H. Ertan Çetingül

The challenge of mapping the human connectome based on diffusion tractography

Tractography based on non-invasive diffusion imaging is central to the study of human brain connectivity. To date, the approach has not been systematically validated in ground truth studies. Based on a simulated human brain data set with ground truth tracts, we organized an open international tractography challenge, which resulted in 96 distinct submissions from 20 research groups. Here, we report the encouraging finding that most state-of-the-art algorithms produce tractograms containing 90% of the ground truth bundles (to at least some extent). However, the same tractograms contain many more invalid than valid bundles, and half of these invalid bundles occur systematically across research groups. Taken together, our results demonstrate and confirm fundamental ambiguities inherent in tract reconstruction based on orientation information alone, which need to be considered when interpreting tractography and connectivity results. Our approach provides a novel framework for estimating reliability of tractography and encourages innovation to address its current limitations.Though tractography is widely used, it has not been systematically validated. Here, authors report results from 20 groups showing that many tractography algorithms produce both valid and invalid bundles.

Tractography-based connectomes are dominated by false-positive connections

Fiber tractography based on non-invasive diffusion imaging is at the heart of connectivity studies of the human brain. To date, the approach has not been systematically validated in ground truth studies. Based on a simulated human brain dataset with ground truth white matter tracts, we organized an open international tractography challenge, which resulted in 96 distinct submissions from 20 research groups. While most state-of-the-art algorithms reconstructed 90% of ground truth bundles to at least some extent, on average they produced four times more invalid than valid bundles. About half of the invalid bundles occurred systematically in the majority of submissions. Our results demonstrate fundamental ambiguities inherent to tract reconstruction methods based on diffusion orientation information, with critical consequences for the approach of diffusion tractography in particular and human connectivity studies in general.

Segmentation of High Angular Resolution Diffusion MRI Using Sparse Riemannian Manifold Clustering

We address the problem of segmenting high angular resolution diffusion imaging (HARDI) data into multiple regions (or fiber tracts) with distinct diffusion properties. We use the orientation distribution function (ODF) to model diffusion and cast the ODF segmentation problem as a clustering problem in the space of ODFs. Our approach integrates tools from sparse representation theory and Riemannian geometry into a graph theoretic segmentation framework. By exploiting the Riemannian properties of the space of ODFs, we learn a sparse representation for each ODF and infer the segmentation by applying spectral clustering to a similarity matrix built from these representations. In cases where regions with similar (resp. distinct) diffusion properties belong to different (resp. same) fiber tracts, we obtain the segmentation by incorporating spatial and user-specified pairwise relationships into the formulation. Experiments on synthetic data evaluate the sensitivity of our method to image noise and to the concentration parameters, and show its superior performance compared to alternative methods when analyzing complex fiber configurations. Experiments on phantom and real data demonstrate the accuracy of the proposed method in segmenting simulated fibers and white matter fiber tracts of clinical importance.

Group action induced averaging for HARDI processing

We consider the problem of processing high angular resolution diffusion images described by orientation distribution functions (ODFs). Prior work showed that several processing operations, e.g., averaging, interpolation and filtering, can be reduced to averaging in the space of ODFs. However, this approach leads to anatomically erroneous results when the ODFs to be processed have very different orientations. To address this issue, we propose a group action induced distance for averaging ODFs, which leads to a novel processing framework on the spaces of orientation (the space of 3D rotations) and shape (the space of ODFs with the same orientation). Experiments demonstrate that our framework produces anatomically meaningful results.

Rotation invariant features for HARDI

Reducing the amount of information stored in diffusion MRI (dMRI) data to a set of meaningful and representative scalar values is a goal of much interest in medical imaging. Such features can have far reaching applications in segmentation, registration, and statistical characterization of regions of interest in the brain, as in comparing features between control and diseased patients. Currently, however, the number of biologically relevant features in dMRI is very limited. Moreover, existing features discard much of the information inherent in dMRI and embody several theoretical shortcomings. This paper proposes a new family of rotation invariant scalar features for dMRI based on the spherical harmonic (SH) representation of high angular resolution diffusion images (HARDI). These features describe the shape of the orientation distribution function extracted from HARDI data and are applicable to any reconstruction method that represents HARDI signals in terms of an SH basis. We further illustrate their significance in white matter characterization of synthetic, phantom and real HARDI brain datasets.

