A framework based on spin glass models for the inference of anatomical connectivity from diffusion-weighted MR data - a technical review

Quantitative mapping of the brain's structural connectivity using diffusion MRI tractography: A review

Diffusion magnetic resonance imaging (dMRI) tractography is an advanced imaging technique that enables in vivo reconstruction of the brain's white matter connections at macro scale. It provides an important tool for quantitative mapping of the brain's structural connectivity using measures of connectivity or tissue microstructure. Over the last two decades, the study of brain connectivity using dMRI tractography has played a prominent role in the neuroimaging research landscape. In this paper, we provide a high-level overview of how tractography is used to enable quantitative analysis of the brain's structural connectivity in health and disease. We focus on two types of quantitative analyses of tractography, including: 1) tract-specific analysis that refers to research that is typically hypothesis-driven and studies particular anatomical fiber tracts, and 2) connectome-based analysis that refers to research that is more data-driven and generally studies the structural connectivity of the entire brain. We first provide a review of methodology involved in three main processing steps that are common across most approaches for quantitative analysis of tractography, including methods for tractography correction, segmentation and quantification. For each step, we aim to describe methodological choices, their popularity, and potential pros and cons. We then review studies that have used quantitative tractography approaches to study the brain's white matter, focusing on applications in neurodevelopment, aging, neurological disorders, mental disorders, and neurosurgery. We conclude that, while there have been considerable advancements in methodological technologies and breadth of applications, there nevertheless remains no consensus about the "best" methodology in quantitative analysis of tractography, and researchers should remain cautious when interpreting results in research and clinical applications.

Mapping Structural Connectivity Using Diffusion MRI: Challenges and Opportunities

Diffusion MRI-based tractography is the most commonly-used technique when inferring the structural brain connectome, i.e., the comprehensive map of the connections in the brain. The utility of graph theory-a powerful mathematical approach for modeling complex network systems-for analyzing tractography-based connectomes brings important opportunities to interrogate connectome data, providing novel insights into the connectivity patterns and topological characteristics of brain structural networks. When applying this framework, however, there are challenges, particularly regarding methodological and biological plausibility. This article describes the challenges surrounding quantitative tractography and potential solutions. In addition, challenges related to the calculation of global network metrics based on graph theory are discussed.Evidence Level: 5Technical Efficacy: Stage 1.

Modelling white matter in gyral blades as a continuous vector field

Many brain imaging studies aim to measure structural connectivity with diffusion tractography. However, biases in tractography data, particularly near the boundary between white matter and cortical grey matter can limit the accuracy of such studies. When seeding from the white matter, streamlines tend to travel parallel to the convoluted cortical surface, largely avoiding sulcal fundi and terminating preferentially on gyral crowns. When seeding from the cortical grey matter, streamlines generally run near the cortical surface until reaching deep white matter. These so-called “gyral biases” limit the accuracy and effective resolution of cortical structural connectivity profiles estimated by tractography algorithms, and they do not reflect the expected distributions of axonal densities seen in invasive tracer studies or stains of myelinated fibres. We propose an algorithm that concurrently models fibre density and orientation using a divergence-free vector field within gyral blades to encourage an anatomically-justified streamline density distribution along the cortical white/grey-matter boundary while maintaining alignment with the diffusion MRI estimated fibre orientations. Using in vivo data from the Human Connectome Project, we show that this algorithm reduces tractography biases. We compare the structural connectomes to functional connectomes from resting-state fMRI, showing that our model improves cross-modal agreement. Finally, we find that after parcellation the changes in the structural connectome are very minor with slightly improved interhemispheric connections (i.e, more homotopic connectivity) and slightly worse intrahemi-spheric connections when compared to tracers.

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.

