Mechanical effects of MitraClip on leaflet stress and myocardial strain in functional mitral regurgitation – A finite element modeling study

Purpose MitraClip is the sole percutaneous device approved for functional mitral regurgitation (MR; FMR) but MR recurs in over one third of patients. As device-induced mechanical effects are a potential cause for MR recurrence, we tested the hypothesis that MitraClip increases leaflet stress and procedure-related strain in sub-valvular left ventricular (LV) myocardium in FMR associated with coronary disease (FMR-CAD). Methods Simulations were performed using finite element models of the LV + mitral valve based on MRI of 5 sheep with FMR-CAD. Models were modified to have a 20% increase in LV volume (↑LV_VOLUME) and MitraClip was simulated with contracting beam elements (virtual sutures) placed between nodes in the center edge of the anterior (AL) and posterior (PL) mitral leaflets. Effects of MitraClip on leaflet stress in the peri-MitraClip region of AL and PL, septo-lateral annular diameter (SLAD), and procedure-related radial strain (Err) in the sub-valvular myocardium were calculated. Results MitraClip increased peri-MitraClip leaflet stress at end-diastole (ED) by 22.3±7.1 kPa (p<0.0001) in AL and 14.8±1.2 kPa (p<0.0001) in PL. MitraClip decreased SLAD by 6.1±2.2 mm (p<0.0001) and increased Err in the sub-valvular lateral LV myocardium at ED by 0.09±0.04 (p<0.0001)). Furthermore, MitraClip in ↑LV_VOLUME was associated with persistent effects at ED but also at end-systole where peri-MitraClip leaflet stress was increased in AL by 31.9±14.4 kPa (p = 0.0268) and in PL by 22.5±23.7 kPa (p = 0.0101). Conclusions MitraClip for FMR-CAD increases mitral leaflet stress and radial strain in LV sub-valvular myocardium. Mechanical effects of MitraClip are augmented by LV enlargement.


Introduction
Functional mitral regurgitation (FMR) in patients with coronary artery disease (FMR-CAD) occurs in 1.2 to 2.1 million patients in the United States and of those more than 400,000 patients have advanced (�2+) FMR-CAD. [1] These numbers are expected to progressively increase as the population ages and more patients survive acute myocardial infarction (MI). [1] Advanced FMR-CAD discovered at cardiac catheterization has a 1-year mortality of approximately 17%. [2] One-year mortality for severe (�3+) FMR-CAD is approximately 40%. [2] MitraClip (Abbott Vascular, Santa Clara, CA) is the sole percutaneous device commercially approved for treatment of FMR. Over 80,000 patients have undergone mitral repair with the MitraClip device in the past decade. [3]. The device approximates the anterior (AL) and posterior leaflets (PL) of the mitral valve, creating a double-barrel mitral orifice as a means of decreasing mitral regurgitation. [4] Two recent trials (COAPT, MITRA-FR) of MitraClip in patients with FMR reported discordant results. MITRA-FR found no difference in mortality and congestive heart failure (CHF) [5], whereas COAPT found that mortality and CHF were lower in MitraClip treated patients. [6] A key issue with MitraClip is recurrence of MR where recurrent advanced MR is present in over one third of FMR patients treated with MitraClip. [7][8][9] Mechanisms responsible for MR recurrence after MitraClip for FMR remain unclear. However, there is reason to believe that LV chamber volume is a primary determinant of recurrent MR after MitraClip. For instance, LV chamber volume was over 25% greater among patients in MITRA-FR (135 ± 35 ml/m 2 ) as compared to COAPT (101 ± 34 ml/m 2 ), paralleling increased rates of residual MR. [5,6] These studies suggest a link between LV chamber size and outcome mediated by mechanical effects of MitraClip including mitral leaflet stress and procedure related tissue stretch in sub-valvular LV myocardium.
Finite element (FE) based computational modeling allows calculation of mitral leaflet stress. For instance, Votta et al. used an FE model of the mitral valve to simulate the effect of edgeedge repair and showed that leaflet stress increases with annular dilatation. [10] Sturla et al. simulated MitraClip in an FE model of human PL prolapse and reported that leaflet stress at peak systole after MitraClip is dependent on LV pressure and that stress was increased with asymmetric device application. [11] Recently, Morgan et al. simulated a FE model of human posterior leaflet prolapse that included the LV + mitral valve and reported that uneven grasp of leaflet tissue by the MitraClip did not increase leaflet stress [12], as well as stresses and strains in the mitral apparatus and adjacent LV wall. To date, however, there have been no FE models of MitraClip in FMR.
This study employed FE models of the LV + mitral valve based on sheep with FMR after postero-lateral MI [13,14] to test the hypothesis that MitraClip increases mitral leaflet stress and procedure-related strain in the sub-valvular LV myocardium.

