Deep Representation Learning for Unsupervised Clustering of Myocardial Fiber Trajectories in Cardiac Diffusion Tensor Imaging

Understanding the complex myocardial architecture is critical for diagnosing and treating heart disease. However, existing methods often struggle to accurately capture this intricate structure from Diffusion Tensor Imaging (DTI) data, particularly due to the lack of ground truth labels and the ambiguous, intertwined nature of fiber trajectories. We present a novel deep learning framework for unsupervised clustering of myocardial fibers, providing a data-driven approach to identifying distinct fiber bundles. We uniquely combine a Bidirectional Long Short-Term Memory network to capture local sequential information along fibers, with a Transformer autoencoder to learn global shape features, with pointwise incorporation of essential anatomical context. Clustering these representations using a density-based algorithm identifies 33 to 62 robust clusters, successfully capturing the subtle distinctions in fiber trajectories with varying levels of granularity. Our framework offers a new, flexible, and quantitative way to analyze myocardial structure, achieving a level of delineation that, to our knowledge, has not been previously achieved, with potential applications in improving surgical planning, characterizing disease-related remodeling, and ultimately, advancing personalized cardiac care.

Fine-tuning Neural-Operator architectures for training and generalization

In this work, we present an analysis of the generalization of Neural Operators (NOs) and derived architectures. We proposed a family of networks, which we name (${\textit{s}}{\text{NO}}+\varepsilon$), where we modify the layout of NOs towards an architecture resembling a Transformer; mainly, we substitute the Attention module with the Integral Operator part of NOs. The resulting network preserves universality, has a better generalization to unseen data, and similar number of parameters as NOs. On the one hand, we study numerically the generalization by gradually transforming NOs into ${\textit{s}}{\text{NO}}+\varepsilon$ and verifying a reduction of the test loss considering a time-harmonic wave dataset with different frequencies. We perform the following changes in NOs: (a) we split the Integral Operator (non-local) and the (local) feed-forward network (MLP) into different layers, generating a {\it sequential} structure which we call sequential Neural Operator (${\textit{s}}{\text{NO}}$), (b) we add the skip connection, and layer normalization in ${\textit{s}}{\text{NO}}$, and (c) we incorporate dropout and stochastic depth that allows us to generate deep networks. In each case, we observe a decrease in the test loss in a wide variety of initialization, indicating that our changes outperform the NO. On the other hand, building on infinite-dimensional Statistics, and in particular the Dudley Theorem, we provide bounds of the Rademacher complexity of NOs and ${\textit{s}}{\text{NO}}$, and we find the following relationship: the upper bound of the Rademacher complexity of the ${\textit{s}}{\text{NO}}$ is a lower-bound of the NOs, thereby, the generalization error bound of ${\textit{s}}{\text{NO}}$ is smaller than NO, which further strengthens our numerical results.