Estimation of Diffusion Properties in Crossing Fiber Bundles

There is an ongoing debate on how to model diffusivity in fiber crossings. We propose an optimization framework for the selection of a dual tensor model and the set of diffusion weighting parameters b, such that both the diffusion shape and orientation parameters can be precisely as well as accurately estimated. For that, we have adopted the Cramér-Rao lower bound (CRLB) on the variance of the model parameters, and performed Monte Carlo simulations. We have found that the axial diffusion λ_|| needs to be constrained, while an isotropic fraction can be modeled by a single parameter f_iso. Under these circumstances, the Fractional Anisotropy (FA) of both tensors can theoretically be independently estimated with a precision of 9% (at SNR=25 ). Levenberg-Marquardt optimization of the Maximum Likelihood function with a Rician noise model approached this precision while the bias was insignificant. A two-element b-vector b = [ 1.0 amp; 3.5 ] · 10³ mm^-2 s was found to be sufficient for estimating parameters of heterogeneous tissue with low error. This has allowed us to estimate consistent FA-profiles along crossing tracts. This work defines fundamental limits for comparative studies to correctly analyze crossing white matter structures.