Experimental protocol
Sheep used to create the finite element models were treated under a protocol approved by the San Francisco Veterans Affairs Institutional Animal Care and Use Committee (IACUC approval number 07-055), in compliance with the "Guide for the Care and Use of Laboratory Animals" prepared by the Institute of Laboratory Animal Resources, National Research Council. [15] Adult sheep underwent postero-lateral MI as previously described. [16] Cardiac magnetic resonance imaging (MRI) showed that infarct area was 21 ± 7% [14] and animals developed mild to moderate FMR-CAD 16 weeks after MI. [16] MRI studies consisted of six radially oriented LV long images in which pixel spacing was 2.08 mm x 2.08 mm.

Anesthesia and pain control
Anesthesia for MI, MRI and sacrifice procedures in chronic animals was similar. Briefly, anesthesia was induced with ketamine (20 mg/ kg intravenous) and maintained with isoflurane (2.2% inhaled). Post-operative pain associated with the MI procedure was controlled with buprenorphine (0.01mg/kg) was given subcutaneously every 6 hours for the first 24 hours and then every 8 to 12 hours for 2 more days. In addition, at the conclusion of the MI and MRI procedures, the incision was infiltrated with a long acting local anesthetic (Bupivacaine 0.5% x 10 ml) and ketorolac 30 mg was given intra-muscularly once and as needed for post-operative pain.

Model construction and constitutive equations
The LV was contoured and meshed as previously described. [17] On average, each model contained 10500 elements with an average element volume of 0.05 ml. Rule-based fiber angles were assigned with myofiber fiber helix angle varying transmurally from −60˚at the epicardium to +60˚at the endocardium. LV myocardium was divided into MI, borderzone, and remote regions (Fig 1A). Active and passive myocardial constitutive laws were previously described by Guccione et al. [18,19] Prior to virtual MitraClip, the passive stiffness parameter, C, and contractility parameter, T max , for MI, borderzone and remote regions were inversely calculated by minimizing the difference between modeled and experimentally determined LV volume and regional strain [20] using established methods. [21] The optimized values for C and T max for MI, borderzone and remote regions were previously reported. [13] The mitral leaflets were contoured and meshed as previously described (Fig 1B). [17] Edge chords were attached to free edge of each leaflet and strut chords were attached to the mid-section of each leaflet, as described by Wenk et al. [17] The mitral leaflets were modeled using a bi-layer soft tissue material ( � MAT_091, LS-DYNA, Livermore Software Technology Corporation (LSTC), Livermore, CA) [22] and the chordae tendineae were modeled with cable elements ( � MAT_071; LSTC).

Loading and boundary conditions
The endocardial surface of the FE model was loaded with animal-specific in-vivo LV end-diastolic and end-systolic pressures. During diastole, the mitral leaflets were loaded with MVPG of -4.1 mm Hg in line with MVPG data after MitraClip from Herrmann et al. [23] During systole, MVPG equaled measured LV end-systolic (ES) pressure.
To isolate the mitral apparatus from boundary condition restrictions, the myocardial elements at the level of the valve were extended 3 elements above the mitral plane. The extended base had diastolic stiffness, C, equal to 0.001 � C of remote myocardium and T max equal to zero.
Homogeneous Dirichlet boundary conditions were applied to nodes at the top of the extended base so that the nodes were fixed in the longitudinal axis but allowed to slide in the mitral plane.

Virtual MitraClip
The MitraClip (NTR, Abbott, Abbott Park, Il) was simulated by attaching leaflet nodes in a rectangular pattern extending from the centers of the leading edge of the central regions of the anterior and posterior leaflets (A2 and P2; Fig 1C). The average body surface area (BSA) of the 5 sheep on which the simulations were based was 1.28±0.04. Given that the normal human BSA is 1.99 [24] the MitraClip arm dimensions (9 mm height and 5 mm width) were indexed to 5.7 x 3.2 mm. A 70% partial grasp MitraClip device in which the leaflet region approximated measured 4.0 x 2.9 mm was also simulated (note that the difference between partial and full grasp is the virtual device height).
Leaflet nodes were attached using 'virtual suture' beam elements (material model: � MAT_071, LS-DYNA) as previously described. [25] Specifically, each virtual suture was modeled as a discrete beam element. A unique feature of � MAT_071 is that an axial tension can be specified for each beam element and this axial tension could mechanically pull the two ends of each element together. After the leaflet coaptation, the virtual sutures were changed to rigid elements using the � DEFORMABLE_ TO_RIGID function in LS-DYNA. Virtual MitraClip was performed at the start of diastole (Fig 2). Simulation of LV diastole and systole then proceeded.

