Apparent diffusion coefficient approximation and diffusion anisotropy characterization in DWI.

We present a new approximation for the apparent diffusion coefficient (ADC) of non-Gaussian water diffusion with at most two fiber orientations within a voxel. The proposed model approximates ADC profiles by product of two spherical harmonic series (SHS) up to order 2 from High Angular Resolution Diffusion-weighted (HARD) MRI data. The coefficients of SHS are estimated and regularized simultaneously by solving a constrained minimization problem. An equivalent but non-constrained version of the approach is also provided to reduce the complexity and increase the efficiency in computation. Moreover we use the Cumulative Residual Entropy (CRE) as a measurement to characterize diffusion anisotropy. By using CRE we can get reasonable results with two thresholds, while the existing methods either can only be used to characterize Gaussian diffusion or need more measurements and thresholds to classify anisotropic diffusion with two fiber orientations. The experiments on HARD MRI human brain data indicate the effectiveness of the method in the recovery of ADC profiles. The characterization of diffusion based on the proposed method shows a consistency between our results and known neuroanatomy.