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

Tianyuan Yao, Zhiyuan Li, Praitayini Kanakaraj, Derek B. Archer, Kurt Schilling, Lori Beason-Held, Susan Resnick, Bennett A. Landman, Yuankai Huo

TL;DR

The paper tackles accurate diffusion MRI microstructure estimation across diverse gradient encodings. It introduces the Polyhedra Encoding Transformer (PE-Transformer), which uses icosahedral resampling to achieve uniform, isotropic q-space sampling and a Vision Transformer–style encoder that leverages orientational information. The model predicts the central-voxel free water fraction and Fiber Orientation Distribution (FOD), outperforming a spherical harmonics CNN and a vanilla Transformer across HCP-ya, BLSA, and MASiVar datasets. Higher-icosahedral tessellations yield the best results, demonstrating robustness across single-shell protocols and highlighting the potential of geometry-aware, data-driven diffusion MRI estimation.

Abstract

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.

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

TL;DR

The paper tackles accurate diffusion MRI microstructure estimation across diverse gradient encodings. It introduces the Polyhedra Encoding Transformer (PE-Transformer), which uses icosahedral resampling to achieve uniform, isotropic q-space sampling and a Vision Transformer–style encoder that leverages orientational information. The model predicts the central-voxel free water fraction and Fiber Orientation Distribution (FOD), outperforming a spherical harmonics CNN and a vanilla Transformer across HCP-ya, BLSA, and MASiVar datasets. Higher-icosahedral tessellations yield the best results, demonstrating robustness across single-shell protocols and highlighting the potential of geometry-aware, data-driven diffusion MRI estimation.

Abstract

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.
Paper Structure (10 sections, 5 equations, 4 figures, 1 table)

This paper contains 10 sections, 5 equations, 4 figures, 1 table.

Table of Contents

  1. INTRODUCTION
  2. METHOD
  3. Icosahedral (ICOSA) Polyhedra
  4. Polyhedra signal resampling
  5. Polyhedra Encoding Transformer
  6. EXPERIMENTS
  7. Data
  8. Baseline methods
  9. RESULTS
  10. CONCLUSION

Figures (4)

  • Figure 1: For the Icosahedral polyhedron family (a,b,c), Icosahedral gradient encoding offers a compelling advantage for diffusion MRI by providing a nearly uniform and isotropic sampling of gradient directions on the unit sphere. The larger ICOSA sets ($N_e > 6$) can be generated by edge bisection and tessellation of the ICOSA6 directions and projection onto a unit sphere for diffusion MRI signal. For spherical harmonics (d,e,f,g shows the fiber ODF one same voxel with 2,4,6 and 8 degrees of spherical harmonics), Higher degrees (e.g., l=8) allow for more detailed representations, but there is a trade-off between capturing detail and introducing noise, as higher-order harmonics may fit noise in the data.
  • Figure 2: The overall design of our proposed PE-Transformer.
  • Figure 3: Qualitative Result. Two subjects from the test cohort are visualized for assessment of fiber orientation distribution estimation. The ACC spatial map depicts the consistency between the estimation and Ground Truth labels (GT) .
  • Figure 4: Qualitative Result. Two subjects from the test cohort are visualized for assessment of free water estimation.