Simulation of LV volume effect
LV volume at early filling was increased by using a pre-inflation step where the LV endocardial surface was loaded with animal-specific LV ED pressure until an increase in LV volume of 20% was achieved. The deformed FE mesh was used as the unloaded geometry of a new "LV_VOLUME model. Simulation of virtual MitraClip was then performed using the new "LV_VOLUME model (Fig 2).

Measured outcomes
Von Mises stress was averaged across anterior and posterior leaflets. Von Mises stress was measured in the one element wide region of elements one element removed from the MitraClip (Peri-MitraClip; Fig 1C). Elements with nodes attached to virtual suture beam elements were excluded to avoid stress concentrations associated with local MitraClip-induced element distortion.
Green-Lagrange strain was calculated where the reference geometry for strain at ED is the pre-operative early-diastolic filling LV shape. [14] E rr at ES is relative to ED. Strain was averaged in a transmural group of elements bounded by the P2 scallop of the mitral valve and extending to a point 1/3 of the distance from the valve to apex (lateral sub-valvular).

Statistical analysis
All values are expressed as mean ± standard deviation and compared by repeated measures analysis using a mixed model to test for both fixed and random effects (PROC MIXED, SAS Studio, SAS Release 9.04, University Edition, SAS Institute, Cary, NC). Models included categorical factors for MitraClip clip size, "LV_VOLUME and leaflet region. ED and ES analyses were done separately and in all simulations the animal/ model number was treated as a random variable. Significance was set at p<0.05. Box and whisker plots were constructed with the whiskers at the minimum and maximum of the group data range. All data points in each group are shown as individual points in the plot.

Results
All FE simulations finished successfully with an average calculation time of 64.7 ± 24.6 minutes. Linear regression of simulation calculation time (CalcTime) with the number of virtual processors (NCPU) was CalcTime = -4.95 NCPU + 95 and reached an approximate minimum at 8 virtual processors.

Mitral leaflet stress
Fig 3 shows representative regional leaflet stress color maps of the mitral valve before and after MitraClip with complete grasp. Changes in leaflet stress are most apparent at LV end-diastole (ED) (Fig 3B), during which stress is concentrated in the clip region and increased stress occurs between the device and the mitral annulus. Leaflet stress was also increased in the peri-MitraClip region at LV end-systole (ES) (Fig 3E) although the effect is less pronounced. Color maps from the volume augmented (20% "LV_VOLUME) FE models (Fig 3C and 3F) have a noticeable increase in leaflet stress compared to baseline (non-augmented) models. Fig 4 shows the quantitative effects of MitraClip on leaflet stress in the anterior and posterior leaflets at baseline and with LV volume augmentation (note that the stress is averaged across all five models). As shown, end-diastolic leaflet stress adjacent to the device increased in all animals. At baseline, MitraClip increased peri-MitraClip leaflet stress in the anterior mitral leaflet by 544% and in the posterior leaflet by 131% (both p<0.0001) (Fig 4A and 4B). The effect of MitraClip in "LV_VOLUME FE models was similar, as evidenced by mean increases of 207 and 85% respectively (both p<0.0001). Lesser effects were evident with respect to device-induced leaflet stress in areas remote from the MitraClip: The effect on the leaflet remote from the MitraClip was not significant (NS) with the exception of the anterior leaflet LV volume augmented models in which MitraClip caused a slight, albeit significant, increase in end-diastolic leaflet stress (56%; p = 0.04).
Computational analyses consistently demonstrated MitraClip effects on mitral leaflet stress to be of lesser magnitude during LV end-systole, irrespective of whether measurements were performed in baseline or LV volume augmented models. In baseline models, MitraClip increased peri-device end-systolic leaflet stress by 29.6% (p = NS) in the anterior leaflet, and by 5.8% (p = NS) in the posterior leaflet (Fig 4 and 4D). LV volume augmentation resulted in slight increments in device-induced effects on systolic leaflet stress immediately adjacent to the MitraClip. In the "LV_VOLUME FE models, MitraClip increased peri-device end-systolic leaflet by 37.4% in the anterior leaflet (p = 0.03), and by 23.3% (p = 0.01) in the posterior leaflet (Fig 4C and 4D). Device-induced effects on end-systolic leaflet stress remote from the Mitra-Clip were non-significant for both the anterior and posterior leaflet.
Leaflet stress results for the partial grasp technique of MitraClip implantation are also provided in Fig 4: As shown, partial grasp impacted leaflet stress in a similar manner to that of complete grasp technique, although device-induced increments in leaflet stress were of lesser magnitude.

