Adaptive kernels for multi-fiber reconstruction

An iterative algorithm for computing gradient directions for white matter fascicles detection in brain MRI

This paper proposes a new iterative algorithm for computing gradient directions (GD) to reconstruct the brain's white matter fascicles. In particular, the proposed algorithm extensively overcomes the limitations of existing approaches like Uniform Gradient Directions and Adaptive Gradient Directions (AGD) for this task. The proposed algorithm uses the AGD approach to have a coarse estimation of the fibers in the initial step, and then a refinement is done using an iterative strategy. We begin with GD distributed uniformly inside a grid of bigger size and larger spacing between the points. Both (grid size and spacing between the points) reduce iteratively. The proposed algorithm has higher chance of capturing the fibers' actual position within the grid at each iteration. Hence, the solution tends to the actual position of fiber in each iteration, leading to a better estimation of fiber orientations. Multiple artificial simulations and real dataset experiments on the human brain and optic chiasm of a rat's brain are performed. The excellent performance of the proposed algorithm at different noises ensures stability and robustness. Hence, after processing the MRI data, the proposed algorithm can accurately reflect the ground truth of white matter fascicles connections in reconstructed images. The proposed algorithm helps resolve the structural complexities of the brain caused due to presence of crossing fascicles to a great extent.

Rotationally-invariant mapping of scalar and orientational metrics of neuronal microstructure with diffusion MRI

We develop a general analytical and numerical framework for estimating intra- and extra-neurite water fractions and diffusion coefficients, as well as neurite orientational dispersion, in each imaging voxel. By employing a set of rotational invariants and their expansion in the powers of diffusion weighting, we analytically uncover the nontrivial topology of the parameter estimation landscape, showing that multiple branches of parameters describe the measurement almost equally well, with only one of them corresponding to the biophysical reality. A comprehensive acquisition shows that the branch choice varies across the brain. Our framework reveals hidden degeneracies in MRI parameter estimation for neuronal tissue, provides microstructural and orientational maps in the whole brain without constraints or priors, and connects modern biophysical modeling with clinical MRI.

A localized Richardson-Lucy algorithm for fiber orientation estimation in high angular resolution diffusion imaging

PURPOSE

Diffusion tensor imaging is widely used for studying neural fiber trajectories in white matter and for quantifying changes in tissue using diffusion properties at each voxel in the brain. To better model the nature of crossing fibers within complex architectures, rather than using a simplified tensor model that assumes only a single fiber direction at each image voxel, a model mixing multiple diffusion tensors is used to profile diffusion signals from high angular resolution diffusion imaging (HARDI) data. Based on the HARDI signal and a multiple tensors model, spherical deconvolution methods have been developed to overcome the limitations of the diffusion tensor model when resolving crossing fibers. The Richardson-Lucy algorithm is a popular spherical deconvolution method used in previous work. However, it is based on a Gaussian distribution, while HARDI data are always very noisy, and the distribution of HARDI data follows a Rician distribution. This current work aims to present a novel solution to address these issues.

METHODS

By simultaneously considering both the Rician bias and neighbor correlation in HARDI data, the authors propose a localized Richardson-Lucy (LRL) algorithm to estimate fiber orientations for HARDI data. The proposed method can simultaneously reduce noise and correct the Rician bias.

RESULTS

Mean angular error (MAE) between the estimated Fiber orientation distribution (FOD) field and the reference FOD field was computed to examine whether the proposed LRL algorithm offered any advantage over the conventional RL algorithm at various levels of noise. Normalized mean squared error (NMSE) was also computed to measure the similarity between the true FOD field and the estimated FOD filed. For MAE comparisons, the proposed LRL approach obtained the best results in most of the cases at different levels of SNR and b-values. For NMSE comparisons, the proposed LRL approach obtained the best results in most of the cases at b-value = 3000 s/mm(2), which is the recommended schema for HARDI data acquisition. In addition, the FOD fields estimated by the proposed LRL approach in regions of fiber crossing regions using real data sets also showed similar fiber structures which agreed with common acknowledge in these regions.

CONCLUSIONS

The novel spherical deconvolution method for improved accuracy in investigating crossing fibers can simultaneously reduce noise and correct Rician bias. With the noise smoothed and bias corrected, this algorithm is especially suitable for estimation of fiber orientations in HARDI data. Experimental results using both synthetic and real imaging data demonstrated the success and effectiveness of the proposed LRL algorithm.

