Patient-Specific Quantification of Normal and Bicuspid Aortic Valve Leaflet Deformations from Clinically Derived Images

Abstract

The clinical benefit of patient-specific modeling of heart valve disease remains an unrealized goal, often a result of our limited understanding of the in vivo milieu. This is particularly true in assessing bicuspid aortic valve (BAV) disease, the most common cardiac congenital defect in humans, which leads to premature and severe aortic stenosis or insufficiency (AS/AI). However, assessment of BAV risk for AS/AI on a patient-specific basis is hampered by the substantial degree of anatomic and functional variations that remain largely unknown. The present study was undertaken to utilize a noninvasive computational pipeline (https://doi.org/10.1002/cnm.3142) that directly yields local heart valve leaflet deformation information using patient-specific real-time three-dimensional echocardiographic imaging (rt-3DE) data. Imaging data was collected for patients with normal tricuspid aortic valve (TAV, n = 8) and those with BAV (n = 5 with fused left and right coronary leaflets and n = 5 with fused right and non-coronary leaflets), from which the medial surface of each leaflet was extracted. The resulting deformation analysis resulted in, for the first time, quantified differences between the in vivo functional deformations of the TAV and BAV leaflets. Our approach was able to capture the complex, heterogeneous surface deformation fields in both TAV and BAV leaflets. We were able to identify and quantify differences in stretch patterns between leaflet types, and found in particular that stretches experienced by BAV leaflets during closure differ from those of TAV leaflets in terms of both heterogeneity as well as overall magnitude. Deformation is a key parameter in the clinical assessment of valvular function, and serves as a direct means to determine regional variations in structure and function. This study is an essential step toward patient-specific assessment of BAV based on correlating leaflet deformation and AS/AI progression, as it provides a means for assessing patient-specific stretch patterns

INTRODUCTION

The aortic valve (AV) resides between the left ventricle and the ascending aorta within the aortic root, functioning to prevent backflow of blood from the aorta into the left ventricle during diastolic filling. The normal tricuspid AV (TAV) is composed of three flexible leaflets, which are designated as the left coronary (L), right coronary (R), and non-coronary (N). In contrast, the bicuspid AV (BAV), a congenital anomaly in which the AV has two leaflets instead of three, is the most common cardiac defect and affects 1–2% of the population, with an approximate 3:1 male predominance.¹¹ BAV phenotypes are distinguished by which pair of normal leaflets appear fused. About 3 in 4 BAVs present with a L–R fusion, while about 1 in 4 present with a R–N fusion; cases of L–N fusion are the rarest, making up only about 3% of cases.¹⁶

BAVs have a significantly increased risk of calcific AV disease (CAVD) and associated mortality. It has been estimated that 30–50% of BAV patients will require surgical intervention at some point in their life.⁹ Surgery is the most common treatment for CAVD induced by symptomatic aortic stenosis (AS), and is less commonly required for aortic insufficiency (AI), ascending aortic aneurysm, and dissection. Almost all patients under the age of 50 and presented with AS are also presented with BAV. In fact, until the age of about 70, BAV patients outnumber those with TAV undergoing replacement for AS. Between 71 and 80 years of age, BAV and TAV occur in approximately equal numbers in symptomatic AS patients, and not until over the age of 80 do TAV patients predominate.⁹ While multiple factors are likely involved in the prevalence of AS in BAV patients and its relation to aortic dissection, the presence of a BAV is consistently a strong risk factor for premature AS.

Due to the widespread availability and routine use of pre-surgical 3D echocardiography, the identification of asymptomatic patients with BAV has become increasingly common. Yet, in spite of the strong clinical association between BAV and AS, it is not currently possible to determine which patients with BAV are at highest risk for developing AS.¹ There is evidence to suggest that abnormal AV leaflet deformation patterns cause changes in valvular interstitial cell (VIC) signaling, which in turn result in the advent and progression of calcification.²⁸ Due to their abnormal morphology and microstructure, it follows that BAV leaflets would indeed be more susceptible to accelerated CAVD. However, to assess the risk of CAVD in a patient, it will be necessary to evaluate the functional deformation state of the AV in real time using clinical imaging data and specialized modeling tools. The development of a rational basis for stratifying patients based on CAVD onset and progression risk will therefore require patient-specific quantification of how each AV leaflet deforms locally over the cardiac cycle. A foundational understanding of the range of deformations typically experienced by different AV leaflet types in vivo is also critical in this effort.

