Computational Assessment of Valvular Dysfunction in Discrete Subaortic Stenosis: A Parametric Study

Abstract

Purpose.

Discrete subaortic stenosis (DSS) is a left-ventricular outflow tract (LVOT) obstruction caused by a membranous lesion. DSS is associated with steep aortoseptal angles (AoSAs) and is a risk factor for aortic regurgitation (AR). However, the etiology of AR secondary to DSS remains unknown. This study aimed at quantifying computationally the impact of AoSA steepening and DSS on aortic valve (AV) hemodynamics and AR.

Methods.

An LV geometry reconstructed from cine-MRI data was connected to an AV geometry to generate a unified 2D LV-AV model. Six geometrical variants were considered: unobstructed (CTRL) and DSS-obstructed LVOT (DSS), each reflecting three AoSA variations (110°, 120°, 130°). Fluid-structure interaction simulations were run to compute LVOT flow, AV leaflet dynamics, and regurgitant fraction (RF).

Results.

AoSA steepening and DSS generated vortex dynamics alterations and stenotic flow conditions. While the CTRL-110° model generated the highest degree of leaflet opening asymmetry, DSS preferentially altered superior leaflet kinematics, and caused leaflet-dependent alterations in systolic fluttering. LVOT steepening and DSS subjected the leaflets to increasing WSS overloads (up to 94% increase in temporal shear magnitude), while DSS also increased WSS bidirectionality on the inferior leaflet belly (+0.30-point in oscillatory shear index). Although AoSA steepening and DSS increased diastolic transvalvular backflow, regurgitant fractions (RF<7%) remained below the threshold defining clinical mild AR.

Conclusions.

The mechanical interactions between AV leaflets and LVOT steepening/DSS hemodynamic derangements do not cause AR. However, the leaflet WSS abnormalities predicted in those anatomies provide new support to a mechanobiological etiology of AR secondary to DSS.

Introduction

Discrete subaortic stenosis (DSS) consists of the progressive obstruction to systolic blood flow due to the formation of a thin fibromuscular ring of tissue in the left ventricular (LV) outflow tract (LVOT). The lesion occurs in 6% of children with congenital heart defects and accounts for 8–30% of total pediatric LVOT obstructions¹. While there have been nearly 400 publications describing the clinical forms of DSS, the pathogenesis of DSS and its complications are largely unknown and the different etiologies proposed to date remain hypothetical. Key characteristics of the lesion are its rapid growth and its association with a high-velocity jet and a high pressure gradient across the LVOT^1,2. One of the hallmarks of DSS is its strong association with LVOT anatomical defects such as a steep aortoseptal angle (AoSA, angle between the long axis of the aorta and the septum)^3–5, which are thought to cause derangement of systolic LVOT blood flow^2,4.

DSS is associated with a spectrum of complications among which the most prevalent, aortic regurgitation (AR), affects 26–81% of the adult DSS patient population^5–8. AR secondary to DSS has been attributed to the extension of fibroelastic strands from the lesion to the adjacent aortic valve (AV) leaflets, resulting in impaired leaflet coaptation due to increased tensile forces toward the LV^9,10. However, long-term follow-up reports of DSS patients challenge this proposed etiology as AR symptoms persist in 20–40% of those undergoing membrane resection^2,5–7. Despite the paucity of clinical data on DSS hemodynamics and secondary valvular insufficiency, information collected to date suggests two possible alternate or concurrent etiologies for DSS-induced AR. First, incomplete leaflet coaptation could be the result of abnormal mechanical interactions between the AV and the stenotic LVOT flow. Supporting clinical evidence for this pathway includes the existence of an asymmetric systolic leaflet stutter and the impingement of the LVOT jet on the ventricular surface of the leaflets^2,11. Second, the pathogenesis of AR secondary to DSS, whose progression includes valvular inflammation, scarring, and ultimate cusp thicknening^12,13, could be the result of the progressive biological adaption of the leaflet tissue to the abnormal DSS hemodynamics. This mechanobiological etiology is supported by the existence of fluid wall shear stress (WSS) abnormalities in LV anatomies prone to DSS¹⁴, the demonstrated sensitivity of AV tissue to its mechanical environment^15,16, and the ability of WSS alterations to promote AV leaflet inflammation and remodeling^17–20. The assessment of those potential etiologies requires the thorough investigation of the hemodynamic interactions between the DSS membrane and the AV leaflets, the fundamental biomechanical mechanisms that underly DSS development, and their potential relationship to AR, which, to date, remains largely unknown.

In vivo imaging techniques such as Doppler echocardiography and phase-contrast magnetic resonance imaging have been used to diagnose and monitor AR progression^6,12, but their limited spatial resolution impedes their ability to accurately quantify leaflet dynamics and small-scale flow features. Benchtop in vitro methods such as particle-image velocimetry have been implemented to assess the interventricular velocity field, spatial velocity gradients, and leaflet kinematics^21,22 at higher spatiotemporal resolutions. However, the need to maintain optical access to the flow and the challenge to mimic the native LV deformation has hampered the accurate characterization of native ventricular and valvular hemodynamics. As an alternative, patient-specific computational fluid dynamics modeling has provided critical insights into valvular function and hemodynamics^23,24. In the context of DSS, computational modeling has been used to assess valvular performance in the presence of subaortic stenosis resulting from hypertrophic cardiomyopathy, and has revealed that the obstruction substantially alters leaflet kinematics, especially during coaptation²⁵. Other computational studies aimed at characterizing AV hemodynamics have provided valuable insights into valvular function and hemodynamics, but have typically implemented simplified upstream LVOT flow conditions^26,27. As revealed by a recent computational study comparing the effects of inlet conditions on valvular and aortic flows²⁸, the prescription of non-native, simplified LVOT flow conditions substantially affected valvular hemodynamics and leaflet WSS, justifying the need for considering native LVOT flow profiles for the accurate computational characterization of AV flow.

To address this need, more focus has been put on the design of unified LV-AV computational models. While the native ventricular wall motion can be directly prescribed as a boundary condition in those models^24,29, the simulations of native AV function and leaflet deformation are still particularly challenging. Previous LV-AV flow simulations have addressed this challenge by either directly prescribing an imposed leaflet displacement as a boundary condition^30,31, or by modeling the valve as a stationary or rigid structure^32–35. Fluid-structure interaction (FSI) modeling strategies, which account for the transfer of momentum between the deforming leaflets and the surrounding blood flow, have provided a more accurate characterization of the native LV-AV hemodynamics^23,36. Although FSI studies have suggested that small-scale structures in the LV are capable of altering leaflet kinematics³⁷, no investigation to date has elucidated the effects of LVOT anatomical derangements or obstructions on AV hemodynamics and function. As suggested by a computational LV model recently published by our group, LVOT flow patterns are sensitive to such derangements, and LVOT obstruction caused by DSS results in a marked increase flow velocity, and the development of a rich and complex vortex dynamics in the LVOT¹⁴. However, the exclusion of the AV and aortic root from that earlier study prevented the investigation of the leaflet kinematics and hemodynamic stresses, which may play a role in AR development. Therefore, the present study aimed at characterizing computationally AV function and hemodynamics in LVOT anatomies prone to DSS (i.e., steep AoSA), and obstructed by DSS in order to provide new mechanistic insights into the clinical association between DSS and AR.

