Automatic cortical sulcal parcellation based on surface principal direction flow field tracking

On the definition, construction, and presentation of the human cerebral sulci: A morphology-based approach

Although the term sulcus is known for almost four centuries, its formal, precise, consistent, constructive, and quantitative definition is practically lacking. As the cerebral sulci (and gyri) are vital in cortical anatomy which, in turn, is central in neuroeducation and neuroimage processing, a new sulcus definition is needed. The contribution of this work is threefold, namely to (1) propose a new, morphology-based definition of the term sulcus (and consequently that of gyrus), (2) formulate a constructive method for sulcus calculation, and (3) provide a novel way for the presentation of sulci. The sulcus is defined here as a volumetric region on the cortical mantle between adjacent gyri separated from them at the levels of their gyral white matter crest lines. Consequently, the sulcal inner surface is demarcated by the crest lines of the gyral white matter of its adjacent gyri. Correspondingly, the gyrus is defined as a volumetric region on the cortical mantle separated from its adjacent sulci at the level of its gyral white matter crest line. This volumetric sulcus definition is conceptually simple, anatomy-based, educationally friendly, quantitative, and constructive. Considering the sulcus as a volumetric object is a major differentiation from other works. Based on the introduced sulcus definition, a method for volumetric sulcus construction is proposed in two, conceptually straightforward, steps, namely, sulcal intersection formation followed by its propagation which steps are to be repeated for every sulcal segment. These sulcal and gyral constructions can be automated by applying existing methods and public tools. As a volumetric sulcus forms an imprint into the white matter, this enables prominent sulcus presentation. Since this type of presentation is novel yet unfamiliar to the reader, also a dual surface presentation was proposed here by employing the spatially co-registered white matter and cortical surfaces. The results were presented as dual surface labeled sulci on eight standard orthogonal views, anterior, left lateral, posterior, right lateral, superior, inferior, medial left, and medial right by using a 3D brain atlas. Moreover, additional 108 labeled images were created with sulcus-oriented views for 27 individual left and right sulci forming 54 dual white matter-cortical surface images strengthening in this way the educational value of the proposed approach. These images were included for public use in the NOWinBRAIN neuroimage repository with over 7700 3D images available at www.nowinbrain.org. The results demonstrated the superiority of white matter surface sulci presentation over the standard cortical surface and cross-sectional presentations in terms of sulcal course, continuity, size, shape, width, depth, side branches, and pattern. To my best knowledge, this is the first work ever presenting the labeling of sulci on all cerebral white matter surfaces as well as on dual white matter-cortical surfaces. Additionally to neuroeducation, three other applications of the proposed approach were discussed, sulcal reference maps, sulcus quantification in terms of new parameters introduced here (sulcal volume, wall skewness, and the number of white matter basins), and an atlas-assisted tool for exploration and studying of cerebral sulci and gyri .

Fundamental functional differences between gyri and sulci: implications for brain function, cognition, and behavior

Folding of the cerebral cortex is a prominent characteristic of mammalian brains. Alterations or deficits in cortical folding are strongly correlated with abnormal brain function, cognition, and behavior. Therefore, a precise mapping between the anatomy and function of the brain is critical to our understanding of the mechanisms of brain structural architecture in both health and diseases. Gyri and sulci, the standard nomenclature for cortical anatomy, serve as building blocks to make up complex folding patterns, providing a window to decipher cortical anatomy and its relation with brain functions. Huge efforts have been devoted to this research topic from a variety of disciplines including genetics, cell biology, anatomy, neuroimaging, and neurology, as well as involving computational approaches based on machine learning and artificial intelligence algorithms. However, despite increasing progress, our understanding of the functional anatomy of gyro-sulcal patterns is still in its infancy. In this review, we present the current state of this field and provide our perspectives of the methodologies and conclusions concerning functional differentiation between gyri and sulci, as well as the supporting information from genetic, cell biology, and brain structure research. In particular, we will further present a proposed framework for attempting to interpret the dynamic mechanisms of the functional interplay between gyri and sulci. Hopefully, this review will provide a comprehensive summary of anatomo-functional relationships in the cortical gyro-sulcal system together with a consideration of how these contribute to brain function, cognition, and behavior, as well as to mental disorders.

