Inference of multiple fiber orientations in high angular resolution diffusion imaging

Abstract

A method is presented that is capable of determining more than one fiber orientation within a single voxel in high angular resolution diffusion imaging (HARDI) data sets. This method is an extension of the Markov chain method recently introduced to diffusion tensor imaging (DTI) analysis, allowing the probability density function of up to 2 intra-voxel fiber orientations to be inferred. The multiple fiber architecture within a voxel is then assessed by calculating the relative probabilities of a 1 and 2 fiber model. It is demonstrated that for realistic signal to noise ratios, it is possible to accurately characterize the directions of 2 intersecting fibers using a 2 fiber model. Diffusion tensor imaging (DTI) has become a very important tool for investigating tissue microstructure (1-3), and is capable of providing information on the nerve fiber directions within imaged voxels. The principal axis of the diffusion tensor coincides with the nerve fiber direction because the anisotropic nature of nerve fibers preferentially allows diffusion in a direction parallel to the fiber. Despite the success of DTI, the standard second order tensor model copes poorly with partial volume effects (4) as it is unable to characterize the directions of crossing fibers (5,6). This has implications for tractography for 2 reasons. First, crossing fibers will lead to erroneous directions being inferred; this will add to other sources of noise in the data and potentially imply false connectivity. Secondly, voxels may appear isotropic with complete loss of directional information (7).High angular resolution diffusion imaging (HARDI) is an alternative to DTI (8). Methods to analyze such diffusion weighted data sets with many gradient encoding directions, which go beyond the traditional second order tensor approach, have been proposed and implemented in the literature. These schemes include the use of tensors above second order (5,9); spherical harmonic (10), harmonic decomposition (11), and spherical deconvolution (12) of the signal; as well as least-square fitting of a Gaussian mixture model of 2 intersecting fibers (13,14) and q-ball imaging (15). Determination of uncertainty of the diffusion tensor is a problem that has received much attention in the literature (16 -20), and this knowledge of the uncertainty in fiber orientation has been incorporated into fiber tracking methods (21).Behrens et al. (22) introduced Bayesian inference to the problem of determining fiber orientation. Using a single fiber model, their algorithm could produce a probability density function (PDF) for the fiber orientation within a given voxel (23). Their algorithm explicitly allows for partial volumes of isotropic material and, perhaps more importantly, allows uncertainty in the fiber orientation to be represented. The algorithm presented here is an extension of this analysis to address the problem of partial volumes in voxels containing 2 distinct fiber orientations, thereby allowing us to directly assess the directions and the separate PDFs of more than 1...

Exploiting peak anisotropy for tracking through complex structures

“…Behrens et al [31], Friman et al [9] and Hosey et al [34] use a Bayesian approach combined with a multicompartment model of diffusion and sample from the marginal posterior distribution of the fibre orientation directly. Jones et al [16,17], Lazar [19] and Haroon et al [13] use statistical bootstrap techniques to obtain samples of the fibreorientation estimate distribution.…”

“…However, this framework suffers from the limitations of the multi-tensor models such as fitting problems and the need to prespecify the number of fibres per voxel. Hosey et al [34] and Behrens et al [33] extend the Bayesian approach from [31] to model up to two fibre-orientation estimates within each voxel.…”

Parametric spherical deconvolution: Inferring anatomical connectivity using diffusion MR imaging

“…Usually, fiber bundles are mapped onto diffusionweighted MR signals by the diffusion tensor model proposed by Basser et al (1994). This approach proved inadequate for describing crossings and branchings of nerve fiber tracts, but it is fairly straightforward to represent several fiber bundles by a sum of multiple diffusion tensors weighted by their respective volume fractions (Tuch et al, 2002;Parker and Alexander, 2003;Hosey et al, 2005). However, a Taylor expansion at b = 0 suggests that the observed data will not provide enough information to resolve the water diffusivity and the volume fraction for small b-values independently (Basser and Jones, 2002).…”

Gibbs tracking: A novel approach for the reconstruction of neuronal pathways

“…The main approach of the current methods of fiber tracking (4,10,(12)(13)(14)(15)(16)(17) is the reconstruction of long neuronal pathways in small successive steps by following the local, voxelwisedefined fiber direction. Starting from local information of the diffusivity, long-distance connections are determined.…”