The computational MV repair evaluation protocol employed in this study contains several key steps: (1) modeling the virtual pathological MV featuring anterior (A2) chordal rupture; (2) using chordal transposition to perform the virtual MV repair; (3) conducting dynamic FE evaluations of the normal (control) and pathological MVs before and after repair (chordal transposition); (4) assessing and comparing the physiological and biomechanical features among the normal, pre-repair, and post-repair models (Fig. 1). The virtual MV models were created using our in-house MV modeling code (MATLAB, MathWorks Inc, USA), and dynamic FE evaluations were conducted by ABAQUS (Version 2017, SIMULIA, Dassault Systems, Waltham, MA, USA).

Fig. 1.

Computational mitral valve (MV) repair evaluation protocol for virtual chordal transposition.

A normal MV model near-end diastole consisted of a saddle-shaped annulus, a single-cusp anterior leaflet, a tri-scalloped posterior leaflet, and marginal and strut chordae tendineae (Fig. 2). The MV annulus was divided into anterior and posterior tracts, featuring a posteromedial–anterolateral distance of 32.0 mm and anterior–posterior distance of 31.5 mm [17, 18]. The leaflet-free margin was defined using a linear combination of sinusoidal functions, and multiple lines were generated connecting the annulus to the leaflet-free margin [21, 22]. A three-dimensional (3D) membrane structure of the MV leaflet was designed, which utilized a non-uniform rational B-spline surface (NURBS) modeling approach [19, 23], and exported to ABAQUS followed by meshing with 4122 triangular 3D shell elements. The normal MV model included 24 marginal chordae and 2 strut chordae. These components played a crucial role in linking the papillary muscles with both leaflets. Each marginal chordae tendineae extended into five marginal chordae, which effectively secured the leaflet along its entire free edge. The two strut chordae were modeled and demonstrated a distinct sequential arrangement pattern of papillary muscle tips, primarily localized to the central region of the anterior leaflet. All the chordae tendineae were represented as 3D line elements (T3D2 element type). In order to construct the pathological MV model with A2 RMCT, four primary chordae in the A2 scallop were selectively excised, as guided by previous clinical reports, resulting in the absence of chordae within the length range of 8–12 mm along the marginal edge of the leaflet [24].

Fig. 2.

Virtual mitral valve (MV) models. (A) Normal MV, (B) MV with A2 ruptured mitral chordae tendineae (RMCT). Pm, posteromedial; A, anterior; Al, anterolateral; P, posterior.

Fig. 3 illustrates the step-by-step process of virtual chordal transposition repair. Initially, virtual quadrangular posterior resection is performed, targeting the posterior (P2) scallop, where the chordae tendineae being transferred to the A2 scallop are connected. A total of four primary marginal chordae were identified for the transfer process, necessitating a 16 mm resection of the P2 scallop, to which these chordae were attached. Subsequently, the detached chordae from the P2 scallop were relocated to the A2 scallop, ensuring alignment in the anterior-to-posterior direction. Then, the transferred chordae were integrated with the elements corresponding to the A2 leaflet free margin, thereby replicating the intricate process of chordae suturing. In the last step of the virtual chordal transposition, the P2 scallop was subjected to plication and suturing. Converging the two excised leaflet edges at the midpoint ensured uniform spacing, while interconnecting the corresponding elements in the leaflet tissue replicated the suturing effect.

Fig. 3.

Computational evaluation protocol for virtual chordal transposition repair. (A) Virtual quadrangular posterior leaflet resection. (B) Virtual chordal transposition. (C) Virtual plication and suturing. Pm, posteromedial; A, anterior; Al, anterolateral; P, posterior.

The identical dynamic FE simulation protocol, which has been rigorously demonstrated and validated in our previous studies, was employed in this study to perform the MV function simulations [17, 18, 19, 20, 23, 25, 26]. Briefly, a Fung-type elastic constitutive model was utilized to accurately represent the anisotropic hyperelastic behavior of the MV leaflet tissue [18, 27, 28]. The relationship between the Green–Lagrange strain (E) and Cauchy stress ($\sigma$) was established as:

(1)$$\sigma =\frac{1}{J}𝐅\frac{\partial W}{\partial E}{𝐅}^T$$

where J represents the determinant of the deformation gradient (F). Moreover, to precisely capture the material characteristics of the leaflets, the strain energy function (W) was defined using four parameters (c, A1, A2, and A3) as follows.

