New Approaches to Estimation of White Matter Connectivity in Diffusion Tensor MRI: Elliptic PDEs and Geodesics in a Tensor-Warped Space

Conductance-Based Structural Brain Connectivity in Aging and Dementia

Background: Structural brain connectivity has been shown to be sensitive to the changes that the brain undergoes during Alzheimer's disease (AD) progression. Methods: In this work, we used our recently proposed structural connectivity quantification measure derived from diffusion magnetic resonance imaging, which accounts for both direct and indirect pathways, to quantify brain connectivity in dementia. We analyzed data from the second phase of Alzheimer's Disease Neuroimaging Initiative and third release in the Open Access Series of Imaging Studies data sets to derive relevant information for the study of the changes that the brain undergoes in AD. We also compared these data sets to the Human Connectome Project data set, as a reference, and eventually validated externally on two cohorts of the European DTI Study in Dementia database. Results: Our analysis shows expected trends of mean conductance with respect to age and cognitive scores, significant age prediction values in aging data, and regional effects centered among subcortical regions, and cingulate and temporal cortices. Discussion: Results indicate that the conductance measure has prediction potential, especially for age, that age and cognitive scores largely overlap, and that this measure could be used to study effects such as anticorrelation in structural connections. Impact statement This work presents a methodology and a set of analyses that open new possibilities in the study of healthy and pathological aging. The methodology used here is sensitive to direct and indirect pathways in deriving brain connectivity measures from diffusion-weighted magnetic resonance imaging, and therefore provides information that many state-of-the-art methods do not account for. As a result, this technique may provide the research community with ways to detect subtle effects of healthy aging and Alzheimer's disease.

Automatic, Age Consistent Reconstruction of the Corpus Callosum Guided by Coherency From In Utero Diffusion-Weighted MRI

Reconstruction of white matter connectivity in the fetal brain from in utero diffusion-weighted magnetic resonance imaging (MRI) faces many challenges, including subject motion, small anatomical scale, and limited image resolution and signal. These issues are compounded by the need to track significant changes in structural connectivity throughout development. We present an automated method for improved reliability and completeness of tract extraction across a wide range of gestational ages, based on the geometry of coherent patterns in streamline tractography, and apply it to the reconstruction of the corpus callosum. This method, focused specifically at addressing the challenges of fetal brain imaging, avoids depending on a tractography atlas, and handles variations in size, shape, and tissue properties of developing brains, both between subjects and across ages. Although tractography from in utero MRI generally suffers from a significant number of misleading and missing pathways, we demonstrate the feasibility of extracting the coherent bundle of the corpus callosum while avoiding inappropriate diversions into other tracts.

Global Diffusion Tractography by Simulated Annealing

OBJECTIVE

Our goal is to develop a robust global tractography method for cardiac diffusion imaging.

METHODS

A graph is stretched over the whole myocardium to represent the fiber structure, and the solutions are minima of a graph energy measuring the fidelity to the data along with the fiber density and curvature. The optimization is performed by a variant of simulated annealing that offers increased design freedom without sacrificing theoretical convergence guarantees.

RESULTS

Numerical experiments on synthetic and real data demonstrate the capability of our tractography algorithm to deal with low angular resolution, highly noisy data. In particular, our algorithm outperforms the Bayesian model-based algorithm of Reisert et al. (NeuroImage, vol. 54, no. 2, 2011) and the graph-based algorithm of Frindel et al. (Magn. Reson. Med., vol. 64, no. 4, 2010) at the noise levels typical of in vivo imaging.

CONCLUSION

The proposed algorithm avoids the drawbacks of local techniques and is very robust to noise, which makes it a promising tool for in vivo diffusion imaging of moving organs.

SIGNIFICANCE

Our approach is global in terms of both the fiber structure representation and the minimization problem. It also allows us to adjust the trajectory density by simply changing the vertex-lattice spacing in the graph model, a desirable feature for multiresolution tractography analysis.

