay.Subsequently, this averaged image was then subtracted from all images of this time point and time delay to eliminate light artifacts.A mask was defined to include was achieved for the measurement field.The detected particle images with 4096 pixels × 3072 pixels were divided into interrogation areas (IA) of 32 pixels × 32 pixels.For each IA, an averaged displacement vector was calculated using the grad level distribution and a cross-correlation algorithm.
The so-called mosaic method [32] was applied to accurately detect the broad range of flow velocities which occurred over the cardiac cycle as well as within the measuring plane at each time point especially during the ejection phase.This approach improved the precision of the results by using a shorter time delay for higher velocities and a longer time delay for low velocities.Subsequentially, by calculating the standard deviation for each time delay in every IA, a valid velocity vector could be selected.
Based on these velocity data for each configuration, the thrombosis risk assessment could be applied as postprocessing routine.

Thrombosis risk assessment
To evaluate the risk of thrombosis, we chose two fluid mechanic predictors -shear induced effect and residence time -that are commonly associated with the thrombosis formation [33,34].Based on previous publication in Borowski et al. [21], we decided to use Eulerian transport equations as a mathematical approach to calculate the surrogate parameters for thrombosis risk evaluation.The Eulerian transport equation was solved by means of a numerical approach.The PIV velocity field was implemented to calculate the convective term of the transport equations.
The first aspect refers to platelet activation caused by shear stress.The occurrence of high shear rates of the blood flow is associated with platelet activation [33].Both, the value of the shear stress and the duration of the shear load, are relevant [35].To estimate the shear influence on thrombogenic potential, we calculated the transport of a passive scalar called shear induced effect (SIE):

+ d𝑣 dx
The diffusive transport of the shear stress was assumed to be negligible [36].The initial concentration of SIE at the inflow was assumed to be zero.Thus, only the shear rates due to the present velocity field in the measurement area within one cardiac cycle was considered.For better comparability, SIE was normalized to the maximum SIE values, which was obtained at corresponding time step.
Another aspect to evaluate the thrombogenic potential of TAVR is the aggregation of platelets due to high residence time.Especially in recirculation and stagnation zones, a high residence time can be expected.The residence time of blood in a defined region can also be calculated using a convection-diffusion equation, as it has been done in some numerical simulation for TAVR [22,37]: )) + 1 The passive scalar was defined as residence time (RT), which increases by the defined time increment through the source term of one at each calculated time step.The distribution of the RT is influenced by the convective and diffusive terms.The diffusivity of blood was also neglected for the calculation of the residence time.A concentration of RT = 0 was specified at the inflow, so that the washout in the vicinity of the TAVR can be derived from the measured velocity field.The residence time at each time point was normalized by the current time of the cardiac cycle (relative blood residence time).
Both transport equations were calculated using a numerical solver provided by the FEATool Multiphysics app (Precise Simulation Ltd., Hong Kong) implemented in Matlab (MathWorks, Massachusetts, USA).Implementing the time-dependent PIV velocity fields as a boundary condition in the fluid domain, a transient numerical simulation was performed to solve the transport equations.For this purpose, the geometry was determined from the masking of the PIV post-processing for which PIV velocity information were available at each time point in the fluid domain.The fluid domain was discretized by triangular elements.For the transient calculation of the scalar transport equations, the "backslash" solver of FEATool was used with a time step size of 0.0001 s and a convergence criterion of 1e-06.

Results
The two-dimensional velocity fields of eight time points of the cardiac cycle are shown in Figures 4 and 5.
The results of the TAVR aligned to the native commissures are shown in Figure 4.In the measured plane, the  systolic jet flow is slightly deflected to the sinusoidal side of the aorta.The jet flow of the TAVR creates recirculation areas at the shear layer, which can already be seen at TP 2. The recirculation zone becomes larger with decreasing jet flow and weakens until it finally dissipated during the diastolic phase (TP3 -TP8).
For comparison, Figure 5 shows the results of the misalignment TAVR.At the beginning of the systole, a slightly increased peak velocity can be detected compared to the aligned TAVR results (aligned: 1.0 m/s vs. misaligned: 1.3 m/s).Furthermore, during the ejection phase (TP2), the jet flow is not diverted towards the sinus side, but to the opposite direction.Consequently, a large recirculation vortex is formed at the sinus side distal the TAVR (TP3 & TP4) so that fluid was transported into the sinus by the vortex formation.
Differences in flow topology could be also identified during diastole.Especially the recirculation area, which also occurred at TP5, was oriented counterclockwise.
Based on the flow field, the local and temporal distribution of SIE and RT in the vicinity of a TAVR were examined to assess the influence of commissural alignment on the thrombogenic potential.As a result of the different flow topologies between aligned and misaligned TAVR, high SIE values were transported to the sinuses in the misaligned case.
The histogram shows the relative area with respect to different SIE values in the ROI, see Figure 8.It can be seen that the shear effect of the misaligned TAVR is higher compared to the aligned positioning.
Figures 9 and 10 show the spatial and temporal results of the Eulerian transport equation for the calculation of the relative RT of blood in the vicinity of a TAVR.
The results of the commissural aligned TAVR are shown in Figure 9.As expected, due to the convective term, the region of low relative RT during systolic phase are located in the jet flow region and also depict the diversion of the flow towards the sinus side of the aorta.After TAVR closure at the onset of diastole, there is also a larger area with lower   9,0% 2,6% 0,0% 0,0% 0,0% 0,0% 0,0% 0,0% Histogramm shear induced effect (SIE) Aligned TAVR 0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0 0% 0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9   relative RT compared to the non-sinus side.However, in the ROI, a large area of high RT is found toward the end of diastole.In the area directly above the ROI, lower values of relative RT can be identified.The local and temporal distribution of relative blood RT with misaligned TAVR shows similar results.A jet flow in this configuration diverted to the non-sinus side, recognizable by a region of low RT.Accordingly, at the beginning of the diastolic phase, the region with lower RT is on the non-sinus side.Identical to the commissural aligned configuration of TAVR, a large area of high RT can be found in the ROI at the end of the diastolic phase for the misaligned TAVR.Increased relative RT values were also identified in the region above the ROI.