Investigating the tradeoffs between spatial resolution and diffusion sampling for brain mapping with diffusion tractography: time well spent?

Interest in mapping white matter pathways in the brain has peaked with the recognition that altered brain connectivity may contribute to a variety of neurologic and psychiatric diseases. Diffusion tractography has emerged as a popular method for postmortem brain mapping initiatives, including the ex-vivo component of the human connectome project, yet it remains unclear to what extent computer-generated tracks fully reflect the actual underlying anatomy. Of particular concern is the fact that diffusion tractography results vary widely depending on the choice of acquisition protocol. The two major acquisition variables that consume scan time, spatial resolution, and diffusion sampling, can each have profound effects on the resulting tractography. In this analysis, we determined the effects of the temporal tradeoff between spatial resolution and diffusion sampling on tractography in the ex-vivo rhesus macaque brain, a close primate model for the human brain. We used the wealth of autoradiography-based connectivity data available for the rhesus macaque brain to assess the anatomic accuracy of six time-matched diffusion acquisition protocols with varying balance between spatial and diffusion sampling. We show that tractography results vary greatly, even when the subject and the total acquisition time are held constant. Further, we found that focusing on either spatial resolution or diffusion sampling at the expense of the other is counterproductive. A balanced consideration of both sampling domains produces the most anatomically accurate and consistent results.

A robust variational approach for simultaneous smoothing and estimation of DTI

Estimating diffusion tensors is an essential step in many applications - such as diffusion tensor image (DTI) registration, segmentation and fiber tractography. Most of the methods proposed in the literature for this task are not simultaneously statistically robust and feature preserving techniques. In this paper, we propose a novel and robust variational framework for simultaneous smoothing and estimation of diffusion tensors from diffusion MRI. Our variational principle makes use of a recently introduced total Kullback-Leibler (tKL) divergence for DTI regularization. tKL is a statistically robust dissimilarity measure for diffusion tensors, and regularization by using tKL ensures the symmetric positive definiteness of tensors automatically. Further, the regularization is weighted by a non-local factor adapted from the conventional non-local means filters. Finally, for the data fidelity, we use the nonlinear least-squares term derived from the Stejskal-Tanner model. We present experimental results depicting the positive performance of our method in comparison to competing methods on synthetic and real data examples.

Detection of crossing white matter fibers with high-order tensors and rank-k decompositions

Fundamental to high angular resolution diffusion imaging (HARDI), is the estimation of a positive-semidefinite orientation distribution function (ODF) and extracting the diffusion properties (e.g., fiber directions). In this work we show that these two goals can be achieved efficiently by using homogeneous polynomials to represent the ODF in the spherical deconvolution approach, as was proposed in the Cartesian Tensor-ODF (CT-ODF) formulation. Based on this formulation we first suggest an estimation method for positive-semidefinite ODF by solving a linear programming problem that does not require special parameterization of the ODF. We also propose a rank-k tensor decomposition, known as CP decomposition, to extract the fibers information from the estimated ODF. We show that this decomposition is superior to the fiber direction estimation via ODF maxima detection as it enables one to reach the full fiber separation resolution of the estimation technique. We assess the accuracy of this new framework by applying it to synthetic and experimentally obtained HARDI data.

Groupwise Registration and Atlas Construction of 4th-Order Tensor Fields Using the ℝ Riemannian Metric

Registration of Diffusion-Weighted MR Images (DW-MRI) can be achieved by registering the corresponding 2nd-order Diffusion Tensor Images (DTI). However, it has been shown that higher-order diffusion tensors (e.g. order-4) outperform the traditional DTI in approximating complex fiber structures such as fiber crossings. In this paper we present a novel method for unbiased group-wise non-rigid registration and atlas construction of 4th-order diffusion tensor fields. To the best of our knowledge there is no other existing method to achieve this task. First we define a metric on the space of positive-valued functions based on the Riemannian metric of real positive numbers (denoted by ℝ(+)). Then, we use this metric in a novel functional minimization method for non-rigid 4th-order tensor field registration. We define a cost function that accounts for the 4th-order tensor re-orientation during the registration process and has analytic derivatives with respect to the transformation parameters. Finally, the tensor field atlas is computed as the minimizer of the variance defined using the Riemannian metric. We quantitatively compare the proposed method with other techniques that register scalar-valued or diffusion tensor (rank-2) representations of the DWMRI.