Group-level cortical surface parcellation with sulcal pits labeling

Sulcal pits are the points of maximal depth within the folds of the cortical surface. These shape descriptors give a unique opportunity to access to a rich, fine-scale representation of the geometry and the developmental milestones of the cortical surface. However, using sulcal pits analysis at group level requires new numerical tools to establish inter-subject correspondences. Here, we address this issue by taking advantage of the geometrical information carried by sulcal basins that are the local patches of surfaces surrounding each sulcal pit. Our framework consists in two phases. First, we present a new method to generate a population-specific atlas of this sulcal basins organi- zation as a fold-level parcellation of the cortical surface. Then, we address the labeling of individual sulcal pits and corresponding basins with respect to this atlas. To assess their validity, we applied these methodological advances on two different populations of healthy subjects. The first database of 137 adults allowed us to compare our method to the state-of-the-art and the second database of 209 children, aged between 0 and 18 years, illustrates the adaptability and relevance of our method in the context of pediatric data showing strong variations in cortical volume and folding.

SPHERICAL U-NET FOR INFANT CORTICAL SURFACE PARCELLATION

In human brain MRI studies, it is of great importance to accurately parcellate cortical surfaces into anatomically and functionally meaningful regions. In this paper, we propose a novel end-to-end deep learning method by formulating surface parcellation as a semantic segmentation task on the sphere. To extend the convolutional neural networks (CNNs) to the spherical space, corresponding operations of surface convolution, pooling and upsampling are first developed to deal with data representation on spherical surface meshes, and then spherical CNNs are constructed accordingly. Specifically, the U-Net and SegNet architectures are transformed to the spherical representation for neonatal cortical surface parcellation. Experimental results on 90 neonates indicate the effectiveness and efficiency of our proposed spherical U-Net, in comparison with the spherical SegNet and the previous patch-wise classification method.

A computational method for longitudinal mapping of orientation-specific expansion of cortical surface in infants

The cortical surface of the human brain expands dynamically and regionally heterogeneously during the first postnatal year. As all primary and secondary cortical folds as well as many tertiary cortical folds are well established at term birth, the cortical surface area expansion during this stage is largely driven by the increase of surface area in two orthogonal orientations in the tangent plane: 1) the expansion parallel to the folding orientation (i.e., increasing the lengths of folds) and 2) the expansion perpendicular to the folding orientation (i.e., increasing the depths of folds). This information would help us better understand the mechanisms of cortical development and provide important insights into neurodevelopmental disorders, but still remains largely unknown due to lack of dedicated computational methods. To address this issue, we propose a novel method for longitudinal mapping of orientation-specific expansion of cortical surface area in these two orthogonal orientations during early infancy. First, to derive the two orientation fields perpendicular and parallel to cortical folds, we propose to adaptively and smoothly fuse the gradient field of sulcal depth and also the maximum principal direction field, by leveraging their region-specific reliability. Specifically, we formulate this task as a discrete labeling problem, in which each vertex is assigned to an orientation label, and solve it by graph cuts. Then, based on the computed longitudinal deformation of the cortical surface, we estimate the Jacobian matrix at each vertex by solving a least-squares problem and derive its corresponding stretch tensor. Finally, to obtain the orientation-specific cortical surface expansion, we project the stretch tensor into the two orthogonal orientations separately. We have applied the proposed method to 30 healthy infants, and for the first time we revealed the orientation-specific longitudinal cortical surface expansion maps during the first postnatal year.

