Spectral principal axis system (SPAS) and tuning of tensor-valued encoding for microscopic anisotropy and time-dependent diffusion in the rat brain

Tensor-valued encoding in diffusion MRI allows probing of microscopic anisotropy in tissue, however, time-dependent diffusion (TDD) can bias results unless b-tensors are carefully tuned to account for TDD. We propose two novel strategies for tuning b-tensors to enable accurate measurements without interference from TDD due to restricted diffusion. The first strategy involves identifying encoding tensor projections that yield equal mean diffusivities (MD), providing robust tuning across a wide range of diffusion spectra. The second strategy uses geometric averaging of signals, ensuring tuning regardless of the diffusion spectra. Importantly, the same encoding waveforms used for geometric averaging to probe microscopic anisotropy (µA) can also generate an independent contrast due to TDD. This is enabled by considering spectral anisotropy of encoding and defining the spectral principal axis system (SPAS), which unfolds TDD as an additional independent dimension in tensor-valued encoding. Projections of encoding waveforms along the SPAS axes allow for the simultaneous acquisition of independent contrasts due to both µA and TDD within a single multidimensional diffusion encoding protocol. Additionally, SPAS projections inherit useful properties from the reference tensor, such as optimized b-value, motion nulling, and minimal concomitant field effects. This framework is demonstrated through simulations of various restricted diffusion compartments. Experimental validation on perfusion-fixed and<i>in vivo</i>rat brains highlights the method's potential for enhanced microstructural specificity. In addition to mapping MD, fractional anisotropy, and unbiased microscopic fractional anisotropy, we propose a model-free approach to independently map µA and TDD. This approach uses a minimal yet highly specific protocol, enabling the identification of distinct µA-TDD contrasts across different brain regions, including details in cortical gray matter, choroid plexus, dentate gyrus of the hippocampus, and white matter.