Comparative neuroanatomy: Integrating classic and modern methods to understand association fibers connecting dorsal and ventral visual cortex

Comparative neuroanatomy studies improve understanding of brain structure and function and provide insight regarding brain development, evolution, and also what features of the brain are uniquely human. With modern methods such as diffusion MRI (dMRI) and quantitative MRI (qMRI), we are able to measure structural features of the brain with the same methods across human and non-human primates. In this review article, we discuss how recent dMRI measurements of vertical occipital connections in humans and macaques can be compared with previous findings from invasive anatomical studies that examined connectivity, including relatively forgotten classic strychnine neuronography studies. We then review recent progress in understanding the neuroanatomy of vertical connections within the occipitotemporal cortex by combining modern quantitative MRI and classical histological measurements in human and macaque. Finally, we a) discuss current limitations of dMRI and tractography and b) consider potential paths for future investigations using dMRI and tractography for comparative neuroanatomical studies of white matter tracts between species. While we focus on vertical association connections in visual cortex in the present paper, this same approach can be applied to other white matter tracts. Similar efforts are likely to continue to advance our understanding of the neuroanatomical features of the brain that are shared across species, as well as to distinguish the features that are uniquely human.

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.

Modelfree global tractography

Tractography based on diffusion-weighted MRI investigates the large scale arrangement of the neurite fibers in brain white matter. It is usually assumed that the signal is a convolution of a fiber specific response function (FRF) with a fiber orientation distribution (FOD). The FOD is the focus of tractography. While in the past the FRF was estimated beforehand and was usually assumed to be fix, more recent approaches estimate the response function during tractography. This work proposes a novel objective function independent of the FRF, just aiming for FOD reconstruction. The objective is integrated into global tractography showing promising results.

An Evolutionary Game Theory Model of Spontaneous Brain Functioning

Our brain is a complex system of interconnected regions spontaneously organized into distinct networks. The integration of information between and within these networks is a continuous process that can be observed even when the brain is at rest, i.e. not engaged in any particular task. Moreover, such spontaneous dynamics show predictive value over individual cognitive profile and constitute a potential marker in neurological and psychiatric conditions, making its understanding of fundamental importance in modern neuroscience. Here we present a theoretical and mathematical model based on an extension of evolutionary game theory on networks (EGN), able to capture brain's interregional dynamics by balancing emulative and non-emulative attitudes among brain regions. This results in the net behavior of nodes composing resting-state networks identified using functional magnetic resonance imaging (fMRI), determining their moment-to-moment level of activation and inhibition as expressed by positive and negative shifts in BOLD fMRI signal. By spontaneously generating low-frequency oscillatory behaviors, the EGN model is able to mimic functional connectivity dynamics, approximate fMRI time series on the basis of initial subset of available data, as well as simulate the impact of network lesions and provide evidence of compensation mechanisms across networks. Results suggest evolutionary game theory on networks as a new potential framework for the understanding of human brain network dynamics.

Disentangling micro from mesostructure by diffusion MRI: A Bayesian approach

Diffusion-sensitized magnetic resonance imaging probes the cellular structure of the human brain, but the primary microstructural information gets lost in averaging over higher-level, mesoscopic tissue organization such as different orientations of neuronal fibers. While such averaging is inevitable due to the limited imaging resolution, we propose a method for disentangling the microscopic cell properties from the effects of mesoscopic structure. We further avoid the classical fitting paradigm and use supervised machine learning in terms of a Bayesian estimator to estimate the microstructural properties. The method finds detectable parameters of a given microstructural model and calculates them within seconds, which makes it suitable for a broad range of neuroscientific applications.

Clarifying Human White Matter

Progress in magnetic resonance imaging (MRI) now makes it possible to identify the major white matter tracts in the living human brain. These tracts are important because they carry many of the signals communicated between different brain regions. MRI methods coupled with biophysical modeling can measure the tissue properties and structural features of the tracts that impact our ability to think, feel, and perceive. This review describes the fundamental ideas of the MRI methods used to identify the major white matter tracts in the living human brain.

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.

Simultaneous multi-scale diffusion estimation and tractography guided by entropy spectrum pathways

We have developed a method for the simultaneous estimation of local diffusion and the global fiber tracts based upon the information entropy flow that computes the maximum entropy trajectories between locations and depends upon the global structure of the multi-dimensional and multi-modal diffusion field. Computation of the entropy spectrum pathways requires only solving a simple eigenvector problem for the probability distribution for which efficient numerical routines exist, and a straight forward integration of the probability conservation through ray tracing of the convective modes guided by a global structure of the entropy spectrum coupled with a small scale local diffusion. The intervoxel diffusion is sampled by multi b-shell multi q-angle diffusion weighted imaging data expanded in spherical waves. This novel approach to fiber tracking incorporates global information about multiple fiber crossings in every individual voxel and ranks it in the most scientifically rigorous way. This method has potential significance for a wide range of applications, including studies of brain connectivity.

