The Variance of DTI-derived Parameters via First-Order Perturbation Methods
Chang L, Pierpaoli C, Basser P
Monte Carlo and Bootstrap methods provide powerful statistical tools for determining the effects of background noise in diffusion weighted imaging (DWI) data on diffusion tensor MR imaging (DTI) -derived parameters, and for optimizing the design of DTI experiments. These empirical methods do not provide analytical relationships between the variance of the distribution of noise in the DWI data and the variance of DTI-derived parameters. Here we use the 1st-order matrix perturbation method to determine how noise in DWI data affects the uncertainty in the estimated tensors. Monte Carlo simulations of DTI experiments are performed to validate these formulae, and to determine their applicability over a broad range of experimental design parameters.