NODDI-SH: a computational efficient NODDI extension for fODF estimation in diffusion MRI

Diffusion Magnetic Resonance Imaging (DMRI) is the only non-invasive imagingtechnique which is able to detect the principal directions of water diffusionas well as neurites density in the human brain. Exploiting the ability ofSpherical Harmonics (SH) to model spherical functions, we propose a newreconstruction model for DMRI data which is able to estimate both the fiberOrientation Distribution Function (fODF) and the relative volume fractions ofthe neurites in each voxel, which is robust to multiple fiber crossings. Weconsider a Neurite Orientation Dispersion and Density Imaging (NODDI) inspiredsingle fiber diffusion signal to be derived from three compartments:intracellular, extracellular, and cerebrospinal fluid. The model, calledNODDI-SH, is derived by convolving the single fiber response with the fODF ineach voxel. NODDI-SH embeds the calculation of the fODF and the neurite densityin a unified mathematical model providing efficient, robust and accurateresults. Results were validated on simulated data and tested on extitin-vivo data of human brain, and compared to and Constrained SphericalDeconvolution (CSD) for benchmarking. Results revealed competitive performancein all respects and inherent adaptivity to local microstructure, while sensiblyreducing the computational cost. We also investigated NODDI-SH performance whenonly a limited number of samples are available for the fitting, demonstratingthat 60 samples are enough to obtain reliable results. The fast computationaltime and the low number of signal samples required, make NODDI-SH feasible forclinical application.