Scattering approach to diffusion quantifies axonal damage in brain injury

Early diagnosis and noninvasive monitoring of neurological disorders require sensitivity to elusive cellular-level alterations that occur much earlier than volumetric changes observable with the millimeter-resolution of medical imaging modalities. Morphological changes in axons, such as axonal varicosities or beadings, are observed in neurological disorders, as well as in development and aging. Here, we reveal the sensitivity of time-dependent diffusion MRI (dMRI) to axonal morphology at the micrometer scale. Scattering theory uncovers the two parameters that determine the diffusive dynamics of water in axons: the average reciprocal cross-section and the variance of long-range cross-sectional fluctuations. This theoretical development allowed us to predict dMRI metrics sensitive to axonal alterations across tens of thousands of axons in seconds rather than months of simulations in a rat model of traumatic brain injury. Our approach bridges the gap between micrometers and millimeters in resolution, offering quantitative, objective biomarkers applicable to a broad spectrum of neurological disorders.

Geometry of the cumulant series in neuroimaging

Water diffusion gives rise to micrometer-scale sensitivity of diffusion MRI (dMRI) to cellular-level tissue structure. The advent of precision medicine and quantitative imaging hinges on revealing the information content of dMRI, and providing its parsimonious basis- and hardware-independent "fingerprint". Here we reveal the geometry of a multi-dimensional dMRI signal, classify all 21 invariants of diffusion and covariance tensors in terms of irreducible representations of the group of rotations, and relate them to tissue properties. Previously studied dMRI contrasts are expressed via 7 invariants, while the remaining 14 provide novel complementary information. We design acquisitions based on icosahedral vertices guaranteeing minimal number of measurements to determine 3-4 most used invariants in only 1-2 minutes for the whole brain. Representing dMRI signals via scalar invariant maps with definite symmetries will underpin machine learning classifiers of brain pathology, development, and aging, while fast protocols will enable translation of advanced dMRI into clinical practice.