Analytical and fast Fiber Orientation Distribution reconstruction in 3D-Polarized Light Imaging.

Three dimensional Polarized Light Imaging (3D-PLI) is an optical technique which allows mapping the spatial fiber architecture of fibrous postmortem tissues, at sub-millimeter resolutions. Here, we propose an analytical and fast approach to compute the fiber orientation distribution (FOD) from high-resolution vector data provided by 3D-PLI. The FOD is modeled as a sum of K orientations/Diracs on the unit sphere, described on a spherical harmonics basis and analytically computed using the spherical Fourier transform. Experiments are performed on rich synthetic data which simulate the geometry of the neuronal fibers and on human brain data. Results indicate the analytical FOD is computationally efficient and very fast, and has high angular precision and angular resolution. Furthermore, investigations on the right occipital lobe illustrate that our strategy of FOD computation enables the bridging of spatial scales from microscopic 3D-PLI information to macro- or mesoscopic dimensions of diffusion Magnetic Resonance Imaging (MRI), while being a means to evaluate prospective resolution limits for diffusion MRI to reconstruct region-specific white matter tracts. These results demonstrate the interest and great potential of our analytical approach.