Brain tractography using Q-ball imaging and graph theory: Improved connectivities through fibre crossings via a model-based approach

Methodological considerations on diffusion MRI tractography in infants aged 0-2 years: a scoping review

Diffusion MRI (dMRI) enables studying the complex architectural organization of the brain's white matter (WM) through virtual reconstruction of WM fiber tracts (tractography). Despite the anticipated clinical importance of applying tractography to study structural connectivity and tract development during the critical period of rapid infant brain maturation, detailed descriptions on how to approach tractography in young infants are limited. Over the past two decades, tractography from infant dMRI has mainly been applied in research settings and focused on diffusion tensor imaging (DTI). Only few studies used techniques superior to DTI in terms of disentangling information on the brain's organizational complexity, including crossing fibers. While more advanced techniques may enhance our understanding of the intricate processes of normal and abnormal brain development and extensive knowledge has been gained from application on adult scans, their applicability in infants has remained underexplored. This may partially be due to the higher technical requirements versus the need to limit scan time in young infants. We review various previously described methodological practices for tractography in the infant brain (0-2 years-of-age) and provide recommendations to optimize advanced tractography approaches to enable more accurate reconstructions of the brain WM's complexity. IMPACT: Diffusion tensor imaging is the technique most frequently used for fiber tracking in the developing infant brain but is limited in capability to disentangle the complex white matter organization. Advanced tractography techniques allow for reconstruction of crossing fiber bundles to better reflect the brain's complex organization. Yet, they pose practical and technical challenges in the fast developing young infant's brain. Methods on how to approach advanced tractography in the young infant's brain have hardly been described. Based on a literature review, recommendations are provided to optimize tractography for the developing infant brain, aiming to advance early diagnosis and neuroprotective strategies.

Cellular Automata Tractography: Fast Geodesic Diffusion MR Tractography and Connectivity Based Segmentation on the GPU

Geodesic based tractography on diffusion magnetic resonance data is a method to devise long distance connectivities among the brain regions. In this study, cellular automata technique is applied to the geodesic tractography problem and the algorithm is implemented on a graphics processing unit. Cellular automaton based method is preferable to current techniques due to its parallel nature and ability to solve the connectivity based segmentation problem with the same computational complexity, which has important applications in neuroimaging. An application to prior-less tracking and connectivity based segmentation of corpus callosum fibers is presented as an example. A geodesic tractography based corpus callosum atlas is provided, which reveals high projections to the cortical language areas. The developed method not only allows fast computation especially for segmentation but also provides a powerful and intuitive framework, suitable to derive new algorithms to perform connectivity calculations and allowing novel applications.

Development of Brain Structural Networks Over Age 8: A Preliminary Study Based on Diffusion Weighted Imaging

Brain structural network changes provide key information about the aging process of the brain. Unfortunately, there has yet to be a detailed characterization of these structural networks across different age groups. Efforts to classify these networks have also been hampered by their reliance on technically limited traditional methods, which are unable to track multiple fiber orientations within a voxel and consequently are prone to false detection and artifacts. In this study, a newly developed Ensemble Average Propagator (EAP) based probabilistic tractography method was applied to construct a structural network, with the strength of the link between any two brain functional regions estimated according to the alignment of the EAP along connecting pathways. Age-related changes in the topological organization of human brain structural networks were thereby characterized across a broad age range (ages 8-75 years). The data from 48 healthy participants were divided into four age groups (Group 1 aged 8-15 years; Group 2 aged 25-35 years; Group 3 aged 45-55 years; and, Group 4 aged 65-75 years; N = 12 per group). We found that the brain structural network continues to strengthen during later adolescence and adulthood, through the first 20-30 years of life. Older adults, aged 65-75, had a significantly less optimized topological organization in their structural network, with decreased global efficiency and increased path lengths versus subjects in other groups. This study suggests that probabilistic tractography based on EAP provides a reliable method to construct macroscale structural connectivity networks to capture the age-associated changes of brain structures.

Construction of brain structural connectivity network using a novel integrated algorithm based on ensemble average propagator