Materials and Methods

LV-AV Geometry

As AR is more commonly observed in adult DSS patients^5–7, cardiac cine-MRI data acquired from a healthy 25-year old male volunteer using a 3T scanner (Discovery MR750w, GE Healthcare, Chicago, IL) were used to reconstruct a two-dimensional (2D) LV geometry. Images were acquired in the 3-chamber view (field of view: 320 mm; spatial resolution: 0.625 mm) on the mid-plane intersecting the apex and mitral/aortic valves. The end-systolic LV anatomic boundary was segmented using Segment³⁸ v2.2 R6435 (Medviso AB, Lund, Sweden), and finalized in SolidWorks (Dassault Systèmes, Vélizy-Villacoublay, France) to produce a spatially-smooth geometry (Figure 1A). The valve structures and papillary muscles were excluded due to the insufficient spatial resolution of the original images.

Figure 1.

Unified left ventricular-aortic valve (LV-AV) model geometry: A) schematic showing the LV-AV assembly, the fluid domain and the bounding fictitious solid shell geometry, B) left ventricular outflow tract (LVOT) geometries with the three aortoseptal angle (AoSA) configurations considered in this study (CTRL: unobstructed LVOT; DSS: LVOT anatomy obstructed with subaortic lesion), and C) AV geometry, leaflet opening angle (θ), and wall shear stress (WSS) characterization sites

Six LV geometrical variants were considered to model an unobstructed (CTRL) and a DSS-obstructed LVOT (DSS), each reflecting three AoSA variations (110°, 120°, 130°) (Figure 1B). The CTRL and DSS geometries enabled the isolation of the hemodynamic impact of the DSS lesion, while the range of AoSAs, which matched that reported by echocardiographic measurements in DSS patients³, was implemented to isolate the hemodynamic impact of LV anatomical defects conducive to DSS development. The membrane was modeled as a compliant structure (length: 10 mm; thickness: 1 mm) mimicking the cross-section of the typical crescent-shaped obstruction³⁹, and was attached to the septal wall 8-mm upstream of the AV¹². This position and those dimensional characteristics resulted in a 25% reduction in luminal diameter, which is consistent with the typical degree of stenosis reported in previous case studies^40,41.

A 2D AV model previously designed by our group²⁶ was attached to the outlet of the LV models to generate unified LV-AV geometries. The valve consisted of two identical leaflets (superior leaflet and inferior leaflet) housed within two symmetric aortic sinuses (Figure 1C). Each leaflet was modeled as a thin structure (uniform thickness: 420 μm) attached to the aortic root along the base of the sinus. Straight orifice extensions were added to the sinotubular junction (length: 29 mm; width: 20.1 mm) and the mitral inlet (length: 2 mm; width: 24.4 mm) to improve numerical stability and allow for downstream hemodynamic development.

Modeling Strategy

Overview

Flow simulations in the six LV-AV geometries required the implementation of different numerical strategies to model: 1) the native motion of the LV wall, 2) the fluid-structure interactions between the AV leaflets and the blood flow, and 3) the fluid-structure interactions between the DSS membrane and the blood flow (DSS models only). In addition, in an effort to effectively isolate the sole effect of LV anatomical defects (i.e., steep AoSA with/without DSS lesion) on valvular hemodynamics and function, the six LV models were subjected to the same LV wall deformations and flow boundary conditions.

LV Wall Motion

LV wall deformation data were generated from the cine-MRI dataset used to reconstruct the initial LV geometry. 29 image frames were captured over one cardiac cycle with a total duration of 0.772 s. The LV wall section located below the LVOT was manually segmented on each frame by fitting a cubic spline contour at the luminal boundary¹⁴. This procedure resulted in 29 spline contours reflecting the native LV deformation over one cardiac cycle. As this temporal resolution was too coarse for adequate hemodynamic assessment, a smaller time step was obtained by first discretizing each contour into 80 nodes and then interpolating the location of each node using a cubic spline between two consecutive time frames^29,42. The strategy was implemented via an automatic MATLAB procedure (The Mathworks Inc., Natick, MA, USA), and resulted in the generation of 60 intermediate positions. One cardiac cycle consisted of 1,766 LV total contours and an effective temporal resolution of 0.4375 ms.

LV Flow Modeling

Following a similar approach to that implemented in our previous work¹⁴, LV flow was computed via a one-way FSI strategy using the commercial software ANSYS 19.2 (ANSYS Inc., Canonsburg, PA, USA). The fluid domain boundary was first reconstructed in ANSYS Mechanical as a fictitious solid shell model. The LV wall displacement calculated in the previous step was then prescribed as a boundary condition for each contour node at each time step. The resulting motion was then transmitted to ANSYS Fluent as a moving wall boundary condition using the ANSYS System Coupling module. As it was only used as a tool to transmit displacement data, the fictitious solid shell was modeled as an isotropic linear elastic material (density: 1000 kg/m³, Young’s Modulus: 10 GPa, Poisson’s ratio: 0.001) to improve structural convergence^14,42.

The flow equations were computed via an arbitrary Lagrangian-Eulerian (ALE) strategy⁴³, in which a dynamic mesh was fixed to the deforming fluid boundary and smoothed/remeshed at each time step to maintain an acceptable grid quality. The governing flow equations consisted of the continuity and Navier-Stokes equations in their ALE forms:

$$\nabla \cdot \overline{\mathbf{V}}=0$$ (1)

and

$${\rho }_f\left\{\frac{\partial \overline{\mathbf{V}}}{\partial t}+\left[\left(\overline{\mathbf{V}}-{\overline{\mathbf{V}}}_w\right)\cdot \nabla \right]\overline{\mathbf{V}}\right\}=\nabla \cdot {\overline{\overline{\mathbf{\tau }}}}_f+{\overline{\mathbf{f}}}_f,$$ (2)

respectively, where $\overline{\mathbf{V}}$ is the fluid velocity vector, ρ_f is the fluid density, ${\overline{\mathbf{V}}}_w$ is the moving mesh velocity vector, ${\overline{\overline{\mathbf{\tau }}}}_f$ is the fluid stress tensor, and ${\overline{\mathbf{f}}}_f$ is the body force per unit volume. Those equations were solved iteratively until the criterion for numerical convergence (continuity residual < 0.001) was reached. Blood was approximated as a laminar, incompressible, Newtonian fluid (ρ_f = 1050 kg/m³; μ = 0.0035 kg/m.s), consistent with previous LV flow simulations^30,31.

