Inferring multiple maxima in intravoxel white matter fiber distribution.

A new methodology is introduced that characterizes the intravoxel orientation distribution function (ODF) based on a single-fiber model of the diffusion MRI signal. Using a Bayesian framework the probability of finding a fiber in a specific orientation is obtained. The proposed ODF estimation relies on a cigar-like diffusion tensor model, the methodology is thus denominated Bayesian cigar-like diffusion tensor (BCDT). This work makes two major contributions: 1) the study of single-fiber models in detecting fibers with different volume fractions in a voxel, and 2) the introduction of the Nth-root correction to improve the detection of fibers with smaller volume fractions, where N is the number of diffusion MRI measurements. It is demonstrated that the incomplete signal modeling fails to reconstruct the relative fiber volume fractions, especially when the intravoxel diffusion profiles have dissimilar contributions to the diffusion MRI signal. In this situation the fibers with smaller contributions are hardly detectable. The BCDT method proposed here reduces this effect by introducing the Nth-root correction, making multiple fibers estimable. The performance of the new methodology is illustrated using synthetic and real data, as well as the data from a phantom of intersecting capillaries.

A Bayesian framework to identify principal intravoxel diffusion profiles based on diffusion-weighted MR imaging.

In this paper we introduce a new method to characterize the intravoxel anisotropy based on diffusion-weighted imaging (DWI). The proposed solution, under a fully Bayesian formalism, deals with the problem of joint Bayesian Model selection and parameter estimation to reconstruct the principal diffusion profiles or primary fiber orientations in a voxel. We develop an efficient stochastic algorithm based on the reversible jump Markov chain Monte Carlo (RJMCMC) method in order to perform the Bayesian computation. RJMCMC is a good choice for this problem because of its ability to jump between models of different dimensionality. This methodology provides posterior estimates of the parameters of interest (fiber orientation, diffusivities etc) unconditional of the model assumed. It also gives an empirical posterior distribution of the number of primary nerve fiber orientations given the DWI data. Different probability maps can be assessed using this methodology: 1) the intravoxel fiber orientation map (or orientational distribution function) that gives the probability of finding a fiber in a particular spatial orientation; 2) a three-dimensional map of the probability of finding a particular number of fibers in each voxel; 3) a three-dimensional MaxPro (maximum probability) map that provides the most probable number of fibers for each voxel. In order to study the performance and reliability of the presented approach, we tested it on synthetic data; an ex-vivo phantom of intersecting capillaries; and DWI data from a human subject.