Accurate Reconstruction of Right Heart Shape and Motion From Cine‐MRI for Image‐Driven Computational Hemodynamics

Figures

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  FIGURE 1. The first row lists the volumetric cine‐MRI series with the corresponding cardiac MRI planes: (a) 2D view of a rotational long axis plane, (a.1) 3D view of the same rotational plane over the reconstructed right ventricles surface, (a.2) scheme of the 18 rotational planes; (b) short axis plane; (c) aortic valve short axis plane; (d) long axis plane. The second row lists the set of 2D long‐axis cine‐MRI: (e) specific view for the right heart evaluation; (f) specific view where the left ventricle, the right atrium, and the aortic root are visible; (g) specific view for the evaluation of the aortic flow; (h) three chambers plane where the pulmonary flow is visible; (i) four chambers view.

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  FIGURE 2. Overall reconstruction procedure. Step 1: Endocardial contours generation from cine‐MRI. Zoom on Step 1 (Section 2.2.1): (1a): manual tracing of the endocardial border (dotted red line on slice Sn¯,k) on every cine‐MRI slice for a fixed time frame; (1b): sketch of the non‐rigid registration algorithm applied to time consecutive slices and deformation of the endocardial contour due to the application of the resulting transformation. Step 2: Morphing procedure. Zoom on Step 2 (Section 2.2.2): (2a): extended and smoothed distance field dx defined on the template surface Λn,j−1, superimposed on the contours set Γn (Section 2.2.2—[i], [ii], [iii]); (2b): representation of the vector field wx defined as in Section 2.2.2—[iv] on the warped template surface Λn,j; (2c): resulting surface at frame n. Step 3: recovery of the endocardial displacement field and representation of the displacement field snx on the reference configurations of RA and RV at the end‐systolic instant. Zoom on Step 3 (Section 2.2.3): (3a): endocardial and epicardial faces of RA (ΛnRA,endo, ΛnRA,epi) and RV (ΛnRV,endo, ΛnRV,epi) superimposed on the level set images of the RA and RV endocardial surfaces; (3b): a sketch…

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  FIGURE 3. Multi‐resolution strategy using the Gaussian filtering with kernel size equal to 21×21,11×11,7×7, and 5×5 pixels. These sizes are obtained by imposing an image shrinking factor of 8,4,2,1 in the procedure proposed by the SimpleElastix library [35] and based on the image spacing. No down‐sampling is applied. The original Sn,k on the left side of the arrow. On the right side, the filtered Sn,k at each resolution level.

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  FIGURE 4. Computational domain and boundary conditions. (a): Representation of the whole right heart Ωt with its boundaries: Ventricle outflow Σoutt; atrial inflows at the superior (green) and inferior (blue) vena cavae Σint; ventricular and atrial endocardium and physical wall of the pulmonary artery Σw; surface of the pulmonary valve's leaflets ΓPVt; surface of the TV's leaflets ΓTVt. (b, c): Tetrahedric volumetric mesh of the RH of the healthy subject and of the ToF patient. (d): Pressure curves at the pulmonary artery and inferior and superior Vena cavae, imposed as boundary conditions; values come from literature [40, 41]. (e, f): TV and PV in open and closed configurations of the healthy subject and of the ToF patient; red square: detail of the tetrahedral mesh of the healthy TV.

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  FIGURE 5. RV reconstruction of a healthy patient. MSMorph‐I: MSMorph technique employing all available cine‐MRI; MSMorph‐II: MSMorph technique employing all available cine‐MRI apart TV‐R cine‐MRI; MSMorph‐III: MSMorph technique employing only SA and LA cine‐MRI; SA‐based: standard reconstruction procedure [32] employing only SA cine‐MRI. Left column: reconstruction of the reference end‐systolic configuration. Central column: reconstruction of the end‐diastolic configuration and spatial distribution of the normal component of the corresponding displacement field. Blue and light blue colors: inward normal displacement; Green, yellow, and red colors: outward normal displacement. Right column: on top, the time evolution of the ventricular volumes normalized w.r.t. body surface area, computed by removing the pulmonary artery; below, the spatial distribution of metric αn defined on the end‐diastolic configurations.

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  FIGURE 6. RA reconstruction of a healthy patient. MSMorph‐I: MSMorph technique employing all available cine‐MRI; MSMorph‐II: MSMorph technique employing all available cine‐MRI apart TV‐R cine‐MRI; MSMorph‐III: MSMorph technique employing only SA and LA cine‐MRI. Left column: reconstruction of the reference end‐systolic configuration. Central column: reconstruction of the end‐diastolic configuration and spatial distribution of the normal component of the corresponding displacement field. Blue and light blue colors: inward normal displacement; Green, yellow, and red colors: outward normal displacement. Right column: on top, the time evolution of the atrial volumes normalized w.r.t. body surface area; below, the spatial distribution of metric αn defined on the end‐diastolic configurations.

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  FIGURE 7. (a, b): Evolution over time of MSD (left) and HDΓ~nΓn (right) for the RA and the RV contours of the healthy subject. The red dotted line indicates the value of the in‐slice resolution, 1.15mm; (c): evolution over time of HDΓ~nΛ~n for the RA and the RV of the healthy subject; Reconstructions of the RA and RV of the healthy subject (in grey) obtained at end systole (d) and at end diastole (e) compared with the reference solution Γ~n (in black). MSMorph‐I scenario.

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  FIGURE 8. RH reconstruction of a healthy subject (H) and a ToF patient (TF). First–second rows: RH reconstructions and intersections of the reconstructed surfaces with the image plane at two instants of the cardiac cycle; first row: healthy subject; second row: ToF patient. Third row: RV and RA volume curves over a heartbeat. Fourth row: curves of RV and RA flow rates over a heartbeat computed as the time derivative of the volumes multiplied by the blood density.

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  FIGURE 9. First row: selected time instants and longitudinal and transversal (in red) sections where velocity is plotted; second row: velocity field on the longitudinal section: Third row: velocity field on the transversal section; fourth row: pressure field on the longitudinal section. Left: healthy subject (H); right: patient with repaired ToF (TF). (a): acceleration phase; (b) systolic peak; (c): deceleration phase.

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  FIGURE 10. Sub‐grid viscosity μsgs normalized w.r.t. the blood viscosity μ on the longitudinal section for H (first row) and TF (second row) at the three selected instants. Windows to focus on vorticity isosurfaces at RVOT created with Q criterion >3000.