Registration-Free Infant Cortical Surface Parcellation using Deep Convolutional Neural Networks

Automatic parcellation of infant cortical surfaces into anatomical regions of interest (ROIs) is of great importance in brain structural and functional analysis. Conventional cortical surface parcellation methods suffer from two main issues: 1) Cortical surface registration is needed for establishing the atlas-to-individual correspondences; 2) The mapping from cortical shape to the parcellation labels requires designing of specific hand-crafted features. To address these issues, in this paper, we propose a novel cortical surface parcellation method, which is free of surface registration and designing of hand-crafted features, based on deep convolutional neural network (DCNN). Our main idea is to formulate surface parcellation as a patch-wise classification problem. Briefly, we use DCNN to train a classifier, whose inputs are the local cortical surface patches with multi-channel cortical shape descriptors such as mean curvature, sulcal depth, and average convexity; while the outputs are the parcellation label probabilities of cortical vertices. To enable effective convolutional operation on the surface data, we project each spherical surface patch onto its intrinsic tangent plane by a geodesic-distance-preserving mapping. Then, after classification, we further adopt the graph cuts method to improve spatial consistency of the parcellation. We have validated our method based on 90 neonatal cortical surfaces with manual parcellations, showing superior accuracy and efficiency of our proposed method.

Joint representation of consistent structural and functional profiles for identification of common cortical landmarks

In the brain mapping field, there have been significant interests in representation of structural/functional profiles to establish structural/functional landmark correspondences across individuals and populations. For example, from the structural perspective, our previous studies have identified hundreds of consistent DICCCOL (dense individualized and common connectivity-based cortical landmarks) landmarks across individuals and populations, each of which possess consistent DTI-derived fiber connection patterns. From the functional perspective, a large collection of well-characterized HAFNI (holistic atlases of functional networks and interactions) networks based on sparse representation of whole-brain fMRI signals have been identified in our prior studies. However, due to the remarkable variability of structural and functional architectures in the human brain, it is challenging for earlier studies to jointly represent the connectome-scale structural and functional profiles for establishing a common cortical architecture which can comprehensively encode both structural and functional characteristics across individuals. To address this challenge, we propose an effective computational framework to jointly represent the structural and functional profiles for identification of consistent and common cortical landmarks with both structural and functional correspondences across different brains based on DTI and fMRI data. Experimental results demonstrate that 55 structurally and functionally common cortical landmarks can be successfully identified.

A COMPUTATIONAL METHOD FOR LONGITUDINAL MAPPING OF ORIENTATION-SPECIFIC EXPANSION OF CORTICAL SURFACE AREA IN INFANTS

The dynamic expansion of the human cortical surface during infancy is largely driven by the increase of surface area in two orthogonal directions: 1) the expansion parallel to the folding orientation (i.e., increasing the lengths of folds) and 2) the expansion perpendicular to the folding orientation (i.e., increasing the depths of folds). The knowledge on this would help us better understand the cortical growth mechanisms and provide important insights into neurodevelopmental disorders, but still remains scarce, due to the lack of dedicated computational methods. To address this issue, we propose a novel method for longitudinal mapping of orientation-specific expansion of cortical surface area in these two orthogonal directions during early infancy. We apply our method to 30 healthy infants, and for the first time reveal the orientation-specific longitudinal cortical surface expansion maps during the first postnatal year.

Confirmation of a gyral bias in diffusion MRI fiber tractography

Diffusion MRI fiber tractography has been increasingly used to map the structural connectivity of the human brain. However, this technique is not without limitations; for example, there is a growing concern over anatomically correlated bias in tractography findings. In this study, we demonstrate that there is a bias for fiber tracking algorithms to terminate preferentially on gyral crowns, rather than the banks of sulci. We investigate this issue by comparing diffusion MRI (dMRI) tractography with equivalent measures made on myelin-stained histological sections. We begin by investigating the orientation and trajectories of axons near the white matter/gray matter boundary, and the density of axons entering the cortex at different locations along gyral blades. These results are compared with dMRI orientations and tract densities at the same locations, where we find a significant gyral bias in many gyral blades across the brain. This effect is shown for a range of tracking algorithms, both deterministic and probabilistic, and multiple diffusion models, including the diffusion tensor and a high angular resolution diffusion imaging technique. Additionally, the gyral bias occurs for a range of diffusion weightings, and even for very high-resolution datasets. The bias could significantly affect connectivity results using the current generation of tracking algorithms.

