The role of stress concentration in calcified bicuspid aortic valve

Abstract

Calcific aortic valve disease (CAVD) is the most common valvular heart disease in the aging population, and is now believed to be a slow, progressive, yet actively regulated process. The disease progression can be divided into two phases: initiation phase associated with lipid deposition and inflammation response, and the later propagation phase with active calcification growth. It has been hypothesized that elevated mechanical stress plays a major role in both phases of disease progression. In order to identify a direct link between leaflet stress and calcification development, we performed patient-specific finite-element (FE) analyses of six bicuspid aortic valves (BAV), where the leaflets, raphe and calcifications were all considered. The results showed that during the initiation phase, calcium buildup is likely to occur along the leaflet-root attachment curve (ATC), and the commissures, which are subject to the most drastic changes in stress during the cardiac cycle. During the propagation phase, the presence of calcification would lead to local stress concentration along its boundary, hence further calcification growth. Three patterns of calcification formation were identified on BAV leaflets: ‘radial’, which extended radially from ATC into the leaflet belly region; ‘commissure to commissure’, which extended circumferentially along the coaptation; and ‘raphe’, which located in the vicinity of the raphe. Furthermore, we found a strong correlation between regions with a high risk of calcium buildup and regions with elevated mechanical stress. The high-risk regions predicted at diastole on the non-calcified leaflet from FE models agreed reasonably well with the in vivo calcification locations, which indicates that patient-specific FE modelling could help us to evaluate the potential risk of calcification formation in the early stage of CAVD.

1. Introduction

Calcific aortic valve disease (CAVD) encompasses a disease continuum ranging from early stage mild leaflet alternation (such as leaflet thickening) to end-stage aortic stenosis (AS), where the movement of heavily calcified aortic valve (AV) leaflets is severely restricted, leading to narrowed valve opening and reduced amount of blood flow through the valve during systole. CAVD is the most common valvular heart disease in the aging population of the developed world with a projected disease of 4.5 million in 2030 [1]. In particular, AS has a prevalence around 0.4% in the general population, and 3.0% in the population over 75 years old [2–4].

The buildup of calcium that leads to AS involves a series of highly complex and tightly regulated processes [5–7], and may be divided into two distinct phases [8]: an early initiation phase dominated by lipid deposition and inflammation, and a later propagation phase characterized by an apparent self-perpetuating cycle of calcium formation and valvular injury [9]. It has been hypothesized that mechanical stress plays an essential role in both phases. During the initiation phase, high stress concentration initiates endothelial damage, which results in infiltration of lipids such as oxidatively modified low-density lipoprotein (LDL) [10] into the subendothelial region [11,12], the establishment of inflammatory responses with T lymphocytes [13,14] and macrophages [11] within the subendothelium and fibrosa, and the formation of extracellular matrix [15] and microcalcifications within the leaflet tissue [11]. During the propagation phase, the presence of calcification causes a compliance mismatch and increased mechanical stress. The tissue injury due to elevated stress could further activate various calcific pathways [16–19] and osteoblast differentiation, which in turn triggers additional calcification formation [20]. Therefore, the propagation phase features a self-perpetuating cycle between tissue injury and calcification growth. Although the link between lipid deposition, inflammation and CAVD progression suggests that statins could be beneficial to AS patients, interestingly, three independent trials [21–23] found that statin therapy failed to halt AS progression, even though it reduced the serum LDL cholesterol concentration by more than one-half [23]. Thus, the result from these trials [21–23] suggests that AV biomechanical factor could play a more important role than lipid deposition and inflammation response in disease progression, especially during the propagation phase.

Detailed investigation of biomechanical factors related with CAVD progression requires computational approaches. The buildup of calcium that leads to AS is a slow, gradual and long-term process, which makes it almost impossible to monitor and investigate initiation and propagation phases in in vivo patients. Ex vivo experimental studies [24–26] employ simplified conditions, which focus on short-term (i.e. days to weeks) responses, and cannot explain many phenomena observed in patients. For example, it is known that calcification occurs mostly on the aortic (versus ventricular) side of the valve; however, most calcification on the aortic side develops only at certain subregions [27], but not all over the leaflet surface. Such heterogeneity of calcium buildup clearly cannot be explained by fluid oscillatory shear stress [24] on the aortic side of the leaflets.