An important task for neuroscience is to accurately construct structural connectivity network of human brain. Tractography constructed based on high angular resolution diffusion imaging (HARDI) provides valuable information of human brain structural connections. Existing algorithms, mainly categorized as deterministic or probabilistic, come with inherent limitations (e.g., fiber direction uncertainty induced by noise, or anatomically unreasonable connections and heavy computational cost). In this study, a novel integrated algorithm was proposed to construct brain structural connectivity network by incorporating the deterministic path planning and probabilistic connection strength estimation, based on ensemble average propagator (EAP). We first estimated EAPs from multi-shell samples using the spherical polar Fourier imaging (SPFI), and then extracted diffusion orientations coinciding with neural fiber tracts. Only under angular constraints, the deterministic path planning algorithm was subsequently used to find all reasonable pathways between pairwise white matter (WM) voxels in different regions of interest (ROIs). Consequently, a train of consecutive WM voxels along each of the identified pathways was determined, and the connection strength of these pathways was computed by integrating their EAP alignment over a solid angle. The connection strength of a pair of WM voxels was assigned as the connection strength with the largest connection possibility. Finally, the connection strength between two ROIs was calculated as the sum of all the connection probabilities of each pair of WM voxels in the ROIs. A comparison against voxel-graph based probabilistic tractography method was performed on Fibercup phantom dataset, and the results demonstrated that the proposed method can produce better structural connection and is more computationally economical. Lastly, three datasets from Human Connectome Project (HCP) S1200 group were tested and their structural connectivity networks were constructed for topological analysis. The results showed great consistency in network metrics with previous WM network studies in healthy adults.

Decoding the microstructural correlate of diffusion MRI

Diffusion imaging has evolved considerably over the past decade. While it provides valuable information about the structural connectivity at the macro- and mesoscopic scale, bridging the gap to the microstructure at the level of single nerve fibers poses an enormous challenge. This is particularly true for the human brain with its large size, its large white-matter volume and availability of histological techniques for studying human whole-brain sections and subsequent 3D reconstruction. Classic post-mortem techniques for studying the fiber architecture of the brain, such as myeloarchitectonic staining or dye tracing, are complemented by novel histological approaches, such as 3D polarized light imaging or optical coherence tomography, enabling unique insight into the fiber architecture from large fiber bundles within deep white matter to single nerve fibers in the cortex. The present review discusses the benefits and challenges of these latest developments in comparison with the classic techniques, with particular focus on the mutual exchange between in vivo and post-mortem diffusion imaging and post-mortem microstructural approaches for understanding the wiring of the brain across different scales.

Building connectomes using diffusion MRI: why, how and but

Why has diffusion MRI become a principal modality for mapping connectomes in vivo? How do different image acquisition parameters, fiber tracking algorithms and other methodological choices affect connectome estimation? What are the main factors that dictate the success and failure of connectome reconstruction? These are some of the key questions that we aim to address in this review. We provide an overview of the key methods that can be used to estimate the nodes and edges of macroscale connectomes, and we discuss open problems and inherent limitations. We argue that diffusion MRI-based connectome mapping methods are still in their infancy and caution against blind application of deep white matter tractography due to the challenges inherent to connectome reconstruction. We review a number of studies that provide evidence of useful microstructural and network properties that can be extracted in various independent and biologically relevant contexts. Finally, we highlight some of the key deficiencies of current macroscale connectome mapping methodologies and motivate future developments.

Diffusion MRI fiber tractography of the brain

The ability of fiber tractography to delineate non-invasively the white matter fiber pathways of the brain raises possibilities for clinical applications and offers enormous potential for neuroscience. In the last decade, fiber tracking has become the method of choice to investigate quantitative MRI parameters in specific bundles of white matter. For neurosurgeons, it is quickly becoming an invaluable tool for the planning of surgery, allowing for visualization and localization of important white matter pathways before and even during surgery. Fiber tracking has also claimed a central role in the field of "connectomics," a technique that builds and studies comprehensive maps of the complex network of connections within the brain, and to which significant resources have been allocated worldwide. Despite its unique abilities and exciting applications, fiber tracking is not without controversy, in particular when it comes to its interpretation. As neuroscientists are eager to study the brain's connectivity, the quantification of tractography-derived "connection strengths" between distant brain regions is becoming increasingly popular. However, this practice is often frowned upon by fiber-tracking experts. In light of this controversy, this paper provides an overview of the key concepts of tractography, the technical considerations at play, and the different types of tractography algorithm, as well as the common misconceptions and mistakes that surround them. We also highlight the ongoing challenges related to fiber tracking. While recent methodological developments have vastly increased the biological accuracy of fiber tractograms, one should be aware that, even with state-of-the-art techniques, many issues that severely bias the resulting structural "connectomes" remain unresolved.

