## 3 Results and Discussion
During the TMVI procedure attempt, LVOT pressure gradients can be measured by by introducing a catheter equipped with sensors into the heart. One sensor is positioned near to the AoV, while another sensor is positioned close to the LV apex [32; 33]. This enables surgeons to observe and measure the intraventricular pressure and the flow velocity at the outflow tract. By evaluating the pressure and flow during the process, it is possible to detect any potential LVOT obstruction. In this study, the pressure gradients (\(\Delta\)P) of different simulations of MV leaflet angulation were investigated as illustrated in Figure 4b. Moreover, the pressure gradient was calculated by taking the difference of LV pressure (at LV cavity) and maximum pressure near AoV. It is obvious that the pressure gradients value increased when anterior leaflet of MV extended into the outflow tract, as seen in Figure 4b for those the cases before AML splitting. In addition, as it was illustrated earlier in Figures 8 and 9, a dropped in pressure gradients was seen in all cases after the laceration of anterior leaflet. The decrease in pressure gradients following the division of the anterior leaflet, as seen in Figure 4b, aligns with the findings published in prior studies [13; 34; 35]. The presence of an artificial valve in the mitral valve, along with the laceration of the anterior leaflet, did not result in the observation of critical LVOT gradients. The MV leaflet splitting approach is crucial because to the occurrence of significant LVOT blockage in up to 22% of patients undergoing transcatheter mitral valve implantation (TMVI) [17; 18]. Figure 5: Illustrations of simulated velocity fields and structural deformations of the LV generic model at four different time during the cardiac cycle, where (**a-d**) are simulated models at angle 0\({}^{\circ}\), 10\({}^{\circ}\), 20\({}^{\circ}\) and 30\({}^{\circ}\), respectively, with the preservation of AML. Figure 6: Snapshots of four time points of flow velocity and LV wall displacement. (**a–d**) show the simulations at angle \(0^{\circ}\), \(10^{\circ}\), \(20^{\circ}\) and \(30^{\circ}\), respectively, after AML splitting. Figure 7: Snapshots of flow velocity profiles at different angulation of MV anterior leaflet, where (**a,b**) illustrate the simulations before and after division of AML, respectively (left-to-right (\(0^{\circ}\), \(10^{\circ}\), \(20^{\circ}\) and \(30^{\circ}\))). Prior to TMVI, it is essential to evaluate the LVOT and MV annulus. This can aid in choosing the optimal size of the MV prosthetic device. The protrusion of the MV device into the LV can cause AML to move excessively towards the outflow tract, resulting in the formation of LVOT obstruction [36; 37]. Our simulations demonstrated the capability of the developed model to simulate occlusion at the LVOT, by showing the effect of this obstruction on flow pattern and pressure gradient. Additionally, simulations after AML splitting were studied to show the importance of this clinical approach in diminishing the LVOT obstruction, as the preservation of subvalvular apparatus of MV is necessary. Preserving the subvalvular apparatus, including native leaflets of MV, during mitral valve surgery, such as TMVI, significantly increases patients' likelihood of surviving the treatment by greatly boosting their capacity to sustain LV function [38; 39]. However, in some cases, LVOT obstruction may exist due to the movement of MV anterior leaflet towards outflow tract. To overcome such as complications, the surgical technique of AML splitting can be a solution to minimize the flow obstruction at LVOT following TMVI [16]. The ALE-FSI technique uses a well-defined fluid-structure interface. This approach directly solves solid and fluid variables to relate fluid-solid interaction. ALE-FSI is used in several vascular simulations [40; 41]. Few models have used the ALE technique to simulate fluid dynamics on mitral leaflets [42; 43; 44].