Fig 1.
Reference biomechanical LV model simulating the full cardiac cycle (a). Synthetic image generation using the model (b). Three different image stacks with tag lines in orthogonal directions are generated by rasterization (1) and then resampled by cropping in k-space and convolved in time (2). Adding noise and changing image resolution by filtering in k-space (c). Image registration showing 3D tagged images superimposed with the warped mesh for different time frames (d).
Fig 2.
Isotropic synthetic images to analyze the effect of image properties.
Images with varying tag distances (in mm) (a), pixel sizes (in mm) (b), and SNRs (c) (values are written at the bottom right corner for each case). Images shown in (a) are noiseless and have 1 mm pixel size. Images in (b) are noiseless and have 7 mm tag distance. For the ones in (c), pixel size and tag distance are 3.5 mm and 7 mm, respectively. Images represent the configuration at end-diastolic time frame.
Fig 3.
Anisotropically resolved synthetic images to analyze the effect of geometrical inconsistencies.
Images with 7 mm tag distance, SNR 20, and 3.5x7.0x7.0 mm 3 pixel size for varying amounts of shift increasing from left to right (values are written at the bottom right corner for each case) on short-axis (a) and long-axis (b) views. IP and TP stand for the direction of shift, in-plane and through-plane, respectively. Images represent the configuration at end-diastolic time frame. The arrows indicate the regions with the largest amount of error due to shift for IP (± 6 IP) and TP (± 6 TP).
Fig 4.
Effect of Tag distance to Pixel size Ratio (TPR) on noiseless isotropic image analysis.
Normalized mean ± standard deviations in displacement error norm (%) plotted as a function of TPR (a). Black curve stands for the errors computed for the images with different pixel sizes keeping the tag distance constant at 7 mm while the red one represents the analysis results with different tag distances where the pixel size is 1 mm. Mean ± standard deviations in component-wise Green-Lagrange strain error as a function of TPR for the best performing regularization strength (b-d). Radial strain component (b) is more sensitive to a change in TPR while the circumferential (c) and the longitudinal (d) components are more accurately measured.
Fig 5.
Effect of SNR on isotropic image analysis.
Results on images with 1 mm pixel size and 7 mm tag distance. Normalized mean ± standard deviations in displacement error norm (%) without regularization (red curve) and with optimal regularization (black curve) (a). Regularization helps decreasing the registration error significantly. Mean ± standard deviations in component-wise Green-Lagrange strain error as a function of SNR which is independent of regularization strength for SNR≥20 (b-d).
Fig 6.
Combined effect of image resolution and SNR on isotropic image analysis.
Results on images with 7 mm tag distance. Normalized mean ± standard deviations in displacement error norm (%) plotted as a function of SNR for different pixel sizes (a). Mean ± standard deviations in component-wise Green-Lagrange strain error as a function of SNR and pixel size (b-d). Combined effect of pixel size and SNR is more pronounced on the radial strain component (b) while there is almost no change in the circumferential (c) and longitudinal (d)components. Legends show the pixel size in mm.
Fig 7.
Effect of image resolution on anisotropically resolved image analysis.
Results on noiseless images with 7 mm tag distance. Normalized mean ± standard deviations in displacement error norm (%) as a function of pixel size (a). Signed averages in Green-Lagrange strain component errors as a function of pixel size (b-d). Radial strain component is the most sensitive to an increase in pixel size (b), while circumferential (c) and the longitudinal (d) components are not affected at all.
Fig 8.
Combined effect of image resolution and SNR on anisotropically resolved image analysis.
Results on images with 7 mm tag distance. Normalized mean ± standard deviations in displacement error norm (%) plotted as a function of SNR for different pixel sizes (a). Mean ± standard deviations in component-wise Green-Lagrange strain error as a function of SNR and pixel size (b-d). Combined effect of increased pixel size and decreased SNR is more pronounced on the radial strain component (b) while there is almost no change in the circumferential (c) and longitudinal (d) components.
Fig 9.
Effect of geometrical inconsistencies.
Results on images with anisotropic pixel size 3.5x7.0x7.0 mm 3 and SNR 20 for 7 mm tag distance. Normalized mean ± standard deviations in displacement error norm (%) plotted as a function of in-plane and through plane shift (in mm) between image stacks (a). Mean ± standard deviations in component-wise Green-Lagrange strain error as a function of in-plane and through plane shift (in mm) between image stacks (b-d). Increasing amount of shift leads to an increased error in radial strain component (b) while there is almost no change in the circumferential (c) and longitudinal (d) components.