The objectives of the present study were thus to (1) develop a clinical imaging modality-based computational modeling pipeline to extract local AV leaflet deformations on a patient-specific basis, and (2) apply the pipeline to a group of human TAV and BAV data to elucidate potential population-level differences in deformation patterns between the valve leaflet types. This study thus serves as a prerequisite for the broader effort to identify sensitive, clinically derivable functional indices that can predict the onset and progression of AV calcification, since leaflet mechanical behavior is a critical metric of the AV’s functional state.

METHODS

Patient Selection

In the present study, adult patients (> 18 years of age) of random sex for which real-time three-dimensional echocardiographic (rt-3DE) images were acquired as part of routine clinical care were considered for inclusion. All imaging was approved by the University of Pennsylvania Institutional Review Board after informed consent was obtained. Exclusion criteria included inadequate rt-3DE image quality and other factors such as the AV anatomy not being fully within the field of view throughout the cardiac cycle, as well as the presence of relevant pathophysiologies including endocarditis, chronic inflammatory disease, and rheumatic fever. Patients with prior AV surgery were also excluded, as well as patients whose rt-3DE images contained stitching artifacts. Moreover, TAV patients were required to have no more than trace AV regurgitation and stenosis, and BAV patients were required to have no more than mild calcification, based on rt-3DE assessment. The 18 total patients whose data were utilized were categorized according to their AV phenotype, namely TAV (n = 8), BAV with L–R fusion (n = 5), and BAV with R-N fusion (n = 5). Key patient characteristics, including age, sex, BMI, presence of primary and secondary cardiac pathologies, and reason for image acquisition are reported in Table 1.

TABLE 1.

Patient characteristics.

	TAV	BAV
Number of patients	8	10
Age [years]	63.3 ± 6.2	44.6 ± 15.4
Male	5 (0.63)	8 (0.80)
Body mass index [kg/m2]	28.9 ± 5.5	27.4 ± 6.5
Hypertension	6 (0.75)	4 (0.40)
Coronary artery disease	3 (0.38)	0
Dilation or aneurysm of the aortic root and/or ascending aorta	0	7 (0.70)
Aortic insufficiency (moderate to severe)	0	7 (0.70)
Other congenital heart defect	0	1 (0.10)
Atrial fibrillation	4 (0.50)	1 (0.10)
Mitral regurgitation or stenosis (moderate to severe)	3 (0.38)	2 (0.2)
Procedure performed after image acquisition:
Heart transplant	5 (0.63)	0
Atrial ablation	2 (0.25)	1 (0.10)
Mitral valve surgery	1 (0.13)	0
Surgery of the aortic valve and/or ascending aorta	0	9 (0.90)
None (routine imaging)	0	1 (0.10)

Image Processing and Geometric Modeling

Images were acquired in full-volume mode over four consecutive cardiac cycles with a 2–7 MHz matrix-array transducer at end-expiration during positive pressure ventilation in anesthetized patients to eliminate motion caused by respiration. The AV leaflets from each data set were manually labeled in each rt-3DE image in ITK-SNAP,²⁹ an open-source software toolkit for medical image segmentation. The L, R, and N leaflets of each TAV were individually traced in the fully open and fully closed phases of the cardiac cycle. Likewise, the non-fused leaflet and fused leaflet in each BAV were traced in the fully open and fully closed phases of the cardiac cycle. Care was taken to include the raphe as a separately labeled region in the segmentation of each fused BAV leaflet (Fig. 1).

FIGURE 1.

Pipeline for AV geometric modeling on a patient-specific basis, starting from noninvasive rt-3DE images of the valve. Full target geometries of the AV obtained through image segmentation (a) are processed using an established deformable medial modeling approach (b), which yields leaflet-specific triangulated mesh models of the leaflet medial surface (c). In addition to describing the AV leaflet medial surface geometry, each leaflet’s geometric model is enriched with a local radius function (d), which defines the pointwise thickness of the leaflet.