Discussion
By performing PIV measurements, we could assess the flow field of an aligned and misaligned TAVR.Furthermore, we evaluated the thrombogenic potential by means of Eulerian hemodynamic criteria.
In general, the fluid mechanical functionality of the TAVR was ensured for both -aligned and misaligned positioning.This result matches with the experimental studies from Salmonsmith et al.They found that the global hemodynamic characteristics of the tested TAVR, such as effective orifice area, the mean transvalvular systolic pressure drop and the forward flow energy losses, fulfills in all configurations the required limits according to the ISO standard [15].However, they found different vortex structures implicating that the aligned configuration could be favorable due the washout of the sinus by means of local vortices.As shown in our results, the circumferential positioning of TAVR could have an impact in the local flow field.Vortex formations which are responsible for blood transport from the main flow to the sinuses were affected be the alignment of the device.In our case the misaligned TAVR promotes the transport of blood into the sinus.But our results indicate that the fluid, which was transported into the sinuses, was previously exposed to high shear values.In the scenario of a blood flow, the platelets could be activated as a result of high shear load.In combination with the high residence time within the sinuses the thrombogenic potential with our proposed assessment model is thus higher in the misaligned case compared to the commissural aligned TAVR.This thesis is supported by clinical findings of Rashid et al., who showed an association between the occurrence of late thrombosis and misalignment [38].
Since commissural alignment in TAVR has only recently become the focus of clinical research, there is a clear gap in understanding the long-term clinical impact of commissural alignment according to Khalid and O'Sullivan [9].
By expanding the patient population to include younger patients, new aspects arise, such as coronary access for further coronary interventions or valve-in-valve implantation [8], which support the relevance of the analysis regarding circumferential positioning of TAVR.Ideally, a THV with low skirt or commissure height that is designed to achieve commissure-to-commissure alignment with the native aortic valve is desirable to facilitate future coronary access after TAVR [39].But still no official instructions from THV manufacturers exist to achieve commissural alignment [40].
Therefore, experimental studies as we described within this manuscript are essential tools for further TAVR investigation to analyze the impact of TAVR positioning on the hemodynamic situation and so on the thrombogenic potential.Further studies will concentrate on the threedimensional measurement of the flow field due to its complex flow topology by means of tomographic PIV.Our results suggest that a holistic approach considering not only washout but also shear induced activation is necessary to reflect the complex hemodynamic situation in TAVR.

Limitations
It should be noted that the experiments were conducted by means of a mono PIV setup, so only two velocity components were measured from the anticipated three-dimensional flow.In addition, flow was measured in a plane placed centrally in the aortic root.However, it can be assumed that those secondary flows also occur transversely to the main flow, which was not considered.The blood substituting fluid has Newtonian properties and thus has no shear rate dependent viscosity.Another limitation is the rigid geometry used as boundary condition for our post-processing routine, meaning that the closure and opening of the valve was not considered by means of a moving boundary.Furthermore, due to difficult optical accessibility, the flow in the neo sinus could not be detected.

Conclusions
In particular, the enhancement of the durability of TAVR for the treatment of younger patients has led to an increased interest in long-term implant failures due to the lifethreatening consequences of implant malfunction.
Our results indicate for the misaligned TAVR that the fluid, which was transported into the sinuses, was previously exposed to high shear values.In the scenario of a blood flow, the platelets could be activated as a result of high shear load.In combination with the high residence time within the sinuses the thrombogenic potential is thus higher in the misaligned case compared to the commissural aligned TAVR.
In addition, it seems to be necessary for the evaluation of the thrombogenic potential of TAVR not only to consider the washout behavior but also the shear history of the blood flow.We found that an Eulerian approach by means of scalar transport equation is suitable to obtain high resolved predictions of different surrogate parameters for experimental results.This post-processing routine can also be adapted to numerical studies and is therefore appropriate for comparison of numerical and experimental studies.
It is generally accepted that both hemodynamic factors raise the thrombogenic potential of cardiovascular implants.We conclude that the implantation strategy regarding implant positioning may influence the TAVR durability and should be critically considered.The presented results indicate that the implantation strategy of a TAVR should not only focus on implantation height with respect to regurgitation but also on the alignment of native and prosthetic commissures.