Improving the accuracy of PGSE DTI experiments using the spatial distribution of b matrix

A novel method for improving the accuracy of diffusion tensor imaging (DTI) is proposed. It takes into account the b matrix spatial variations, which can be easily determined using a simple anisotropic diffusion phantom. In opposite to standard numerical procedure of the b matrix calculation that requires the exact knowledge of amplitudes, shapes and time dependencies of diffusion gradients, the new method, which we call BSD-DTI (B-matrix spatial distribution in DTI), relies on direct measurements of its space-dependent components. The proposed technique was demonstrated on the Bruker Biospec 94/20USR system, using the spin echo diffusion sequence to image an isotropic water phantom and an anisotropic capillary phantom. The accuracy of the diffusion tensor determination was improved by an overall factor of about 8 for the isotropic water phantom.

Improving DTI tractography by including diagonal tract propagation

Tractography algorithms have been developed to reconstruct likely WM pathways in the brain from diffusion tensor imaging (DTI) data. In this study, an elegant and simple means for improving existing tractography algorithms is proposed by allowing tracts to propagate through diagonal trajectories between voxels, instead of only rectilinearly to their facewise neighbors. A series of tests (using both real and simulated data sets) are utilized to show several benefits of this new approach. First, the inclusion of diagonal tract propagation decreases the dependence of an algorithm on the arbitrary orientation of coordinate axes and therefore reduces numerical errors associated with that bias (which are also demonstrated here). Moreover, both quantitatively and qualitatively, including diagonals decreases overall noise sensitivity of results and leads to significantly greater efficiency in scanning protocols; that is, the obtained tracts converge much more quickly (i.e., in a smaller amount of scanning time) to those of data sets with high SNR and spatial resolution. Importantly, the inclusion of diagonal propagation adds essentially no appreciable time of calculation or computational costs to standard methods. This study focuses on the widely-used streamline tracking method, FACT (fiber assessment by continuous tracking), and the modified method is termed "FACTID" (FACT including diagonals).

Quantitative assessment of a framework for creating anatomical brain networks via global tractography

Interregional connections of the brain measured with diffusion tractography can be used to infer valuable information regarding both brain structure and function. However, different tractography algorithms can generate networks that exhibit different characteristics, resulting in poor reproducibility across studies. Therefore, it is important to benchmark different tractography algorithms to quantitatively assess their performance. Here we systematically evaluated a newly introduced tracking algorithm, global tractography, to derive anatomical brain networks in a fiber phantom, 2 post-mortem macaque brains, and 20 living humans, and compared the results with an established local tracking algorithm. Our results demonstrated that global tractography accurately characterized the phantom network in terms of graph-theoretic measures, and significantly outperformed the local tracking approach. Results in brain tissues (post-mortem macaques and in vivo humans), however, showed that although the performance of global tractography demonstrated a trend of improvement, the results were not vastly different than that of local tractography, possibly resulting from the increased fiber complexity of real tissues. When using macaque tracer-derived connections as the ground truth, we found that both global and local algorithms generated non-random patterns of false negative and false positive connections that were probably related to specific fiber systems and largely independent of the tractography algorithm or tissue type (post-mortem vs. in vivo) used in the current study. Moreover, a close examination of the transcallosal motor connections, reconstructed via either global or local tractography, demonstrated that the lateral transcallosal fibers in humans and macaques did not exhibit the denser homotopic connections found in primate tracer studies, indicating the need for more robust brain mapping techniques based on diffusion MRI data.