Therefore, patient-specific biomechanical analysis will be performed in this study using finite-element (FE) analysis. To investigate the relationship between leaflet stress and calcification development, we selected AS patients with bicuspid aortic valve (BAV), a congenital cardiac anomaly with a prevalence of 0.5–2.0% in the general population [28–30]. Compared with patients with a normal tricuspid AV (TAV), BAV patients almost universally develop valvular calcification at a younger age with a more rapid progression, and they account for nearly 50% of all AS cases [30,31]. This could be due to a combined effect of both genetic factors [32,33] and biomechanical factors [27,29,34]. For example, mutations of the NOTCH1 gene, which have been associated with BAV development, could lead to a later upregulation of osteoblast-specific genes and consequent calcium deposits [32]. On the other hand, the abnormal BAV morphologies could lead to additional stress concentration [35,36], followed by the accelerated tissue damage and calcification formation. In this scenario, patient-specific stress analysis using FE modelling could help us to better understand the biomechanical factors associated with CAVD progression towards AS. Previous FE analyses of BAV were limited to idealized or simplified geometries of the leaflets [35–38]. Furthermore, these studies have not considered the calcification in their analysis.

The objective of this study is hence to perform a detailed patient-specific FE analysis of BAV to investigate the relationship between mechanical stress concentration and calcium buildup related to CAVD progression. Patient-specific geometries were directly reconstructed from multi-slice computed tomography (MSCT) images, including leaflets, raphe and calcification. We assumed that the basic, un-calcified BAV leaflet morphologies would not change significantly over time, i.e. during the calcification initiation and propagation phase. Based on this assumption, we first used the un-calcified BAV leaflet morphologies to estimate the leaflet stress during the initiation phase, and compared the locations of stress concentrations with the in vivo calcification locations to elicit their correlations. Next, an FE analysis was performed with the inclusion of calcifications to estimate the stress during the propagation phase and its effect on calcium buildup. By comparing the stress distribution pattern obtained from FE analysis with the actual in vivo calcification locations of patients, we obtained a direct link between leaflet stress and CAVD progression, observed several patterns of calcification growth, and identified a critical stress value above which calcium is likely to build up.

2. Methods

2.1. Patient clinical data

A variety of BAV classification systems have been proposed based on descriptions of valve phenotypes [39–43]. Here, we adopted the classification system by Sievers & Schmidtke [43]. As seen in table 1, clinical data from six BAV patients (3 type 0 BAV, 3 type 1 BAV and no type 2 BAV) between the age of 57 and 82 were collected retrospectively from Emory University Hospital (Atlanta, GA) (n = 5) and the Hartford Hospital (Hartford, CT) (n = 1), under the Institutional Review Broad (IRB) approvals. Type 0 and type 1 BAV refer to a BAV with no raphe and one raphe, respectively (cf. figure 1a). All BAV patients had severe AS, with moderate to severe calcifications, and were treated with TAVR. In this study, we focused on the FE analysis of BAV biomechanics prior to TAVR. For the patients at Emory University Hospital, the MSCT images were acquired using a Siemens SOMATOM Definition Flash CT scanner, with an in-plane spatial resolution between 0.62 × 0.62 mm and 0.93 × 0.93 mm, and a slice thickness of 1.0 mm. For the patient at Hartford Hospital, the MSCT images were acquired using a GE LightSpeed 64-channel volume CT scanner, with an in-plane resolution of 0.82 × 0.82 mm, and a slice thickness of 0.625 mm. The CT images were aligned with axial, coronal and sagittal views (cf. figure 1b), and were typically obtained at 10 phases (time points) over the cardiac cycle for each patient. Clinical examination reports recorded patients' cardiac physiology and clinical metrics, such as the systolic and diastolic pressure gradients, left ventricular ejection fraction, AV effective orifice area, etc.

Table 1.

