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

Abstract Time- or frequency-dependent (“restricted”) diffusion potentially provides useful information about cellular-scale structures in the brain but is challenging to interpret because of intravoxel tissue heterogeneity. Multidimensional diffusion-relaxation correlation MRI with tensor-valued diffusion encoding enables characterization of intravoxel heterogeneity in terms of nonparametric distributions of diffusion tensors and nuclear relaxation rates, and was recently augmented with explicit consideration of frequency-dependence to resolve the effects of restricted diffusion for distinct populations of tissue water. The simplest acquisition protocols for tensor-valued encoding unintentionally cover a frequency range of a factor 2-3, which can be extended in a more controlled way with oscillating gradient waveforms. 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 narrower ranges that may be insufficient to observe 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 4·109 sm−2, the inclusion of frequency-dependence drastically reduces 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 = 3·109 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.