White Matter Fiber Tractography Using Nonuniform Rational B-Splines Curve Fitting

The study of neural connectivity has grown rapidly in the past decade. Revealing brain anatomical connection improves not only clinical measures but also cognition understanding. In order to achieve this goal, we have to track neural fiber pathways first. Aiming to estimate 3D fiber pathways more accurately from orientation distribution function (ODF) fields, we presented a novel tracking method based on nonuniform rational B-splines (NURBS) curve fitting. First, we constructed ODF fields from high angular resolution diffusion imaging (HARDI) datasets using diffusion orientation transform (DOT) method. Second, under the angular and length constraints, the consecutive diffusion directions were extracted along each fiber pathway starting from a seed voxel. Finally, after the coordinates of the control points and their corresponding weights were determined, NURBS curve fitting was employed to track fiber pathways. The performance of the proposal has been evaluated on the tractometer phantom and real brain datasets. Based on several measure metrics, the resulting fiber pathways show promising anatomic consistency.

Tracking and validation techniques for topographically organized tractography

Topographic regularity of axonal connections is commonly understood as the preservation of spatial relationships between nearby neurons and is a fundamental structural property of the brain. In particular the retinotopic mapping of the visual pathway can even be quantitatively computed. Inspired from this previously untapped anatomical knowledge, we propose a novel tractography method that preserves both topographic and geometric regularity. We make use of parameterized curves with Frenet-Serret frame and introduce a highly flexible mechanism for controlling geometric regularity. At the same time, we incorporate a novel local data support term in order to account for topographic organization. Unifying geometry with topographic regularity, we develop a Bayesian framework for generating highly organized streamlines that accurately follow neuroanatomy. We additionally propose two novel validation techniques to quantify topographic regularity. In our experiments, we studied the results of our approach with respect to connectivity, reproducibility and topographic regularity aspects. We present both qualitative and quantitative comparisons of our technique against three algorithms from MRtrix3. We show that our method successfully generates highly organized fiber tracks while capturing bundle anatomy that are geometrically challenging for other approaches.

Newly observed anterior thalamocortical fiber of the thalamus using 7.0T super-resolution magnetic resonance tractography and its implications for the classical Papez circuit

Here, we have employed recently developed super-resolution tractography using 7.0T-MRI to analyze the fine structures involved in thalamocortical connections, something that has proved difficult using conventional techniques. We detail a newly observed thalamocortical pathway connecting the anterior nucleus of the thalamus and the cingulate cortex not via the internal capsule but via the septal area. The observed pathway is believed to be a classical pathway of the Papez circuit but had not been previously identified.

Analytic tractography: A closed-form solution for estimating local white matter connectivity with diffusion MRI

White matter structures composed of myelinated axons in the living human brain are primarily studied by diffusion-weighted MRI (dMRI). These long-range projections are typically characterized in a two-step process: dMRI signal is used to estimate the orientation of axon segments within each voxel, then these local orientations are linked together to estimate the spatial extent of putative white matter bundles. Tractography, the process of tracing bundles across voxels, either requires computationally expensive (probabilistic) simulations to model uncertainty in fiber orientation or ignores it completely (deterministic). Furthermore, simulation necessarily generates a finite number of trajectories, introducing "simulation error" to trajectory estimates. Here we introduce a method to analytically (via a closed-form solution) take an orientation distribution function (ODF) from each voxel and calculate the probabilities that a trajectory projects from a voxel into each directly adjacent voxels. We validate our method by demonstrating experimentally that probabilistic simulations converge to our analytically computed transition probabilities at the voxel level as the number of simulated seeds increases. We then show that our method accurately calculates the ground-truth transition probabilities from a publicly available phantom dataset. As a demonstration, we incorporate our analytic method for voxel transition probabilities into the Voxel Graph framework, creating a quantitative framework for assessing white matter structure, which we call "analytic tractography". The long-range connectivity problem is reduced to finding paths in a graph whose adjacency structure reflects voxel-to-voxel analytic transition probabilities. We demonstrate that this approach performs comparably to the current most widely-used probabilistic and deterministic approaches at a fraction of the computational cost. We also demonstrate that analytic tractography works on multiple diffusion sampling schemes, reconstruction method or parameters used to define paths. Open source software compatible with popular dMRI reconstruction software is provided.

Connectome sensitivity or specificity: which is more important?

Connectomes with high sensitivity and high specificity are unattainable with current axonal fiber reconstruction methods, particularly at the macro-scale afforded by magnetic resonance imaging. Tensor-guided deterministic tractography yields sparse connectomes that are incomplete and contain false negatives (FNs), whereas probabilistic methods steered by crossing-fiber models yield dense connectomes, often with low specificity due to false positives (FPs). Densely reconstructed probabilistic connectomes are typically thresholded to improve specificity at the cost of a reduction in sensitivity. What is the optimal tradeoff between connectome sensitivity and specificity? We show empirically and theoretically that specificity is paramount. Our evaluations of the impact of FPs and FNs on empirical connectomes indicate that specificity is at least twice as important as sensitivity when estimating key properties of brain networks, including topological measures of network clustering, network efficiency and network modularity. Our asymptotic analysis of small-world networks with idealized modular structure reveals that as the number of nodes grows, specificity becomes exactly twice as important as sensitivity to the estimation of the clustering coefficient. For the estimation of network efficiency, the relative importance of specificity grows linearly with the number of nodes. The greater importance of specificity is due to FPs occurring more prevalently between network modules rather than within them. These spurious inter-modular connections have a dramatic impact on network topology. We argue that efforts to maximize the sensitivity of connectome reconstruction should be realigned with the need to map brain networks with high specificity.

