Statistical assessment of non-Gaussian diffusion models

In human brain diffusion measurements, there are deviations from monoexponential signal decay at high values of the diffusion-weighting factor b. This is known as non-Gaussian diffusion and can provide novel kinds of image contrast. We evaluated quantitatively the goodness-of-fit of five popular diffusion models. Because of the Rician signal distribution and physiological noise, the measurement errors are unknown. This precludes standard χ(2) testing. By repeating the measurement 25 times, the errors were estimated. Hypothesis testing based on the residual after least squares curve fitting was then carried out. Systematic errors originating from the Rician signal bias were eliminated in the fitting procedure. We performed diffusion measurements on four healthy volunteers with b-values ranging from 0 to 5000 s/mm(2) . The data were analyzed voxelwise. The null hypothesis of a given model being adequate was rejected, if the residual after fitting exceeded a limit that corresponds to a significance level of 1%. The fraction of rejected voxels depended strongly on the number of free model parameters. The rejected fraction was: monoexponential model with two parameters, 94%; statistical model with three parameters, 29%; stretched exponential model with three parameters, 35%; cumulant model with three parameters, 48%; cumulant model with four parameters, 11%; biexponential model with four parameters, 2.9%.