An Implementation of Patient-Specific Biventricular Mechanics Simulations With a Deep Learning and Computational Pipeline

Figure 1. The segmentation network is implemented as a stack of blocks illustrated here. The encode and decode paths along with the skip connection are defined in the same block. The “Next Layer” is either another such block or the bottom encoding block comprised of convolution/normalisation/activation sequences. The overall structure of the network is shown on the right, with the dimensions of tensors passing between layers given relative to an input of shape (1, N, W).

Figure 2. The valve estimation network is composed primarily of a series of densely-connected convolutional layers. Each dense block is composed of three residual units containing 2D convolutions using progressively larger dilation rates. A final convolution reduces the spatial dimension of the volume by 2. The regression network is implemented as a sequence of densely-connected blocks followed by a series of small fully-connected networks relating the final output volume to each landmark coordinate. (A) Residual unit, (B) dilated dense block, (C) network definition.

Figure 3. Short and long-axis cine MR images are simultaneously fed into two neural networks, one for labelling the LV blood pool (red), LV myocardium (green), and RV blood pool (blue) and the second labelling ten valve landmarks throughout the cardiac cycle. The segmentations are converted to labelled contours and a biventricular template surface mesh is fitted to the labelled contours. Volumes, derived from the network generated cavity labels, as well as valve annuli motion are used as boundary conditions in the biomechanical simulations. Passive parameters are optimised by minimising the difference between the model and imaged geometries at end-diastole.

Figure 4. Boxplots illustrate dice scores for each label: LV blood pool (LV), LV myocardium (Myo), and RV blood pool are shown for the healthy volunteers (V), DCM patients (D), and HCM patients (H). The centre line of each boxplot represents the median and the whiskers denote the 25th and 75th percentiles.

Figure 5. Boxplots of valve annotation errors for all 10 valve landmarks are shown for selected healthy volunteers (V), DCM patients (D), and HCM patients (H) in which valve landmarks were manually identified over the entire cardiac cycle. Each boxplot represents errors throughout the cardiac cycle. The centre line of each boxplot represents the median and the whiskers denote the 25th and 75th percentiles. The 10 valve landmarks correspond to those shown in Figure 3, Valve Landmark Identification.

Figure 6. Three representative cases for the healthy volunteer, DCM and HCM groups are shown below with models fit to the neural network segmentations. Model surfaces at end-systole (purple) are overlayed on a single long-axis and short-axis image.

Figure 7. Mean active fibre stress over the cardiac cycle in both the LV and RV for a single case (v1) illustrating the active stress distribution over the entire heart at three points during active contraction: early systole (t = 50 ms), peak active contraction (t = 230 ms), and end-systole (t = 360 ms). The bullseye plot shows the regional distribution of mean active fibre stress over the 17 AHA regions at end-systole.

Figure 8. Mean fibre stretch over the cardiac cycle is shown for both the LV and RV for a single case (v1). Fibre stretch over the cardiac cycle is also plotted for nine time points with the reference state model (ES) shown as a wireframe mesh. The bullseye plot illustrates differences in regional stretch at the end-systolic state in the 17 AHA regions.

Figure 9. (A) Mean active fibre stress and (B) fibre stretch over the cardiac cycle in 16 AHA regions of the LV for healthy (black), DCM (blue), and HCM (red) groups.

Figure 10. Selected long-axis images which were part of the 12 cases (h1, h4, d2, d4) used in this study which demonstrate poor image quality due to imaging artefacts. In the first row, the LV blood pool and myocardial segmentations obtained using the neural network are overlain on top of each image to qualitatively show the impact of the image quality on the network segmentation. In the second row, the final fitted model surface is shown on top of the image.