After slice-by-slice manual segmentations of the leaflets were performed in ITK-SNAP, the 3D segmentations were smoothed with convert3D, an ITK-SNAP companion tool that provides command-line implementation of common Insight Toolkit image processing filters (Figs. 2a and 2b). A Gaussian kernel of 1 mm was used, followed by qualitative verification that the smoothing corrected any extraneous ridges and surface noise produced during slice-by-slice manual segmentation without reducing important details such as the raphe, leaflet free margin, and commissural zones. In order to obtain a geometric model of each AV leaflet, a medial axis representation of each leaflet (the medial axis being the surface midway between the aortic and ventricular surfaces) was obtained from the segmented images. To accomplish this, we used an established inverse skeletonization approach, referred to as continuous medial representation (cm-rep),³⁰ to define the non-branching medial surface of each leaflet based on its rt-3DE segmentation (Fig. 2), using procedures described previously in detail.[20] An initial coarse mesh of the leaflet’s medial surface was obtained by manually triangulating the Voronoi skeleton of the segmented/smoothed rt-3DE image (Fig. 2c). For fused leaflets, the triangles associated with the raphe were manually identified. Note that this process is subject-specific since the initial coarse mesh is manually created, and thus neither the number of nodes nor the element size are exactly conserved across different patients. Then, we performed two iterations of Loop subdivision,¹⁵ which refined the mesh sufficiently to accurately capture the local geometry even in regions of higher curvature (Fig. 2d). The refined mesh was fitted using the cm-rep methodology described in Pouch et al.,²⁰ in order to refine the shape representation and enforce constraints on the medial and boundary geometry. Cm-rep describes the shape of an object in terms of its medial surface(s) and a scalar function r defined on the medial surface (Fig. 2e). In this case, the value of r at any location on the medial surface of an AV leaflet is the distance between that location on the medial surface and the closest point(s) on the outer surface boundary of the leaflet. Cm-rep is an inverse skeletonization approach since the boundary of the leaflet can be analytically reconstructed from its medial axis representation, as defined by the medial surface and radius function r. The technique deforms a pre-defined medial template of the leaflet to a specific instance of the imaged leaflet geometry. The template’s medial surface is deformed and the associated radius function is optimized to maximize the volumetric overlap between the boundary reconstructed from the deforming template and the rt-3DE segmentation.²⁰

FIGURE 2.

Detailed methodology for converting segmented rt-3DE images to a cm-rep of each leaflet. (a) Segmentations of the leaflets in the rt-3DE image were obtained. (b) The raw rt-3DE segmentation of each leaflet was smoothed with a Gaussian kernel. (c) 3D Voronoi skeletonization was performed to obtain an approximate medial surface of the segmented leaflet and a triangulated mesh of the medial surface was manually generated on the Voronoi skeleton.²⁰ This mesh served as an initialization, or deformable template, for medial modeling of the leaflet. We defined all AV leaflets in this study to have a non-branching medial axis. In fused BAV leaflets, we manually labeled the mesh triangles located at the raphe. (d) To obtain the final medial axis representation, the template was refined using Loop subdivision.¹⁵ (e) The coordinates and associated radius (r) value at each node were optimized to maximize the volumetric overlap between the smoothed segmentation and a closed boundary reconstructed from the medial model as described in Ref. [20].

Image-Based Deformation Estimation

To determine diastolic deformation fields over the complete AV leaflet surface noninvasively, we extended a previously validated image-based deformation estimation method developed by our group for the mitral valve.^18,21 This method yields detailed local deformation information over the entire leaflet surface directly from clinically derived in vivo images (Fig. 3). An essential feature of our approach is that it does not require physical markers to determine surface deformations. We thus did not require any material point correspondence between open-state and closed-state images when estimating diastolic deformations. Instead, we exploited the fact that the subject-specific closed-state geometry of the leaflets can be precisely acquired from diastolic scans, and used the finite element (FE) method to impose pressure loading conditions and an approximated finite elastic behavior of the leaflet only as a regularizer to map the open-state leaflet geometry to its closed state. This approach is a substantial improvement over marker-based measurements because it provides a deformation field over the entire leaflet surface, rather than just within regions enclosed by markers. The closure simulation was configured such that the local leaflet thickness was prescribed using the image-based radius function r, and a homogeneous nonlinear isotropic constitutive model was assigned to the leaflet material.²¹ Moreover, the displacement of the basal attachment and free edge boundaries were prescribed using cubic spline curves parameterized uniformly by arc length. Note that the basal attachment and free edge provide natural boundary conditions that help to constrain the process of morphing the open-state leaflet to its closed state. While pressurizing the open-state valve mesh, we penalized any mismatch between the simulated and true (i.e. imaged) closed shapes of the leaflets using a local corrective pressure field, which was at any instance and location linearly proportional to the shortest distance between the AV mesh and the true AV medial surface (Fig. 3b). In this way, the loading conditions on the leaflet are iteratively optimized so as to match the imaged closed-state geometry (Fig. 3c). This approach for noninvasive, image-based deformation estimation was extensively validated in both atrioventricular and semilunar heart valves against ground-truth and fiducial marker-based measurements of local deformation (see²¹ and Appendix).