Estimating Fiber Orientation Distribution Functions in 3D-Polarized Light Imaging

Research of the human brain connectome requires multiscale approaches derived from independent imaging methods ideally applied to the same object. Hence, comprehensible strategies for data integration across modalities and across scales are essential. We have successfully established a concept to bridge the spatial scales from microscopic fiber orientation measurements based on 3D-Polarized Light Imaging (3D-PLI) to meso- or macroscopic dimensions. By creating orientation distribution functions (pliODFs) from high-resolution vector data via series expansion with spherical harmonics utilizing high performance computing and supercomputing technologies, data fusion with Diffusion Magnetic Resonance Imaging has become feasible, even for a large-scale dataset such as the human brain. Validation of our approach was done effectively by means of two types of datasets that were transferred from fiber orientation maps into pliODFs: simulated 3D-PLI data showing artificial, but clearly defined fiber patterns and real 3D-PLI data derived from sections through the human brain and the brain of a hooded seal.

Structural Brain Network: What is the Effect of LiFE Optimization of Whole Brain Tractography?

Structural brain networks constructed based on diffusion-weighted MRI (dMRI) have provided a systems perspective to explore the organization of the human brain. Some redundant and nonexistent fibers, however, are inevitably generated in whole brain tractography. We propose to add one critical step while constructing the networks to remove these fibers using the linear fascicle evaluation (LiFE) method, and study the differences between the networks with and without LiFE optimization. For a cohort of nine healthy adults and for 9 out of the 35 subjects from Human Connectome Project, the T 1-weighted images and dMRI data are analyzed. Each brain is parcellated into 90 regions-of-interest, whilst a probabilistic tractography algorithm is applied to generate the original connectome. The elimination of redundant and nonexistent fibers from the original connectome by LiFE creates the optimized connectome, and the random selection of the same number of fibers as the optimized connectome creates the non-optimized connectome. The combination of parcellations and these connectomes leads to the optimized and non-optimized networks, respectively. The optimized networks are constructed with six weighting schemes, and the correlations of different weighting methods are analyzed. The fiber length distributions of the non-optimized and optimized connectomes are compared. The optimized and non-optimized networks are compared with regard to edges, nodes and networks, within a sparsity range of 0.75-0.95. It has been found that relatively more short fibers exist in the optimized connectome. About 24.0% edges of the optimized network are significantly different from those in the non-optimized network at a sparsity of 0.75. About 13.2% of edges are classified as false positives or the possible missing edges. The strength and betweenness centrality of some nodes are significantly different for the non-optimized and optimized networks, but not the node efficiency. The normalized clustering coefficient, the normalized characteristic path length and the small-worldness are higher in the optimized network weighted by the fiber number than in the non-optimized network. These observed differences suggest that LiFE optimization can be a crucial step for the construction of more reasonable and more accurate structural brain networks.

Ensemble Tractography

Tractography uses diffusion MRI to estimate the trajectory and cortical projection zones of white matter fascicles in the living human brain. There are many different tractography algorithms and each requires the user to set several parameters, such as curvature threshold. Choosing a single algorithm with specific parameters poses two challenges. First, different algorithms and parameter values produce different results. Second, the optimal choice of algorithm and parameter value may differ between different white matter regions or different fascicles, subjects, and acquisition parameters. We propose using ensemble methods to reduce algorithm and parameter dependencies. To do so we separate the processes of fascicle generation and evaluation. Specifically, we analyze the value of creating optimized connectomes by systematically combining candidate streamlines from an ensemble of algorithms (deterministic and probabilistic) and systematically varying parameters (curvature and stopping criterion). The ensemble approach leads to optimized connectomes that provide better cross-validated prediction error of the diffusion MRI data than optimized connectomes generated using a single-algorithm or parameter set. Furthermore, the ensemble approach produces connectomes that contain both short- and long-range fascicles, whereas single-parameter connectomes are biased towards one or the other. In summary, a systematic ensemble tractography approach can produce connectomes that are superior to standard single parameter estimates both for predicting the diffusion measurements and estimating white matter fascicles.