The boundary conditions at the mitral inlet and aortic outlet consisted of transient and spatially uniform velocity profiles derived from the time-rate of change in LV volume imposed by the wall deformation captured from MRI. The diastolic (0 < t < 0.480 s) to systolic (0.480 < t < 0.772 s) ratio was approximately 2:1, and mitral valve closure was simulated by enforcing zero flow velocity at the mitral inlet. A pressure condition was applied to the aortic leaflet surface during diastole in ANSYS Mechanical to assist valve closure despite the absence of aortic flow pressure in the model. This pressure was progressively ramped from 0 Pa during the deceleration phase (t = 0.68 s) to 500 Pa at the end of systole (t = 0.772 s) to achieve numerical convergence and realistic leaflet closure.

AV-Flow and DSS-Flow Interactions

The dynamics of the AV leaflets and the DSS membrane were computed via a two-way FSI modeling strategy, which accounted for the transfer of momentum between those structures and the surrounding blood flow. The compliant AV leaflets were approximated using an isotropic linear elastic material model (Young’s modulus: 0.37 MPa, Poisson’s ratio: 0.4), which has been shown to mimic realistic leaflet function in 2D²⁶. Due to the unavailability of mechanical test data on DSS lesions, the DSS membrane was approximated using the same material model and properties as the AV leaflets.

The leaflets and lesion deformations were computed by solving the structure momentum equation:

$${\rho }_s\stackrel{\mathbf{..}}{{\overline{\mathbf{d}}}_s}=\nabla \cdot {\overline{\overline{\mathbf{\tau }}}}_s+{\overline{\mathbf{f}}}_s,$$ (3)

where ρ_s is the structure density, ${\overline{\mathbf{d}}}_s$ is the local structure displacement vector, ${\overline{\overline{\mathbf{\tau }}}}_s$ is the structure stress tensor, and ${\overline{\mathbf{f}}}_s$ is the body force per unit volume of either the leaflet or DSS lesion domain. Those equations were coupled to the flow equations (1) and (2) by enforcing continuity of displacements, velocities (no-slip), and traction at the fluid-structure interfaces:

$$\{\begin{array}{l}{\overline{\mathbf{d}}}_s={\overline{\mathbf{d}}}_f\hfill \\ {\stackrel{.}{\overline{\mathbf{d}}}}_s=\overline{\mathbf{V}}\hfill \\ {\overline{\overline{\mathbf{\tau }}}}_s\cdot {\widehat{\mathbf{n}}}_s={\overline{\overline{\mathbf{\tau }}}}_f\cdot {\widehat{\mathbf{n}}}_f\hfill \end{array},$$ (4)

respectively, where ${\overline{\mathbf{d}}}_f$ is the local fluid displacement, and ${\widehat{\mathbf{n}}}_s$ and ${\widehat{\mathbf{n}}}_f$ are the leaflet/lesion and fluid unit normal vectors to the fluid-structure interface. The resulting system of equations (1) – (4) were solved iteratively at each time step. Progress of the coupled solution was monitored by assessing the root mean square (RMS) of the normalized change in data transfer values between successive iterations. Convergence at each time step was considered achieved when the change in data transfer quantities resulted in RMS < 0.01.

Computational Domains Discretization

The fluid domain was discretized using unstructured wedge cells. Following a mesh sensitivity analysis conducted previously in a similar LV geometry¹⁴, a characteristic cell size of 175 μm was adopted to discretize the fluid domain. This cell size resulted in grid sizes of 328,587, 331,830, and 335,535 cells for the CTRL-130°, −120°, and −110° models, respectively, and 323,371, 336,212, and 335,828 cells for the DSS-130°, −120°, and −110° models, respectively. The structural domains occupied by the AV leaflets and the DSS membrane were discretized using unstructured tetrahedral cells. An appropriate grid resolution for the AV leaflets was determined by comparing the total deformation and von Mises stresses predicted under steady peak-systolic flow conditions using increasingly refined mesh sizes (153 to 802 elements per leaflet). Mesh independence was considered reached when a change in total deformation and von Mises stress between two consecutive grid sizes became smaller than 5% and 10%, respectively. Those criteria were met as the number of elements was increased from 368 to 516, which resulted in a 1.3 % and 9.9% change in total deformation and von Mises stress, respectively. Therefore, each leaflet was discretized using 368 elements to produce mesh-independent results. Based on a previous mesh sensitivity analysis conducted on a similar DSS lesion and LV geometry¹⁴, the membrane structural domain was discretized using 556 elements.

Hemodynamic Analysis

Velocity and Vorticity

LV flow was characterized in terms of the in-plane velocity vector field $({\overline{\mathbf{V}}}_{12})$ and the out-of-plane vorticity $({\overline{\Omega }}_{12})$ field defined as:

$${\overline{\mathbf{V}}}_{12}=u_1{\widehat{\mathbf{e}}}_{\mathbf{1}}+u_2{\widehat{\mathbf{e}}}_{\mathbf{2}}$$ (5)

and

$${\overline{\mathbf{\Omega }}}_{\mathbf{12}}=\left(\frac{\partial u_2}{\partial x_1}-\frac{\partial u_1}{\partial x_2}\right){\widehat{\mathbf{e}}}_{\mathbf{3}},$$ (6)

respectively, where u_i is the instantaneous velocity component along the direction x_i.

Leaflet WSS

To investigate local WSS alterations on each leaflet, the ventricular surface was discretized into three circumferentially aligned regions (width: 4 mm) representing the leaflet base, belly, and tip (see Figure 1C).

WSS characteristics were then captured using the instantaneous WSS component τ₁₂, the temporal shear magnitude (TSM), and the oscillatory shear index (OSI) defined as:

$${\mathbf{\tau }}_{12}=\mu \left(\frac{\partial u_1}{\partial x_2}+\frac{\partial u_2}{\partial x_1}\right),$$ (7)

$$TSM=\frac{1}{T}{\int }_0^T\left|{\tau }_{12}\right|dt,$$ (8)

and

$$OSI=\frac{1}{2}\left[1-\frac{\left|{\int }_0^T{\tau }_{12}dt\right|}{{\int }_0^T\left|{\tau }_{12}\right|dt}\right],$$ (9)

respectively, where T is the cardiac period. The TSM characterized the time-averaged magnitude of the WSS over one cardiac cycle, while the OSI quantified the oscillatory nature of the WSS signal (OSI=0: purely pulsatile/unidirectional; OSI=0.5: purely oscillatory/bidirectional).

