Tracking and validation techniques for topographically organized tractography

Surface-Based Probabilistic Fiber Tracking in Superficial White Matter

The short association fibers or U-fibers travel in the superficial white matter (SWM) beneath the cortical layer. While the U-fibers play a crucial role in various brain disorders, there is a lack of effective tools to reconstruct their highly curved trajectory from diffusion MRI (dMRI). In this work, we propose a novel surface-based framework for the probabilistic tracking of fibers on the triangular mesh representation of the SWM. By deriving a closed-form solution to transform the spherical harmonics (SPHARM) coefficients of 3D fiber orientation distributions (FODs) to local coordinate systems on each triangle, we develop a novel approach to project the FODs onto the tangent space of the SWM. After that, we utilize parallel transport to realize the intrinsic propagation of streamlines on SWM following probabilistically sampled fiber directions. Our intrinsic and surface-based method eliminates the need to perform the necessary but challenging sharp turns in 3D compared with conventional volume-based tractography methods. Using data from the Human Connectome Project (HCP), we performed quantitative comparisons to demonstrate the proposed algorithm can more effectively reconstruct the U-fibers connecting the precentral and postcentral gyrus than previous methods. Quantitative validations were then performed on post-mortem MRIs to show the reconstructed U-fibers from our method more faithfully follow the SWM than volume-based tractography. Finally, we applied our algorithm to study the parietal U-fiber connectivity changes in autosomal dominant Alzheimer's disease (ADAD) patients and successfully detected significant associations between U-fiber connectivity and disease severity.

Supervised tractogram filtering using Geometric Deep Learning

A tractogram is a virtual representation of the brain white matter. It is composed of millions of virtual fibers, encoded as 3D polylines, which approximate the white matter axonal pathways. To date, tractograms are the most accurate white matter representation and thus are used for tasks like presurgical planning and investigations of neuroplasticity, brain disorders, or brain networks. However, it is a well-known issue that a large portion of tractogram fibers is not anatomically plausible and can be considered artifacts of the tracking procedure. With Verifyber, we tackle the problem of filtering out such non-plausible fibers using a novel fully-supervised learning approach. Differently from other approaches based on signal reconstruction and/or brain topology regularization, we guide our method with the existing anatomical knowledge of the white matter. Using tractograms annotated according to anatomical principles, we train our model, Verifyber, to classify fibers as either anatomically plausible or non-plausible. The proposed Verifyber model is an original Geometric Deep Learning method that can deal with variable size fibers, while being invariant to fiber orientation. Our model considers each fiber as a graph of points, and by learning features of the edges between consecutive points via the proposed sequence Edge Convolution, it can capture the underlying anatomical properties. The output filtering results highly accurate and robust across an extensive set of experiments, and fast; with a 12GB GPU, filtering a tractogram of 1M fibers requires less than a minute.

Reconstructing the somatotopic organization of the corticospinal tract remains a challenge for modern tractography methods

The corticospinal tract (CST) is a critically important white matter fiber tract in the human brain that enables control of voluntary movements of the body. The CST exhibits a somatotopic organization, which means that the motor neurons that control specific body parts are arranged in order within the CST. Diffusion magnetic resonance imaging (MRI) tractography is increasingly used to study the anatomy of the CST. However, despite many advances in tractography algorithms over the past decade, modern, state-of-the-art methods still face challenges. In this study, we compare the performance of six widely used tractography methods for reconstructing the CST and its somatotopic organization. These methods include constrained spherical deconvolution (CSD) based probabilistic (iFOD1) and deterministic (SD-Stream) methods, unscented Kalman filter (UKF) tractography methods including multi-fiber (UKF2T) and single-fiber (UKF1T) models, the generalized q-sampling imaging (GQI) based deterministic tractography method, and the TractSeg method. We investigate CST somatotopy by dividing the CST into four subdivisions per hemisphere that originate in the leg, trunk, hand, and face areas of the primary motor cortex. A quantitative and visual comparison is performed using diffusion MRI data (N = 100 subjects) from the Human Connectome Project. Quantitative evaluations include the reconstruction rate of the eight anatomical subdivisions, the percentage of streamlines in each subdivision, and the coverage of the white matter-gray matter (WM-GM) interface. CST somatotopy is further evaluated by comparing the percentage of streamlines in each subdivision to the cortical volumes for the leg, trunk, hand, and face areas. Overall, UKF2T has the highest reconstruction rate and cortical coverage. It is the only method with a significant positive correlation between the percentage of streamlines in each subdivision and the volume of the corresponding motor cortex. However, our experimental results show that all compared tractography methods are biased toward generating many trunk streamlines (ranging from 35.10% to 71.66% of total streamlines across methods). Furthermore, the coverage of the WM-GM interface in the largest motor area (face) is generally low (under 40%) for all compared tractography methods. Different tractography methods give conflicting results regarding the percentage of streamlines in each subdivision and the volume of the corresponding motor cortex, indicating that there is generally no clear relationship, and that reconstruction of CST somatotopy is still a large challenge. Overall, we conclude that while current tractography methods have made progress toward the well-known challenge of improving the reconstruction of the lateral projections of the CST, the overall problem of performing a comprehensive CST reconstruction, including clinically important projections in the lateral (hand and face areas) and medial portions (leg area), remains an important challenge for diffusion MRI tractography.