Diffusion MRI and tractography opened a new avenue for studying white matter fascicles and their tissue properties in the living human brain. There are many different tractography methods, and each requires the user to set several parameters. A limitation of tractography is that the results depend on the selection of algorithms and parameters. Here, we analyze an ensemble method, Ensemble Tractography (ET), that reduces the effect of algorithm and parameter selection. ET creates a large set of candidate streamlines using an ensemble of algorithms and parameter values and then selects the streamlines with strong support from the data using a global fascicle evaluation method. Compared to single parameter connectomes, ET connectomes predict diffusion MRI signals better and cover a wider range of white matter volume. Importantly, ET connectomes include both short- and long-association fascicles, which are not typically found together in single-parameter connectomes.

Training shortest-path tractography: Automatic learning of spatial priors

Tractography is the standard tool for automatic delineation of white matter tracts from diffusion weighted images. However, the output of tractography often requires post-processing to remove false positives and ensure a robust delineation of the studied tract, and this demands expert prior knowledge. Here we demonstrate how such prior knowledge, or indeed any prior spatial information, can be automatically incorporated into a shortest-path tractography approach to produce more robust results. We describe how such a prior can be automatically generated (learned) from a population, and we demonstrate that our framework also retains support for conventional interactive constraints such as waypoint regions. We apply our approach to the open access, high quality Human Connectome Project data, as well as a dataset acquired on a typical clinical scanner. Our results show that the use of a learned prior substantially increases the overlap of tractography output with a reference atlas on both populations, and this is confirmed by visual inspection. Furthermore, we demonstrate how a prior learned on the high quality dataset significantly increases the overlap with the reference for the more typical yet lower quality data acquired on a clinical scanner. We hope that such automatic incorporation of prior knowledge and the obviation of expert interactive tract delineation on every subject, will improve the feasibility of large clinical tractography studies.

Strengths and weaknesses of state of the art fiber tractography pipelines--A comprehensive in-vivo and phantom evaluation study using Tractometer

Many different tractography approaches and corresponding isolated evaluation attempts have been presented over the last years, but a comparative and quantitative evaluation of tractography algorithms still remains a challenge, particularly in-vivo. The recently presented evaluation framework Tractometer is the first attempt to approach this challenge in a quantitative, comparative, persistent and open-access way. Tractometer is currently based on the evaluation of several global connectivity and tract-overlap metrics on hardware phantom data. The work presented in this paper focuses on extending Tractometer with a metric that enables the assessment of the local consistency of tractograms with the underlying image data that is not only applicable to phantom dataset but allows the quantitative and purely data-driven evaluation of in-vivo tractography. We furthermore present an extensive reference-based evaluation study of 25,000 tractograms obtained on phantom and in-vivo datasets using the presented local metric as well as all the methods already established in Tractometer. The experiments showed that the presented local metric successfully reflects the behavior of in-vivo tractography under different conditions and that it is consistent with the results of previous studies. Additionally our experiments enabled a multitude of conclusions with implications for fiber tractography in general, including recommendations regarding optimal choice of a local modeling technique, tractography algorithm, and parameterization, confirming and complementing the results of earlier studies.

The influence of construction methodology on structural brain network measures: A review

Structural brain networks based on diffusion MRI and tractography show robust attributes such as small-worldness, hierarchical modularity, and rich-club organization. However, there are large discrepancies in the reports about specific network measures. It is hypothesized that these discrepancies result from the influence of construction methodology. We surveyed the methodological options and their influences on network measures. It is found that most network measures are sensitive to the scale of brain parcellation, MRI gradient schemes and orientation model, and the tractography algorithm, which is in accordance with the theoretical analysis of the small-world network model. Different network weighting schemes represent different attributes of brain networks, which makes these schemes incomparable between studies. Methodology choice depends on the specific study objectives and a clear understanding of the pros and cons of a particular methodology. Because there is no way to eliminate these influences, it seems more practical to quantify them, optimize the methodologies, and construct structural brain networks with multiple spatial resolutions, multiple edge densities, and multiple weighting schemes.

Unraveling the multiscale structural organization and connectivity of the human brain: the role of diffusion MRI

The structural architecture and the anatomical connectivity of the human brain show different organizational principles at distinct spatial scales. Histological staining and light microscopy techniques have been widely used in classical neuroanatomical studies to unravel brain organization. Using such techniques is a laborious task performed on 2-dimensional histological sections by skilled anatomists possibly aided by semi-automated algorithms. With the recent advent of modern magnetic resonance imaging (MRI) contrast mechanisms, cortical layers and columns can now be reliably identified and their structural properties quantified post-mortem. These developments are allowing the investigation of neuroanatomical features of the brain at a spatial resolution that could be interfaced with that of histology. Diffusion MRI and tractography techniques, in particular, have been used to probe the architecture of both white and gray matter in three dimensions. Combined with mathematical network analysis, these techniques are increasingly influential in the investigation of the macro-, meso-, and microscopic organization of brain connectivity and anatomy, both in vivo and ex vivo. Diffusion MRI-based techniques in combination with histology approaches can therefore support the endeavor of creating multimodal atlases that take into account the different spatial scales or levels on which the brain is organized. The aim of this review is to illustrate and discuss the structural architecture and the anatomical connectivity of the human brain at different spatial scales and how recently developed diffusion MRI techniques can help investigate these.