Patient information: the gender, age, BAV type, peak transvalvular diastolic and systolic pressures for all patients. A schematic of different types of BAV can be found in figure 1a. Type 0 and type 1 refer to BAV with no raphe and one raphe, respectively. In addition, L, R and N refer to the left, right and non-coronary leaflets, respectively. A-P refers to BAV where the orientation of leaflet free edge is anterior–posterior. LAT refers to BAV where the orientation of leaflet free edge is lateral. L-R refers to BAV where the left and right coronary leaflets are fused, while R-N refers to BAV where the right and non-coronary leaflets are fused.

patient ID	gender	age	type of BAV	transvalvular diastolic pressure gradient (mmHg)	transvalvular systolic pressure gradient (mmHg)
A	F	82	0 A-P	57	90
B	F	75	0 LAT	60	106
C	M	71	0 A-P	60	35
D	M	69	1 R-N	54	65
E	F	62	1 L-R	77	95
F	M	57	1 L-R	78	71

Figure 1.

BAV types and geometry reconstruction. (a) Schematic of normal TAV, type 0 and type 1 BAV. Black and red lines represent the leaflet free edge and raphe, respectively; (b) representative CT image of the BAV in axial, sagittal and coronal views; (c) reconstructed BAV models of six patients. Here and below, the orientation of each BAV model follows the schematic in (a).

2.2. Patient-specific geometry reconstruction

The patient-specific BAV geometries were segmented from MSCT images at both end-systole and mid-diastole using Amira-Avizo (Thermo Fisher Scientific, MA) and three-dimensional Slicer (www.slicer.org) software. The initial, reference state was chosen at the end-systole, where the leaflets are partially open and assumed to be stress-free. FE meshes were, therefore, generated at end-systole using HyperMesh (Altair Engineering, Inc., MI) software. The models were composed of 8-node brick elements (C3D8R) for the BAV leaflets and 4-node tetrahedral elements (C3D4) for the raphe and calcification regions. Three layers of elements were used across the leaflet thickness, with a uniform total thickness of 0.75 mm, which is typical for human AV leaflets [44]. As seen in figure 1c, the reconstructed BAV models comprise the non-fused leaflet, fused leaflet, the calcification and the raphe. For patient D, the raphe (or a raphe-like structure) is close to the commissure region of the fused leaflet; for patients E and F, the raphe is more prominent and extends along the radial direction into the belly region of the fused leaflet. The BAV and calcification shared the same nodes on the tissue–calcification boundary, thus guaranteeing full-interface displacement continuity, and avoiding contact-related and kinematic constraints-related issues in FE simulations. More details on BAV model reconstruction can be found in appendix A.

2.3. Finite-element modelling

2.3.1. Modelling of valve material properties

While the material properties for leaflet tissue could vary among patients, one representative set of human leaflet material properties was adopted for this study [45]. In particular, the mechanical response of the leaflet tissue was modelled with a modified version of the anisotropic hyperplastic Holzapfel–Gasser–Ogden (MHGO) material model [46,47]. Valve tissues were assumed to be composed of a matrix material with two families of embedded fibres, each consisting of a preferred direction. The strain energy function, W, can be expressed as

$$\begin{array}{rl}W& =C_{10}\{\exp [C_{01}({\overline{I}}_1-3)-1]\}\\ & +\frac{k_1}{2k_2}\sum _{i=1}^2\left[\exp \left\{k_2{\left[\kappa {\overline{I}}_1+(1-3\kappa ){\overline{I}}_{4i}-1\right]}^2\right\}-1\right]\\ & +\frac{1}{D}{(J-1)}^{2}i=1,\hspace{0.17em}2,\end{array}$$ 2.1

where C₁₀, C₀₁ are the matrix parameters, k₁, k₂ are the material parameters, D is a material constant which enforces incompressibility, ${\overline{I}}_1$ and ${\overline{I}}_{4i}$ are the strain invariants, which describe the matrix material and the fibre family properties, respectively, κ is a dispersion parameter which determines the level of dispersion in the fibre orientations and J is the determinant of the deformation gradient. The mean local fibre directions are assumed symmetric with respect to the circumferential axis of the local coordinate system. Local coordinate systems were defined for each leaflet, and the local fibre orientations were defined through ${\overline{I}}_{4i}={\mathit{m}}_{0_i}\cdot \mathit{C}{\mathit{m}}_{0_i}$, where C is the right Cauchy Green tensor, with ${\mathit{m}}_{0_1}=[\text{cos}\theta ,\text{sin}\theta ,0]$ and ${\mathit{m}}_{0_2}=[\text{cos}\theta ,-\text{sin}\theta ,0]$, and θ defines the angle between one of the mean local fibre direction and the circumferential direction of the local coordinate system. The anisotropic hyperelastic material model was implemented into ABAQUS/Explicit 2016 (SIMULIA, Providence, RI) with a user sub-routine VUANISOHYPER [48–50], where the material model parameters are summarized in table 2. For simplicity, this set of parameters was used to describe the material properties of both the leaflets and the raphe.