Diffusion MRI at 25: exploring brain tissue structure and function

Diffusion MRI (or dMRI) came into existence in the mid-1980s. During the last 25 years, diffusion MRI has been extraordinarily successful (with more than 300,000 entries on Google Scholar for diffusion MRI). Its main clinical domain of application has been neurological disorders, especially for the management of patients with acute stroke. It is also rapidly becoming a standard for white matter disorders, as diffusion tensor imaging (DTI) can reveal abnormalities in white matter fiber structure and provide outstanding maps of brain connectivity. The ability to visualize anatomical connections between different parts of the brain, non-invasively and on an individual basis, has emerged as a major breakthrough for neurosciences. The driving force of dMRI is to monitor microscopic, natural displacements of water molecules that occur in brain tissues as part of the physical diffusion process. Water molecules are thus used as a probe that can reveal microscopic details about tissue architecture, either normal or in a diseased state.

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.

Quantitative evaluation of 10 tractography algorithms on a realistic diffusion MR phantom

As it provides the only method for mapping white matter fibers in vivo, diffusion MRI tractography is gaining importance in clinical and neuroscience research. However, despite the increasing availability of different diffusion models and tractography algorithms, it remains unclear how to select the optimal fiber reconstruction method, given certain imaging parameters. Consequently, it is of utmost importance to have a quantitative comparison of these models and algorithms and a deeper understanding of the corresponding strengths and weaknesses. In this work, we use a common dataset with known ground truth and a reproducible methodology to quantitatively evaluate the performance of various diffusion models and tractography algorithms. To examine a wide range of methods, the dataset, but not the ground truth, was released to the public for evaluation in a contest, the "Fiber Cup". 10 fiber reconstruction methods were evaluated. The results provide evidence that: 1. For high SNR datasets, diffusion models such as (fiber) orientation distribution functions correctly model the underlying fiber distribution and can be used in conjunction with streamline tractography, and 2. For medium or low SNR datasets, a prior on the spatial smoothness of either the diffusion model or the fibers is recommended for correct modelling of the fiber distribution and proper tractography results. The phantom dataset, the ground truth fibers, the evaluation methodology and the results obtained so far will remain publicly available on: http://www.lnao.fr/spip.php?rubrique79 to serve as a comparison basis for existing or new tractography methods. New results can be submitted to fibercup09@gmail.com and updates will be published on the webpage.

Connectivity-based parcellation of the cortical mantle using q-ball diffusion imaging

This paper exploits the idea that each individual brain region has a specific connection profile to create parcellations of the cortical mantle using MR diffusion imaging. The parcellation is performed in two steps. First, the cortical mantle is split at a macroscopic level into 36 large gyri using a sulcus recognition system. Then, for each voxel of the cortex, a connection profile is computed using a probabilistic tractography framework. The tractography is performed from q fields using regularized particle trajectories. Fiber ODF are inferred from the q-balls using a sharpening process focusing the weight around the q-ball local maxima. A sophisticated mask of propagation computed from a T1-weighted image perfectly aligned with the diffusion data prevents the particles from crossing the cortical folds. During propagation, the particles father child particles in order to improve the sampling of the long fascicles. For each voxel, intersection of the particle trajectories with the gyri lead to a connectivity profile made up of only 36 connection strengths. These profiles are clustered on a gyrus by gyrus basis using a K-means approach including spatial regularization. The reproducibility of the results is studied for three subjects using spatial normalization.

A novel global tractography algorithm based on an adaptive spin glass model

This paper introduces a novel framework for global diffusion MRI tractography inspired from a spin glass model. The entire white matter fascicle map is parameterized by pieces of fibers called spins. Spins are encouraged to move and rotate to align with the main fiber directions, and to assemble into longer chains of low curvature. Moreover, they have the ability to adapt their quantity in regions where the spin concentration is not sufficient to correctly model the data. The optimal spin glass configuration is retrieved by an iterative minimization procedure, where chains are finally assimilated to fibers. As a result, all brain fibers appear as growing simultaneously until they merge with other fibers or reach the domain boundaries. In case of an ambiguity within a region like a crossing, the contribution of all neighboring fibers is used determine the correct neural pathway. This framework is tested on a MR phantom representing a 45 degrees crossing and a real brain dataset. Notably, the framework was able to retrieve the triple crossing between the callosal fibers, the corticospinal tract and the arcuate fasciculus.

