Incorporating Torsion Into 3D Geometric Reconstruction of Left‐Ventricle From 2D Echocardiography and Its Impact on Hemodynamics

FIGURE 1. (a) Time history of basal and apical rotations along with computed twist over a cardiac cycle. (b) Temporal interpolation of intermediate shape (Z) capturing deformation and rotation of a simplified basal SA section.

FIGURE 2. (a) LV system during diastole with triangulated surface mesh immersed in a background cartesian grid. Assembly of the approximated geometries (aorta, left atrium, and LV lid) with the 3D reconstructed LV chamber during (b) diastole and (c) systole phases, respectively.

FIGURE 3. (a) Comparison of sono crystals placement with 3D reconstructed LV surface at early systole along with time history of shortest distances (error) computed between mid SA crystals and LV surface. (b) Peak diastole cycle‐to‐cycle variation of velocity line plots at different locations on a background vorticity contour. (c) Cycle‐to‐cycle comparison of volume‐averaged mean velocity components. (d) eloss versus grid size plots for torsion OFF configuration. (e) Time history of volume‐averaged residence time across cardiac cycles.

FIGURE 4. Comparison of Doppler velocity measurements with the velocity magnitude from numerical simulation (a) at aortic orifice during systole and (b) at mitral orifice during diastole. (c) Plane independent study: Time history of area‐averaged velocity on different planes near aortic orifice during systole shows negligible difference. (d) Time history of twist and flow rate. View of LV from the apex at (X) zero and (Y) peak twist to visualize torsion. (e) Decomposition of the velocity u at a point on the LV surface into its cylindrical, that is, radial ur, tangential (torsional) ut, and axial uz, components.

FIGURE 5. A cross‐section shape analysis. (a, b) Eccentricity time series over the cardiac cycle for the basal, mid‐ventricular, and apical sections. (c–e) Representative basal, mid, and apical cross‐sections, respectively, at t/T=0.5, showing the SA contour (solid), fitted ellipse (red dashed), and area‐equivalent circle (blue dotted).

FIGURE 6. Nondimensional WSS magnitude contours on the LV surface split along the A3C view (row 1 and row 2) and 3D view of OSI contours (row 3) on the reconstructed LV chamber for Torsion ON and Torsion OFF cases. WSS is visualized at several cardiac instants t/T: (a) early systole; (b) mid systole; (c) early diastole; and (d) mid diastole.

FIGURE 7. Limiting streamlines (black), showing the shear stress direction on the walls, and surface velocity streamlines (red) are plotted on the LV surface split along the A3C view at several cardiac instants t/T: (a) early systole; (b) mid systole; (c) early diastole; and (d) mid diastole.

FIGURE 8. Comparison of nondimensional contours of residence time, vorticity, and velocity plotted on the mid‐plane along the A3C view at several cardiac instants t/T: (a) early systole; (b) mid systole; (c) early diastole; and (d) mid diastole.

FIGURE 9. Time history of volume fraction for different categories of residence time. The colors denote the residence time, while the solid and dashed lines denote the torsion OFF and ON cases, respectively.