Table 2.

The parameters used in the MHGO material model. R² describes the goodness of the fit based on the experiments.

MHGO model parameters	C10 (kPa)	C01	k1 (kPa)	k2	θ(°)	D (kPa−1)	κ	R2
	0.1347	11.21	11.33	28.59	22.07	5.00 × 10−4	4.54 × 10−7	0.81

For a normal TAV, the collagen fibres on the leaflets are typically orientated circumferentially from commissure to commissure, and nearly parallel to the free edge [51–53]. However, for a fused leaflet with raphe of BAV, the fibres in the raphe region are typically disoriented [34,54]. It has been reported that the orientation of the fibres can be almost 45° (instead of parallel) to the free edge. In the raphe, the fibres from the opposite side can merge at a 90° angle [34]. Therefore, the local coordinate system was defined accordingly: for the leaflet without raphe, the circumferential axis of the local coordinate system was set to be nearly parallel to the free edge; while for the leaflet with raphe, the circumferential axis was set to be approximately +45° and −45° to the free edge on both sides of the raphe, forming a 90° angle at the raphe. The calcification was assumed to be homogeneous, isotropic and linear elastic, with a Young's modulus of 12.6 MPa and a Poisson's ratio of 0.3 [55].

2.3.2. Loading and boundary conditions

Patient-specific FE modelling was performed in ABAQUS/Explicit 2016 (SIMULIA, Providence, RI) for all six BAV patients to analyse valve biomechanics during both valve opening and closure. The initial reference state was chosen at end-systole where the leaflets were partially open and assumed to be stress-free. For valve opening, the leaflet-root attachment curve (ATC) was fixed since its movement throughout systole was found to be negligible, and a mean transvalvular systolic pressure was applied on the ventricular surface of the BAV leaflets. For valve closure, nodal displacements were prescribed at each ATC as kinematic boundary conditions, which described the motion of the aortic root from end-systole to mid-diastole. In addition, a mean transvalvular diastolic pressure was applied to the aortic surface of the BAV leaflets.

Patient-specific values of the transvalvular pressure were obtained from pre-operative clinical reports (table 1). The nodal displacement of each node along the ATC from end-systole to mid-diastole was calculated based on the geometries reconstructed from MSCT images at both phases. Since the FE analysis only focused on quasi-static state when the valve was fully open (at peak-systole) and fully closed (at mid-diastole), rather than the dynamics of the valve over the entire cardiac cycle, the pressure and the nodal displacements were applied linearly, rather than following the physiological curve. In specific, for each FE simulation, the pressure and nodal displacements were ramped from zero to the target value. After the FE simulation finished, the deformed geometry was obtained, and the stress and strain values were extracted and analysed.

2.3.3. Finite-element analyses with and without calcification

We assume that the calcifications do not change the morphology of the original BAV leaflets significantly. Therefore, FE simulations were first performed in the BAV models without calcification, which represent the initiation phase prior to calcium buildup.

In order to investigate the propagation phase of calcification formation, and how the presence of calcification further affects the valve dynamics, FE simulations were performed in the BAV models that included calcifications reconstructed from the MSCT images.

3. Results

3.1. Finite-element model validation

In order to validate the FE simulation, at mid-diastole, the deformed BAV leaflet geometries obtained from simulation with calcifications were compared with the geometries segmented directly from the MSCT images, considered herein as the ground truth. Point-to-mesh distance metric [45] was used to quantify the error distance between a point on one surface and the other surface. In particular, the mid-surfaces (between the aortic and the ventricular side) of the leaflets from FE simulations were extracted, and compared with the ground truth geometries. As shown in figure 2, the deformed BAV geometries were in reasonable agreement with the ground truth geometries. The mean point-to-mesh error distance was less than 2.0 mm for all patients.

Figure 2.