Stochastic DT-MRI connectivity mapping on the GPU

We present a method for stochastic fiber tract mapping from diffusion tensor MRI (DT-MRI) implemented on graphics hardware. From the simulated fibers we compute a connectivity map that gives an indication of the probability that two points in the dataset are connected by a neuronal fiber path. A Bayesian formulation of the fiber model is given and it is shown that the inversion method can be used to construct plausible connectivity. An implementation of this fiber model on the graphics processing unit (GPU) is presented. Since the fiber paths can be stochastically generated independently of one another, the algorithm is highly parallelizable. This allows us to exploit the data-parallel nature of the GPU fragment processors. We also present a framework for the connectivity computation on the GPU. Our implementation allows the user to interactively select regions of interest and observe the evolving connectivity results during computation. Results are presented from the stochastic generation of over 250,000 fiber steps per iteration at interactive frame rates on consumer-grade graphics hardware.

Preliminary experience with visualization of intracortical fibers by focused high-resolution diffusion tensor imaging

BACKGROUND AND PURPOSE

The inherent low anisotropy of gray matter and the lack of adequate imaging sensitivity and resolution has, so far, impeded depiction of axonal fibers to their intracortical origin or termination. We tested the hypothesis that an experimental approach with high-resolution diffusion tensor imaging (DTI) provides anisotropic data for fiber tractography with sufficient sensitivity to visualize in vivo the fine distribution of white matter bundles at the intracortical level.

MATERIALS AND METHODS

We conducted phantom measurements of signal-to-noise ratio (SNR) and obtained diffusion tensor maps of the occipital lobe in 6 healthy volunteers using a dedicated miniature phased array detector at 3T. We reconstructed virtual fibers using a standard tracking algorithm.

RESULTS

The coil array provided a SNR of 8.0 times higher at the head surface compared with a standard quadrature whole head coil. Diffusion tensor maps could be obtained with an in-plane resolution of 0.58 x 0.58 mm(2). The axonal trajectories reconstructed from the diffusion data penetrate into the cortical ribbon perpendicular to the pial surface. This is the expected pattern for the terminations of thalamocortical afferent fibers to the middle layers of the occipital cortex and is consistent with the known microstructural organization of the mammalian cerebral cortex.

CONCLUSION

High-resolution DTI reveals intracortical anisotropy with a distinct parallel geometrical order, perpendicular to the pial surface, consistent with structures that may be identified as the terminal afferents in cortical gray matter.

A Bayesian framework for global tractography

We readdress the diffusion tractography problem in a global and probabilistic manner. Instead of tracking through local orientations, we parameterise the connexions between brain regions at a global level, and then infer on global and local parameters simultaneously in a Bayesian framework. This approach offers a number of important benefits. The global nature of the tractography reduces sensitivity to local noise and modelling errors. By constraining tractography to ensure a connexion is found, and then inferring on the exact location of the connexion, we increase the robustness of connectivity-based parcellations, allowing parcellations of connexions that were previously invisible to tractography. The Bayesian framework allows a direct comparison of the evidence for connecting and non-connecting models, to test whether the connexion is supported by the data. Crucially, by explicit parameterisation of the connexion between brain regions, we infer on a parameter that is shared with models of functional connectivity. This model is a first step toward the joint inference on functional and anatomical connectivity.

Probabilistic anatomical connectivity derived from the microscopic persistent angular structure of cerebral tissue

Recently developed methods to extract the persistent angular structure (PAS) of axonal fibre bundles from diffusion-weighted magnetic resonance imaging (MRI) data are applied to drive probabilistic fibre tracking, designed to provide estimates of anatomical cerebral connectivity. The behaviour of the PAS function in the presence of realistic data noise is modelled for a range of single and multiple fibre configurations. This allows probability density functions (PDFs) to be generated that are parametrized according to the anisotropy of individual fibre populations. The PDFs are incorporated in a probabilistic fibre-tracking method to allow the estimation of whole-brain maps of anatomical connection probability. These methods are applied in two exemplar experiments in the corticospinal tract to show that it is possible to connect the entire primary motor cortex (M1) when tracing from the cerebral peduncles, and that the reverse experiment of tracking from M1 successfully identifies high probability connection via the pyramidal tracts. Using the extracted PAS in probabilistic fibre tracking allows higher specificity and sensitivity than previously reported fibre tracking using diffusion-weighted MRI in the corticospinal tract.