(2)$$\begin{array}{c}\hfill \mathrm{W}=\frac{\mathrm{c}}{2}\left[{\mathrm{e}}^{\mathrm{Q}}-1\right],\mathrm{Q}={\mathrm{A}}_1{\mathrm{E}}_{11}^2+{\mathrm{A}}_2{\mathrm{E}}_{22}^2+2{\mathrm{A}}_3{\mathrm{E}}_{11}{\mathrm{E}}_{22}\hfill \end{array}$$

the leaflet tissue elements were approximated as nearly incompressible and hyperelastic (J = det F = 1). In accordance, the stress–strain correlation was formulated as follows:

(3)$${\sigma }_c=\left(2E_{11}+1\right)c\exp (Q)\left(A_1{E}_{11}+A_3{E}_{22}\right)$$

(4)$${\sigma }_r=\left(2E_{22}+1\right)c\exp (Q)\left(A_3{E}_{11}+A_2{E}_{22}\right)$$

the primary material coordinates considered in our analysis were the fiber directions spanning the surface of the leaflet, namely, the circumferential ($\sigma$${}_{\text{c}}$) and radial ($\sigma$${}_{\text{r}}$) directions. To accurately capture the mechanical response of the leaflet tissue, we incorporated experimentally derived material parameters from a previous investigation [29] into the Fung-type hyperelastic constitutive model, which was then integrated into the ABAQUS platform. The anterior leaflet had a thickness of 0.69 mm, while the posterior leaflet had a thickness of 0.51 mm [30]. Next, the Ogden models were employed to characterize the nonlinear hyperelastic properties of the strut and marginal chordae [31]. The cross-sectional areas assigned to the strut, anterior marginal, and posterior marginal chordae were 0.61 mm${}^2$, 0.29 mm${}^2$, and 0.27 mm${}^2$, respectively [31]. To ensure accurate simulations, the virtual MV models were assigned appropriate values for Poisson’s ratio (0.48) and density (1100 kg/m${}^3$) [23, 32, 33].

Subsequently, dynamic FE analyses were conducted to assess the MV functions before and after repair. A physiological transvalvular pressure gradient was applied to the simulations throughout an entire cardiac cycle (duration = 1.8 seconds, end-systolic pressure = 126 mmHg [34]). To accurately represent the coaptation between the two leaflets, self-contact within each leaflet, and the interaction between the leaflets and chordae during the cardiac cycle, the penalty method was utilized to implement the general contact algorithm (friction coefficient of 0.05) [26].

In order to assess the impact of the MV repair technique, an analysis of the leaflet stress distribution, the stress distribution along the chordae, and the coaptation between the leaflets was conducted across the entire cardiac cycle. Specifically, the biomechanical properties of the normal MV and the pathological MV before and after chordal transposition were compared during peak systole. Both quantitative and qualitative assessments were performed to evaluate the functional and morphological characteristics of these models. Geometric variables, including coaptation length and coaptation angle, were also examined. Coaptation length was defined as the distance from the free margin of the anterior leaflet to the highest point of the leaflet coaptation at peak systole. The coaptation angle was determined by connecting the top of the leaflet coaptation with the anteroposterior (A–P) line.

Successful simulation of virtual chordal transposition repair was carried out for the pathological MV model presenting an A2 chordal rupture. Fig. 4A illustrates the MV morphologies at end-diastole for the normal MV and the pathological MV before and after chordal transposition. The pathological MV model clearly exhibited A2 chordal rupturing and a substantial anterior leaflet flail (Fig. 4A). Conversely, the post-virtual chordal transposition MV model revealed a considerable reduction in the total annulus length, equivalent to the length of the excised P2 leaflet.

Fig. 4.

MV morphologies and leaflet stress distributions. (A) MV morphologies at end-diastole for the normal, pre-repair, and post-repair MV models. (B) Leaflet stress distributions near peak systole. Pm, posteromedial; A, anterior; Al, anterolateral; P, posterior; MV, mitral valve.

Fig. 4B displays the leaflet stress distributions near peak systole for the normal, pre-repair, and post-repair MV models. In order to facilitate a comparison among these models, a reference maximum stress value (0.4 MPa) was established to visualize the MV models [19]. In the normal MV, the notable stress values were observed in the circumferential direction within the anterior saddle-horn region, reaching a maximum stress of 0.6 MPa. The pathological MV model with an A2 chordal rupture exhibited a stress distribution resembling that of the normal MV in the anterior leaflet region, with a maximum stress of 0.61 MPa. However, the P2 leaflet region in the pre-repair MV displayed a relatively higher stress distribution compared to the normal MV. Additionally, following virtual chordae transposition repair, there was a substantial reduction in the overall stress throughout the leaflet region, effectively mitigating the high-stress distribution observed in the pre-repair P2 scallop. Moreover, the considerable stresses identified in the radial direction within the central zone of the anterior leaflet were effectively alleviated in both the normal and pathological MVs. The maximum leaflet stress value of 0.37 MPa was found after the virtual chordal transposition and fell below the designated threshold for maximum stress. This reduction indicates a substantial decrease of 60.6% in comparison to the maximum stress detected in the pathological MV.

