Diffusion Maps Clustering for Magnetic Resonance Q-Ball Imaging Segmentation

International audienceWhite matter fiber clustering aims to get insight about anatomical structures in order to generate atlases, perform clear visualizations, and compute statistics across subjects, all important and current neuroimaging problems. In this work, we present a diffusion maps clustering method applied to diffusion MRI in order to segment complex white matter fiber bundles. It is well known that diffusion tensor imaging (DTI) is restricted in complex fiber regions with crossings and this is why recent high-angular resolution diffusion imaging (HARDI) such as Q-Ball imaging (QBI) has been introduced to overcome these limitations. QBI reconstructs the diffusion orientation distribution function (ODF), a spherical function that has its maxima agreeing with the underlying fiber populations. In this paper, we use a spherical harmonic ODF representation as input to the diffusion maps clustering method.We first show the advantage of using diffusion maps clustering over classical methods such as N-Cuts and Laplacian eigenmaps. In particular, our ODF diffusion maps requires a smaller number of hypothesis from the input data, reduces the number of artifacts in the segmentation, and automatically exhibits the number of clusters segmenting the Q-Ball image by using an adaptive scalespace parameter.We also show that our ODF diffusion maps clustering can reproduce published results using the diffusion tensor (DT) clustering with N-Cuts on simple synthetic images without crossings. On more complex data with crossings, we show that our ODF-based method succeeds to separate fiber bundles and crossing regions whereas the DT-based methods generate artifacts and exhibit wrong number of clusters. Finally, we show results on a real-brain dataset where we segment well-known fiber bundles

Mapping Topographic Structure in White Matter Pathways with Level Set Trees

Fiber tractography on diffusion imaging data offers rich potential for describing white matter pathways in the human brain, but characterizing the spatial organization in these large and complex data sets remains a challenge. We show that level set trees---which provide a concise representation of the hierarchical mode structure of probability density functions---offer a statistically-principled framework for visualizing and analyzing topography in fiber streamlines. Using diffusion spectrum imaging data collected on neurologically healthy controls (N=30), we mapped white matter pathways from the cortex into the striatum using a deterministic tractography algorithm that estimates fiber bundles as dimensionless streamlines. Level set trees were used for interactive exploration of patterns in the endpoint distributions of the mapped fiber tracks and an efficient segmentation of the tracks that has empirical accuracy comparable to standard nonparametric clustering methods. We show that level set trees can also be generalized to model pseudo-density functions in order to analyze a broader array of data types, including entire fiber streamlines. Finally, resampling methods show the reliability of the level set tree as a descriptive measure of topographic structure, illustrating its potential as a statistical descriptor in brain imaging analysis. These results highlight the broad applicability of level set trees for visualizing and analyzing high-dimensional data like fiber tractography output

Spectral Clustering en IRM de diffusion pour Retrouver les Faisceaux de la Matière Blanche

White matter fiber clustering allows to get insight about anatomical structures in order to generate atlases, perform clear visualizations and compute statistics across subjects, all important and current neuroimaging problems. In this work, we present a Diffusion Maps clustering method applied to diffusion MRI in order to cluster and segment complex white matter fiber bundles. It is well-known that Diffusion Tensor Imaging (DTI) is restricted in complex fiber regions with crossings and this is why recent High Angular Resolution Diffusion Imaging (HARDI) such has Q-Ball Imaging (QBI) have been introduced to overcome these limitations. QBI reconstructs the diffusion orientation distribution function (ODF), a spherical function that has its maxima agreeing with the underlying fiber populations. In this paper, we introduce the usage of the Diffusion Maps technique and show how it can be used to directly cluster set of fiber tracts, that could be obtained through a streamline tractography for instance, and how it can also help in segmenting fields of ODF images, obtained through a linear and regularized ODF estimation algorithm based on a spherical harmonics representation of the Q-Ball data. We first show the advantage of using Diffusion Maps clustering over classical methods such as N-Cuts and Laplacian Eigenmaps in both cases. In particular, our Diffusion Maps requires a smaller number of hypothesis from the input data, reduces the number of artifacts in fiber tract clustering and ODF image segmentation and automatically exhibits the number of clusters in both cases by using an adaptive scale-space parameter. We also show that our ODF Diffusion Maps clustering can reproduce published results using the diffusion tensor (DT) clustering with N-Cuts on simple synthetic images without crossings. On more complex data with crossings, we show that our ODF-based method succeeds to separate fiber bundles and crossing regions whereas the DT-based methods generate artifacts and exhibit wrong number of clusters. Finally, we illustrate the potential of our approach on a real brain dataset where we successfully segment well-known fiber bundles

