Optimized Quantification of Diffusional Non-Gaussianity in the Human Brain

PurposeTo test the performance of three existing models of diffusional non-Gaussianity and introduce a new model. Materials and MethodsQuantitative measures of diffusional non-Gaussianity provide clinically useful information. Three-parameter mathematical models are particularly relevant, because they assign one parameter to non-Gaussianity, one to diffusivity and one to the signal in the absence of diffusion weighting. One such model is the cumulant expansion, where the logarithm of the signal is approximated by a Taylor series. Convergence may be blocked by singularities in the complex b-plane. To overcome this problem, we replace the Taylor series by a Pade approximant, which can model singularities. The resulting signal model is denoted the Pade exponent model. Analyzing diffusion-weighted brain data from four volunteers, we compare the performance of the Pade exponent model with the statistical model, the stretched exponential model and the cumulant expansion. With voxelwise hypothesis testing, we calculate the fraction of voxels where the models fail to describe the data. ResultsWith 16 b-values in the range [0,5000] s/mm(2), the fractions of rejected voxels in white / gray matter are: statistical model, 41 / 20%; stretched exponential model, 68 / 16.6%; cumulant expansion, 58 / 37%; Pade exponent, 5.2 / 16.1%. The parameters of the Pade exponent model do not depend strongly on the range of measured b-values. ConclusionThe Pade exponent model describes non-Gaussian diffusion data with high precision over a wide range of b-values.