MR characterization of compartment shape anisotropy (CSA)

INTRODUCTION The orientational dependence of the diffusion-weighted MR signal intensity has been exploited to characterize the integrity and orientation of white-matter pathways in the brain. Anisotropy observed in traditional single pulsed field gradient (single-PFG) acquisitions is primarily a product of the interaction betweeen cellular membranes and diffusing water molecules suggesting the restricting character of the membranes [1]. Thus, such anisotropy is observed when the cells have an elongated structure. Moreover, any incoherence in the orientation of a collection of cells leads to a decrease in the observed anisotropy. Consequently, the measured anisotropy in singlePFG scans emerges from the interplay between the anisotropy of the cells (hereafter referred to as compartment shape anisotropy, CSA) and the coherence in the population of cells (hereafter referred to as ensemble anisotropy, EA). There is yet another mechanism of anisotropy at a sub-compartmental length scale, which is induced by the restricting barriers [2], called microscopic anisotropy (μA). Figure 1 illustrates when these different mechanisms of anisotropy may be encountered. When the cells are spherical, only μA can be observed. A randomly oriented population of anisotropic cells will in addition exhibit CSA. Finally, if the anisotropic cells have any orientational preference in their alignment, all three mechanisms of diffusion anisotropy coexist. It was shown recently that μA and EA can be probed simultaneously and differentiated using the double-PFG pulse sequences [2], a realization of which is depicted in Figure 2. Such a development led to the inference of an apparent compartment size using the double-PFG experiment with arbitrary timing parameters and small gradient strengths. In this study, we extend the theory of restricted diffusion to account for CSA as well.