FIGURE 3.

Pipeline for acquiring the deformed (i.e. closed, fully loaded) state on a per-leaflet basis. (a) First, the open- and closed-state medial surface geometries are acquired from rt-3DE (Figs. 1 and 2), shown here for a TAV. (b) Throughout the FE simulation, boundary displacement, bulk leaflet pressurization, and shape enforcement are precisely coordinated to ensure accuracy and stability. (c) During closure, the loading conditions on the leaflet are adjusted locally using a corrective pressure field that is proportional to the signed distance d between any point and the nearest location on the true closed surface.²¹ This local pressure continually pushes the simulated leaflet surface toward the true closed configuration and thus enforces the true closed shape by the end of the simulation. Representative surface geometries and cross sections are shown for the open state, the onset of shape enforcement, the final simulated closed state, and the true closed state.

Post-processing and Statistical Analysis

To detect statistically significant differences in deformation between leaflet types, as well as to express stretches in terms of anatomic directions (circumferential/radial), we mapped our leaflet geometries to the parametric space of a B-spline surface,^2,19 which registered the stretch values from each original 3D valve geometry to a 2D domain with orthogonal coordinates that were correspondent across all leaflets (Fig. 4a). Splines provide a good method for comparing and averaging results between leaflets and leaflet types because they can represent arbitrary surface geometries as mappings from a single parametric space, namely the unit square $\in {ℝ}^2$ with coordinates (u, v) [19]. This allowed direct comparison between physical points on different leaflets that correspond to the same parametric location.

FIGURE 4.

(a) Spline surfaces are defined parametrically in R² based on the spline coordinates (u, v), from which circumferential and radial directions are defined locally. This spline surface can then be morphed to the leaflet surface in 3D via least-squares fitting, to allow projection of stretch results onto the anatomic directions and averaging of results across subjects for each leaflet type. (b) Pipeline for enforcing material point correspondence between open- and closed-state spline surfaces. Nodes on the open and closed triangulated leaflet meshes are treated as material points (i.e. correspondent between configurations), due to the fact that the closed-state nodes are obtained through a FE simulation, which uses finite elasticity to determine the deformed nodal positions. To maintain this correspondence between the open and closed spline surfaces, the parametric locations of the mesh nodes in the open state were maintained using equality constraints during the closed-state fitting process.

The spline surface fitting process consisted of three major steps: (1) fitting the leaflet boundary in the undeformed (i.e. open/systolic) configuration, (2) fitting the interior leaflet points in the undeformed configuration, and (3) fitting the deformed configuration.² We first fit each undeformed leaflet boundary (basal attachment and free edge) with a spline curve and registered each mesh node on the boundary to this curve. We then created a ruled spline surface between these open-state spline curves, parameterized the interior mesh nodes to this surface, and performed least-squares fitting. In order to assign a spline parametric location (u_i, v_i) to each physical point (mesh node), we used a Newton-Raphson scheme to compute the spline parameters that minimized the projected distance between the mesh node and the spline surface.¹⁹ This technique applied to parameterizing both the boundary and interior points (Fig. 4a). Note that the spline surface that is fit to the leaflet has an analytical form, and is thus a C²-continuous function of (u, v) (the discretized grid representation shown throughout Fig. 4 is merely illustrative, meant to more clearly show the relation between the parametric space and the real-world leaflet geometry).

Using the spline parameterization acquired from fitting the undeformed leaflet mesh, we fit the deformed FE node spatial coordinates while enforcing the nodal parametric locations to remain unchanged (Fig. 4b). Fitting the deformed configuration differed from fitting the undeformed configuration only in that no projection operation was used to parameterize the deformed FE nodes. Rather, the parametric locations of each FE node in the deformed configuration were assigned a priori using the optimized parametric locations acquired from fitting the undeformed configuration (Fig. 4b).

