Mesh U-Nets for 3D Cardiac Deformation Modeling

Abstract

During a cardiac cycle, the heart anatomy undergoes a series of complex 3D deformations, which can be analyzed to diagnose various cardiovascular pathologies including myocardial infarction. While volume-based metrics such as ejection fraction are commonly used in clinical practice to assess these deformations globally, they only provide limited information about localized changes in the 3D cardiac structures. The objective of this work is to develop a novel geometric deep learning approach to capture the mechanical deformation of complete 3D ventricular shapes, offering potential to discover new image-based biomarkers for cardiac disease diagnosis. To this end, we propose the mesh U-Net, which combines mesh-based convolution and pooling operations with U-Net-inspired skip connections in a hierarchical step-wise encoder-decoder architecture, in order to enable accurate and efficient learning directly on 3D anatomical meshes. The proposed network is trained to model both cardiac contraction and relaxation, that is, to predict the 3D cardiac anatomy at the end-systolic phase of the cardiac cycle based on the corresponding anatomy at end-diastole and vice versa. We evaluate our method on a multi-center cardiac magnetic resonance imaging (MRI) dataset of 1021 patients with acute myocardial infarction. We find mean surface distances between the predicted and gold standard anatomical meshes close to the pixel resolution of the underlying images and high similarity in multiple commonly used clinical metrics for both prediction directions. In addition, we show that the mesh U-Net compares favorably to a 3D U-Net benchmark by using 66% fewer network parameters and drastically smaller data sizes, while at the same time improving predictive performance by 14%. We also observe that the mesh U-Net is able to capture subpopulation-specific differences in mechanical deformation patterns between patients with different myocardial infarction types and clinical outcomes.

Appendices

A 3D U-Net

In this section, we describe in greater detail the training and validation procedure of the 3D U-Net [6] used for both the end-diastolic and end-systolic prediction tasks. First, we convert the mesh representations of the cardiac anatomies of the whole dataset into voxelgrids to allow for the same dataset to be used for both the 3D U-Net and mesh U-Net evaluation. We achieve this by voxelizing the 3D meshes and placing them in the center of 128 $\times$ 128 $\times$ 128 voxelgrids where each voxel is encoded as either background (value: “0") or left ventricular myocardium (value: “1"). We then select a 3D U-Net architecture and train it using binary cross entropy as a loss function. Next, we pass the unseen test data through the trained 3D U-Net and convert the resulting predictions and corresponding gold standard anatomies from voxelgrid to 3D surface mesh representations with the marching cubes algorithm [20]. Finally, we use the obtained mesh representations to calculate both surface distances and Hausdorff distances between the meshes predicted by the 3D U-Net and the respective gold standard meshes.

B Subpopulation-Specific Deformations

We display the results of the subpopulation-specific training experiments using the Hausdorff distance as a quantitative metric in Fig. 4.

Fig. 4.

Hausdorff distance distributions achieved by mesh U-Nets trained on one subpopulation and evaluated on unseen test dataset of the same subpopulation (blue color) and the complementary subpopulation (orange color). Plots are shown for both ED and ES prediction tasks (columns) and both STEMI and MACE population splits (rows). p-values for KS-test: <0.0001 (ED prediction for both STEMI and MACE); <0.001 (ES prediction for STEMI); <0.005 (ES prediction for MACE). (Color figure online)