Distribution of point-to-mesh error distance between the deformed leaflets obtained from FE simulations and the ground truth geometries reconstructed from MSCT images at mid-diastole. The mean error distances and the standard deviations were 1.71 ± 1.26 mm, 1.39 ± 0.90 mm, 1.42 ± 0.97 mm, 1.50 ± 1.00 mm, 1.79 ± 1.14 mm and 1.48 ± 0.92 mm for patients A, B, C, D, E and F, respectively.

3.2. Finite-element analysis without calcification: the initiation phase of calcium buildup

Figures 3 and 4 present the maximum principal strain and stress distributions of the leaflets at diastole, respectively, while table 3 summarizes the corresponding average values, where the average values exclude top 1% of elements with extreme high (non-physiological) values [56]. For fused leaflets with raphe, two average values were reported, one that only considered the leaflets, and the other which also included the raphe region (table 3). The strain and stress patterns and their average values varied among the patients due to patient-specific geometries, as well as loading and boundary conditions. At diastole, when the fused and non-fused leaflets are nearly symmetric (patients A, B and D), the average strain and stress between the two leaflets were close; when the two leaflets are asymmetric (patients C, E and F), the average values between the two leaflets showed more variations.

Figure 3.

Leaflet strain distribution for the FE models without calcification at diastole.

Figure 4.

Leaflet stress distribution for the FE models without calcification at diastole.

Table 3.

Average values of strain and tensile and compressive stress at diastole over the non-fused and fused leaflets without calcifications. For fused leaflets, the values in parentheses are the average values over both the leaflet and the raphe.

	patient ID	A	B	C	D	E	F
non-fused leaflet	strain	0.170	0.149	0.156	0.151	0.181	0.163
	tensile stress (kPa)	73.05	113.68	58.47	46.37	129.2	136.67
	compressive stress (kPa)	−4.59	−2.41	−3.44	−0.94	−11.66	−7.64
fused leaflet	strain	0.169	0.151	0.201	0.152 (0.146)	0.173 (0.191)	0.171 (0.187)
	tensile stress (kPa)	72.28	107.09	93.97	50.53 (46.49)	79.99 (109.63)	101.44 (187.94)
	compressive stress (kPa)	−3.8	−8.94	−15.15	−2.5 (−23.7)	−5.94 (−50.0)	−6.96 (−57.9)

In general, peak strain and stress values were observed locally along the leaflet ATC and at the commissure, where the leaflets are subjected to great flexion. Along the leaflet ATC, the regions of high strain and stress extend radially into the belly region, while at the commissure, these regions extend circumferentially along the coaptation line from commissure to commissure. These results were consistent with previous ex vivo experimental observations [34]. For leaflets with raphe, the strain and stress distribution patterns are more complex. In particular, the presence of a prominent raphe (patients E and F) can lead to additional folding, and hence high strain and stress values in its vicinity.

Figure 5 presents the maximum principal stress distribution during valve opening. It is evident that even without the presence of calcification, BAV is naturally stenotic, with the typical ‘fish-mouth’ (instead of nearly round) shape for the orifice. In general, the stresses were higher in the belly region, and peak stresses were observed near the central part of the free edges, where the leaflet was being stretched the most. With the presence of the prominent raphe, the stress distribution became highly asymmetric between the non-fused and the fused leaflet. For all patients, it is notable that the leaflet ATC and the commissure regions on the aortic side were mostly subject to compressive stresses during systole. Since these regions were subject to peak tensile stresses during diastole, this suggests that these regions (along the ATC and the commissure) experience the most drastic stress variation during a cardiac cycle.

Figure 5.

Aortic view (a) and the side view (b) of stress distribution for the FE models without calcification at systole.

3.3. Finite-element analysis with calcification: the propagation phase of calcification formation

Figures 6 and 7 present the leaflet maximum principal strain and stress distributions at diastole, respectively, while table 4 summarizes the corresponding average values. In addition, figure 8 presents the maximum principal stress distribution at systole. Compared with figures 3–5, it is clear that the calcification affects both the BAV morphology and the biomechanical response significantly during the entire cardiac cycle. Firstly, the deformed geometries were altered with the presence of calcifications. For all patients, the curvature of the leaflet free edge at the coaptation region decreased locally where calcifications were nearby, as the stiffer calcification restricted the leaflet motion. At diastole, for the two type 1 L-R patients (patients E and F) with prominent raphe, both the calcifications and the raphe restricted the movement of the fused leaflet, and this combined effect caused an incomplete leaflet coaptation at diastole. At systole, the valve opening area became even smaller with the presence of calcifications (figure 8), leading to moderate to severe AS. Secondly, compared with the leaflets without calcifications, the stress and strain became highly non-uniform with the presence of calcifications. In addition to the regions along ATC and commissure, the peak values for both tensile and compressive stresses were also found in the vicinity of the calcification.

