Physics-Informed Reconstruction of Transmural Myocardial Deformation from 3D Echocardiography: Validation Against Cardiac MRI

Figures

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  Fig. 1. Workflow for LV segmentation: A 3D Echocardiography: Volumetric images captured using a Philips matrix-array probe by expert sonographers; B Clinical Image Processing: 3D segmentation and speckle tracking via TomTec-Arena (TTA); C Segmentation Results: Final volumetric endocardial and epicardial surfaces serving as the geometric basis for the proposed strain analysis

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  Fig. 2. End-systolic CMR segmentations performed in Medis Suite MR, displaying long-axis (A2C, A3C, and A4C) and short-axis (mitral valve, papillary muscles, and apex) cross-sections

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  Fig. 3. Sensitivity analysis of optimization weights αvol,αtrack,αsmooth. A Area-normalized tracking error Etrackavg post-optimization remains within range of the initial epicardial and endocardial segmentations across all parameter combinations. B Volume incompressibility, measured by rms (J − 1) , demonstrates that higher αvol consistently improves volume preservation. C Heatmaps illustrate post-optimization improvement ratios mapped across cyclic parameter pairings: the optimized epicardial tracking error Etrack relative to the initial epicardium is shown over αvol vs. αsmooth; the optimized volume error Evol relative to the initial segmentation is mapped over αsmooth vs. αtrack ; and the optimized smoothness error Esmooth relative to the first optimization iteration is mapped over αtrack vs. αvol

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  Fig. 4. Validation over cardiac cycle. Global longitudinal strain (GLS) and global circumferential strain (GCS) over the normalized cardiac cycle for a representative healthy left ventricle (A, B) and a left ventricle with pulmonary arterial hypertension (PAH; C, D). In each panel, we compare the endocardial strain obtained from 3D echocardiography (3D Echo Endo) with the volume-weighted transmural strain computed across the endocardial, mid-wall, and epicardial layers, evaluated both from the initial epicardial segmentation (Myo Pre) and from the physics-informed epicardial reconstruction (Myo Post). These are plotted against the corresponding long-axis CMR feature-tracking estimates of endocardial and myocardial strain (CMR (LAX) Endo, CMR (LAX) Myo). Longitudinal and circumferential directions are defined relative to the ventricular long axis, and all strains are Lagrangian and referenced to end-diastole, so each curve closes over the cycle. To place the two modalities on a common timeline, we apply a two-segment piecewise-linear time warp to each trace that holds end-diastole at the cycle boundaries and maps each modality’s end-systole onto a shared normalized time, taken as the…

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  Fig. 5. Segmental myocardial strain at end-systole (ES) before and after optimization. The bulls-eye plots compare pre-optimization and post-optimization spatial maps for myocardial longitudinal strain (left panels) and myocardial circumferential strain (right panels). Data are presented for the patient with pulmonary arterial hypertension (PAH, top row) and the healthy subject (bottom row). Pre-optimization maps represent the initial strains derived from vertex tracking prior to applying the soft volume conservation constraint

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  Fig. 6. Principal strain analysis of the healthy LV. All bulls-eye maps visualize spatial distributions at end-systole using a 16-segment model over the endocardium (Endo) and epicardium (Epi). A–C Principal Strains: Bulls-eye maps illustrating primary contraction ( λ1−1 ), secondary contraction ( λ2−1 ), and transmural principal strain λ3−1. D Average Principal Strains: Temporal variation of the three volume-averaged principal strains over the normalized cardiac cycle (t/T). The average is computed as a weighted mean of strains from individual tetrahedra, using their undeformed volumes as weights. E Primary Contraction Orientation: Bulls-eye maps showing the signed helix angle (−90° to 90°) formed by the principal eigenvector v1 relative to the circumferential direction in the short-axis plane. The circumferential direction is defined via the right-hand rule (thumb pointing from apex to mitral valve); positive angles indicate v1 tilts toward the base, while negative angles indicate a tilt toward the apex. F Transmural Alignment: A single bulls-eye map displaying the acute angle, ∠(v1epi,v1endo), between the epicardial and endocardial directions of primary contraction

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  Fig. 7. Principal strain analysis derived from 3D echocardiography. The strain lines indicate the direction of maximum contraction and are color-coded by the depth (0 on the endocardium and 1 on the epicardium). The results shown in the figure correspond to the healthy left ventricle (LV). The mitral and aortic valves are labeled as MV and AV, respectively, to aid spatial orientation