Leaflet Kinematics

Leaflet kinematics were characterized by tracking the instantaneous leaflet opening angle (θ, Figure 1C) between valve opening (t = 0.5 s) and the onset of valve closure (t = 0.7 s). The maximum (θ_max) and average (θ_avg) leaflet opening angles were captured over this time interval for each leaflet, and the degree of systolic flutter was quantified as the range of opening angles predicted for each leaflet over this period. The degree of leaflet symmetry was estimated by quantifying the R-squared (R²) value between the instantaneous opening angles of the inferior and superior leaflets defined as⁴⁴:

$$R^2={\left(\frac{{\sum }_{i=1}^n\left({\theta }_{\text{sup},i}-{\overline{\theta }}_{\text{sup}}\right)\left({\theta }_{\text{inf},i}-{\overline{\theta }}_{\text{inf}}\right)}{\sqrt{{\sum }_{i=1}^n{\left({\theta }_{\text{sup},i}-{\overline{\theta }}_{\text{sup}}\right)}^2{\sum }_{i=1}^n{\left({\theta }_{\text{inf},i}-{\overline{\theta }}_{\text{inf}}\right)}^2}}\right)}^2,$$ (10)

where n is the number of temporal data points evaluated, and ${\overline{\theta }}_{\text{sup}}$ and ${\overline{\theta }}_{\text{inf}}$ represent the sample mean for the respective leaflet angles ( R² = 1: perfectly symmetric, R² = 0 : perfectly asymmetric).

Valvular Regurgitation

Valvular regurgitation was quantified in terms of the regurgitant fraction (RF),

$$RF=\frac{S{V}_{LVOT}-S{V}_{MV}}{S{V}_{LVOT}},$$ (11)

where SV_LVOT and SV_MV are the LVOT and MV stroke volume, respectively. Consistent with the technique used in the clinic for Doppler echocardiography-based AR assessment⁴⁵, those quantities were estimated as the product of the velocity-time integral over the aortic and mitral annulus, respectively, and the aortic and mitral annulus cross-sectional area, respectively,

$$S{V}_{LVOT}=\left({\int }_{systole}{\overline{\mathbf{V}}}_{12}\cdot {\widehat{\mathbf{n}}}_{\mathbf{aa}}dt\right)\times A_{aa}$$ (12)

and

$$S{V}_{MV}=\left({\int }_{\mathit{\text{diastole}}}{\overline{\mathbf{V}}}_{12}\cdot {\widehat{\mathbf{n}}}_{\mathbf{ma}}dt\right)\times A_{ma},$$ (13)

where ${\widehat{\mathbf{n}}}_{\mathrm{aa}}$ and ${\widehat{\mathbf{n}}}_{\mathrm{ma}}$ are the unit vectors normal to the line representing the aortic and mitral annulus, respectively, and A_aa and A_ma are the aortic and mitral annulus cross-sectional areas, respectively. SV_LVOT and SV_MV were then obtained by multiplying this quantity by the annulus cross-sectional area (A_aa = 20.1mm²; A_ma = 24.4 mm²), which was approximated as rectangular in this 2D representation. The RF values predicted in both groups were expressed relative to the value computed in the CTRL-130° model.

Results

Each model was run for four cardiac cycles to achieve temporal convergence. The data described in this section were captured during the last cycle.

Vorticity and Velocity Fields

Animations of the mean velocity vector and vorticity contour fields predicted during systole in all three models are included in Online Resource 1. Snapshots of the LVOT flow field predicted during the acceleration phase, at peak systole, during the deceleration phase, and during leaflet coaptation are shown in Figure 2.

Figure 2.

Snapshots of the velocity vector and vorticity contour fields captured in the control (CTRL) and discrete subaortic stenosis (DSS) groups during diastole (t = 0.45 s), the acceleration phase (t = 0.55 s), at peak systole (t = 0.60 s), during the deceleration phase (t = 0.68 s), and during coaptation (t = 0.77 s)

The presence of the AV had a weak impact on the upstream interventricular hemodynamics, as suggested by the strong similarities between the global flow structures captured by the model and those reported in our previous work in the absence of AV¹⁴. Diastolic filling in the CTRL models was dominated by the formation of similar clockwise (CW) vortices within the LVOT (v₁). The increased convective acceleration of the mitral jet combined with the flow separation from the sharp mitral-aortic junction contributed to the formation of this vortex, which migrated toward the LVOT later during late diastole due to flow deceleration. The dominant CW vortex (v₁) had essentially the same size, position, and magnitude in all CTRL models. In contrast, the DSS models predicted the entrapment of this vortex between the membrane and the valve, which resulted in its radial elongation. In addition, the interactions between the DSS membrane and the diastolic LV flow resulted in alternating vortex shedding patterns from the lesion tip, whose frequency (~25 Hz) was substantially higher than that of the cardiac cycle (1.3 Hz). The vortex dynamics predicted in the DSS models was marked by the formation, growth, migration, and eventual attenuation of smaller counterclockwise (CCW, v₂) and CW (v₃) vortices in the LVOT, and their interactions with the initial CW vortex (v₁).

The flow conditions predicted in the different geometries generated case-specific AV systolic hemodynamics. AoSA steepening in the CTRL group was characterized by both increased flow asymmetry and average vorticity magnitude (up to 47% increase vs. CTRL-130°). The combination of the DSS lesion and decreasing AoSA exacerbated both flow asymmetry and average vorticity magnitude (up to 69% increase vs. CTRL-130°; up to 26% increase vs. DSS-130°). During the acceleration phase (t = 0.55 s), shear layers extended from the tip of the leaflets as a result of the increased orifice jet momentum. The interaction between the ejected blood flow and the nearly stagnant aortic flow caused the shear layers to roll up within the sinuses and to form a near-symmetric vortex pair. AoSA steepening caused the vortex pairs to become larger and more rotational, and this effect was more pronounced in the DSS group. Consistent with previous observations¹⁴, vortex shedding from the lesion in the DSS group caused the formation of a downstream CCW recirculation bubble, which became entrapped in the region bounded by the DSS membrane and the inferior leaflet. As the AoSA steepened, the increase in flow rotationality skewed the LVOT jet toward the superior leaflet.