Human brain asymmetry in microstructural connectivity demonstrated by diffusional kurtosis imaging

Structural asymmetry of whole brain white matter (WM) pathways, i.e., the connectome, has been demonstrated using fiber tractography based on diffusion tensor imaging (DTI). However, DTI-based tractography fails to resolve axonal fiber bundles that intersect within an imaging voxel, and therefore may not fully characterize the extent of asymmetry. The goal of this study was to assess structural asymmetry with tractography based on diffusional kurtosis imaging (DKI), which improves upon DTI-based tractography by delineating intravoxel crossing fibers. DKI images were obtained from 42 healthy subjects. By using automatic segmentation, gray matter (GM) was parcellated into anatomically defined regions of interest (ROIs). WM pathways were reconstructed with both DKI- and DTI-based tractography. The connectivity between the ROIs was quantified with the streamlines connecting the ROIs. The asymmetry index (AI) was utilized to quantify hemispheric differences in the connectivity of cortical ROIs and of links interconnecting cortical ROIs. Our results demonstrated that leftward asymmetrical ROIs and links were observed in frontal, parietal, temporal lobes, and insula. Rightward asymmetrical ROI and links were observed in superior frontal lobe, cingulate cortex, fusiform, putamen, and medial temporal lobe. Interestingly, these observed structural asymmetries were incompletely identified with DTI-based tractography. These results suggest that DKI-based tractography can improve the identification of asymmetrical connectivity patterns, thereby serving as an additional tool in the evaluation of the structural bases of functional lateralization.

Structural degree predicts functional network connectivity: a multimodal resting-state fMRI and MEG study

Communication between neuronal populations in the human brain is characterized by complex functional interactions across time and space. Recent studies have demonstrated that these functional interactions depend on the underlying structural connections at an aggregate level. Multiple imaging modalities can be used to investigate the relation between the structural connections between brain regions and their functional interactions at multiple timescales. We investigated if consistent modality-independent functional interactions take place between brain regions, and whether these can be accounted for by underlying structural properties. We used functional MRI (fMRI) and magnetoencephalography (MEG) recordings from a population of healthy adults together with a previously described structural network. A high overlap in resting-state functional networks was found in fMRI and especially alpha band MEG recordings. This overlap was characterized by a strongly interconnected functional core network in temporo-posterior brain regions. Anatomically realistically coupled neural mass models revealed that this strongly interconnected functional network emerges near the threshold for global synchronization. Most importantly, this functional core network could be explained by a trade-off between the product of the degrees of structurally-connected regions and the Euclidean distance between them. For both fMRI and MEG, the product of the degrees of connected regions was the most important predictor for functional network connectivity. Therefore, irrespective of the modality, these results indicate that a functional core network in the human brain is especially shaped by communication between high degree nodes of the structural network.

Diffusion tensor imaging and tractography of the human language pathways: moving into the clinical realm

The functional correlates of anatomical derangements are of interest to the neurological clinician. Diffusion tensor tractography (DTT) is a relatively new tool in the arsenal of functional neuroimaging, by which to assess white matter tracts in the brain. While much import has been given to tracking corticospinal tracts in neurological disease, studying language pathway interconnections using DTT has largely remained in the research realm. Hardware and software advances have allowed this tool to ease into clinical practice, with several radiologists, neurologists, and neurosurgeons now familiar with its applications. DTT images, although visually appealing, are founded in mathematical equations and assumptions, and require a more than basic understanding of principles and limitations before they can be integrated into routine clinical practice. Cognitive pathways like that of language, that are normally hard to assess and especially more so when pathologically affected, have been at the receiving end of several opposing and often controversial hypotheses, and the past decade has seen the clarification, validation or rejection of several of these by the in vivo charting of functional connectivity using DTT. The focus of this review is to illustrate DTT of the language pathways with emphasis on practical considerations, clinical applications, and limitations.