FASSt : Filtering via Symmetric Autoencoder for Spherical Superficial White Matter Tractography

Superficial white matter (SWM) plays an important role in functioning of the human brain, and it contains a large amount of cortico-cortical connections. However, the difficulties of generating complete and reliable U-fibers make SWM-related analysis lag behind relatively matured Deep white matter (DWM) analysis. With the aid of some newly proposed surface-based SWM tractography algorithms, we have developed a specialized SWM filtering method based on a symmetric variational autoencoder (VAE). In this work, we first demonstrate the advantage of the spherical representation and generate these spherical tracts using the triangular mesh and the registered spherical surface. We then introduce the Filtering via symmetric Autoencoder for Spherical Superficial White Matter tractography (FASSt) framework with a novel symmetric weights module to perform the filtering task in a latent space. We evaluate and compare our method with the state-of-the-art clustering-based method on diffusion MRI data from Human Connectome Project (HCP). The results show that our proposed method outperform these clustering methods and achieves excellent performance in groupwise consistency and topographic regularity.

Flow-based Geometric Interpolation of Fiber Orientation Distribution Functions

The fiber orientation distribution function (FOD) is an advanced model for high angular resolution diffusion MRI representing complex fiber geometry. However, the complicated mathematical structures of the FOD function pose challenges for FOD image processing tasks such as interpolation, which plays a critical role in the propagation of fiber tracts in tractography. In FOD-based tractography, linear interpolation is commonly used for numerical efficiency, but it is prone to generate false artificial information, leading to anatomically incorrect fiber tracts. To overcome this difficulty, we propose a flowbased and geometrically consistent interpolation framework that considers peak-wise rotations of FODs within the neighborhood of each location. Our method decomposes a FOD function into multiple components and uses a smooth vector field to model the flows of each peak in its neighborhood. To generate the interpolated result along the flow of each vector field, we develop a closed-form and efficient method to rotate FOD peaks in neighboring voxels and realize geometrically consistent interpolation of FOD components. By combining the interpolation results from each peak, we obtain the final interpolation of FODs. Experimental results on Human Connectome Project (HCP) data demonstrate that our method produces anatomically more meaningful FOD interpolations and significantly enhances tractography performance.

Anatomically informed multi-level fiber tractography for targeted virtual dissection

OBJECTIVES

Diffusion-weighted MRI can assist preoperative planning by reconstructing the trajectory of eloquent fiber pathways, such as the corticospinal tract (CST). However, accurate reconstruction of the full extent of the CST remains challenging with existing tractography methods. We suggest a novel tractography algorithm exploiting unused fiber orientations to produce more complete and reliable results.

METHODS

Our novel approach, referred to as multi-level fiber tractography (MLFT), reconstructs fiber pathways by progressively considering previously unused fiber orientations at multiple levels of tract propagation. Anatomical priors are used to minimize the number of false-positive pathways. The MLFT method was evaluated on synthetic data and in vivo data by reconstructing the CST while compared to conventional tractography approaches.

RESULTS

The radial extent of MLFT reconstructions is comparable to that of probabilistic reconstruction: [Formula: see text] for the left and [Formula: see text] for the right hemisphere according to Wilcoxon test, while achieving significantly higher topography preservation compared to probabilistic tractography: [Formula: see text].