Hitting the right target : noninvasive localization of the subthalamic nucleus motor part for specific deep brain stimulation

Deep brain stimulation of the subthalamic nucleus (STN) has gained momentum as a therapy for advanced Parkinson’s disease. The stimulation effectively alleviates the patients’ typical motor symptoms on a long term, but can give rise to cognitive and psychiatric adverse effects as well. Based on primate studies, the STN has been divided into three functionally different parts, which were distinguished by their afferent and efferent connections. The largest part is the motor area, followed by an associative and a limbic area. The serious adverse effects on cognition and behavior occurring after deep brain stimulation are assumed to be caused by electrical current spread to the associative and limbic areas of the STN. Therefore, selective stimulation of the motor part of the STN seems crucial, both to obtain the best possible therapeutic effect on the motor symptoms and to minimize the debilitating effects on cognition and behavior. However, current medical imaging techniques do not yet facilitate the required accurate identification of the STN itself, let alone its different functional areas. The final target for DBS is still often adjusted using intraoperative electrophysiology. Therefore, in this thesis we aimed to improve imaging for deep brain stimulation using noninvasive MRI protocols, in order to identify the STN and its motor part. We studied the advantages and drawbacks of already available noninvasive methods to target the STN. This review did not lead to a straightforward conclusion; identification of the STN motor part remained an open question. In follow-up on this question, we investigated the possibility to distinguish the different functional STN parts based on their connectivity information. Three types of information were carefully analyzed in this thesis. First, we looked into the clustering of local diffusion information within the STN region. We visually inspected the complex diffusion profiles, derived from postmortem rat brain data with high angular resolution, and augmented this manual segmentation method using k-means and graph cuts clustering. Because the weighing of different orders of diffusion information in the traditionally used L2 norm on the orientation distribution functions (ODFs) remained an open issue, we developed a specialized distance measure, the so-called Sobolev norm. This norm does not only take into account the amplitudes of the diffusion profiles, but also their extrema. We showed it to perform better than the L2 norm on synthetic phantom data and real brain (thalamus) data. The research done on this topic facilitates better classification by clustering of gray matter structures in the (deep) brain. Secondly, we were the first to analyze the STN’s full structural connectivity, based on probabilistic fiber tracking in diffusion MRI data of healthy volunteers. The results correspond well to topical literature on STN projections. Furthermore, we assessed the structural connectivity per voxel of the STN seed region and discovered a gradient in connectivity to the premotor cortex within the STN. While going from the medial to the lateral part of the STN, the connectivity increases, confirming the expected lateral location of the STN motor part. Finally, the connectivity analysis produced evidence for the existence of a "hyperdirect" pathway between the motor cortex and the STN in humans, which is very useful for future research into stimulation targets. The results of these experiments indicate that it is possible to find the motor part of the STN as specific target for deep brain stimulation using structural connectivity information acquired in a noninvasive way. Third and last, we studied functional connectivity using resting state functional MRI data of healthy volunteers. The resulting significant clusters provided us with the first complete description of the STN’s resting state functional connectivity, which corresponds with the expectations based on available literature. Moreover, we performed a reverse regression procedure with the average time series signals in motor and limbic areas as principal regressors. The results were analyzed for each STN voxel separately and also showed mediolateral gradients in functional connectivity within the STN. The lateral STN part exhibited more motor connectivity, while the medial part seemed to be more functionally connected to limbic brain areas, as described in neuronal tracer studies. These results show that functional connectivity analysis also is a viable noninvasive method to find the motor part of the STN. The work on noninvasive MRI methods for identification of the STN and its functional parts, as presented in this thesis, thus contributes to future specific stimulation of the motor part of the STN for deep brain stimulation in patients with Parkinson’s disease. This may help to maximize the motor effects and minimize severe cognitive and psychiatric side effects