Active delineation of Meyer's loop using oriented priors through MAGNEtic tractography (MAGNET)

Streamline tractography algorithms infer connectivity from diffusion MRI (dMRI) by following diffusion directions which are similarly aligned between neighboring voxels. However, not all white matter (WM) fascicles are organized in this manner. For example, Meyer's loop is a highly curved portion of the optic radiation (OR) that exhibits a narrow turn, kissing and crossing pathways, and changes in fascicle dispersion. From a neurosurgical perspective, damage to Meyer's loop carries a potential risk of inducing vision deficits to the patient, especially during temporal lobe resection surgery. To prevent such impairment, achieving an accurate delineation of Meyer's loop with tractography is thus of utmost importance. However, current algorithms tend to under-estimate the full extent of Meyer's loop, mainly attributed to the aforementioned rule for connectivity which requires a direction to be chosen across a field of orientations. In this article, it was demonstrated that MAGNEtic Tractography (MAGNET) can benefit Meyer's loop delineation by incorporating anatomical knowledge of the expected fiber orientation to overcome local ambiguities. A new ROI-mechanism was proposed which supplies additional information to streamline reconstruction algorithms by the means of oriented priors. Their results showed that MAGNET can accurately generate Meyer's loop in all of our 15 child subjects (8 males; mean age 10.2 years ± 3.1). It effectively improved streamline coverage when compared with deterministic tractography, and significantly reduced the distance between the anterior-most portion of Meyer's loop and the temporal pole by 16.7 mm on average, a crucial landmark used for preoperative planning of temporal lobe surgery. Hum Brain Mapp 38:509-527, 2017. © 2016 Wiley Periodicals, Inc.

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.

Adaptive Riemannian metrics for improved geodesic tracking of white matter

We present a new geodesic approach for studying white matter connectivity from diffusion tensor imaging (DTI). Previous approaches have used the inverse diffusion tensor field as a Riemannian metric and constructed white matter tracts as geodesics on the resulting manifold. These geodesics have the desirable property that they tend to follow the main eigenvectors of the tensors, yet still have the flexibility to deviate from these directions when it results in lower costs. While this makes such methods more robust to noise, it also has the serious drawback that geodesics tend to deviate from the major eigenvectors in high-curvature areas in order to achieve the shortest path. In this paper we formulate a modification of the Riemannian metric that results in geodesics adapted to follow the principal eigendirection of the tensor even in high-curvature regions. We show that this correction can be formulated as a simple scalar field modulation of the metric and that the appropriate variational problem results in a Poisson's equation on the Riemannian manifold. We demonstrate that the proposed method results in improved geodesics using both synthetic and real DTI data.

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.

Tumor invasion margin on the Riemannian space of brain fibers

Gliomas are one of the most challenging tumors to treat or control locally. One of the main challenges is determining which areas of the apparently normal brain contain glioma cells, as gliomas are known to infiltrate for several centimeters beyond the clinically apparent lesion visualized on standard CT or MRI. To ensure that radiation treatment encompasses the whole tumour, including the cancerous cells not revealed by MRI, doctors treat a volume of brain extending 2cm out from the margin of the visible tumour. This expanded volume often includes healthy, non-cancerous brain tissue. Knowing that glioma cells preferentially spread along nerve fibers, we propose the use of a geodesic distance on the Riemannian manifold of brain fibers to replace the Euclidean distance used in clinical practice and to correctly identify the tumor invasion margin. To compute the geodesic distance we use actual DTI data from patients with glioma and compare our predicted growth with follow-up MRI scans. Results show improvement in predicting the invasion margin when using the geodesic distance as opposed to the 2cm conventional Euclidean distance.

Measures for pathway analysis in brain white matter using diffusion tensor images

In this paper we discuss new measures for connectivity analysis of brain white matter, using MR diffusion tensor imaging. Our approach is based on Riemannian geometry, the viability of which has been demonstrated by various researchers in foregoing work. In the Riemannian framework bundles of axons are represented by geodesics on the manifold. Here we do not discuss methods to compute these geodesics, nor do we rely on the availability of geodesics. Instead we propose local measures which are directly computable from the local DTI data, and which enable us to preselect viable or exclude uninteresting seed points for the potentially time consuming extraction of geodesics. If geodesics are available, our measures can be readily applied to these as well. We consider two types of geodesic measures. One pertains to the connectivity saliency of a geodesic, the second to its stability with respect to local spatial perturbations. For the first type of measure we consider both differential as well as integral measures for characterizing a geodesic's saliency either locally or globally. (In the latter case one needs to be in possession of the geodesic curve, in the former case a single tangent vector suffices.) The second type of measure is intrinsically local, and turns out to be related to a well known tensor in Riemannian geometry.