Figure 6.

Leaflet strain distribution for the FE models with calcification at diastole.

Figure 7.

Leaflet stress distribution for the FE models with calcification at diastole.

Table 4.

Average values of strain and tensile and compressive stress at diastole over the non-fused and fused leaflets with calcifications. For the fused leaflet, the values in parentheses are the average values over both the leaflet and the raphe.

	patient ID	A	B	C	D	E	F
non-fused leaflet	strain	0.177	0.156	0.159	0.144	0.166	0.166
	tensile stress (kPa)	35.24	102.59	62.89	27.70	69.95	55.19
	compressive stress (kPa)	−25.88	−10.31	−3.37	−2.32	−8.25	−62.03
fused leaflet	strain	0.175	0.147	0.187	0.126 (0.108)	0.177 (0.194)	0.171 (0.182)
	tensile stress (kPa)	87.38	57.27	89.47	14.71 (20.42)	77.46 (147.70)	79.68 (212.77)
	compressive stress (kPa)	−8.40	−7.27	−14.40	−5.31 (−18.02)	−14.20 (−49.75)	−7.81 (−40.5)

Figure 8.

Aortic view (a) and the side view (b) of stress distribution for the FE models with calcification at systole.

4. Discussion

4.1. The relationship between stress concentration and calcium buildup

It has been hypothesized that regional stress concentrations could cause structural damage on the leaflet microstructure and play an important role in CAVD progression during both the initiation and the propagation phases of calcium buildup [8,27]. While FE analyses have become a powerful tool to explore valve biomechanics, there is still a lack of direct and detailed evidence on how the biomechanics affects valvular calcification development. In particular, the ‘critical’ stress above which the leaflet becomes prone to calcium buildup is unclear, and it is challenging to predict the local regions on the leaflet where the calcium is more likely to build up. BAV patients were usually selected for FE study of AS since they tend to develop AS more rapidly. Most of the previous studies using FE modelling were limited to idealized geometries of the leaflets [36,37]. Although Conti et al. [35] and Dallard et al. [38] used clinical data, the geometries were not reconstructed directly from clinical images. Except for the study of Dallard et al. [38], most of the previous studies simply modelled the raphe region with an arbitrarily added thickness along the straight fused line. Most importantly, although BAV patients are typically heavily calcified, none of these previous studies included patient-specific calcifications. Thus, this study marks the first comprehensive study of BAV biomechanics based on detailed patient-specific geometries that include the leaflets, raphe and calcifications, which gives us the opportunity to investigate the relationship between valve biomechanics and calcium buildup.

In the initiation phase, in order to describe valve biomechanics prior to calcium buildup, FE modelling was performed for BAVs without calcifications. The results showed that the regions along the ATC and commissure experienced peak tensile stresses during diastole (figure 4), and compressive stresses during systole (figure 5). In addition, for the fused leaflet, peak tensile and compressive stresses were also observed in the vicinity of the raphe. Therefore, calcium buildup is more likely to initiate in these regions due to the most drastic stress variations during a cardiac cycle. Indeed, the small pieces of calcification observed in patients E and F, which were likely at their initiation phase, were found in these regions.

In the propagation phase, in order to describe the interaction between the calcification and the leaflet tissue, the same mesh grid nodes were shared on the tissue–calcification boundary, which guarantees displacement continuity at the interface. It was found that the existence of calcification could accelerate the CAVD progression, since it leads to a compliance mismatch and hence stress concentration along its boundary, which would cause further injury and calcium buildup. This is consistent with the hypothesis that the propagation phase features a self-perpetuating cycle of calcium formation and valvular injury [8]. Overall, our patient-specific FE simulations suggested a direct link between elevated stress levels and calcification initiation and propagation in CAVD progression.