Simultaneous ODF estimation and tractography in HARDI

We consider the problem of tracking white matter fibers in high angular resolution diffusion imaging (HARDI) data while simultaneously estimating the local fiber orientation profile. Prior work showed that an unscented Kalman filter (UKF) can be used for this problem, yet existing algorithms employ parametric mixture models to represent water diffusion and to define the state space. To address this restrictive model dependency, we propose to extend the UKF to HARDI data modeled by orientation distribution functions (ODFs), a more generic diffusion model. We consider the spherical harmonic representation of the HARDI signal as the state, enforce nonnegativity of the ODFs, and perform tractography using the directions at which the ODFs attain their peaks. In simulations, our method outperforms filtered two-tensor tractography at different levels of noise by achieving a reduction in mean Chamfer error of 0.05 to 0.27 voxels; it also produced in vivo fiber tracking that is consistent with the neuroanatomy.

Sparse Riemannian manifold clustering for HARDI segmentation

We address the problem of segmenting high angular resolution diffusion images of the brain into cerebral regions corresponding to distinct white matter fiber bundles. We cast this problem as a manifold clustering problem in which distinct fiber bundles correspond to different submanifolds of the space of orientation distribution functions (ODFs). Our approach integrates tools from sparse representation theory into a graph theoretic segmentation framework. By exploiting the Riemannian properties of the space of ODFs, we learn a sparse representation for the ODF at each voxel and infer the segmentation by applying spectral clustering to a similarity matrix built from these representations. We evaluate the performance of our method via experiments on synthetic, phantom and real data.

Online agglomerative hierarchical clustering of neural fiber tracts

We consider the problem of clustering neural fiber pathways, produced from diffusion MRI data via tractography, into different bundles. Existing clustering methods often suffer from the burden of computing pairwise fiber (dis)similarities, which escalates quadratically as the number of fiber pathways increases. To address this challenge, we adopt the scenario of clustering data streams into the fiber clustering framework. Specifically, we propose to use an online hierarchical clustering method, which yields a framework similar to doing clustering while simultaneously performing tractography. We evaluate the proposed method through experiments on phantom and real diffusion MRI data. Experiments on phantom data evaluate the sensitivity of our method to initialization and show its superior performance compared with alternative methods. Experiments on real data demonstrate the accuracy in clustering selected white matter fiber tracts into anatomically consistent bundles.

Estimation of multimodal orientation distribution functions from cardiac MRI for tracking Purkinje fibers through branchings

The inclusion of the free-running Purkinje network in computational simulations provides a significant insight into understanding the mechanisms of cardiac pathophysiologies. However, its automatic extraction is challenging due to the presence of abundant local complexities. We thereby introduce a novel algorithm to track the Purkinje fibers in high resolution magnetic resonance (MR) images. Our formulation successively identifies local fiber orientations by using a nonlinear oriented filter. Specifically, the filter is used to compute several local profiles, from which one can estimate the orientation distribution function (ODF). The algorithm then determines the directions to be followed by detecting the modes of the local ODF using different spherical clustering methods. We quantitatively compare the accuracy of the tracked fibers with manually delineated anatomical structures.

An algebraic solution to rotation recovery in HARDI from correspondences of orientation distribution functions

We consider the problem of aligning high angular resolution diffusion images characterized by orientation distribution functions (ODFs). We cast this problem as an optimization problem where we seek the rotation that aligns the source and target ODFs. This rotation induces a linear transformation of the spherical harmonic coefficients of the ODFs, which can be parametrized by the rotation Euler angles. We propose an algebraic approach to estimate this transformation from a number of ODF correspondences. We evaluate the proposed method on synthetic ODFs as well as on a diffusion MR phantom dataset.