Mitral annular geometry
LV annular diameter, as measured from the septum to the lateral wall (SLAD), before and after MitraClip implantation are shown in Fig 5. MitraClip reduced LV end-diastolic SLAD by 18.7% (p<0.0001) and 21.1% (p<0.0001) in baseline and LV volume augmented models respectively. Lesser, albeit significant, reductions in LV end-systolic SLAD occurred in both baseline and volume augmented models (8.3%, and 9.0% % respectively; both p<0.0001). The effect of LV size was not significant at ED but was significant at ES (p = 0.03). Fig 6 shows representative color maps of change in LV end-diastolic myocardial radial strain (E rr ) after simulated MitraClip with complete grasp. Note the change in E rr in the P2 region (white rectangle) with highest intensity in the P2 endocardium. Note also that intensity is increased in the LV volume augmented model.  (Fig 7A) and endocardium (Fig 7B) at end-diastole, and in sub-valvular myocardium at end-systole (Fig 7C): As shown, MitraClip increased E rr at end-diastole by 138% in sub-valvular myocardium, and by 131% in baseline and LV volume augmented models respectively (both p<0.0001). MitraClip yielded even larger effects on endocardial end-diastolic E rr , as evidenced by increases of 230% and 186% in baseline and LV volume augmented models respectively (both p<0.001), corresponding to absolute increments of 0.052 ±0.035 and 0.044±0.049. Conversely, MitraClip decreased end-systolic E rr at ES in lateral subvalvular myocardium by 41.9% and 45.1% in baseline and LV volume augmented models respectively (both p<0.001) (Fig 7C). The effect of LV size was not significant at ED or at ES.

Sub-valvular myocardial strain
The quantitative effect of MitraClip on longitudinal strain (E ll ) is shown in S1 Fig. The pattern of effect on E ll is similar to that of radial strain but inverted, meaning that longitudinal strain generally decreased post-procedure. Different than E rr , the effect of LV size was significant at ED and ES.

Discussion
The principal finding of this study is that MitraClip implantation for FMR increases both enddiastolic and end-systolic mitral leaflet stress in the peri-device region: As a consequence, septo-lateral annular diameter was decreased and E rr in the P2 sub-valvular myocardium was increased at end-diastole (ED) and decreased at end-systole (ES). Mechanical effects of Mitra-Clip are augmented by in the enlarged LV, as leaflet stress and E rr were further increased in "LV_VOLUME models at end-diastole.

Leaflet stress
Regarding the underlying mechanism of MitraClip action, it should be noted that mitral leaflet stress is a function of leaflet and annular geometry, leaflet material properties, and loading conditions. MitraClip pulls the anterior and posterior leaflet edges together, thus inducing stress on the mitral leaflets that would be expected to increase in proportion to the amount of tissue gathered by the MitraClip (Fig 8 illustrates proposed mechanism).
Increased LV volume is associated with annular enlargement and greater papillary muscle displacement. Simulation of LV volume effect in this study using "LV_VOLUME FE models confirms that pre-procedure increase in LV volume increases MitraClip-associated leaflet stress. Of note, the LV volume index at ES of sheep used in this study was approximately 40 ml/ m 2 -a value lower than the volume index of most patients with FMR. It is worth noting that increased trans-mitral gradient after MitraClip has been shown to predict poor composite outcomes including heart failure and death. [26] It is likely that those patients have leaflet stress and strain in the sub-valvular LV wall in excess of values determined in this study. Further studies are warranted to test these concepts.

MitraClip durability
There is substantial evidence that mitral leaflet stress causes leaflet remodeling. Mitral leaflet thickening occurs with volume loading associated with pregnancy [27] and with leaflet tethering insufficient to cause MR [28] and also in sheep [29] and humans with FMR associated with increased LV sphericity, mitral tenting and annular size [30]. Along these lines, it is interesting that the EVEREST investigators found a difference between FMR and degenerative mitral regurgitation (DMR) in healing response when the MitraClip was explanted > 30 days after implantation. [31] Specifically, MitraClip implanted for FMR had thicker fibrous capsules and greater tissue bridge extending over the arms of the clip. [31] There are also reports of acute leaflet perforation after MitraClip for FMR. [32] While usually considered a technical complication, acute perforation may be a function of leaflet stress since tissue rupture is more likely at high stress and strain levels. Taken together, these data support the concept that recurrent MR after MitraClip for FMR is impacted by device-induced leaflet stress.