Gyral net: A new representation of cortical folding organization

One distinct feature of the cerebral cortex is its convex (gyri) and concave (sulci) folding patterns. Due to the remarkable complexity and variability of gyral/sulcal shapes, it has been challenging to quantitatively model their organization patterns. Inspired by the observation that the lines of gyral crests can form a connected graph on each brain hemisphere, we propose a new representation of cortical gyri/sulci organization pattern - gyral net, which models cortical architecture from a graph perspective, starting with nodes and edges obtained from the reconstructed cortical surfaces. A novel computational framework is developed to efficiently and automatically construct gyral nets from surface meshes, and four measurements are devised to quantify the folding patterns. Using an MRI dataset for autism study as a test bed, we identified reduced local connectivity cost and increased curviness of gyral net bilaterally on the parietal lobe, occipital lobe, and temporal lobe in autistic patients. Additionally, we found that the cortical thickness and the gyral straightness of gyral joints are higher than the rest of gyral crest regions. The proposed representation offers a new tool for a comprehensive and reliable characterization of the cortical folding organization. This novel computational framework will enable large-scale analyses of cortical folding patterns in the future.

Elucidating functional differences between cortical gyri and sulci via sparse representation HCP grayordinate fMRI data

The highly convoluted cerebral cortex is characterized by two different topographic structures: convex gyri and concave sulci. Increasing studies have demonstrated that cortical gyri and sulci exhibit different structural connectivity patterns. Inspired by the intrinsic structural differences between gyri and sulci, in this paper, we present a data-driven framework based on sparse representation of fMRI data for functional network inferences, then examine the interactions within and across gyral and sulcal functional networks and finally elucidate possible functional differences using graph theory based properties. We apply the proposed framework to the high-resolution Human Connectome Project (HCP) grayordinate fMRI data. Extensive experimental results on both resting state fMRI data and task-based fMRI data consistently suggested that gyri are more functionally integrated, while sulci are more functionally segregated in the organizational architecture of cerebral cortex, offering novel understanding of the byzantine cerebral cortex.

Joint prediction of longitudinal development of cortical surfaces and white matter fibers from neonatal MRI

The human brain can be modeled as multiple interrelated shapes (or a multishape), each for characterizing one aspect of the brain, such as the cortex and white matter pathways. Predicting the developing multishape is a very challenging task due to the contrasting nature of the developmental trajectories of the constituent shapes: smooth for the cortical surface and non-smooth for white matter tracts due to changes such as bifurcation. We recently addressed this problem and proposed an approach for predicting the multishape developmental spatiotemporal trajectories of infant brains based only on neonatal MRI data using a set of geometric, dynamic, and fiber-to-surface connectivity features. In this paper, we propose two key innovations to further improve the prediction of multishape evolution. First, for a more accurate cortical surface prediction, instead of simply relying on one neonatal atlas to guide the prediction of the multishape, we propose to use multiple neonatal atlases to build a spatially heterogeneous atlas using the multidirectional varifold representation. This individualizes the atlas by locally maximizing its similarity to the testing baseline cortical shape for each cortical region, thereby better representing the baseline testing cortical surface, which founds the multishape prediction process. Second, for temporally consistent fiber prediction, we propose to reliably estimate spatiotemporal connectivity features using low-rank tensor completion, thereby capturing the variability and richness of the temporal development of fibers. Experimental results confirm that the proposed variants significantly improve the prediction performance of our original multishape prediction framework for both cortical surfaces and fiber tracts shape at 3, 6, and 9 months of age. Our pioneering model will pave the way for learning how to predict the evolution of anatomical shapes with abnormal changes. Ultimately, devising accurate shape evolution prediction models that can help quantify and predict the severity of a brain disorder as it progresses will be of great aid in individualized treatment planning.