Figure 1 :
Figure 1: Setup of the hydrodynamic circulation loop (pulse duplicator system) to simulate physiological and pathophysiological flow and pressure conditions.

Figure 2 :
Figure 2: Comparison of implantation configuration for the commissural aligned TAVR (left) and the commissural misaligned TAVR (right) in the aortic root model as side view and top view.

Figure 3 :
Figure 3: Arrangement of the PIV setup with the pulse duplicator system, the laser light sheet optic, and the CMOS camera (left), and visualization of a particle image of TAVR flow within the aortic root model with the region of interest in the sinus (right).

Figure 4 :
Figure 4: PIV-measured velocity fields at eight time points within the cardiac cycle using a 2D2C-PIV setup.The velocity magnitude is color-scaled and the flow direction is shown by the two-dimensional velocity vectors.The TAVR was implanted in alignment with the native commissures.Time point (TP) 1: acceleration during systolic phase, TP 2: developed jet during systolic phase; TP 3 and 4: deceleration of the flow after valve closure during early diastolic phase; TP 5: growth of recirculation zone; TP 6 to 8: backflow in the sinuses.

Figure 5 :
Figure 5: PIV measured velocity fields at several time points within the cardiac cycle using a 2D2C PIV setup.The velocity magnitude is color-scaled and the flow direction is shown by the two-dimensional velocity vectors.The TAVR was implanted in a 60 • misalignment with the native commissures, time point (TP) 1: acceleration during systolic phase, TP 2: developed jet during systolic phase; TP 3 and 4: deceleration of the flow after valve closure during early diastolic phase; TP 5: growth of recirculation zone; TP 6 to 8: backflow in the sinuses.

Figures 6
Figures 6 and 7 show the local distribution of SIE at eight time points for the commissural aligned and misaligned TAVR, respectively.It can be seen in both configurations that increased SIE values occurred at the shear layer of the systolic jet.Furthermore, high SIE values occurred at the boundary of recirculation zones.As a result of the different flow topologies between aligned and misaligned TAVR, high SIE values were transported to the sinuses in the misaligned case.The histogram shows the relative area with respect to different SIE values in the ROI, see Figure8.It can be seen that the shear effect of the misaligned TAVR is higher compared to the aligned positioning.Figures9 and 10show the spatial and temporal results of the Eulerian transport equation for the calculation of the relative RT of blood in the vicinity of a TAVR.The results of the commissural aligned TAVR are shown in Figure9.As expected, due to the convective term, the region of low relative RT during systolic phase are located in the jet flow region and also depict the diversion of the flow towards the sinus side of the aorta.After TAVR closure at the onset of diastole, there is also a larger area with lower

Figure 6 :
Figure 6: Local distribution of the shear induced effect at several time points within the cardiac cycle for the commissural aligned TAVR, time point (TP) 1: acceleration during systolic phase, TP 2: developed jet during systolic phase; TP 3 and 4: deceleration of the flow after valve closure during early diastolic phase; TP 5: growth of recirculation zone; TP 6 to 8: backflow in the sinuses.

Figure 7 :
Figure 7: Local distribution of the shear induced effect at several time points within the cardiac cycle for the commissural misaligned TAVR, time point (TP) 1: acceleration during systolic phase, TP 2: developed jet during systolic phase; TP 3 and 4: deceleration of the flow after valve closure during early diastolic phase; TP 5: growth of recirculation zone; TP 6 to 8: backflow in the sinuses.

Figure 8 :
Figure 8: Histogram of the relative area with respect to different SIE values in the ROI.

Figure 9 :
Figure 9: Local distribution of relative blood residence time at some time points in the cardiac cycle for TAVR aligned with native commissures, time point (TP) 1: acceleration during systolic phase, TP 2: developed jet during systolic phase; TP 3 and 4: deceleration of the flow after valve closure during early diastolic phase; TP 5: growth of recirculation zone; TP 6 to 8: backflow in the sinuses.

Figure 10 :
Figure 10: Local distribution of relative blood residence time at some time points in the cardiac cycle for TAVR misaligned with native commissures (rotation 60 • ), time point (TP) 1: acceleration during systolic phase, TP 2: developed jet during systolic phase; TP 3 and 4: deceleration of the flow after valve closure during early diastolic phase; TP 5: growth of recirculation zone; TP 6 to 8: backflow in the sinuses.

Figure 11 :
Figure 11: Histogram of relative blood residence time in the region of interest (ROI) after one cardiac cycle comparing commissural aligned TAVR (left) versus commissural misaligned TAVR (right).