Manifold-driven Grouping of Skeletal Muscle Fibers

In this report, we present a manifold clustering method for the classification of fibers obtained from diffusion tensor images (DTI) of the human skeletal muscle. To this end, we propose the use of angular Hilbertian metrics between multivariate normal distributions to define a family of distances between tensors that we generalize to fibers. The obtained metrics between fiber tracts encompasses both diffusion and localization information. As far as clustering is concerned, we use two methods. The first approach is based on diffusion maps and k-means clustering in the spectral embedding space. The second approach uses a linear programming formulation of prototype-based clustering. This formulation allows for classification over manifolds without the necessity to embed the data in low dimensional spaces and determines automatically the number of clusters. The experimental validation of the proposed framework is done using a manually annotated significant dataset of DTI of the calf muscle for healthy and diseased subjects

Improving the Tractography Pipeline: on Evaluation, Segmentation, and Visualization

Recent advances in tractography allow for connectomes to be constructed in vivo. These have applications for example in brain tumor surgery and understanding of brain development and diseases. The large size of the data produced by these methods lead to a variety problems, including how to evaluate tractography outputs, development of faster processing algorithms for tractography and clustering, and the development of advanced visualization methods for verification and exploration. This thesis presents several advances in these fields. First, an evaluation is presented for the robustness to noise of multiple commonly used tractography algorithms. It employs a Monte–Carlo simulation of measurement noise on a constructed ground truth dataset. As a result of this evaluation, evidence for obustness of global tractography is found, and algorithmic sources of uncertainty are identified. The second contribution is a fast clustering algorithm for tractography data based on k–means and vector fields for representing the flow of each cluster. It is demonstrated that this algorithm can handle large tractography datasets due to its linear time and memory complexity, and that it can effectively integrate interrupted fibers that would be rejected as outliers by other algorithms. Furthermore, a visualization for the exploration of structural connectomes is presented. It uses illustrative rendering techniques for efficient presentation of connecting fiber bundles in context in anatomical space. Visual hints are employed to improve the perception of spatial relations. Finally, a visualization method with application to exploration and verification of probabilistic tractography is presented, which improves on the previously presented Fiber Stippling technique. It is demonstrated that the method is able to show multiple overlapping tracts in context, and correctly present crossing fiber configurations

Characterising population variability in brain structure through models of whole-brain structural connectivity

Models of whole-brain connectivity are valuable for understanding neurological function. This thesis seeks to develop an optimal framework for extracting models of whole-brain connectivity from clinically acquired diffusion data. We propose new approaches for studying these models. The aim is to develop techniques which can take models of brain connectivity and use them to identify biomarkers or phenotypes of disease. The models of connectivity are extracted using a standard probabilistic tractography algorithm, modified to assess the structural integrity of tracts, through estimates of white matter anisotropy. Connections are traced between 77 regions of interest, automatically extracted by label propagation from multiple brain atlases followed by classifier fusion. The estimates of tissue integrity for each tract are input as indices in 77x77 ”connectivity” matrices, extracted for large populations of clinical data. These are compared in subsequent studies. To date, most whole-brain connectivity studies have characterised population differences using graph theory techniques. However these can be limited in their ability to pinpoint the locations of differences in the underlying neural anatomy. Therefore, this thesis proposes new techniques. These include a spectral clustering approach for comparing population differences in the clustering properties of weighted brain networks. In addition, machine learning approaches are suggested for the first time. These are particularly advantageous as they allow classification of subjects and extraction of features which best represent the differences between groups. One limitation of the proposed approach is that errors propagate from segmentation and registration steps prior to tractography. This can cumulate in the assignment of false positive connections, where the contribution of these factors may vary across populations, causing the appearance of population differences where there are none. The final contribution of this thesis is therefore to develop a common co-ordinate space approach. This combines probabilistic models of voxel-wise diffusion for each subject into a single probabilistic model of diffusion for the population. This allows tractography to be performed only once, ensuring that there is one model of connectivity. Cross-subject differences can then be identified by mapping individual subjects’ anisotropy data to this model. The approach is used to compare populations separated by age and gender