DISCUSSION

MLFT provides a novel way to reconstruct fiber pathways by adding the capability of including branching pathways in fiber tractography. Thanks to its robustness, feasible reconstruction extent and topography preservation, our approach may assist in clinical practice as well as in virtual dissection studies.

Connectivity gradients on tractography data: Pipeline and example applications

Gray matter connectivity can be described in terms of its topographical organization, but the differential role of white matter connections underlying that organization is often unknown. In this study, we propose a method for unveiling principles of organization of both gray and white matter based on white matter connectivity as assessed using diffusion magnetic ressonance imaging (MRI) tractography with spectral embedding gradient mapping. A key feature of the proposed approach is its capacity to project the individual connectivity gradients it reveals back onto its input data in the form of projection images, allowing one to assess the contributions of specific white matter tracts to the observed gradients. We demonstrate the ability of our proposed pipeline to identify connectivity gradients in prefrontal and occipital gray matter. Finally, leveraging the use of tractography, we demonstrate that it is possible to observe gradients within the white matter bundles themselves. Together, the proposed framework presents a generalized way to assess both the topographical organization of structural brain connectivity and the anatomical features driving it.

The functional characterization of callosal connections

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The functional characterization of callosal connections is informed by anatomical data.

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Callosal connections play a conditional driving role depending on the brain state and behavioral demands.

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Callosal connections play a modulatory function, in addition to a driving role.

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The corpus callosum participates in learning and interhemispheric transfer of sensorimotor habits.

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The corpus callosum contributes to language processing and cognitive functions.

The brain operates through the synaptic interaction of distant neurons within flexible, often heterogeneous, distributed systems. Histological studies have detailed the connections between distant neurons, but their functional characterization deserves further exploration. Studies performed on the corpus callosum in animals and humans are unique in that they capitalize on results obtained from several neuroscience disciplines. Such data inspire a new interpretation of the function of callosal connections and delineate a novel road map, thus paving the way toward a general theory of cortico-cortical connectivity. Here we suggest that callosal axons can drive their post-synaptic targets preferentially when coupled to other inputs endowing the cortical network with a high degree of conditionality. This might depend on several factors, such as their pattern of convergence-divergence, the excitatory and inhibitory operation mode, the range of conduction velocities, the variety of homotopic and heterotopic projections and, finally, the state-dependency of their firing. We propose that, in addition to direct stimulation of post-synaptic targets, callosal axons often play a conditional driving or modulatory role, which depends on task contingencies, as documented by several recent studies.

Parallel Transport Tractography

Tractography is an important technique that allows the in vivo reconstruction of structural connections in the brain using diffusion MRI. Although tracking algorithms have improved during the last two decades, results of validation studies and international challenges warn about the reliability of tractography and point out the need for improved algorithms. In propagation-based tracking, connections have traditionally been modeled as piece-wise linear segments. In this work, we propose a novel propagation-based tracker that is capable of generating geometrically smooth ( C1 ) curves using parallel transport frames. Notably, our approach does not increase the complexity of the propagation problem that remains two-dimensional. Moreover, our tracker has a novel mechanism to reduce noise related propagation errors by incorporating topographic regularity of connections, a neuroanatomic property of many brain pathways. We ran extensive experiments and compared our approach against deterministic and other probabilistic algorithms. Our experiments on FiberCup and ISMRM 2015 challenge datasets as well as on 56 subjects of the Human Connectome Project show highly promising results both visually and quantitatively. Open-source implementations of the algorithm are shared publicly.

On the cortical connectivity in the macaque brain: A comparison of diffusion tractography and histological tracing data

Diffusion-weighted magnetic resonance imaging (DW-MRI) tractography is a non-invasive tool to probe neural connections and the structure of the white matter. It has been applied successfully in studies of neurological disorders and normal connectivity. Recent work has revealed that tractography produces a high incidence of false-positive connections, often from "bottleneck" white matter configurations. The rich literature in histological connectivity analysis studies in the macaque monkey enables quantitative evaluation of the performance of tractography algorithms. In this study, we use the intricate connections of frontal, cingulate, and parietal areas, well established by the anatomical literature, to derive a symmetrical histological connectivity matrix composed of 59 cortical areas. We evaluate the performance of fifteen diffusion tractography algorithms, including global, deterministic, and probabilistic state-of-the-art methods for the connectivity predictions of 1711 distinct pairs of areas, among which 680 are reported connected by the literature. The diffusion connectivity analysis was performed on a different ex-vivo macaque brain, acquired using multi-shell DW-MRI protocol, at high spatial and angular resolutions. Across all tested algorithms, the true-positive and true-negative connections were dominant over false-positive and false-negative connections, respectively. Moreover, three-quarters of streamlines had endpoints location in agreement with histological data, on average. Furthermore, probabilistic streamline tractography algorithms show the best performances in predicting which areas are connected. Altogether, we propose a method for quantitative evaluation of tractography algorithms, which aims at improving the sensitivity and the specificity of diffusion-based connectivity analysis. Overall, those results confirm the usefulness of tractography in predicting connectivity, although errors are produced. Many of the errors result from bottleneck white matter configurations near the cortical grey matter and should be the target of future implementation of methods.

