Porous or biological materials comprise a multitude of micro-domainscontaining water. Diffusion-weighted magnetic resonance measurements are sensitive to the anisotropy of the thermal motion of such water. This anisotropy can bedue to the domain shape, as well as the (lack of) dispersion in their orientations.Averaging over measurements that span all orientations is a trick to suppress thelatter, thereby untangling it from the influence of the domains’ anisotropy on thesignal. Here, we consider domains whose anisotropy is modeled as being the resultof a Hookean (spring) force, which has the advantage of having a Gaussian diffusionpropagator while still confining the spatial range for the diffusing particles. In fact,this confinement model is the effective model of restricted diffusion when diffusion isencoded via gradients of long durations, making the model relevant to a broad rangeof studies aiming to characterize porous media with microscopic subdomains. In thisstudy, analytical expressions for the powder-averaged signal under this assumptionare given for so-called single and double diffusion encoding schemes, which sensitize the MR signal to the diffusive displacement of particles in, respectively, one ortwo consecutive time intervals. The signal for one-dimensional diffusion is shownto exhibit power-law dependence on the gradient strength while its coefficient bearssignatures of restricted diffusion.

The orientationally-averaged diffusion magnetic resonance (MR) signal acquired at high diffusion weighting shows great potential for answering fundamental questions about neural tissue microstructure[1]. The noise-induced bias in the magnitude-valued signal and angular resolution limitations in diffusion encoding are among the challenges in obtaining an accurate estimate. Here, we present a data processing framework for computing the orientationally-averaged diffusion signal that corrects the noise induced bias and accounts for the low angular resolution of the acquisition. Noise correction is performed using a statistical transformation framework [2] that converts the noisy MR signal from a noncentralChi distribution to a noisy Gaussian one. Weights for each of the probing directions are computed to improve the rotationally invariant representation of the sample. Synthetic data, generated to mimic diffusion acquisitions with different noise levels and number of acquisition directions, were used to test the data processing framework. The performance of the framework was evaluated by comparing the processed data with the analytical solution of the orientationally-averaged signal. Results show that the computation of the orientationally-averaged signal benefits from both the noise correction and the weighted averaging, especially in the low signal regime. This work provides a tool for processing high diffusion-weighted MR signals whose interpretation could improve our knowledge about neural tissue microstructure.

[1] Özarslan E, Yolcu C, Herberthson M, Knutsson H, Westin CF. Influence of the size and curvedness ofneural projections on the orientationally averaged diffusion MR signal. Front Phys, 2018; 6:17.

[2] Koay CG, Özarslan E, Basser PJ. A signal transformational framework for breaking the noise floorand its applications in MRI. J Magn Reson 2009; 197(2):108–119.

Neuronal and glial projections can be envisioned to be tubes of infinitesimal diameter as far as diffusion magnetic resonance (MR) measurements via clinical scanners are concerned. Recent experimental studies indicate that the decay of the orientationally-averaged signal in white-matter may be characterized by the power-law, Ē(q) ∝ q−1, where q is the wavenumber determined by the parameters of the pulsed field gradient measurements. One particular study by McKinnon et al. [1] reports a distinctively faster decay in gray-matter. Here, we assess the role of the size and curvature of the neurites and glial arborizations in these experimental findings. To this end, we studied the signal decay for diffusion along general curves at all three temporal regimes of the traditional pulsed field gradient measurements. We show that for curvy projections, employment of longer pulse durations leads to a disappearance of the q−1 decay, while such decay is robust when narrow gradient pulses are used. Thus, in clinical acquisitions, the lack of such a decay for a fibrous specimen can be seen as indicative of fibers that are curved. We note that the above discussion is valid for an intermediate range of q-values as the true asymptotic behavior of the signal decay is Ē(q) ∝ q−4 for narrow pulses (through Debye-Porod law) or steeper for longer pulses. This study is expected to provide insights for interpreting the diffusion-weighted images of the central nervous system and aid in the design of acquisition strategies.