Increased flow asymmetry became apparent in the DSS models downstream of the AV at peak systole (t = 0.60 s). While the CTRL group continued to generate near-symmetric vortices from the leaflet tips, the shedding of those vortices in the DSS group resulted in increased flow rotationality in the wake of the superior leaflet, in an AoSA-dependent manner. As compared to the CTRL-130° model, steeper models resulted in large vortical structures around the valvular jet, and generated stenotic conditions in the sinus region (up to 37% increase in peak-systolic velocity and 37% reduction in effective orifice area (EOA) vs. CTRL-130°). In the DSS group, the acceleration of the flow toward the AV washed out the CCW recirculation bubble entrapped in the LVOT, and caused its impingement toward the base and belly regions of the inferior leaflet. AoSA steepening in the DSS group predicted similar stenotic AV flow conditions (up to 40% increase in peak-systolic velocity and 36% reduction in EOA vs. DSS-130°). The combined effect of AoSA abnormalities and DSS resulted in a similar increase in peak-systolic velocity but a marked reduction in EOA (up to 39% increase in peak-systolic velocity and 49% reduction in EOA vs. CTRL-130°). Vortices emanating or shed from the tip of the leaflets migrated toward the sinus wall and caused flow redirection back into the sinuses. In the CTRL and DSS groups, the largest AoSA (130°) gave rise to the formation of only one secondary vortex near the inferior (q_inf) and superior (q_sup) sinus wall, respectively. In contrast, the increased sinus recirculation caused by AoSA steepening led to the development of two secondary vortices (w_inf and w_sup) in both groups.

The peak-systolic flow features persisted until the deceleration phase (t = 0.68 s), after which the decrease in ejection velocity caused the vortices formed near the tip of the leaflets to migrate downstream of the AV. Large-scale coherent flow structures were still visible near the leaflets in the CTRL models, and interaction of the shed vortices and sinus wall resulted in either the formation (CTRL-130°) or maintenance (CTRL°−120 and −110°) of secondary vortices in the wake of the leaflets (w_sup and w_inf, respectively). The DSS models, meanwhile, generated asymmetric and disorganized vortices downstream of the valve. The secondary vortices formed at peak systole were maintained throughout this phase but migrated further into the sinus cavities. Interestingly, AoSA steepening in this group was also accompanied by the formation of another pair of vortices in the inferior sinus region (d₁), which expanded and migrated further into the sinus as the AoSA steepened. In all models, coaptation (t = 0.77 s) was characterized by the rapid closure of the AV, and the shedding of new vortex pairs in the wake of the leaflets. The vortex dynamics predicted during valve closure mimicked the ejection characteristics, with the formations of near-symmetric vortices in the CTRL groups and asymmetric vortices in the DSS models. The unobstructed models (i.e., CTRL group) generated vortex pairs that were more diffuse, and spanned nearly the entire length of the sinus cavities. Conversely, the DSS group generated vortices that were focally concentrated and aligned on the long-axis of the aorta. AoSA steepening in the DSS group resulted in the formation of increasingly large and rotating vortices in the superior sinus region. While the CTRL models predicted the breakdown and diffusion of their secondary vortical structures into the surrounding flow, the secondary vortex pairs observed in the DSS group (with the exception of the DSS-120°) were maintained throughout coaptation and migrated deeper into the sinus.

Leaflet Kinematics

The opening angles for both leaflets were tracked throughout the cardiac cycle in each model (Figure 3). Regardless of the LVOT anatomy, the leaflets experienced systolic fluttering, which began immediately after the valve opening (t = 0.5 s) and persisted throughout ejection until the onset of valve closure (t = 0.7 s). The maximum and average leaflet opening angle, the angular range of systolic flutter for each leaflet, and the degree of leaflet asymmetry for each model are reported in Table 1. Regardless of the model, the superior and inferior leaflets exhibited essentially similar kinematics (<13% and <15% difference in θ_max and θ_avg, respectively) and synchronous opening (R²>0.81).

Figure 3.

Time history of the instantaneous superior and inferior leaflet opening angles captured in the control (CTRL) and discrete subaortic stenosis (DSS) groups

Table 1.

Leaflet kinematic predictions: opening angle, systolic flutter range, and degree of asymmetry characteristics

LV model	leaflet	θmax (°)	θavg. (°)	systolic flutter range (°)	R2
CTRL-130°	inferior	83.2	73.9	14.9	0.96
	superior	76.1	70.9	9.4
DSS-130°	inferior	79.1	73.9	8.0	0.92
	superior	71.1	64.1	11.3
CTRL-120°	inferior	80.3	68.8	19.0	0.90
	superior	74.5	68.6	10.3
DSS-120°	inferior	72.9	68.3	8.9	0.86
	superior	82.3	66.7	23.0
CTRL-110°	inferior	82.4	65.7	25.8	0.81
	superior	75.9	67.8	12.6
DSS-110°	inferior	72.3	65.5	12.0	0.90
	superior	73.4	63.9	13.9

AoSA steepening also had only a moderate effect on leaflet opening characteristics (<15% and <12% difference in θ_max and θ_ave, respectively_, vs. group-matched 130° model), but a more pronounced impact on the degree of systolic flutter. In fact, in the CTRL group, AoSA steepening increased substantially but unequally the degree of systolic flutter of the superior and inferior leaflet (up to 34% and 73% increase, respectively, vs. CTRL-130° leaflets), and resulted in increasing asynchrony in leaflet opening (up to 0.15-point decrease in R² vs. CTRL-130°). In the DSS group, AoSA steepening also generated an asymmetric increase in systolic flutter on the superior and inferior leaflets (up to 103% increase and 50% increase, respectively, vs. DSS-130° leaflets), but maintained a relatively synchronous leaflet opening (less than 0.06-point decrease in R² vs. DSS130°). The presence of the DSS lesion did not affect leaflet kinematics across all AoSAs (<13% and <10% difference in θ_max and θ_ave, respectively, vs. CTRL models). In contrast, it created leaflet-specific alterations in systolic flutter (up to 123% increase and 53% decrease in degree of superior and inferior leaflet systolic flutter, respectively, vs. CTRL models).

Systolic WSS Characteristics

Peak-Systolic WSS Magnitude

The peak-systolic (t = 0.60 s) WSS magnitudes predicted in the base, belly, and tip regions of the superior and inferior leaflets for all models are shown in Figure 4. As reported in previous AV leaflet WSS studies, the leaflet WSS magnitude exhibited a strong spatial dependence as shown by the progressive increase from the leaflet base to the tip. Peak-systolic WSS magnitudes predicted over the base and belly regions of the superior and inferior leaflets were essentially similar in the CTRL group (<11% difference between both leaflets) and DSS groups (<13% difference). The tip regions of the superior and inferior leaflets were, however, subjected to more contrasted WSS magnitudes in the DSS group (up to 20% difference between both leaflets).

