Geometry Does Impact on the Plane Strain Directions of the Human Left Ventricle, Irrespective of Disease

Figures

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  Figure 1. Cartoon showing the torque generation in LV muscular wall. (A) Epicardial fibers (black) have a left-handed helical pattern, while the endocardial ones (red) have a right-handed helical pattern. As a consequence, the hoop component of the contraction generates a torque around the vertical axis of the LV: epicardial fibers yield a clockwise torque, while the endocardial ones yield a counterclockwise torque. (B) Cross section of the LV at diastole, when contraction is null. (C) Cross section of the LV at systole, when contraction is high. If the contractile force is equal in the epicardial and endocardial fibers, the epicardial torque (black) is larger than the endocardial one (red), being different from the lever arm.

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  Figure 2. The 3D-STE can track the position of thousands of landmarks during the heart’s cycle. (Left Panel) Left: Typical 3D-STE landmarks output, i.e. the discretization of LV surfaces using the position of the landmarks tracked by the 3D-STE; each LV surface is segmented in 36 planes along the axial direction (base to apex); planes are equally divided into 36 sections along hoop direction. (Right Panel) Top: Example of PSD patterns as evaluated by using the original 3D-STE data. Bottom: PSD orientations and PSs are displayed on the American Heart Association (AHA) bull’s-eye 16-segment model. Modified from [19].

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  Figure 3. The relationships between full 3D tensor U (and its principal directions), its projection U¯p on the local surface tangent plane and the classic radial, circumferential and longitudinal 3D-STE strains. Modified from [10].

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  Figure 4. (a) First order neighborhood (in blue) relative to the evaluation point (in red) in a landmark-grid detail (either Endo- or Epi-) showed in the undeformed (diastole) and deformed state (systole). (b) Plane strain tensor U¯p is calculated on the red point using the displacement vectors of the blue ones. The PSD v^p is then identified upon the eigen decomposition of U¯p. Then, the angle αp is computed with regard to the circumferential direction (dotted line). Modified from [19].

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  Figure 5. Per-category and per-landmark median values of αp absolute values in degrees for both Epi- and Endocardium. Regions are colored according to the color bar at top left. Abbreviations: Control healthy subjects (CNT), Cirrhosis (CRR), Aortic regurgitation (AR), Myocardial infarction of inferior wall (MI-INF), Myocardial infarction of anterior wall (MI-ANT), Mutation carriers for hypertrophic cardiomyopathy with LV hypertrophy (HCM), Secondary ventricular hypertrophy (SVH), Mutation carriers for hypertrophic cardiomyopathy without LV hypertrophy (G+LVH−), Atrial fibrillation without ventricular hypertrophy (AFLVH−), Atrial fibrillation with ventricular hypertrophy (AFLVH+), Hypertension without LV hypertrophy (HTLVH−), and Hypertension with LV hypertrophy (HTLVH+).

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  Figure 6. Per-category and per-landmark median values of λ1p for both Epi- and Endocardium. Regions are colored according to the color bar at top left. Abbreviations: Control healthy subjects (CNT), Cirrhosis (CRR), Aortic regurgitation (AR), Myocardial infarction of inferior wall (MI-INF), Myocardial infarction of anterior wall (MI-ANT), Mutation carriers for hypertrophic cardiomyopathy with LV hypertrophy (HCM), Secondary ventricular hypertrophy (SVH), Mutation carriers for hypertrophic cardiomyopathy without LV hypertrophy (G+LVH−), Atrial fibrillation without ventricular hypertrophy (AFLVH−), Atrial fibrillation with ventricular hypertrophy (AFLVH+), Hypertension without LV hypertrophy (HTLVH−), and Hypertension with LV hypertrophy (HTLVH+).