During peak systole, the chordal stress distributions were assessed and compared among the normal MV and the pathological MV before and after chordal transposition (Fig. 5A). Fig. 5B displays the unfolded chordal stress distributions, which were centered on the A2 scallop and bisected at the midpoint of the P2 scallop. In the normal MV, relatively higher chordal stress values were primarily localized in the A2 and P2 leaflet regions rather than the entire chordae, while no abrupt stress variations were noted within the specific chordae. The maximum chordal stress value was 0.81 MPa in the normal MV. In contrast, the pre-repair MV featuring A2 RMCT demonstrated a marked increase in chordal stresses on the two intact chordae, adjacent to the ruptured A2 chordae, which reached a maximum chordal stress value of 1.17 MPa. The P2 region of the pathological MV showed a relatively higher stress distribution in comparison to the normal MV, while other areas displayed a comparable chordal stress distribution. Following the virtual chordal transposition repair procedure, the post-repair MV displayed a large reduction in the high chordal stress values within both the A2 and P2 leaflet regions, where the maximum stress value only reached 0.78 MPa, thereby indicating a lower chordal stress level compared to the normal MV. Particularly noteworthy were the dramatically decreased chordal stress values identified in the intact chordae that were located adjacent to the ruptured A2 chordae. The chordal stress distributions in the A2 and P2 leaflet regions of the post-repair MV demonstrated relatively uniform stress values without any large fluctuations, thereby resembling that of the normal MV.

Fig. 5.

Chordal stress distributions. (A) Chordal stress distributions near peak systole for the normal, pre-repair, and post-repair MV models. (B) Unfolded chordal stress distributions. MV, mitral valve; Pm, posteromedial; A, anterior; Al, anterolateral; P, posterior.

Fig. 6 presents the visualization and identification of leaflet coaptation at peak systole, thereby enabling a qualitative comparison of the performance between the normal MV and the pathological MV, both before and after chordal transposition. The normal MV exhibited complete coaptation, while the pathological MV exhibited pronounced anterior leaflet prolapse resulting from the A2 chordal rupture, which was accompanied by a distinct area of MR. Remarkably, in the post-repair MV, successful restoration of the anterior leaflet prolapse and complete recovery of the coaptation were both clearly observed, which surpassed the coaptation performance by the normal MV. The virtual chordal transposition repair facilitated the junction between the two leaflets, effectively restoring the leaflet coaptation.

Fig. 6.

Leaflet coaptation near peak systole for the normal, pre-repair, and post-repair MV models. MV, mitral valve; Pm, posteromedial; A, anterior; Al, anterolateral; P, posterior.

Assessing the morphological attributes of the normal MV and the pathological MV, both before and after the chordal transposition, at the fully closed position enabled a strategic examination of the coaptation lengths and coaptation angles of the two leaflets (Fig. 7). For enhanced visualization and quantitative analysis of the leaflet coaptation length, the cross-sectional edges of the leaflets in the A2–P2 plane were color-coded, with the anterior leaflet depicted in blue and the posterior leaflet depicted in red. During peak systole, the normal MV showed a leaflet coaptation length of 5.97 mm, while no leaflet contact was observed in the pathological MV featuring A2 RMCT (Fig. 7A). Remarkably, the leaflet coaptation length of the repaired MV with chordal transposition was completely restored and measured 6.37 mm. Furthermore, the post-repair MV demonstrated a reduced anterior leaflet coaptation angle of 4.0°, in comparison to the normal MV (8.8°), whereas the posterior leaflet coaptation angle increased to 43.3° in the post-repair MV, surpassing the normal MV (31.5°) (Fig. 7B). These findings provide evidence that chordal transposition repair effectively eliminated the severe anterior leaflet prolapse.

Fig. 7.

(A) Coaptation lengths and (B) coaptation angles near peak systole for the normal, pre-repair, and post-repair MV models. The cross-sectional edge of the anterior leaflet in the A–P plane is visualized in blue, while the posterior leaflet is in red. A, anterior; P, posterior; MV, mitral valve. Blue star, no coaptation.