MR tractography with diffusion tensor imaging in clinical routine

Using MRI, we demonstrated that the depiction of the cerebral white matter fiber tracts has become a routine procedure. Diffusion tensor (DT) sequences may be analyzed with combined volume analysis and tractography extraction software, giving indirect visualization of white matter connections. We obtained DT data from 20 subjects with normal MR imaging and five patients presenting cerebral diseases such as brain tumors, multiple sclerosis and stroke, with five patients explored on two different MR scanners. Data were transferred to dedicated workstations for anatomical realignment, determination of voxel eigenvectors and calculation of fiber tract orientations in a region of interest. In all subjects, axonal directions underlying the main neuronal pathways could be delineated. Comparisons between diseased regions and contralateral areas demonstrated changes in voxel anisotropy in injured regions, revealing possible preferential fiber orientations within diffuse T2 hyperintensities. Rapid data processing allows imaging of the normal and diseased fiber pathways as part of the routine MRI examination. Therefore, it appears that whenever white matter disease is suspected a tractography can be performed with this fast and simple method that we proved to be reliable and reproducible.

Fiber tracking in q-ball fields using regularized particle trajectories

Most of the approaches dedicated to fiber tracking from diffusion-weighted MR data rely on a tensor model. However, the tensor model can only resolve a single fiber orientation within each imaging voxel. New emerging approaches have been proposed to obtain a better representation of the diffusion process occurring in fiber crossing. In this paper, we adapt a tracking algorithm to the q-ball representation, which results from a spherical Radon transform of high angular resolution data. This algorithm is based on a Monte-Carlo strategy, using regularized particle trajectories to sample the white matter geometry. The method is validated using a phantom of bundle crossing made up of haemodialysis fibers. The method is also applied to the detection of the auditory tract in three human subjects.

Mathematical framework for simulating diffusion tensor MR neural fiber bundles

White matter (WM) fiber tractography (i.e., the reconstruction of the 3D architecture of WM fiber pathways) is known to be an important application of diffusion tensor magnetic resonance imaging (DT-MRI). For the quantitative evaluation of several fiber-tracking properties, such as accuracy, noise sensitivity, and robustness, synthetic ground-truth DT-MRI data are required. Moreover, an accurate simulated phantom is also required for optimization of the user-defined tractography parameters, and objective comparisons between fiber-tracking algorithms. Therefore, in this study a mathematical framework for simulating DT-MRI data, based on the physical properties of WM fiber bundles, is presented. We obtained a model of a WM fiber bundle by parameterizing the various features that characterize this bundle. We then evaluated three different synthetic DT-MRI models using experimental data in order to test the proposed methodology, and to determine the optimum model and parameter settings for constructing a realistic simulated DT-MRI phantom. Several examples of how the mathematical framework can be applied to compare fiber-tracking algorithms are presented.

Sulcal pattern and morphology of the superior temporal sulcus

The superior temporal sulcus (STs) is the main sulcal landmark of the external temporal cortex and is very important for functional (posterior language areas on the left) mapping and surgery. The methodology we use is based on the extraction of the 3D shape of sulci and their separation into subunits called sulcal roots. Seventeen normal brains (male: 11, female: 6, age: 22-60) were systematically analyzed. Additionally, parameters generated by visual observation were recorded. Non-parametric statistics were performed to evaluate the variation of the STs and influence of side, handedness and sex. We found that the 3D architecture of the STs was consistent with our generic model in four sulcal roots and four "plis de passage" (PP) and significant differences between right and left hemispheres. These morphological differences may be related to the language-relevant cortical areas difference and are pertinent for defining the limits of morphometric variability of the STs in "normal humans".