Multidirectional and Topography-based Dynamic-scale Varifold Representations with Application to Matching Developing Cortical Surfaces

The human cerebral cortex is marked by great complexity as well as substantial dynamic changes during early postnatal development. To obtain a fairly comprehensive picture of its age-induced and/or disorder-related cortical changes, one needs to match cortical surfaces to one another, while maximizing their anatomical alignment. Methods that geodesically shoot surfaces into one another as currents (a distribution of oriented normals) and varifolds (a distribution of non-oriented normals) provide an elegant Riemannian framework for generic surface matching and reliable statistical analysis. However, both conventional current and varifold matching methods have two key limitations. First, they only use the normals of the surface to measure its geometry and guide the warping process, which overlooks the importance of the orientations of the inherently convoluted cortical sulcal and gyral folds. Second, the 'conversion' of a surface into a current or a varifold operates at a fixed scale under which geometric surface details will be neglected, which ignores the dynamic scales of cortical foldings. To overcome these limitations and improve varifold-based cortical surface registration, we propose two different strategies. The first strategy decomposes each cortical surface into its normal and tangent varifold representations, by integrating principal curvature direction field into the varifold matching framework, thus providing rich information of the orientation of cortical folding and better characterization of the complex cortical geometry. The second strategy explores the informative cortical geometric features to perform a dynamic-scale measurement of the cortical surface that depends on the local surface topography (e.g., principal curvature), thereby we introduce the concept of a topography-based dynamic-scale varifold. We tested the proposed varifold variants for registering 12 pairs of dynamically developing cortical surfaces from 0 to 6 months of age. Both variants improved the matching accuracy in terms of closeness to the target surface and the goodness of alignment with regional anatomical boundaries, when compared with three state-of-the-art methods: (1) diffeomorphic spectral matching, (2) conventional current-based surface matching, and (3) conventional varifold-based surface matching.

Topography-Based Registration of Developing Cortical Surfaces in Infants Using Multidirectional Varifold Representation

Cortical surface registration or matching facilitates atlasing, cortical morphology-function comparison and statistical analysis. Methods that geodesically shoot surfaces into one another, as currents or varifolds, provide an elegant mathematical framework for generic surface matching and dynamic local features estimation, such as deformation momenta. However, conventional current and varifold matching methods only use the normals of the surface to measure its geometry and guide the warping process, which overlooks the importance of the direction in the convoluted cortical sulcal and gyral folds. To cope with the stated limitation, we decompose each cortical surface into its normal and tangent varifold representations, by integrating principal curvature direction field into the varifold matching framework, thus providing rich information for the direction of cortical folding and better characterization of the cortical geometry. To include more informative cortical geometric features in the matching process, we adaptively place control points based on the surface topography, hence the deformation is controlled by points lying on gyral crests (or "hills") and sulcal fundi (or "valleys") of the cortical surface, which are the most reliable and important topographic and anatomical landmarks on the cortex. We applied our method for registering the developing cortical surfaces in 12 infants from 0 to 6 months of age. Both of these variants significantly improved the matching accuracy in terms of closeness to the target surface and the precision of alignment with regional anatomical boundaries, when compared with several state-of-the-art methods: (1) diffeomorphic spectral matching, (2) current-based surface matching and (3) original varifold-based surface matching.

Construction of 4D high-definition cortical surface atlases of infants: Methods and applications

