NODDI is a popular diffusion MRI technique that estimates indices about tissue microstructure. However it makes a priori assumptions, particularly fixing intrinsic diffusivity (DI) to be the same throughout the brain. We aim to validate this assumption by combining NODDI with mcDESPOT, which enables an independent estimation of the CSF volume fraction. By doing this, we enable NODDI to estimate voxel-wise maps of DI as well as of the perpendicular diffusivity by removing the tortuosity constraint. Our estimated DI maps show that the assumed value is more suitable for white matter than gray matter and resulted in sharper contrast in neurite density maps but noisier orientation dispersion (ODI) maps. Removing the tortuosity assumption restored the ODI but degraded the quality of the neurite density map.