4.2. Predictions of calcification formation with critical stress

The FE analysis performed in this study enabled us to identify a critical stress level, which can be used to predict local regions where calcium buildup is likely to occur. Figure 9 presents the stress distribution on non-calcified leaflets based on FE modelling, where the ‘high-risk’ region (shown in light grey) is defined as the region where the stress is above a threshold value. The predicted high-risk region depends on the choice of the threshold value. In particular, as the threshold value increases, the corresponding high-risk region shrinks. The optimal threshold, i.e. the critical value, is, therefore, identified when the ratio A_o/A_h becomes the largest, where A_o is the overlap area between the high-risk region and the actual calcification location and A_h is the entire high-risk region area. For the six BAV patients in this study, it was found that the critical stress value was 1.40 ± 0.08 times the (base level) average stress over the leaflets.

Figure 9.

Stress distribution patterns based on the critical value (left) and the actual patient geometries (right) for each patient. The region where the stress is higher than the critical value (hence has a high risk of developing calcifications) is shown in light grey and the rest of the leaflet is shown in black.

In addition, several distribution patterns were identified for high-risk regions. The first one was the ‘radial’ pattern, which extended radially from ATC into the belly region. The second one was the ‘commissure to commissure’ pattern, which extended circumferentially along the coaptation. Both patterns were consistent with previous findings of Thubrikar et al. [27]. In addition, a third pattern was observed for BAV with raphe, which extended along the raphe. Compared with the calcification locations of the six patients, it can be seen from figure 9 that the high-risk regions predicted based on non-calcified leaflet stress distribution agreed reasonably well with the actual calcification locations. While not shown here, a similar analysis was performed based on the strain distribution, but we failed to identify a critical strain value with which the associated high-risk regions agreed well with the actual calcification locations. Therefore, our FE modelling suggests that the stress is a more effective biomechanical indicator for calcium buildup. Overall, patient-specific FE modelling could help us to predict local regions with a high risk of calcium buildup using the stress distribution on non-calcified leaflets at valve closure, and to potentially evaluate the risk of calcification formation.

4.3. Bicuspid aortic valve versus tricuspid aortic valve

Compared with TAV, BAV has quite different morphology due to its abnormal structure. In general, BAV leaflets are found to show more folding and creasing, which is consistent with previous experimental observations [34,57] and numerical simulations [35,37]. During systole, the TAV leaflets are fully open, forming a nearly circular shape orifice; while the BAV leaflets form a much smaller ‘fish-mouth’ shape orifice (figure 5), indicating that the BAV is stenotic by nature. During diastole, the coaptation contact lines at the free edge are nearly straight for TAV; however, they are curved for BAV (figure 3). Furthermore, the presence of a raphe added additional stiffness to the fused leaflet [38], leading to more complex flexure in the leaflet. For example, additional folding was observed near the raphe along the radial direction, as the two halves of the fused leaflet bulged towards the ventricle.

While both genetic factors [32,33] and biomechanical factors [27,29,34] could contribute to the more rapid calcification formation in BAV than TAV, our FE simulations enabled us to isolate and compare the biomechanical response between BAV and TAV. In particular, the patient-specific FE analysis of normal TAV performed by Liang et al. [45] provided an ideal comparison since their simulations were performed with the same leaflet material properties as those used in this study. Compared to their results, the overall peak stress of BAV at diastole increased two- to three-fold, even without the presence of calcification. This increase in the peak stress of the BAV leaflet was consistent with previous simulation results of BAV using both idealized geometries [36] and patient-specific geometries [35]. This significantly elevated stress level in BAV is likely to be one of the causes that BAV is more prone to calcium buildup and almost universally develops heavy calcifications.

