Augmented Equivariant Mesh Networks for Anatomical Segmentation

Accurate patient-specific tetrahedral cardiac meshes are essential for in-silico trials, yet common segmentation-then-modelling pipelines can blur thin-wall anatomy and offer limited cross-case correspondence. We propose HeartVolMesh, which lifts each template vertex to an anisotropic Gaussian kernel and uses a 3D CNN-GNN to predict per-vertex displacements and Cholesky-parameterized covariances from volumetric images. Training is guided by a covariance-aware negative log-likelihood loss with lightweight mesh regularization. For volumetric meshing, we warp a fixed tetrahedral template to the reconstructed surface via staged alignment, non-rigid registration, and deformation propagation, preserving connectivity and correspondence by construction, with resolution controlled by template density. Experiments show consistent gains over deformation-based baselines in surface mesh accuracy and volumetric mesh fidelity.

Computational models of the human heart are widely used to study electromechanical and fluid-dynamical cardiac function and to support applications such as in silico clinical trials. However, most studies remain limited to single or patient-specific anatomies, restricting the inclusion of population-level variability required for uncertainty quantification. A key challenge is translating medical-image segmentations, which may contain artifacts, mesh defects or disjoint domains, into topologically coherent geometries suitable for multiphysics simulations. In this work, we present a semi-automatic pipeline that converts CT-based segmentations into simulation-ready cardiac meshes within a few minutes while preserving anatomical and topological consistency. Building on modern deep learning segmentation methods, the framework incorporates a template-based registration stage to regularize artifacts and enforce mesh-quality constraints. A Chamfer-distance morphing strategy deforms a high-quality template toward each segmented heart, matching individual chambers while preserving topology. The resulting meshes are watertight, isotopological, and endowed with consistent point-to-point correspondence. The pipeline is validated on 58 healthy cardiac CT scans, including all cardiac chambers and proximal vessel segments. The resulting meshes can be represented in a unified shape space, enabling the construction of a statistical shape model of the heart and major vessels. Principal Component Analysis shows that a low-dimensional latent space efficiently captures population variability, while Gaussian Mixture Modeling enables synthetic anatomy generation. Overall, the proposed framework (released open-source) provides a pathway from raw segmentations to simulation-ready cardiac geometries, enabling anatomically consistent virtual cohorts for large-scale in silico studies.

This work demonstrates a full reproduction and extension of MNet, a hybrid 2D/3D convolutional network designed for anisotropic medical image segmentation. The original architecture was re-implemented within the nnU-Net framework to verify its reported performance and robustness to variable voxel spacing, known as anisotropy. Experiments were conducted on PROMISE prostate MRI and a controlled subset of LiTS liver CT under matched preprocessing and compute constraints. The reproduced MNet achieved a Dice similarity coefficient (DSC) of 89.0 +/- 0.9% on PROMISE, within 0.8% of the published result, and 94.3 +/- 1.9% / 54.6 +/- 3.1% for liver and tumor segmentation on LiTS, respectively. Two lightweight extensions were further introduced: (1) a learned Fusion Gating mechanism enabling adaptive 2D-3D feature blending, and (2) a VMamba state-space module for efficient long-range depth modelling. The Spatial Gating variant improved DSC by +0.8% with less than 3% inference overhead, while VMamba improved performance consistency, reducing PROMISE Dice variation to +/- 0.7% and achieving the strongest LiTS liver performance at 95.8% Dice. Both extensions preserved MNet robustness to anisotropy, with delta Dice = 1.5% across 1-4 mm voxel spacing. Overall, the study confirms MNet reproducibility and demonstrates that adaptive fusion and state-space modelling have the potential to further strengthen segmentation reliability under anisotropic conditions. However, further tests are required to provide definitive conclusions.