Figure 4.

Comparison of the peak-systolic wall shear stress (WSS) values on each leaflet for all models (inner horizontal line within each box indicates average value).

Temporal Shear Magnitude

The WSS characteristics captured on the ventricular surface of each leaflet are shown in Table 1. 3D surface plots are also provided (Figure 5) to give a visual aid for highlighting the model- and leaflet-specific differences outlined in this section.

Figure 5.

3D surface plots of the regional time-averaged wall shear stress (WSS) characteristics

Regardless of the model, comparison of the TSM predictions in the base, belly, and tip regions of both leaflets demonstrated the spatial dependence of the WSS, as evidenced by the progressive increase in WSS magnitude along the radial direction (up to 228% increase in TSM between base and tip). In addition, the models predicted essentially similar surface-averaged WSS magnitude on both leaflets (<7% difference in TSM between both leaflets across all models).

Comparison of the TSM predictions across all AoSAs revealed the strong dependence of the WSS magnitude on the LVOT anatomy. In fact, AoSA steepening resulted in substantial WSS overloads on both leaflets (CTRL and DSS superior leaflet: up to 48% and 78% increase in surface-averaged TSM, respectively, vs. group-matched 130° model; CTRL and DSS inferior leaflet: up to 41% and 69% increase, respectively). Analysis of the regional leaflet TSM revealed two distinct trends in the CTRL and DSS groups. In the CTRL group, AoSA steepening subjected all regions of both leaflets to WSS overloads (>11% increase in TSM vs. CTRL-130°). In the DSS group, the asymmetric hemodynamic environment generated by the lesion subjected nearly all regions of the superior leaflet (except the base of the DSS-110° leaflet) to WSS overload regardless of the degree of steepening (>14% increase in TSM vs. DSS-130°), while subjecting the inferior leaflet to AoSA-dependent, site-specific alterations in WSS magnitude.

TSM predictions in the DSS models suggested the existence of similar WSS overloads on both leaflets (up to 39% increase in surface-averaged TSM in DSS-130° vs. CTRL-130°), which were progressively attenuated under AoSA steepening (<15% increase in surface-averaged TSM in DSS-130° vs. CTRL-130°). However, inspection of the regional TSM predictions revealed substantial differences in WSS distributions over both leaflets. In fact, regardless of the degree of steepening, the flow skewness generated by DSS subjected all regions of the superior leaflet to WSS overloads (>7% increase in TSM vs. CTRL models). In contrast, while only the base of the inferior leaflet was exposed to increased WSS magnitude, the overload (>31% in TSM vs. CTRL models) was much greater than on the superior leaflet.

Oscillatory Shear Index

OSI predictions on the ventricular leaflet surface in all CTRL models revealed the existence of an essentially unidirectional WSS environment (OSI<0.11). In contrast, the hemodynamic abnormalities generated by the DSS lesion subjected the leaflets to increased bidirectionality. This was particularly marked in the base and belly regions of the inferior leaflet in the DSS-120° model (OSI = 0.35 and 0.25, respectively) and the belly region of the inferior leaflet in the CTRL-130° models (OSI = 0.27). OSI predictions in the CTRL models were weakly affected by AoSA steepening (less than 0.1-point difference in regional OSI across all CTRL models). While a similar trend was observed on the superior leaflet in the DSS group (less than 0.04-point difference in regional OSI across all DSS models), the moderate steepening introduced by the DSS-120° model subjected the base of the inferior leaflet to a substantially higher degree of WSS bidirectionality (0.30-point increase in regional OSI vs. DSS-130°). The combination of AoSA steepening and LVOT obstruction weakly impacted the predicted WSS bidirectionality on the superior leaflet (< 0.09-point difference in regional OSI between the groups). The interactions between the inferior leaflet and the vortex dynamic alterations caused by the DSS lesion resulted in a higher degree of WSS oscillation on the leaflet base and belly in the DSS-120° model (0.29- and 0.22-point increase in OSI, respectively vs. CTRL group) and on the leaflet belly in the DSS-130° and DSS-110° models (0.25- and 0.14-point increase in OSI, respectively vs. CTRL group).

Aortic Regurgitation

RF values computed in all models are shown in Table 2. Using the CTRL-130° regurgitant volume as a baseline, the CTRL and DSS models predicted trivial amounts of regurgitation (RF< 7%), well below the clinical threshold defining mild AR (RF=30%)⁴⁵.

Table 2.

Systolic wall shear stress (WSS) characteristics and regurgitant fraction (RF)

		TSM (Pa)			OSI
LV model	leaflet	base	belly	tip	base	belly	tip	RF (%)
CTRL-130°	inferior	2.20	3.02	5.25	0.07	0.02	0.05	0.0
	superior	2.18	2.86	5.32	0.03	0.02	0.04
DSS-130°	inferior	4.27	2.62	7.67	0.05	0.27	0.03	6.6
	superior	3.16	4.40	6.05	0.03	0.02	0.03
CTRL-120°	inferior	2.44	4.34	8.02	0.06	0.02	0.05	6.0
	superior	2.47	5.86	6.99	0.07	0.11	0.03
DSS-120°	inferior	4.45	4.87	8.43	0.35	0.25	0.13	0.0
	superior	4.12	6.60	7.76	0.01	0.02	0.07
CTRL-110°	inferior	2.45	4.51	7.20	0.07	0.02	0.03	4.2
	superior	2.51	4.69	6.35	0.04	0.01	0.01
DSS-110°	inferior	3.22	4.38	7.17	0.13	0.16	0.01	4.7
	superior	3.10	5.03	7.51	0.03	0.01	0.04

Discussion

This computational study aimed at assessing the impact of AoSA abnormalities and DSS on AV hemodynamics and function by performing FSI simulations in a unified LV-AV model, and evidenced that both DSS and AoSA abnormalities affect, to some degree, the functionality of the AV and the spatial distribution of the leaflet WSS. Specifically, this analysis demonstrates: 1) the remarkable impact of DSS and DSS-prone LVOT anatomies on subaortic flow and vortex dynamics; 2) the causality between AoSA steepening/DSS LVOT abnormalities and AV leaflet kinematic alterations; 3) the inability of those leaflet kinematic derangements to generate clinical AR levels; and 4) the existence of altered WSS patterns on AV leaflets in DSS and DSS-prone LVOT anatomies. This demonstration, even in its qualitative form, is not only novel to the DSS research community, it also provides for the first time a plausible explanation of the association between AR and DSS.

