Explicit differentiable slicing and global deformation for cardiac mesh reconstruction

Three-dimensional (3D) mesh reconstruction of the cardiac anatomy from medical images is useful for shape and motion measurements and biophysics simulations. However, 3D medical images are often acquired as 2D slices that are sparsely sampled (e.g., large slice spacing) and noisy, and 3D mesh reconstruction on such data is a challenging task. Traditional voxel-based approaches utilize non-differentiable pre- and post-processing that compromises fidelity to images, while mesh-level deep learning approaches require large 3D mesh annotations that are difficult to obtain. Differentiable cross-domain supervision from 2D images to 3D meshes is therefore crucial for enabling end-to-end optimization in medical imaging. While there have been attempts to approximate the voxelization and slicing of meshes that are being optimized, there has not yet been a method for directly using 2D slices to supervise 3D mesh reconstruction in a differentiable manner. Here, we propose a novel explicit differentiable voxelization and slicing (DVS) algorithm allowing gradient backpropagation to a 3D mesh from its slices, which facilitates refined mesh optimization directly supervised by the losses defined on 2D images. Further, we propose an innovative framework for extracting patient-specific left ventricle (LV) meshes from medical images by coupling DVS with a graph harmonic deformation (GHD) mesh morphing descriptor of cardiac shape that naturally preserves mesh quality and smoothness during optimization. The proposed framework achieves state-of-the-art performance in cardiac mesh reconstruction tasks from densely sampled (CT) as well as sparsely sampled (MRI stack with few slices) images, outperforming alternatives, including Marching Cubes, statistical shape models, algorithms with vertex-based mesh morphing algorithms and alternative methods for image-supervision of mesh reconstruction. Experimental results demonstrate that our method achieves an overall Dice score of 90% during a sparse fitting on multi-datasets. The proposed method can further quantify clinically useful parameters such as ejection fraction and global myocardial strains, closely matching the ground truth and outperforming the traditional voxel-based approach in sparse images.