Fast and accurate connectivity analysis between functional regions based on DT-MRI

Diffusion tensor and functional MRI data provide insight into function and structure of the human brain. However, connectivity analysis between functional areas is still a challenge when using traditional fiber tracking techniques. For this reason, alternative approaches incorporating the entire tensor information have emerged. Based on previous research employing pathfinding for connectivity analysis, we present a novel search grid and an improved cost function which essentially contributes to more precise paths. Additionally, implementation aspects are considered making connectivity analysis very efficient which is crucial for surgery planning. In comparison to other algorithms, the presented technique is by far faster while providing connections of comparable quality. The clinical relevance is demonstrated by reconstructed connections between motor and sensory speech areas in patients with lesions located in between.

A volumetric approach to quantifying region-to-region white matter connectivity in diffusion tensor MRI

In this paper we present a volumetric approach for quantitatively studying white matter connectivity from diffusion tensor magnetic resonance imaging (DT-MRI). The proposed method is based on a minimization of path cost between two regions, defined as the integral of local costs that are derived from the full tensor data along the path. We solve the minimal path problem using a Hamilton-Jacobi formulation of the problem and a new, fast iterative method that computes updates on the propagating front of the cost function at every point. The solutions for the fronts emanating from the two initial regions are combined, giving a voxel-wise connectivity measurement of the optimal paths between the regions that pass through those voxels. The resulting high-connectivity voxels provide a volumetric representation of the white matter pathway between the terminal regions. We quantify the tensor data along these pathways using nonparametric regression of the tensors and of derived measures as a function of path length. In this way we can obtain volumetric measures on white-matter tracts between regions without any explicit integration of tracts. We demonstrate the proposed method on several fiber tracts from DT-MRI data of the normal human brain.

Finsler tractography for white matter connectivity analysis of the cingulum bundle

In this paper, we present a novel approach for the segmentation of white matter tracts based on Finsler active contours. This technique provides an optimal measure of connectivity, explicitly segments the connecting fiber bundle, and is equipped with a metric which is able to utilize the directional information of high angular resolution data. We demonstrate the effectiveness of the algorithm for segmenting the cingulum bundle.

A Hamilton-Jacobi-Bellman approach to high angular resolution diffusion tractography

This paper describes a new framework for white matter tractography in high angular resolution diffusion data. A direction-dependent local cost is defined based on the diffusion data for every direction on the unit sphere. Minimum cost curves are determined by solving the Hamilton-Jacobi-Bellman using an efficient algorithm. Classical costs based on the diffusion tensor field can be seen as a special case. While the minimum cost (or equivalently the travel time of a particle moving along the curve) and the anisotropic front propagation frameworks are related, front speed is related to particle speed through a Legendre transformation which can severely impact anisotropy information for front propagation techniques. Implementation details and results on high angular diffusion data show that this method can successfully take advantage of the increased angular resolution in high b-value diffusion weighted data despite lower signal to noise ratio.

Capturing intraoperative deformations: research experience at Brigham and Women's Hospital

During neurosurgical procedures the objective of the neurosurgeon is to achieve the resection of as much diseased tissue as possible while achieving the preservation of healthy brain tissue. The restricted capacity of the conventional operating room to enable the surgeon to visualize critical healthy brain structures and tumor margin has lead, over the past decade, to the development of sophisticated intraoperative imaging techniques to enhance visualization. However, both rigid motion due to patient placement and nonrigid deformations occurring as a consequence of the surgical intervention disrupt the correspondence between preoperative data used to plan surgery and the intraoperative configuration of the patient's brain. Similar challenges are faced in other interventional therapies, such as in cryoablation of the liver, or biopsy of the prostate. We have developed algorithms to model the motion of key anatomical structures and system implementations that enable us to estimate the deformation of the critical anatomy from sequences of volumetric images and to prepare updated fused visualizations of preoperative and intraoperative images at a rate compatible with surgical decision making. This paper reviews the experience at Brigham and Women's Hospital through the process of developing and applying novel algorithms for capturing intraoperative deformations in support of image guided therapy.