In neuroimaging, cortical surface atlases play a fundamental role for spatial normalization, analysis, visualization, and comparison of results across individuals and different studies. However, existing cortical surface atlases created for adults are not suitable for infant brains during the first two postnatal years, which is the most dynamic period of postnatal structural and functional development of the highly-folded cerebral cortex. Therefore, spatiotemporal cortical surface atlases for infant brains are highly desired yet still lacking for accurate mapping of early dynamic brain development. To bridge this significant gap, leveraging our infant-dedicated computational pipeline for cortical surface-based analysis and the unique longitudinal infant MRI dataset acquired in our research center, in this paper, we construct the first spatiotemporal (4D) high-definition cortical surface atlases for the dynamic developing infant cortical structures at seven time points, including 1, 3, 6, 9, 12, 18, and 24 months of age, based on 202 serial MRI scans from 35 healthy infants. For this purpose, we develop a novel method to ensure the longitudinal consistency and unbiasedness to any specific subject and age in our 4D infant cortical surface atlases. Specifically, we first compute the within-subject mean cortical folding by unbiased groupwise registration of longitudinal cortical surfaces of each infant. Then we establish longitudinally-consistent and unbiased inter-subject cortical correspondences by groupwise registration of the geometric features of within-subject mean cortical folding across all infants. Our 4D surface atlases capture both longitudinally-consistent dynamic mean shape changes and the individual variability of cortical folding during early brain development. Experimental results on two independent infant MRI datasets show that using our 4D infant cortical surface atlases as templates leads to significantly improved accuracy for spatial normalization of cortical surfaces across infant individuals, in comparison to the infant surface atlases constructed without longitudinal consistency and also the FreeSurfer adult surface atlas. Moreover, based on our 4D infant surface atlases, for the first time, we reveal the spatially-detailed, region-specific correlation patterns of the dynamic cortical developmental trajectories between different cortical regions during early brain development.

Spatiotemporal patterns of cortical fiber density in developing infants, and their relationship with cortical thickness

The intrinsic relationship between the convoluted cortical folding and the underlying complex whiter matter fiber connections has received increasing attention in current neuroscience studies. Recently, the axonal pushing hypothesis of cortical folding has been proposed to explain the finding that the axonal fibers (derived from diffusion tensor images) connecting to gyri are significantly denser than those connecting to sulci in both adult human and non-human primate brains. However, it is still unclear about the spatiotemporal patterns of the fiber density on the cortical surface of the developing infant brains from birth to 2 years of age, which is the most dynamic phase of postnatal brain development. In this paper, for the first time, we systemically characterized the spatial distributions and longitudinal developmental trajectories of the cortical fiber density in the first 2 postnatal years, via joint analysis of longitudinal structural and diffusion tensor imaging from 33 healthy infants. We found that the cortical fiber density increases dramatically in the first year and then keeps relatively stable in the second year. Moreover, we revealed that the cortical fiber density on gyral regions was significantly higher at 0, 1, and 2 years of age than that on sulcal regions in the frontal, temporal, and parietal lobes. Meanwhile, the cortical fiber density was strongly positively correlated with cortical thickness at several three-hinge junction regions of gyri. These results significantly advanced our understanding of the intrinsic relationship between the cortical folding, cortical thickness and axonal wiring during early postnatal stages.

Spatial Patterns, Longitudinal Development, and Hemispheric Asymmetries of Cortical Thickness in Infants from Birth to 2 Years of Age

Cortical thickness (CT) is related to normal development and neurodevelopmental disorders. It remains largely unclear how the characteristic patterns of CT evolve in the first 2 years. In this paper, we systematically characterized for the first time the detailed vertex-wise patterns of spatial distribution, longitudinal development, and hemispheric asymmetries of CT at 0, 1, and 2 years of age, via surface-based analysis of 219 longitudinal magnetic resonance images from 73 infants. Despite the dynamic increase of CT in the first year and the little change of CT in the second year, we found that the overall spatial distribution of thin and thick cortices was largely present at birth, and evolved only modestly during the first 2 years. Specifically, the precentral gyrus, postcentral gyrus, occipital cortex, and superior parietal region had thin cortices, whereas the prefrontal, lateral temporal, insula, and inferior parietal regions had thick cortices. We revealed that in the first year thin cortices exhibited low growth rates of CT, whereas thick cortices exhibited high growth rates. We also found that gyri were thicker than sulci, and that the anterior bank of the central sulcus was thicker than the posterior bank. Moreover, we showed rightward hemispheric asymmetries of CT in the lateral temporal and posterior insula regions at birth, which shrank gradually in the first 2 years, and also leftward asymmetries in the medial prefrontal, paracentral, and anterior cingulate cortices, which expanded substantially during this period. This study provides the first comprehensive picture of early patterns and evolution of CT during infancy.