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  Figure 7. Per-category and per-landmark median values of λ2p for both Epi- and Endocardium. Regions are colored according to the color bar at top left. Abbreviations: Control healthy subjects (CNT), Cirrhosis (CRR), Aortic regurgitation (AR), Myocardial infarction of inferior wall (MI-INF), Myocardial infarction of anterior wall (MI-ANT), Mutation carriers for hypertrophic cardiomyopathy with LV hypertrophy (HCM), Secondary ventricular hypertrophy (SVH), Mutation carriers for hypertrophic cardiomyopathy without LV hypertrophy (G+LVH−), Atrial fibrillation without ventricular hypertrophy (AFLVH−), Atrial fibrillation with ventricular hypertrophy (AFLVH+), Hypertension without LV hypertrophy (HTLVH−), and Hypertension with LV hypertrophy (HTLVH+).

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  Figure 8. Per-category and per-landmark median values Δk measuring Endo-Epi αp absolute differences. For each category all landmark locations were subjected to the Wilcoxon paired nonparametric test (i.e., endo- vs. epi-). Regions are colored according to the color bar at top left; Δk < −40 are colored in black: Δk > 0 and with a significant test (very limited) are colored in violet; Δk with a non-significant test are colored in cyan if <0, in white if >0. Abbreviations: Control healthy subjects (CNT), Cirrhosis (CRR), Aortic regurgitation (AR), Myocardial infarction of inferior wall (MI-INF), Myocardial infarction of anterior wall (MI-ANT), Mutation carriers for hypertrophic cardiomyopathy with LV hypertrophy (HCM), Secondary ventricular hypertrophy (SVH), Mutation carriers for hypertrophic cardiomyopathy without LV hypertrophy (G+LVH−), Atrial fibrillation without ventricular hypertrophy (AFLVH−), Atrial fibrillation with ventricular hypertrophy (AFLVH+), Hypertension without LV hypertrophy (HTLVH−), and Hypertension with LV hypertrophy (HTLVH+).

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  Figure 9. Differences ΔkCNT − Δkother between αp values of control group and other categories. Landmarks with no significant differences are colored in cyan. Abbreviations: Cirrhosis (CRR), Aortic regurgitation (AR), Myocardial infarction of inferior wall (MI-INF), Myocardial infarction of anterior wall (MI-ANT), Mutation carriers for hypertrophic cardiomyopathy with LV hypertrophy (HCM), Secondary ventricular hypertrophy (SVH), Mutation carriers for hypertrophic cardiomyopathy without LV hypertrophy (G+LVH−), Atrial fibrillation without ventricular hypertrophy (AFLVH−), Atrial fibrillation with ventricular hypertrophy (AFLVH+), Hypertension without LV hypertrophy (HTLVH−), and Hypertension with LV hypertrophy (HTLVH+).

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  Figure 10. Relationship between Endo/Epi RMS static curvature ratio in systole (in abscissa) and Endo-Epi αp differences (per category and per-landmark median values). Blue lines represent regression lines with confidence intervals. Points are colored according to their affiliation to “parallels” in the context of LV topology shown in Figure 2: cyan at the base, yellow-green in the middle, red in the apex. The vertical lines at x = 1 and the horizontal one at y = 0 indicate the upper and lower limits (respectively) within which we expect to see the ranges of these variables. CNT behave consistently with this expectation (i.e., Endo/Epi RMS curvature ratio always >1 and αp differences always <1). The other categories do the same with a few exceptions.

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  Figure 11. Relationship between Endo/Epi RMS static curvature ratio in diastole (in abscissa) and Endo-Epi αp differences (per category and per-landmark median values). Blue lines represent regression lines with confidence intervals. Points are colored according to their affiliation to “parallels” in the context of LV topology shown in Figure 2: cyan at the base, yellow-green in the middle, red in the apex. The vertical lines at x = 1 and the horizontal one y = 0 indicate the upper and lower limits (respectively) within which we expect to see the ranges of these variables. CNT behave consistently with this expectation (i.e., Endo/Epi RMS curvature ratio always >1 and αp differences always <1). The other categories do the same with a few exceptions.