Geometry of the cumulant series in diffusion MRI

Area of Science:

• Biomedical Imaging
• Quantitative MRI
• Diffusion MRI (dMRI)

Background:

• dMRI offers micron-scale sensitivity to cellular tissue structure.
• Precision medicine and quantitative imaging require understanding dMRI's information content and developing hardware-independent fingerprints.

Purpose of the Study:

• To explore the geometry and topology of dMRI signals based on rotational symmetry.
• To identify irreducible components and invariants of cumulant tensors for relating to tissue properties.
• To improve dMRI-based classification of diseases and enable faster clinical protocols.

Main Methods:

• Analysis of dMRI signal geometry and acquisition topology using SO(3) symmetry.
• Identification of irreducible components and invariants for cumulant tensors.
• Development of shortest acquisition protocols using icosahedral vertices.
• Classification of multiple sclerosis using kurtosis invariants in a large cohort.

Main Results:

• Established a full set of invariants for cumulant tensors, linking them to tissue properties.
• Demonstrated improved multiple sclerosis classification by including all kurtosis invariants (1189 subjects).
• Designed rapid whole-brain acquisition protocols (1-2 minutes) to capture key invariants.

Conclusions:

• Scalar invariant maps with defined symmetries can underpin machine learning for pathology, development, and aging.
• Fast dMRI protocols facilitate the clinical translation of advanced diffusion imaging techniques.
• This work provides a framework for a parsimonious, hardware-independent dMRI fingerprint.