Object-based morphometry of the cerebral cortex

Most of the approaches dedicated to automatic morphometry rely on a point-by-point strategy based on warping each brain toward a reference coordinate system. In this paper, we describe an alternative object-based strategy dedicated to the cortex. This strategy relies on an artificial neuroanatomist performing automatic recognition of the main cortical sulci and parcellation of the cortical surface into gyral patches. A set of shape descriptors, which can be compared across subjects, is then attached to the sulcus and gyrus related objects segmented by this process. The framework is used to perform a study of 142 brains of the International Consortium for Brain Mapping (ICBM) database. This study reveals some correlates of handedness on the size of the sulci located in motor areas, which was not detected previously using standard voxel based morphometry.

Coordinate-based versus structural approaches to brain image analysis

A basic issue in neurosciences is to look for possible relationships between brain architecture and cognitive models. The lack of architectural information in magnetic resonance images, however, has led the neuroimaging community to develop brain mapping strategies based on various coordinate systems without accurate architectural content. Therefore, the relationships between architectural and functional brain organizations are difficult to study when analyzing neuroimaging experiments. This paper advocates that the design of new brain image analysis methods inspired by the structural strategies often used in computer vision may provide better ways to address these relationships. The key point underlying this new framework is the conversion of the raw images into structural representations before analysis. These representations are made up of data-driven elementary features like activated clusters, cortical folds or fiber bundles. Two classes of methods are introduced. Inference of structural models via matching across a set of individuals is described first. This inference problem is illustrated by the group analysis of functional statistical parametric maps (SPMs). Then, the matching of new individual data with a priori known structural models is described, using the recognition of the cortical sulci as a prototypical example.

Diffusion MRI of complex neural architecture

While functional brain imaging methods can locate the cortical regions subserving particular cognitive functions, the connectivity between the functional areas of the human brain remains poorly understood. Recently, investigators have proposed a method to image neural connectivity noninvasively using a magnetic resonance imaging method called diffusion tensor imaging (DTI). DTI measures the molecular diffusion of water along neural pathways. Accurate reconstruction of neural connectivity patterns from DTI has been hindered, however, by the inability of DTI to resolve more than a single axon direction within each imaging voxel. Here, we present a novel magnetic resonance imaging technique that can resolve multiple axon directions within a single voxel. The technique, called q-ball imaging, can resolve intravoxel white matter fiber crossing as well as white matter insertions into cortex. The ability of q-ball imaging to resolve complex intravoxel fiber architecture eliminates a key obstacle to mapping neural connectivity in the human brain noninvasively.

A framework to study the cortical folding patterns

This paper describes a decade-long research program focused on the variability of the cortical folding patterns. The program has developed a framework of using artificial neuroanatomists that are trained to identify sulci from a database. The framework relies on a renormalization of the brain warping problem, which consists in matching the cortices at the scale of the folds. Another component of the program is the search for the alphabet of the folding patterns, namely, a list of indivisible elementary sulci. The search relies on the study of the cortical folding process using antenatal imaging and on backward simulations of morphogenesis aimed at revealing traces of the embryologic dimples in the mature cortical surface. The importance of sulcal-based morphometry is illustrated by a simple study of the correlates of handedness on asymmetry indices. The study shows for instance that the central sulcus is larger in the dominant hemisphere.

Fiber tracking: principles and strategies - a technical review

The state of the art of reconstruction of the axonal tracts in the central nervous system (CNS) using diffusion tensor imaging (DTI) is reviewed. This relatively new technique has generated much enthusiasm and high expectations because it presently is the only approach available to non-invasively study the three-dimensional architecture of white matter tracts. While there is no doubt that DTI fiber tracking is providing exciting new opportunities to study CNS anatomy, it is very important to understand its limitations. In this review we therefore assess the basic principles and the assumptions that need to be made for each step of the study, including both data acquisition and the elaborate fiber reconstruction algorithms. Special attention is paid to situations where complications may arise, and possible solutions are reviewed. Validation issues and potential future directions and improvements are also discussed.

From the diffusion coefficient to the diffusion tensor

With diffusion tensor MRI one has access to the organization in space of tissue microstructural components. This outstanding potential adds, however, another layer of complexity to the diffusion MRI data acquisition and analysis processes. Over the last few years many articles have been published dealing with those matters. This special issue is thus timely to provide readers with the synthesis and the overall viewpoints from leading contributors to the field.