Study of Connectivity in the Brain Using the Full Diffusion Tensor from MRI

3D stochastic completion fields for mapping connectivity in diffusion MRI

The 2D stochastic completion field algorithm, introduced by Williams and Jacobs [1], [2], uses a directional random walk to model the prior probability of completion curves in the plane. This construct has had a powerful impact in computer vision, where it has been used to compute the shapes of likely completion curves between edge fragments in visual imagery. Motivated by these developments, we extend the algorithm to 3D, using a spherical harmonics basis to achieve a rotation invariant computational solution to the Fokker-Planck equation describing the evolution of the probability density function underlying the model. This provides a principled way to compute 3D completion patterns and to derive connectivity measures for orientation data in 3D, as arises in 3D tracking, motion capture, and medical imaging. We demonstrate the utility of the approach for the particular case of diffusion magnetic resonance imaging, where we derive connectivity maps for synthetic data, on a physical phantom and on an in vivo high angular resolution diffusion image of a human brain.

A Hough transform global probabilistic approach to multiple-subject diffusion MRI tractography

A global probabilistic fiber tracking approach based on the voting process provided by the Hough transform is introduced in this work. The proposed framework tests candidate 3D curves in the volume, assigning to each one a score computed from the diffusion images, and then selects the curves with the highest scores as the potential anatomical connections. The algorithm avoids local minima by performing an exhaustive search at the desired resolution. The technique is easily extended to multiple subjects, considering a single representative volume where the registered high-angular resolution diffusion images (HARDI) from all the subjects are non-linearly combined, thereby obtaining population-representative tracts. The tractography algorithm is run only once for the multiple subjects, and no tract alignment is necessary. We present experimental results on HARDI volumes, ranging from simulated and 1.5T physical phantoms to 7T and 4T human brain and 7T monkey brain datasets.

Rotation invariant completion fields for mapping diffusion MRI connectivity

Partial differential equations have been successfully used for fibre tractography and for mapping connectivity indices in the brain. However, the current implementation of methods which require 3D orientation to be tracked can suffer from serious shortcomings when invariance to 3D rotation is desired. In this paper we focus on the 3D stochastic completion field and introduce a new methodology to solve the underlying PDE in a manner that achieves rotation invariance. The key idea is to use spherical harmonics to solve the Fokker-Planck equation representing the evolution of the probability density function of a 3D directional random walk. We validate the new approach by presenting improved connectivity indices on synthetic data, on the MICCAI 2009 Fibre Cup phantom and on a biological phantom comprised of two rat spinal chords in a crossing configuration.

Diffusion simulation-based fiber tracking using time-of-arrival maps: a comparison with standard methods

OBJECT

We propose a new tracking method based on time-of-arrival (TOA) maps derived from simulated diffusion processes.

MATERIALS AND METHODS

The proposed diffusion simulation-based tracking consists of three steps that are successively evaluated on small overlapping sub-regions in a diffusion tensor field. First, the diffusion process is simulated for several time steps. Second, a TOA map is created to store simulation results for the individual time steps that are required for the tract reconstruction. Third, the fiber pathway is reconstructed on the TOA map and concatenated between neighboring sub-regions. This new approach is compared with probabilistic and streamline tracking. All methods are applied to synthetic phantom data for an easier evaluation of their fiber reconstruction quality.

RESULTS

The comparison of the tracking results did show severe problems for the streamline approach in the reconstruction of crossing fibers, for example. The probabilistic method was able to resolve the crossing, but could not handle strong curvature. The new diffusion simulation-based tracking could reconstruct all problematic fiber constellations.

CONCLUSION

The proposed diffusion simulation-based tracking method used the whole tensor information of a neighborhood of voxels and is, therefore, able to handle problematic tracking situations better than established methods.

A physical model for DT-MRI based connectivity map computation

In this study we address the problem of extracting a robust connectivity metric for brain white matter. We defined the connectivity problem as an energy minimization task, by associating the DT-field to a physical system composed of nodes and springs, with their constants defined as a function of local structure. Using a variational approach we formulated a fast and stable map evolution, which utilizes an anisotropic kernel smoothing scheme equivalent to a diffusion PDE. The proposed method provides connectivity maps that correlate with normal anatomy on real patient data.

White matter fiber tractography via anisotropic diffusion simulation in the human brain

A novel approach to noninvasively tracing brain white matter fiber tracts is presented using diffusion tensor magnetic resonance imaging (DT-MRI). This technique is based on successive anisotropic diffusion simulations over the human brain, which are utilized to construct three dimensional diffusion fronts. The fiber pathways are determined by evaluating the distance and orientation from the fronts to their corresponding diffusion seeds. Synthetic and real DT-MRI data are employed to demonstrate the tracking scheme. It is shown that the synthetic tracts are accurately replicated, and several major white matter fiber pathways can be reproduced noninvasively, with the tract branching being allowed. Since simulating the diffusion process, which is truly a physical phenomenon reflecting the underlying architecture of cerebral tissues, makes full use of the diffusion tensor data, including both the magnitude and orientation information, the proposed approach is expected to enhance robustness and reliability in white matter fiber reconstruction.

Analysis of MR diffusion weighted images

Diffusion-weighted MR images provide information that is present in no other imaging modality. Whilst some of this information may be appreciated visually in diffusion weighted images, much of it may be extracted only with the aid of data post-processing. This review summarizes the methods available for interpreting diffusion weighted imaging (DWI) information using the diffusion tensor and other models of the DWI signal. This is followed by an overview of methods that allow the estimation of fibre tract orientation and that provide estimates of the routes and degree of anatomical cerebral white matter connectivity.

DT-MRI denoising and neuronal fiber tracking

Diffusion tensor imaging can provide the fundamental information required for viewing structural connectivity. However, robust and accurate acquisition and processing algorithms are needed to accurately map the nerve connectivity. In this paper, we present a novel algorithm for extracting and visualizing the fiber tracts in the CNS, specifically in the brain. The automatic fiber tract mapping problem will be solved in two phases, namely a data smoothing phase and a fiber tract mapping phase. In the former, smoothing of the diffusion-weighted data (prior to tensor calculation) is achieved via a weighted TV-norm minimization, which strives to smooth while retaining all relevant detail. For the fiber tract mapping, a smooth 3D vector field indicating the dominant anisotropic direction at each spatial location is computed from the smoothed data. Neuronal fibers are then traced by calculating the integral curves of this vector field. Results are expressed using three modes of visualization: (1) Line integral convolution produces an oriented texture which shows fiber pathways in a planar slice of the data. (2) A streamtube map is generated to present a 3D view of fiber tracts. Additional information, such as degree of anisotropy, can be encoded in the tube radius, or by using color. (3) A particle system form of visualization is also presented. This mode of display allows for interactive exploration of fiber connectivity with no additional preprocessing.

Estimating distributed anatomical connectivity using fast marching methods and diffusion tensor imaging

A method is presented for determining paths of anatomical connection between regions of the brain using magnetic resonance diffusion tensor information. Level set theory, applied using fast marching methods, is used to generate three-dimensional time of arrival maps, from which connection paths between brain regions may be identified. The method is demonstrated in the normal brain and it is shown that major white matter tracts may be elucidated and that multiple connections and tract branching are allowed. Maps of connectivity between brain regions are also determined. Four options are described for estimating the degree of connectivity between regions.