A 4D continuous representation of myocardial velocity fields from tissue phase mapping magnetic resonance imaging

Figures

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  Fig 1. B-spline interpolation and approximation. a) Interpolation of a sampled, noise-contaminated sinusoid, using LBS (crosses) and CBS (dashed line). The continuous, noise free sinusoid is shown as a solid line b) Approximation a sampled, noise-contaminated sinusoid, using LBS (crosses) and CBS (dashed line).

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  Fig 2. Velocity fields with varying levels of added noise. Illustration of the different levels of noise added to the velocity field. Here, the y-component of the field from a mid-ventricular slice early in systole is shown. The z-axis points in the through-plane direction.

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  Fig 3. Material point trajectories with end systolic displacement and end point error. A graphical representation of the end point error, and end systolic displacement, for a hypothetical LV material point trajectory. For illustration purposes we show 2D projections of the estimated trajectories, displacements and EPEs, viewed from a mid-ventricular short axis.

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  Fig 4. Bland-Altman analysis. Bland-Altman plots comparing the y-component of the original velocity field with different synthetic fields. Only Bland-Altman plots from processing with a scale conversion factor of Δxyz = 60/50 is shown.

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  Fig 5. Field approximations and residual fields. Approximations of the y-component of the velocity field and their associated residual fields in early systole, with different B-spline basis, level of noise, and scale conversion factor. The section highlighted by the red circle illustrates discrepancies between the original and synthetic fields in the border between the LV anterior free wall and the chest wall.

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  Fig 6. Material point trajectories. a) Anatomical short axis image of the heart at the onset of systole. The red box represents an arbitrary area of interest that has been used to compare trajectories between schemes. b) 2D projections of LV material point trajectories integrated based on the original velocity field, c) zoomed in view on the area of interest of the trajectories in (b), d-h) trajectories integrated in velocity field with 10% added noise with different B-spline basis functions and scale conversion factors (Δxyz), and i-m) trajectories integrated in a velocity field with 20% added noise with different B-spline basis functions and scale conversion factors.

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  Fig 7. End point errors. End point error distributions of LV material point trajectories integrated based on the acquired- and synthetic velocity fields, representing different levels of imaging noise and choice of scale conversion (i.e. noise reduction), Δxyz. All fields were integrated using the Euler method with nearest-neighbor interpolation. Here, Δxyz = 1, corresponds to an unfiltered data set. The central mark indicates the median, and the bottom and top edges of the box indicate the 25th and 75th percentiles, respectively. The whiskers extend to the most extreme data points not considered outliers by MATLAB’s boxplot function. The plot axes are scaled to show the body of the box plots more clearly, and do not display extreme outliers >3mm.

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  Fig 8. End systolic displacements. End systolic displacement distributions of LV material point trajectories integrated based on the acquired- and synthetic velocity fields, representing different levels of imaging noise and choice of scale conversion. The plot axes are scaled to show the body of the box plots more clearly, and do not display extreme outliers.

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  Fig 9. Accuracy of trajectories integrated in a continuous field. End point error distributions of LV material point trajectories integrated in a continuous representation of the field. Here we compare nearest-neighbor interpolation, LBS interpolation, and CBS interpolation. The trajectories were integrated with the Euler method, using a step size equal to the temporal sampling interval of the acquired TPM data.