Optimized quantification of diffusional non-gaussianity in the human brain

To test the performance of three existing models of diffusional non-Gaussianity and introduce a new model.

Quantitative 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 Padé approximant, which can model singularities. The resulting signal model is denoted the Padé exponent model. Analyzing diffusion-weighted brain data from four volunteers, we compare the performance of the Padé 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.

With 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%; Padé exponent, 5.2 / 16.1%. The parameters of the Padé exponent model do not depend strongly on the range of measured b-values.

The Padé exponent model describes non-Gaussian diffusion data with high precision over a wide range of b-values.