4.4. Limitations

There are several limitations in this study. First, although patient-specific geometries were reconstructed from MSCT images, patient-specific material properties were not obtained. Leaflet material properties were assumed the same as normal TAV leaflets [45], where only one set of material properties derived from experimental ex vivo data of human cadaver heart tissues were used to describe all the patients in this study. Moreover, the tissue material properties were assumed to be homogeneous, and the raphe was assumed to have the same material properties as the leaflet, while the material properties could vary throughout different regions of the leaflets within one patient. Second, following the common practice of patient-specific FE simulations of heart valves [35,45], quantitative validation was just performed at valve closure, and the thickness of leaflets was assumed uniform [58] due to the low spatial resolution of MSCT images. However, variations in leaflet thickness have been reported for BAV, such as thickened free edge of the fused leaflet with raphe [34]. Therefore, for more accurate predictions, future studies should consider the spatial variations in the tissue properties and leaflet thickness, with more accurate calcification properties. Finally, the FE simulations only included the valve, not the aortic root. The prescribed nodal displacements at the valve ATC did not accurately describe the full interaction between the valve and the aortic root, which could contribute to some elevated stress observed along ATC in the simulations. More accurate simulations will require patient-specific fluid–structure interaction (FSI) modelling that includes the valve, the aortic root and hemodynamic field. Such FSI modelling is being performed in our group and will be discussed in following publications.

5. Conclusion

We performed patient-specific FE analysis for human BAV from MSCT images. Compared to TAV patients, the results show that BAV has a smaller opening at systole, and more flexure throughout the leaflet at diastole, with curved coaptation contact line at the free edges, and additional folding along the prominent raphe. The abnormal morphology of BAV affects the stress level significantly, leading to much higher peak stress than that of TAV. This biomechanical factor could be one of the causes that BAV is more likely to develop heavy calcifications.

FE simulation results showed a clear link between leaflet stress level and calcium buildup in CAVD progression. During the initiation phase, the calcium buildup is likely to occur at the regions along the ATC, the commissure, and in the vicinity of raphe, which are subject to drastic stress variations during a cardiac cycle. In the propagation phase, the local stress concentration induced by the presence of calcification could play a central role in the self-perpetuating cycle of calcification formation and valvular injury. Three patterns were identified for calcification formation: ‘radial’, which extended radially from ATC into the belly region; ‘commissure to commissure’, which extended circumferentially along the coaptation; and ‘raphe’, located in the vicinity of the raphe. Furthermore, we found a strong correlation between regions with a high risk of calcium buildup, and regions with elevated mechanical stress (rather than strain). The high-risk region could be identified with a critical stress, which was approximately 1.4 times the leaflet average stress. The high-risk regions predicted at diastole on the non-calcified leaflet from FE models agreed reasonably well with the in vivo calcification locations, which indicates that patient-specific FE modelling could help us to potentially evaluate the risk of calcification formation in the early stage of CAVD.

Appendix A. Bicuspid aortic valve model reconstruction

Patient-specific BAV structures were identified and semi-automatically segmented from the rest of the heart using Hounsfield intensity thresholding, region growing techniques and manual pixel editing tools. Data segmentation was initiated at a threshold level of approximately 180 Hounsfield units (HU). For the three type 1 BAV patients, the raphe was identified where the leaflet tissue was clearly thickened, and reconstructed based on the HU histogram of the MSCT scans; having a threshold level similar to the BAV leaflets, as can be seen in figure 1b. Initially, a two-dimensional mesh (S4 shell elements) of the ventricular surface of the BAV leaflets was created, before creating the three-dimensional solid mesh using the element offset tool available in HyperMesh (Altair Engineering, Inc., MI) software. After a mesh convergence study, the individual element size for the BAV models was set to 0.25 mm. Mesh size was refined until stress results were independent of mesh size, with results showing a variation within 5%. The total number of elements used for the leaflets, raphe and calcification was on average 54 600, 24 200 and 170 000, respectively.

Data accessibility

All relevant data are within the paper and as electronic supplementary material.

Authors' contributions

T.Q. roles: conceptualization, methodology, data analysis, investigation, project administration, validation, visualization, writing—original draft, writing—review and editing. A.C. roles: data analysis, investigation, writing—review and editing. W.M. roles: investigation, writing—review and editing. B.B. roles: data analysis, writing—review and editing. N.K. roles: resources, writing—review and editing. S.L. roles: resources, writing—review and editing. W.S. roles: conceptualization, funding acquisition, investigation, project administration, resources, supervision, writing—review and editing. All authors gave final approval for publication and agree to be held accountable for the work performed therein.

Competing interests

W.S. is a co-founder and serves as the Chief Scientific Advisor of Dura Biotech. He has received compensation and owns equity in the company. The remaining authors have nothing to disclose.