Finally, we computed stretch in both spline parametric directions, which corresponded to the circumferential ($\widehat{u}$) and radial ($\widehat{v}$) anatomic directions (Fig. 4a). Specifically, we computed the stretch in a given parametric direction at a given spline parametric location by computing the ratio of the surface derivative magnitudes in the given parametric direction between deformed and undeformed configurations. Let S(u, v) be the physical point of a spline surface corresponding to the parameter point (u, v) and {S_u(u, v), S_v(u, v)} be the parametric derivatives of that surface at that parametric point in the $\widehat{u}$ and $\widehat{v}$ directions respectively. Denoting the spline surface fit for the undeformed configuration as S⁰, the stretch in the $\widehat{u}$ direction λ_u is

$${\lambda }_u\left(u,v\right)=\sqrt{\frac{S_u{\left(u,v\right)}^T{S}_u\left(u,v\right)}{S_u^0{\left(u,v\right)}^T{S}_u^0\left(u,v\right)}},$$ (1)

while the stretch in the $\widehat{v}$ direction λ_v is

$${\lambda }_v\left(u,v\right)=\sqrt{\frac{S_v{\left(u,v\right)}^T{S}_v\left(u,v\right)}{S_v^0{\left(u,v\right)}^T{S}_v^0\left(u,v\right)}}.$$ (2)

Note that all stretch values presented herein represent a length ratio; therefore, values greater than 1 denote extension, while values less than 1 denote compression along the direction indicated.

The ability to compare locally correspondent stretch values between subjects enabled the averaging and statistical analysis of the obtained stretch results. The Dunn–Šidák method²⁵ was used to test for pairwise differences in mean stretches between leaflet types averaged over the entire leaflet surface, using the adjusted p-value p_adj = 1 − (1 − p)ⁿ, where n is the total number of pairwise comparisons performed (n = 21 in the present study, corresponding to all pairwise comparisons for 7 observed leaflet types). Mean differences were considered statistically significant when p_adj<0.05. Additionally, to better elucidate localized changes in stretch, we performed Welch’s t-tests pointwise for every parametric location (u, v) between each TAV leaflet type and their corresponding BAV leaflet types, both fused and non-fused, examining circumferential and radial stretch as variables of interest. The resulting maps of pointwise p-values were then used to qualitatively identify regions of each leaflet in which circumferential and/or radial stretch were most likely to differ between corresponding TAV and BAV phenotypes.

RESULTS

One advantage of the present method is the ability to quantify local leaflet deformation fields in substantial detail. This allowed us to reveal some interesting differences in the directional stretches, which demonstrated substantial regions over which deformation in TAV leaflets differed significantly from their fused and non-fused BAV counterparts (Figs. 5, 6 and 7). Generally, stretch fields in the TAV were smoother and showed less regional and inter-leaflet variations (Figs. 5 and 6a). In contrast, the BAV showed much more pronounced differences across different tissue regions, especially in the fused leaflets near the raphe (Figs. 5 and 6b, 6c).

FIGURE 5.

Representative stretch fields at full closure for a TAV and a BAV, showing local maximum and minimum in-plane stretch magnitudes and directions. Differences by leaflet type are qualitatively apparent; note especially that in the raphe of the BAV, the maximum in-plane stretch is substantially lower than over the rest of the fused leaflet.

FIGURE 6.

Key study results, showing mean circumferential and radial stretch fields for (a) TAV patients, (b) BAV patients with L–R fusion, and (c) BAV patients with R–N fusion, averaged across each leaflet type using the spline surface parameterization. Note the large differences between the BAV leaflets and their TAV counterparts, as well as the visible effect of the raphe (central) region on the circumferential stretch field of L–R (R–L) and R–N (N–R) leaflets.

FIGURE 7.

Group-wise stretches in (a) the principal directions and (b) the anatomic circumferential and radial directions, averaged per leaflet. While no differences were found within TAV or BAV leaflet types, several differences were detected between TAV and BAV leaflet types (*padj<0.05, where the endpoints of the corresponding horizontal lines denote the two leaflet types whose difference in means is statistically significant). Most notably, large significant differences in circumferential stretch were detected between TAV leaflets and leaflets from BAVs with L–R fusion. This suggests that TAV and BAV in vivo deformation patterns differ substantially. No significant pairwise differences were detected in the radial direction, in which mean stretches were generally greater but also substantially more variable.

