title: Optimized quantification of diffusional non-gaussianity in the human brain.
abstract: OBJECTIVE
  To test the performance of three existing models of diffusional non-Gaussianity and introduce a new model.
  
  
  METHODS
  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.
  
  
  RESULTS
  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.
  
  
  CONCLUSIONS
  The Padé exponent model describes non-Gaussian diffusion data with high precision over a wide range of b-values.
authors.affiliation: Clinic of Radiology and Nuclear Medicine, St. Olav's Hospital HF, Trondheim, Norway.
authors.forename: Anders
authors.initials: A
authors.lastname: Kristoffersen
mesh_terms: D000328:Adult; D000465:Algorithms; D001921:Brain / Q000033:anatomy & histology*; D003198:Computer Simulation; D038524:Diffusion Magnetic Resonance Imaging / Q000379:methods*; D005260:Female; D006801:Humans; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D008297:Male; D008959:Models, Neurological; D015233:Models, Statistical; D016011:Normal Distribution; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity
keywords: Padé approximant; cumulant expansion; goodness of fit; multiexponential diffusion; non-Gaussian diffusion; white matter