Procedure-related strain and post-MitraClip LV remodeling
Gathering of leaflet tissue by the MitraClip applies traction to leaflet, annulus and adjacent sub-valvular myocardium and subsequently increases leaflet stress, decreases the SL annular dimension and in turn increases radial strain, E rr, in the adjacent sub-valvular myocardium as seen in Fig 8. The predominant effect on the LV wall is constraint of the myocardium which prevents wall thinning during diastole. As a consequence, systolic wall thickening is decreased, sarcomeres in the sub-valvular myocardium are not stretched and systolic wall thickening is decreased via the Starling mechanism.
It is known that volume and pressure overload associated stress and strain stimulate hypertrophy [33] and remodeling after myocardial infarction. [34] In-vitro studies suggest that a 10% strain level is sufficient for growth of myocyte sheets via serial sarcomere deposition. [35] MitraClip increases E rr in the endocardium to near 5% at the end of diastole but it is unclear if this amount of diastolic thickening is sufficient to cause or accelerate LV remodeling in the sub-valvular myocardium. Pantoja et al. studied the effect of UA on procedure related strain in the LV wall and showed that UA significantly increased longitudinal strain in the proximal lateral LV wall. [14] Specifically, the largest effect of UA on E ll occurred in the proximal-lateral endocardial surface, where strains increased from 0.0345 ± 0.0206 to 0.1117 ± 0.0480 (p = 0.0057). Pantoja et al., did not measure the effect of UA on annular shape but when compared with MitraClip, the magnitude of annular reduction was likely significantly larger and annular reduction extended across the entire posterior annulus.

Amount of MitraClip tissue grasp
MitraClip NTR with both partial and complete grasp was simulated in this study where compared to the partial grasp, the complete grasp had overall larger effect on leaflet stress, SL dimension and E rr in LV sub-valvular myocardium. Based on this observation, we anticipate that compared to MitraClip NTR (9 x 5mm), MitraClip XTR (12 x 5mm) will cause even larger leaflet stress concentration and more positive E rr at ED and cause an even larger reduction in the SL dimension at ED.

Study limitations
The primary limitation of this study is that our calculations were not optimized with experimental data obtained after MitraClip. On the other hand, SL annular dimension at end-diastole decreases between 2.8 to 4 mm in patients with FMR after MitraClip [36][37][38] and Lurz et al. found that the MRI-measured radial strain averaged across all sectors at the mitral valve level decreased from 15.4 to 9.6% after MitraClip in a cohort of mostly FMR patients. [39] These findings show that our simulations are in agreement with clinical results. Second, the MR jet location was not measured in the sheep used in the current study. [16] Three-dimensional echocardiography has been performed on sheep with postero-lateral MI [40,41] but MR jet location has not been reported. [40,41] On the other hand, Hidalgo et al found that 41% in patients with FMR undergoing MitraClip had an MR jet in the A2P2 region and 45.5% had a jet that spanned the A2P2-A3P3 region. [37] This supports the contention that postero-lateral MI is associated with leaflet restriction along the entire A2P2 A3P3 section rather than at A2P2 or A3P3 separately. Location of the virtual MitraClip at A2P2 in the current study is therefore reasonable.
Finally, leaflet stresses at ED and ES were examined in the current study, although Rabbah et al. observed that leaflet stress was greatest during peak systole. [42] Future planned analyses will include stress at peak systole.

Conclusions and future directions
Finite element simulations performed in this study demonstrate that MitraClip increases peri-MitraClip leaflet stress at both ED and ES when performed for FMR. Subsequent traction on the mitral annulus causes the SL dimension to decrease and endocardial strain in the adjacent LV wall at ED is increased. Further, mechanical effects of MitraClip on leaflet stress and subvalvular LV strain are augmented in the enlarged LV.
Increased mitral leaflet stress and procedure-related strain in the sub-valvular myocardium may contribute to mitral leaflet and LV remodeling after MitraClip. Future clinical studies are warranted to clinically test device-induced mechanical effects as predictors of procedural success for patients undergoing MitraClip.