Spherical tensor diffusion encoding with spectral specificity and isotropy

Motivation: Lack of spectral selectivity in spherical tensor diffusion encoding impairs the specificity of the measurement. Goal(s): The goal of this work was to design diffusion gradient waveforms yielding a spherical b-tensor with frequency-specific and isotropic spectral projections. Approach: Gradient waveform designs derived from oscillating gradient diffusion methodology were conceived by shifting and overlapping cosine-modulated trapezoidal oscillations along the three coordinate axes to achieve orthonormality of the b-tensor. Results: The proposed gradient waveforms achieved frequency-specific and isotropic diffusion encoding, permitting frequency-dependent diffusion measurements in the in vivo human brain in the same manner as is conventionally performed using multidirectional linear tensor diffusion encoding. Impact: The proposed diffusion gradient waveforms for spectrally specific and isotropic spherical tensor encoding offer selective frequency measurements that can isolate the signatures of time-dependent diffusion, thereby enabling the study of diffusion dispersion in the framework of tensor-valued encoding.