Frequency-dependence in multidimensional diffusion-relaxation correlation MRI of the brain: overfitting or meaningful parameter?

Time- or frequency-dependent ("restricted") diffusion potentially provides useful information about cellular-scale structures in the brain but is challenging to interpret because of the intravoxel tissue heterogeneity. Frequency-dependence was recently incorporated in a multidimensional diffusion-relaxation correlation MRI framework relying on tensor-valued diffusion encoding at multiple frequencies, as well as variable echo and repetition times, to give model-free characterization of intravoxel heterogeneity by Monte Carlo data inversion into nonparametric distributions of frequency-dependent diffusion tensors and nuclear relaxation rates. While microimaging equipment with high-amplitude magnetic field gradients allows exploration of frequencies from tens to hundreds of Hz, clinical scanners with more moderate gradient capabilities are limited to a narrow frequency range, which may be insufficient to observe effects of restricted diffusion for brain tissues. We here investigate the effects of including or omitting frequency-dependence in the data inversion from isotropic and anisotropic liquids, excised tumor tissue, ex vivo mouse brain, and in vivo human brain. For microimaging measurements covering a wide frequency range, from 35 to 320 Hz at b-values over 4{middle dot}109 sm-2, the inclusion of frequency-dependence drastically reduces the fit residuals and avoids bias in the diffusion metrics for tumor and brain voxels with micrometer-scale structures. Conversely, for the case of in vivo human brain investigated in the narrow frequency range from 5 to 11 Hz at b = 3{middle dot}109 sm-2, analyses with and without inclusion of frequency-dependence yield similar fit residuals and diffusion metrics for all voxels. These results indicate that frequency-dependent inversion may be generally applied to diffusion-relaxation correlation MRI data with and without observable effects of restricted diffusion.