Geometry of the cumulant series in diffusion MRI

TL;DR

This paper explores the geometric structure of the cumulant series in diffusion MRI, identifying invariants that improve tissue classification and enabling rapid, hardware-independent imaging protocols for clinical use.

Contribution

It introduces a geometric framework based on SO(3) symmetry to identify invariants of cumulant tensors, enhancing tissue classification and enabling fast, efficient MRI protocols.

Findings

Including all kurtosis invariants improves multiple sclerosis classification.

Designed shortest acquisition protocols using icosahedral vertices for rapid imaging.

Scalar invariant maps with symmetries will support machine learning in pathology and development.

Abstract

Water diffusion gives rise to micron-scale sensitivity of diffusion MRI (dMRI) to cellular-level tissue structure. Precision medicine and quantitative imaging depend on uncovering the information content of dMRI and establishing its parsimonious hardware-independent fingerprint. Based on the rotational SO(3) symmetry, we study the geometry of the dMRI signal and the topology of its acquisition, identify irreducible components and a full set of invariants for the cumulant tensors, and relate them to tissue properties. Including all kurtosis invariants improves multiple sclerosis classification in a cohort of 1189 subjects. We design the shortest acquisitions based on icosahedral vertices to determine the most used invariants in only 1-2 minutes for whole brain. Representing dMRI via scalar invariant maps with definite symmetries will underpin machine learning classifiers of pathology, development, and aging, while fast protocols will enable translation of advanced dMRI into clinic.