LVOT Steepening and DSS Generate Stenotic Hemodynamics and Alter AV Leaflet Kinematics

Flow simulations in the DSS LVOT anatomies demonstrated the dramatic impact of AoSA steepening and the DSS lesion on AV and aortic root hemodynamics. The DSS lesion contributed to the development of asymmetric hemodynamics, supra-valvular stenotic flow conditions, and rich and complex vortex dynamics. Similar flow derangements have been reported in the LVOT of DSS patients using Doppler echocardiography⁴⁶, and have been described as hallmarks of DSS^2,5. Those observations are also consistent with the increased flow skewness and asymmetry reported in the ascending aorta downstream of an obstructed LVOT by a previous computational study²⁵. Furthermore, the peak-systolic flow velocity in the CTRL and DSS groups, which ranged from 0.63 to 0.79 m/s and 0.88 to 0.98 m/s, respectively, are consistent with those reported in vivo (peak velocity: 1.0 to 1.5 m/s)^47,48.

An important result evidenced by the simulations is the dramatic impact of AoSA steepening on aortic root hemodynamics. While the moderate steepening of 20° considered in the CTRL-110° model resulted in a slightly lower degree of flow disorder and rotationality than that predicted in the DSS group, it generated a similar degree of stenosis. The persistence of abnormal stenotic hemodynamics in a steep LVOT without a DSS membrane, which mimics post-resection LVOT anatomy, suggests that resection is not able to restore normal LVOT hemodynamics. This observation may have some important implications in the mechanisms leading to DSS recurrence and AR progression post resection.

The flow derangements caused by LVOT steepening and DSS also subjected the AV leaflets to substantial kinematic alterations during opening, which resulted in increased leaflet asymmetry. Interestingly, AoSA steepening exacerbated the degree of leaflet asymmetry while maintaining the same maximum leaflet opening angles as those predicted in the less steep LVOTs. This result suggests that the stenosis predicted downstream of the steep LVOT is primarily caused by the interactions between the valvular jet and the vortex dynamics captured in this model rather than a physical obstruction at the valve level. Although DSS resulted in contrasted leaflet fluttering, it reduced the overall degree of leaflet asymmetry during opening. The average leaflet opening angles predicted in this study are in good agreement with values reported in bileaflet mechanical heart valve models^25,31,36 (<14% difference).

LVOT Steepening and DSS Subject AV Leaflets to WSS Overloads and Increased Bidirectionality

Despite the 2D approximation made in the study, the WSS characteristics predicted on the ventricular leaflet surface are consistent with those reported in previous 3D numerical and experimental investigations^27,30,49,50. Leaflet peak WSS predictions reported in this study ranged from 51.9 to 181.2 dyn/cm² in the CTRL group, and are in agreement with laser Doppler velocimetry measurements on a trileaflet polyurethane valve under steady flow⁴⁹ (maximum WSS: 79 dyn/cm²), and on a prosthetic valve under transient flow conditions⁵⁰ (maximum WSS: 64 – 71 dyn/cm²). In addition, the present simulations demonstrated the spatial dependence of the leaflet WSS environment, as evidenced by the 3.3-fold increase in TSM predicted from the base toward the tip of both leaflets. A similar trend was reported in a 3D FSI valve model published by our group (2.9-fold increase in TSM between the leaflet base and tip)²⁷. In addition, the OSI predictions extracted from the CTRL group (OSI<0.11) suggest the typical unidirectional, pulsatile nature of the ventricular WSS previously reported computationally^26,27,51 (0<OSI<0.17). It is important to note that the simplifications and the parametric approach implemented in the present study were necessary to effectively capture the isolated and combined effects of DSS and AoSA steepening on the leaflets. Therefore, while the raw quantitative predictions should be interpreted with caution, the predicted trends are more relevant and meaningful.

An important observation suggested by the models is the dramatic impact of the LVOT anatomy on the leaflet WSS environment. The moderate LVOT steepening in the CTRL group subjected both leaflets to remarkable WSS overloads without affecting the pulsatile nature of the WSS environment. The presence of a DSS lesion exacerbated the degree of WSS overload but also caused a net increase in WSS bidirectionality on the inferior leaflet. While the long-term effects of such alterations remain to be determined, valve leaflets have been shown to respond to WSS alterations by triggering cell-mediated biological pathways. In particular, while the normal WSS environment promotes the maintenance of valvular homeostasis, WSS magnitude and/or pulsatility abnormalities have been associated with the onset of disease states^{15,16,52–54}.

Implications for the Pathogenesis of AR Secondary to DSS

Two hypothetical pathways have been proposed to explain AR induction in the adult DSS patient population: 1) a mechanical pathway by which LVOT anatomical abnormalities could cause leaflet kinematic derangements and improper leaflet coaptation; and 2) a long-term mechanobiological pathway by which the hemodynamic alterations caused by LVOT anatomical abnormalities on the leaflets could translate into altered valvular biology, loss of homeostasis, leaflet structural degeneration, and improper coaptation. The flow simulations described in this study provide important insights into the validity of those hypothetical etiologies.

Leaflet Kinematic Derangements Caused by DSS and DSS-Prone LVOT Hemodynamics Do Not Generate Clinical AR

In support of the mechanical etiology, the simulations evidenced the dramatic impact of LVOT steepening and DSS on AV leaflet kinematics. The moderate steepening considered in this study restricted the range of systolic flutter and generated an asymmetric opening of the leaflets. Consistent with other computational reports²⁵, the addition of the DSS lesion particularly affected the kinematics of the inferior leaflet, but resulted interestingly in a lesser degree of leaflet asymmetry during opening. Despite those important kinematic alterations, the levels of AR computed in the models (RF<7%) remained well below the clinical threshold associated with mild AR (RF=30%)⁴⁵. This result suggests that the leaflet kinematic derangements associated with DSS-prone and DSS LVOT anatomies alone do not substantially hamper valvular function and are not able to cause clinically significant levels of valvular insufficiency. However, this conclusion needs to be taken with caution as the present 2D models may not capture the full complexity of the native 3D LV-AV flow, and may underestimate the actual increase in regurgitant flow caused by the DSS lesion. A future study implementing 3D LV, LVOT and AV geometries is needed to address this important question.