Group-averaging stretch values along the principal directions showed that the minimum in-plane stretch across all BAV leaflet types tended to be lower than in the TAV (Fig. 7a), though statistical significance was only achieved when comparing the TAV’s non-coronary leaflet with the BAV’s fused L-R leaflet (TAV mean = 0.927 ± 0.019; BAV mean 0.731 ± 0.030; p_adj ± 0.018). Patterns of the TAV and BAV diastolic stretches were more readily apparent when the deformation field was projected and group-averaged in the anatomic directions, revealing strong differences especially in the circumferential direction (Figs. 6 and 7). TAV leaflet deformation patterns demonstrated some intra-leaflet variability, but modest inter-leaflet variations (Fig. 6a). Generally, TAV leaflets showed lower circumferential stretches at the basal attachment and in the vicinity of nodule of Arantius; this latter finding is consistent with the known thicker tissues that compose the nodule. In contrast to the TAV, differences in deformation patterns across several BAV leaflet types were apparent. In particular, BAV leaflets of all types exhibited lower levels of circumferential stretch compared to TAV, though radial stretch patterns were more similar (Figs. 6b, 6c). Moreover, while the directional stretches of all three TAV leaflet types were very similar, the stretch fields of BAV leaflets were more distinct. Within the fused BAV leaflets, the presence of the raphe resulted in lower local diastolic stretches in the circumferential direction, on average (Figs. 6b, 6c and 7b). Generally, fused leaflet stretch fields were also substantially more heterogeneous compared to both TAV and non-fused BAV leaflets, perhaps also resulting from the localized effects of the raphe.

In the case of L–R fusion, the circumferential stretch patterns in the non-coronary leaflet qualitatively resembled those in the non-coronary leaflet of the TAV, but were lower in magnitude (Fig. 6b); this difference was found to be statistically significant when circumferential stretches were averaged over each leaflet type (Fig. 7b; TAV mean = 1.056 ± 0.028; BAV mean = 0.916 ± 0.019; p_adj = 0.038). The effects of the raphe in the L–R (equivalently, R–L) fused leaflet clearly demonstrated reduced circumferential stretch, especially in the central region (Fig. 6b). Averaged over the entire leaflet surface, the difference in mean circumferential stretch between the TAV R leaflets and the BAV L–R leaflets were statistically significant (Fig. 7b; TAV mean = 1.040 ± 0.020; BAV mean = 0.938 ± 0.016; p_adj = 0.043). The fused R–N (equivalently, N–R) leaflet experienced circumferential compression (Fig. 6c; mean = 0.934 ± 0.034), although this did not translate to a significant difference in mean stretch compared to TAV R (p_adj = 0.492) or TAV N (p_adj = 0.370) leaflets. Similarly, the “normal” left coronary leaflet deformations in BAVs with R–N fusion trended lower in magnitude compared to the normal TAV L leaflet (Fig. 6c), but did not reach statistical significance when averaged over the entire leaflet for either the circumferential (TAV mean = 1.034 ± 0.019; BAV mean = 0.960 ± 0.045; p_adj = 0.987) or radial (TAV mean = 1.102 ± 0.036; BAV mean = 0.979 ± 0.044; p_adj = 0.729) directions. In contrast to the circumferential direction, the effects of either BAV abnormality on radial stretches were more variable for all leaflet types, and no significant pairwise differences were found in mean radial stretch (Fig. 7b). We also noted that shear strains were consistently small, with no detected differences between TAV and BAV (mean shear angle 10° for all leaflet types). Overall, these results suggest that while the three normal TAV leaflets deform very similarly in vivo, TAV and BAV deformation patterns differ substantially.

Pointwise analysis of directional stretches supported the above trends, showing substantial regions over which deformation in TAV leaflets differed significantly from their fused and non-fused BAV counterparts (Fig. 8). Differences in circumferential stretch were more significant than differences in radial stretch for most pairs of TAV/BAV leaflets, and broadly encompassed the center region of the leaflet (Fig. 8a). In contrast, significant differences in radial stretch were more concentrated in the commissural regions, as well as along the basal attachment and free edge (Fig. 8b). Interestingly, no regional differences in circumferential stretch were detected between TAV and non-fused BAV L leaflets (i.e. in BAVs with R–N fusion), although strong differences were found between TAV and non-fused BAV N leaflets (i.e. in BAVs with L–R fusion). In the radial direction, however, this trend reversed, highlighting the complexity, heterogeneity, and variability of BAV deformation fields across different fusion types.

