Massively Multidimensional Diffusion-Relaxation Correlation MRI

Diverse approaches such as oscillating gradients, tensor-valued encoding, and diffusion-relaxation correlation have been used to study microstructure and heterogeneity in healthy and pathological biological tissues. Recently, acquisition schemes with free gradient waveforms exploring both the frequency-dependent and tensorial aspects of the encoding spectrum b(omega) have enabled estimation of nonparametric distributions of frequency-dependent diffusion tensors. These "D(omega)-distributions" allow investigation of restricted diffusion for each distinct component resolved in the diffusion tensor trace, anisotropy, and orientation dimensions. Likewise, multidimensional methods combining longitudinal and transverse relaxation rates, R-1 and R-2,R- with (omega-independent) D-distributions capitalize on the component resolution offered by the diffusion dimensions to investigate subtle differences in relaxation properties of sub-voxel water populations in the living human brain, for instance nerve fiber bundles with different orientations. By measurements on an ex vivo rat brain, we here demonstrate a "massively multidimensional" diffusion-relaxation correlation protocol joining all the approaches mentioned above. Images acquired as a function of the magnitude, normalized anisotropy, orientation, and frequency content of b(omega), as well as the repetition time and echo time, yield nonparametric D(omega)-R-1-R-2-distributions via a Monte Carlo data inversion algorithm. The obtained per-voxel distributions are converted to parameter maps commonly associated with conventional lower-dimensional methods as well as unique statistical descriptors reporting on the correlations between restriction, anisotropy, and relaxation.