Fast approximate stochastic tractography

Many different probabilistic tractography methods have been proposed in the literature to overcome the limitations of classical deterministic tractography: (i) lack of quantitative connectivity information; and (ii) robustness to noise, partial volume effects and selection of seed region. However, these methods rely on Monte Carlo sampling techniques that are computationally very demanding. This study presents an approximate stochastic tractography algorithm (FAST) that can be used interactively, as opposed to having to wait several minutes to obtain the output after marking a seed region. In FAST, tractography is formulated as a Markov chain that relies on a transition tensor. The tensor is designed to mimic the features of a well-known probabilistic tractography method based on a random walk model and Monte-Carlo sampling, but can also accommodate other propagation rules. Compared to the baseline algorithm, our method circumvents the sampling process and provides a deterministic solution at the expense of partially sacrificing sub-voxel accuracy. Therefore, the method is strictly speaking not stochastic, but provides a probabilistic output in the spirit of stochastic tractography methods. FAST was compared with the random walk model using real data from 10 patients in two different ways: 1. the probability maps produced by the two methods on five well-known fiber tracts were directly compared using metrics from the image registration literature; and 2. the connectivity measurements between different regions of the brain given by the two methods were compared using the correlation coefficient ρ. The results show that the connectivity measures provided by the two algorithms are well-correlated (ρ = 0.83), and so are the probability maps (normalized cross correlation 0.818 ± 0.081). The maps are also qualitatively (i.e., visually) very similar. The proposed method achieves a 60x speed-up (7 s vs. 7 min) over the Monte Carlo sampling scheme, therefore enabling interactive probabilistic tractography: the user can quickly modify the seed region if he is not satisfied with the output without having to wait on average 7 min.

Three-dimensional interactive and stereotactic human brain atlas of white matter tracts

We present a human brain atlas of white matter (WM) tracts containing 40 major tracts, which is three-dimensional (3D), segmented, labeled, interactive, stereotactic and correlated to structure and vasculature. We consider: (1) WM accuracy by correlating WM tracts to underlying neuroanatomy and quantifying them; (2) balance between realism and completeness by processing a sequence of track volumes generated for various parameters with the increasing track number to enable a tract "shape convergence". MPRAGE and DTI in 64 directions of the same subject were acquired on 3 Tesla. The method has three steps: DTI-MPRAGE registration, 3D tract generation from DTI, to WM reconstruction from MPRAGE to parcellation into 17 components. 82 track volumes were generated for a wide spectrum of parameter values: Fractional Anisotropy threshold in [0.0125, 0.55] and trajectory angle lower than 45°, 60°, 65°, 70°, 75°, 80°, 85°, 90°. For each tract, a sequence of track volumes was processed to create/edit contours delineating this tract to achieve its shape convergence. The parcellated tracts were grouped into commissures, associations, projections and posterior fossa tracts, and labeled following Terminologia Anatomica. To facilitate that, a dedicated tract editor is developed which processes multiple track volumes, handles tracts in three representations (tracks, contours, envelopes); provides editing/visualization simultaneously on axial, coronal, sagittal planes; enables tract labeling and coloring; and provides numerous tools (track counting, smoothing and length thresholding; representation conversion and saving; structural atlas support). A stereotactic tract atlas along with parcellated WM was developed to explore in real-time any individual tract or their groups along with surrounding neuroanatomy.

Fasciculography: robust prior-free real-time normalized volumetric neural tract parcellation

Fiber tracking in diffusion tensor magnetic resonance images (DTIs) reveals 3-D structural connectivity of the brain conveniently and thus is a viable tool for investigating neural differences. Unfortunately, local noise, image artifacts and numerical tracking errors during integration-based techniques are cumulative. Prematurely terminated fibers and under-sampled fiber bundles result in incomplete reconstruction of white matter fiber tracts and hence incorrect anatomical measurements. Quantitative cross-subject tract analysis, which is critical for abnormality detection, is complicated by inefficient and inaccurate tract reconstruction and normalization from fiber bundles. Because of the above problems, we propose a parcellation method that aims for lower sensitivity to initialization and local orientation error by directly segmenting full white matter tracts (Fasciculography), rather than reconstructing individual curves, from diffusion tensor fields. A fast, robust volumetric, and intrinsically normalized solution is achieved by noise-filtering using a generic parametrized tract model to prevent premature tract termination. At the same time, orientation information reduces the search space, significantly speeding up the tract parcellation process with less human intervention. Detailed comparisons against streamline tracking, shortest-path tracking, and nonrigid registration using synthetic and real DTIs confirmed the superior properties of Fasciculography. Since a normalized tract can be delineated interactively in a just few seconds using the proposed method, accurate high volume tract comparisons become feasible.

Tractography: where do we go from here?