Asymmetric fiber trajectory distribution estimation using streamline differential equation

Fiber orientation distribution estimation with diffusion magnetic resonance imaging (dMRI) is critical in white matter fiber tractography which is most commonly based on symmetric crossing structures. Ambiguous spatial correspondence between estimated diffusion directions and fiber geometry, such as asymmetric crossing, bending, fanning, or kissing, makes tractography challenging. Consequently, numerous tracts suggest intertwined connections in unexpected regions of the white matter or actually stop prematurely in the white matter. In this work, we propose a novel asymmetric fiber trajectory distribution (FTD) function defined on neighboring voxels based on a streamline differential equation from fluid mechanics. The spatial consistency with intra- and inter-voxel constraints is derived for FTD estimation by introducing the concept of divergence. At a local level, the FTD is a series of curve flows that minimize the energy function, characterizes the relations between fibers and joint fiber fragments within the same fiber bundle. Experiments are performed on FiberCup phantom, ISMRM 2015 Tractography challenge data, and in vivo brain dMRI data for qualitative and quantitative evaluations. Results show that our approach can reveal continuous asymmetric FTD details that are potentially useful for robust tractography.

Mapping Short Association Fibers in the Early Cortical Visual Processing Stream Using In Vivo Diffusion Tractography

Short association fibers (U-fibers) connect proximal cortical areas and constitute the majority of white matter connections in the human brain. U-fibers play an important role in brain development, function, and pathology but are underrepresented in current descriptions of the human brain connectome, primarily due to methodological challenges in diffusion magnetic resonance imaging (dMRI) of these fibers. High spatial resolution and dedicated fiber and tractography models are required to reliably map the U-fibers. Moreover, limited quantitative knowledge of their geometry and distribution makes validation of U-fiber tractography challenging. Submillimeter resolution diffusion MRI—facilitated by a cutting-edge MRI scanner with 300 mT/m maximum gradient amplitude—was used to map U-fiber connectivity between primary and secondary visual cortical areas (V1 and V2, respectively) in vivo. V1 and V2 retinotopic maps were obtained using functional MRI at 7T. The mapped V1–V2 connectivity was retinotopically organized, demonstrating higher connectivity for retinotopically corresponding areas in V1 and V2 as expected. The results were highly reproducible, as demonstrated by repeated measurements in the same participants and by an independent replication group study. This study demonstrates a robust U-fiber connectivity mapping in vivo and is an important step toward construction of a more complete human brain connectome.

Topographic Filtering of Tractograms as Vector Field Flows

While diffusion MRI (dMRI) is currently the most widely used in vivo imaging tool for studying brain connectivity, the biological validity of the tractography techniques based on dMRI is often debated. The wide presence of topographic regularity in various brain circuits provides a unique opportunity to examine and improve the reliability of tractography results. In this work, we develop a novel framework for the analysis of the topographic regularity of brain connectivity generated by modern FOD-based tractography techniques. Our method is based on the consistency between the mathematical property of smooth vector field flows and topographically regular fiber tracts. The main idea of our method is that we compute a principal vector field (PVF) for a given tractogram from the FODs by solving a Markov Random Field problem. By quantifying the consistency between each tract and the PVF, we develop a Vector Flow Deviation (VFD) measure and apply it to filter out topographically irregular tracts. In our experiments, we successfully applied our method to remove irregular fiber tracts in two fiber bundles with known connectopy: the visual pathway and the colossal motor pathway, which were reconstructed from the multi-shell diffusion imaging data of the Human Connectome Project (HCP). We also performed quantitative evaluation based on a G²SD distance proposed in previous work to quantitatively demonstrate the effectiveness of our filtering method.