Leaflet WSS Alterations Caused by DSS and DSS-Prone LVOT Hemodynamics Are Conducive to AV Inflammation and Remodeling

The WSS alterations generated on the ventricular surface of the leaflets by the steep LVOT and the DSS lesion are particularly conducive to valvular disease^17,18, and therefore provide increased support to a mechanobiological etiology of AR in DSS patients. In fact, biological studies conducted in our lab have shown that exposure of porcine AV leaflets to supraphysiologic WSS magnitudes (similar to those predicted in the current study) promote both inflammatory and remodeling states via endothelial activation, increased paracrine signaling, and catabolic enzyme secretion and activity^19,20,55. Interestingly, the inflammatory and degenerative states linked to those biological changes are similar to those responsible for tissue inflammation, scarring, redundancy and thickening reported in valves excised from DSS patients and causing impaired coapatation^2,56,57. Exposure of the leaflet ventricularis to oscillatory flow has been associated with biological alterations marked by an overall reduction in leaflet collagen content and an increase in glycosaminoglycan content⁵⁸. Those changes in extracellular matrix composition are similar to those associated with myxomatous valvular degeneration⁵⁹, which has been observed in leaflets excised from a bull-terrier cohort with DSS¹³, and which could cause the typical AV leaflet thickening observed in DSS patients^2,5,6,60. The WSS overloads imposed by the steep LVOT and DSS on both leaflets, and the increased degree of WSS bidirectionality imposed by DSS on the inferior leaflet may trigger similar biological pathways, and lead ultimately to the degeneration of the leaflet structure, impaired motion and coaptation. The exposure of AV leaflets to the WSS characteristics predicted by this study in the steep and DSS LVOTs using the same shear stress bioreactors^61–63 as those implemented in our ex vivo studies would enable the characterization of the valvular biological changes induced by DSS hemodynamics. The combination of those structural changes and the observed leaflet kinematic abnormalities caused by DSS and LVOT steepening may accelerate and amplify AR progression.

The particular presentation of AR in DSS patients provides additional support for this mechanobiological etiology. While DSS affects the pediatric population, AR is much more prevalent and severe in the adult DSS patients^5–8. The main difference between those two populations is the amount of time between initial diagnosis and resection. In the pediatric DSS population, the time from diagnosis to resection is usually short (~2.7 years)^12,64, which may limit the mechanobiological impact of DSS on leaflet function and justify the low incidence of AR. In contrast, in the adult DSS population, resection is typically performed 9 years after initial diagnosis⁵. As a result, the increased time of exposure of AV leaflets to DSS-induced WSS abnormalities would likely cause irreversible biological changes contributing to the progressive development of AR. The important role played by time in the severity of DSS-induced AR has been evidenced in two patient cohorts showing increases in AR prevalence from 32 to 54% over an average follow-up period of 3.7 years⁶⁵, and from 47 to 55% over a 10-year period⁶⁴.

Lastly, the mechanobiological etiology would also explain the worsening of AR symptoms commonly observed post-resection¹². In fact, the flow simulations performed in the steep LVOT in the absence of DSS lesion, and therefore mimicking the results of the resection procedure, evidenced the persistence of supraphysiologic WSS levels on both leaflets. Those abnormalities may have the potential to trigger the mechanobiological cascades leading to AR.

Limitations

Several approximations were made in this study, and need to be taken into consideration to interpret the findings.

First, the 2D LV-AV representation implemented in this study did not permit to capture the three-dimensionality of valvular and ventricular flows. However, the 2D approximation was adequate to capture both the main cardiac flow features and the characteristics of the dominant WSS component acting along the leaflet radial direction^31,66,67. In this context, this modeling approach is not only appropriate to address the specific needs of this parametric study, it also enabled the implementation of sophisticated FSI modeling strategies to capture realistic leaflet motion and lesion deformation in response to native LV wall motion. Nevertheless, future 3D simulations are needed to capture the full complexity of the physics linking LVOT abnormalities, DSS and valvular function. In addition, the decision to design an idealized AV geometry was motivated by the need to isolate the effects of DSS and/or AoSA steepening on AV flow and function while discarding any geometrical variability inherent to patient-specific reconstructions.

In addition, consistent with previous LV-AV simulations^30,31,36,37, the sinus and aortic walls were modeled as rigid to reduce the overall complexity of the simulations and improve numerical convergence. While the native expansion/contraction of the wall may contribute to a momentum transfer to the fluid downstream of the valve, the focus of this study was on the characterization of the upstream flow, with a particular focus on the FSIs between the leaflet ventricularis and LVOT flow. Therefore, the small range of native radial wall motion is not expected to alter substantially the trends observed in the present analysis.

In an effort to limit the overall complexity and computational cost of the models, turbulence was not modeled in this study. The implementation of a laminar model is consistent with previous computational studies in isolated^{25,27,68–70} and unified LV-AV^{23,30,31,36,71} geometries. In addition, a recent study revealed a close agreement between AV flow predictions obtained using a shear-stress transport k-ω model and a laminar flow approximation⁷². Nevertheless, turbulence is a hallmark of DSS hemodynamics, and has been suggested to impact leaflet dynamics³⁷. Therefore, turbulence modeling should be considered in future studies aimed at characterizing the impact of DSS on AV hemodynamics.

While native AV leaflet tissue is known to be non-linear due to the progressive locking of the collagen fibers under increasing loads, this study approximated the leaflets as linear and elastic. This simplification, however, is not expected to alter substantially the predicted AV hemodynamic and WSS characteristics reported in this study during systole since during this phase the leaflets experience only moderate strains^73,74. In addition, the study approximated the DSS lesion with a similar linear elastic material model, which may not capture the complexity of the native tissue. This approximation was made due to the lack of mechanical characterization of DSS membranes. Mechanical test data are needed to better characterize the dynamics of DSS lesions.

Lastly, the effects of LVOT steepening and DSS were quantified by considering three AoSA values and a single DSS membrane morphology/position. However, LVOT steepening covers a wide range of AoSAs^75–77, and the membrane that causes DSS can present as a fibromuscular ring of tissue, an incomplete shelf or a ridge-like structure^40,60,78. Although further parametric studies could be performed to characterize more exhaustively the full spectrum of hemodynamic abnormalities caused by AoSA steepening and DSS, this level of details was not needed in the context of the present study, which aimed at establishing causality between AoSA steepening/DSS and alteration of valvular mechanics.

Abbreviations

ALE

Arbitrary Lagrangian-Eulerian

AoSA

Aortoseptal angle

AR

Aortic regurgitation

AV

Aortic valve

CCW

Counterclockwise

CTRL

Control group

CW

Clockwise

DSS

Discrete subaortic stenosis

EOA

Effective orifice area

FSI

Fluid-structure interaction

LV

Left ventricle

LVOT

Left ventricular outflow tract

OSI

Oscillatory shear index

RF

Regurgitant fraction

RMS

Root mean square

TSM

Temporal shear magnitude

WSS

Wall shear stress