FIGURE 8.

Maps illustrating the significance of local differences in (a) circumferential and (b) radial stretch between each TAV leaflet type and their corresponding BAV leaflet types, both fused and non-fused. Herein, color is proportional to log₁₀(p), where p is the p-value resulting from the pointwise t-test. Regions with lower p (i.e. colored more red) show more consistent differences in stretch.

DISCUSSION

General Overview and Novelty

In the present study, we have developed an integrated computational image analysis pipeline that can be used within a clinical setting to produce a detailed map of local AV leaflet deformations based on patient-specific rt-3DE scans. To acquire diastolic deformation fields across the entire AV leaflet surface noninvasively, we utilized a previously validated image-based stretch estimation method,²¹ which yields local stretch information directly from clinical-quality in vivo images through the use of an FE-based geometric morphing protocol. Following this procedure, we parameterized each AV leaflet surface in both the open and closed states using a 2D spline surface domain (Fig. 4a), which allowed for averaging results across subjects and expressing stretches in terms of systematically defined anatomically relevant directions (Fig. 6). We note that during the spline fitting process, corresponding FE mesh nodes were explicitly mapped to the same parametric location on the spline surface. This parametric correspondence between the FE nodes in both the open and closed states was necessary to guarantee accurate and physically realistic results when computing stretch between the configurations. More specifically, while the mesh nodes in both states can be treated as material points on the leaflet surface due to our utilization of the FE method to infer the deformed configuration, spline surface parametric locations from separate fits generally cannot be assumed to maintain material point correspondence. Our approach thus represents a substantial improvement over previous attempts to determine in vivo tissue stretches using spline fitting alone.^2,6,7

Our results demonstrated that our technique was able to infer the complex, non-uniform leaflet deformation field of the AV. Based on the observed spatial resolution of the resultant stretch field, this approach is sufficiently sensitive to capture the patient-specific heterogeneity in the in-plane deformations of both TAV and BAV leaflets (Fig. 5). Averaging over the leaflet, our results agree well with previous computational estimates of TAV and BAV deformations.²⁶ Importantly, however, the present study is the first to yield such detailed estimates of local TAV/BAV deformations derived directly from clinical images. At the population level, we were also able to identify and quantify differences in stretch patterns between leaflet types, and found in particular that stretches experienced by BAV leaflets during closure differ from those of TAV leaflets in terms of both heterogeneity as well as overall magnitude (Figs. 5, 6 and 7).

Clinical and Pathological Context

Deformation, and specifically cyclic physiological stretch, has been demonstrated to have a notable impact on heart valve function, leaflet tissue maintenance, and adaptive remodeling.^5,17 In the context of BAV functional assessment and prognosis, the methods and results from the present study thus pave the way for the development of critically important clinical tools, with the goal of improving prediction of BAV calcification risk, facilitating patient stratification, and optimizing personalized therapeutic approaches for CAVD. Still, mechanical assessment is but one factor among several that are vital to our understanding of this complex disease. Other mechanisms for BAV-related AI and AS are associated with altered flow patterns and higher tissue stresses. Moreover, although there is no known genetic cause in the majority of individuals, BAV is associated with an enriched familial inheritance, with current evidence suggesting 9–15% incidence among first-degree relatives of BAV patients.^10,12

Clearly, developing a deeper understanding of BAV-related disease progression and pathophysiological mechanisms requires a multi-pronged approach, combining patient-specific biomechanical assessment with a strong foundation in AV mechanobiology, to elucidate bidirectional links between tissue deformation and cellular/sub-cellular biological responses (e.g. cell signaling, biosynthesis, extracellular matrix remodeling). Importantly, the resident VICs within the AV leaflet are largely responsible for maintaining the mechanical environment of the heart valves through their signaling and contractile properties, and VIC dysregulation is associated with a number of valve diseases.[3] We have noted profound microstructural deviations in human explanted BAVs from their highly consistent TAV counterparts,¹ which suggest that the VIC microenvironments in various locations on BAV leaflets are quite different than in the normal TAV. We and others have also clearly established the role of local mechanical stimuli as major regulators of VIC function.^{4,13,14,23,24} This result suggests that the BAV VIC microenvironment plays a major role in the underlying mechanisms and propensity of BAV patients to develop AI and AS. However, the presence of multiple, interdependent interaction pathways connecting VICs with their surrounding microenvironment can complicate systematic study of this complex question. When coupled with the challenge of directly measuring physiologically relevant VIC behaviors, this has hampered purely experimental investigations that seek to unravel contributions of genetic and mechanical environments to BAV pathologies. Thus, there is a critical need to improve the quantification of VIC mechanics and signaling in BAV leaflets. In the absence of such knowledge, the development of alternative strategies for treating or preventing BAV-associated pathologies will likely remain elusive.

