Polyhedra Encoding Transformers: Enhancing Diffusion MRI Analysis Beyond Voxel and Volumetric Embedding

Diffusion-weighted Magnetic Resonance Imaging (dMRI) is an essential tool in neuroimaging. It is arguably the sole noninvasive technique for examining the microstructural properties and structural connectivity of the brain. Recent years have seen the emergence of machine learning and data-driven approaches that enhance the speed, accuracy, and consistency of dMRI data analysis. However, traditional deep learning models often fell short, as they typically utilize pixel-level or volumetric patch-level embeddings similar to those used in structural MRI, and do not account for the unique distribution of various gradient encodings. In this paper, we propose a novel method called Polyhedra Encoding Transformer (PE-Transformer) for dMRI, designed specifically to handle spherical signals. Our approach involves projecting an icosahedral polygon onto a unit sphere to resample signals from predetermined directions. These resampled signals are then transformed into embeddings, which are processed by a transformer encoder that incorporates orientational information reflective of the icosahedral structure. Through experimental validation with various gradient encoding protocols, our method demonstrates superior accuracy in estimating multi-compartment models and Fiber Orientation Distributions (FOD), outperforming both conventional CNN architectures and standard transformers.