Diffusion tractography offers enormous potential for the study of human brain anatomy. However, as a method to study brain connectivity, tractography suffers from limitations, as it is indirect, inaccurate, and difficult to quantify. Despite these limitations, appropriate use of tractography can be a powerful means to address certain questions. In addition, while some of tractography's limitations are fundamental, others could be alleviated by methodological and technological advances. This article provides an overview of diffusion magnetic resonance tractography methods with a focus on how future advances might address challenges in measuring brain connectivity. Parts of this review are somewhat provocative, in the hope that they may trigger discussions possibly lacking in a field where the apparent simplicity of the methods (compared to their functional magnetic resonance imaging counterparts) can hide some fundamental issues that ultimately hinder the interpretation of findings, and cast doubt as to what tractography can really teach us about human brain anatomy.

Quantifying the link between anatomical connectivity, gray matter volume and regional cerebral blood flow: an integrative MRI study

Background

In the graph theoretical analysis of anatomical brain connectivity, the white matter connections between regions of the brain are identified and serve as basis for the assessment of regional connectivity profiles, for example, to locate the hubs of the brain. But regions of the brain can be characterised further with respect to their gray matter volume or resting state perfusion. Local anatomical connectivity, gray matter volume and perfusion are traits of each brain region that are likely to be interdependent, however, particular patterns of systematic covariation have not yet been identified.

Methodology/Principal Findings

We quantified the covariation of these traits by conducting an integrative MRI study on 23 subjects, utilising a combination of Diffusion Tensor Imaging, Arterial Spin Labeling and anatomical imaging. Based on our hypothesis that local connectivity, gray matter volume and perfusion are linked, we correlated these measures and particularly isolated the covariation of connectivity and perfusion by statistically controlling for gray matter volume. We found significant levels of covariation on the group- and regionwise level, particularly in regions of the Default Brain Mode Network.

Conclusions/Significance

Connectivity and perfusion are systematically linked throughout a number of brain regions, thus we discuss these results as a starting point for further research on the role of homology in the formation of functional connectivity networks and on how structure/function relationships can manifest in the form of such trait interdependency.

A Bayesian model of shape and appearance for subcortical brain segmentation

Automatic segmentation of subcortical structures in human brain MR images is an important but difficult task due to poor and variable intensity contrast. Clear, well-defined intensity features are absent in many places along typical structure boundaries and so extra information is required to achieve successful segmentation. A method is proposed here that uses manually labelled image data to provide anatomical training information. It utilises the principles of the Active Shape and Appearance Models but places them within a Bayesian framework, allowing probabilistic relationships between shape and intensity to be fully exploited. The model is trained for 15 different subcortical structures using 336 manually-labelled T1-weighted MR images. Using the Bayesian approach, conditional probabilities can be calculated easily and efficiently, avoiding technical problems of ill-conditioned covariance matrices, even with weak priors, and eliminating the need for fitting extra empirical scaling parameters, as is required in standard Active Appearance Models. Furthermore, differences in boundary vertex locations provide a direct, purely local measure of geometric change in structure between groups that, unlike voxel-based morphometry, is not dependent on tissue classification methods or arbitrary smoothing. In this paper the fully-automated segmentation method is presented and assessed both quantitatively, using Leave-One-Out testing on the 336 training images, and qualitatively, using an independent clinical dataset involving Alzheimer's disease. Median Dice overlaps between 0.7 and 0.9 are obtained with this method, which is comparable or better than other automated methods. An implementation of this method, called FIRST, is currently distributed with the freely-available FSL package.

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.

Conserved and variable architecture of human white matter connectivity

Whole-brain network analysis of diffusion imaging tractography data is an important new tool for quantification of differential connectivity patterns across individuals and between groups. Here we investigate both the conservation of network architectural properties across methodological variation and the reproducibility of individual architecture across multiple scanning sessions. Diffusion spectrum imaging (DSI) and diffusion tensor imaging (DTI) data were both acquired in triplicate from a cohort of healthy young adults. Deterministic tractography was performed on each dataset and inter-regional connectivity matrices were then derived by applying each of three widely used whole-brain parcellation schemes over a range of spatial resolutions. Across acquisitions and preprocessing streams, anatomical brain networks were found to be sparsely connected, hierarchical, and assortative. They also displayed signatures of topo-physical interdependence such as Rentian scaling. Basic connectivity properties and several graph metrics consistently displayed high reproducibility and low variability in both DSI and DTI networks. The relative increased sensitivity of DSI to complex fiber configurations was evident in increased tract counts and network density compared with DTI. In combination, this pattern of results shows that network analysis of human white matter connectivity provides sensitive and temporally stable topological and physical estimates of individual cortical structure across multiple spatial scales.