In the future, it should be noted that abnormal BAV hemodynamics have been implicated as an additional contributor to BAV-associated CAVD.^8,28 This has been speculated to result from abnormal wall shear stress levels that occur as a result of the altered flow patterns around the fused leaflet structures. Thus, building upon the present study, it will be necessary to develop a detailed, comprehensive understanding of TAV and BAV biosolid/fluid function as well as its relation to the clinically obtained 3D dynamic AV geometry and deformation patterns.

Limitations

The scope of the present study is limited in several respects. First, the application of our approach depends on having knowledge of the true systolic and diastolic shapes of the leaflet surface, which must be acquired through real-time imaging. In this regard, the pipeline we have detailed in the present study is not itself predictive in the traditional sense, but rather is meant to serve as a noninvasive tool to measure the current cyclic stretch patterns experienced by the AV. Despite this limitation, we believe that the deformation trends we have elucidated here will ultimately correlate with VIC-level biosynthetic phenomena responsible for the maintenance and remodeling of the leaflet tissues.⁴ Our method will thus facilitate the prediction of long-term calcification risk indirectly through the prediction of consequent biological responses within the leaflet tissue. Toward this goal, a related limitation of our current approach arises from the structural homogenization used in our computational models, which restricts what conclusions can be directly drawn at the tissue and cell levels. For investigations at this scale, a more detailed microstructural model must be used, to account for in-plane and transmural heterogeneity in composition and fiber architecture throughout the tissue.²² The current spatial–temporal resolution of the rt-3DE modality used also precludes analysis of the dynamic deformations of the leaflets over the entire cardiac cycle, thus limiting the present study to analysis of the fully closed diastolic configuration (wherein the leaflets are fairly static). We note, however, that the fully closed state is where the leaflets experience their greatest tension, and thus this is the most relevant configuration for investigating stress-driven remodeling mechanisms. An additional consideration for future work is the investigation of sex differences, particularly in the BAV groups, since this may further elucidate nuances in the presentation and mechanobiological behavior of BAV leaflets compared to their TAV counterparts. This will require larger sample sizes, however, since BAV is substantially more common in males by about a 3:1 ratio,¹¹ as reflected also by our own sample of patients (Table 1).

Conclusions and Future Work

Deformation is a key parameter in the clinical assessment of valvular function, and serves as a direct means to determine regional variations in structure and function. In the present study, we have developed a computational modeling pipeline that can directly yield local deformation information using patient-specific AV geometric data derived from rt-3DE, the most common noninvasive imaging modality used to assess cardiac tissues. Additionally, we have created the first database detailing local in vivo leaflet deformations in patients with TAV and two types of BAV, and we have quantified differences in functional deformation between TAV and BAV leaflets. This study is an essential step toward patient-specific assessment of BAV based on correlating leaflet deformation and AS/AI progression, as it provides a means for assessing patient-specific stretch patterns.

APPENDIX

The image-based stretch estimation method employed in the present study has been previously validated for valvular tissues against both in vitro and in vivo fiducial marker-based deformation metrics.²¹ However, previous validation studies were performed only for the mitral valve, whose geometry is substantially distinct from that of the AV. To further validate our approach for the specific application to the AV, we applied the stretch estimation method to a computationally generated spline surface geometry of a bioprosthetic TAV implant.^27,31 While the bioprosthetic AV has an idealized geometry by design, this validation approach had the advantage of allowing for the comparison of our estimated stretch fields to ground-truth local stretch maps for the modeled TAV, which were obtained via isogeometric analysis.³¹ Resulting stretches from this validation study showed that our technique was able to accurately capture the complex, heterogeneous leaflet deformation field of the AV (Fig. 9). Specifically, our noninvasive method was able to yield stretch estimates within 5% of their ground-truth value over the entire leaflet surface.

FIGURE 9.

In-plane stretch in the normal TAV, showing the capability of the method to capture substantial regional heterogeneity as well as directional differences in stretch.