Anatomy-guided Dense Individualized and Common Connectivity-based Cortical Landmarks (A-DICCCOL)

Establishment of structural and functional correspondences of human brain that can be quantitatively encoded and reproduced across different subjects and populations is one of the key issues in brain mapping. As an attempt to address this challenge, our recently developed Dense Individualized and Common Connectivity-based Cortical Landmarks (DICCCOL) system reported 358 connectional landmarks, each of which possesses consistent DTI-derived white matter fiber connection pattern that is reproducible in over 240 healthy brains. However, the DICCCOL system can be substantially improved by integrating anatomical and morphological information during landmark initialization and optimization procedures. In this paper, we present a novel anatomy-guided landmark discovery framework that defines and optimizes landmarks via integrating rich anatomical, morphological, and fiber connectional information for landmark initialization, group-wise optimization and prediction, which are formulated and solved as an energy minimization problem. The framework finally determined 555 consistent connectional landmarks. Validation studies demonstrated that the 555 landmarks are reproducible, predictable, and exhibited reasonably accurate anatomical, connectional, and functional correspondences across individuals and populations and thus are named anatomy-guided DICCCOL or A-DICCCOL. This A-DICCCOL system represents common cortical architectures with anatomical, connectional, and functional correspondences across different subjects and would potentially provide opportunities for various applications in brain science.

AUTOMATIC PARCELLATION OF CORTICAL SURFACES USING RANDOM FORESTS

Automatic and accurate parcellation of cortical surfaces into anatomically and functionally meaningful regions is of fundamental importance in brain mapping. In this paper, we propose a new method leveraging random forests and graph cuts methods to parcellate cortical surfaces into a set of gyral-based regions, using multiple surface atlases with manual labels by experts. Specifically, our method first takes advantage of random forests and auto-context methods to learn the optimal utilization of cortical features for rough parcellation and then the graph cuts method to further refine the parcellation for improved accuracy and spatial consistency. Particularly, to capitalize on random forests, we propose a novel definition of Haar-like features on cortical surfaces based on spherical mapping. The proposed method has been validated on cortical surfaces from 39 adult brain MR images, each with 35 regions manually labeled by a neuroanatomist, achieving the average Dice ratio of 0.902, higher than the-state-of-art methods.

Simultaneous and consistent labeling of longitudinal dynamic developing cortical surfaces in infants

The human cerebral cortex develops extremely dynamically in the first 2years of life. Accurate and consistent parcellation of longitudinal dynamic cortical surfaces during this critical stage is essential to understand the early development of cortical structure and function in both normal and high-risk infant brains. However, directly applying the existing methods developed for the cross-sectional studies often generates longitudinally-inconsistent results, thus leading to inaccurate measurements of the cortex development. In this paper, we propose a new method for accurate, consistent, and simultaneous labeling of longitudinal cortical surfaces in the serial infant brain MR images. The proposed method is explicitly formulated as a minimization problem with an energy function that includes a data fitting term, a spatial smoothness term, and a temporal consistency term. Specifically, inspired by multi-atlas based label fusion, the data fitting term is designed to integrate the contributions from multi-atlas surfaces adaptively, according to the similarities of their local cortical folding with that of the subject cortical surface. The spatial smoothness term is then designed to adaptively encourage label smoothness based on the local cortical folding geometries, i.e., allowing label discontinuity at sulcal bottoms (which often are the boundaries of cytoarchitecturally and functionally distinct regions). The temporal consistency term is to adaptively encourage the label consistency among the temporally-corresponding vertices, based on their similarity of local cortical folding. Finally, the entire energy function is efficiently minimized by a graph cuts method. The proposed method has been applied to the parcellation of longitudinal cortical surfaces of 13 healthy infants, each with 6 serial MRI scans acquired at 0, 3, 6, 9, 12 and 18months of age. Qualitative and quantitative evaluations demonstrated both accuracy and longitudinal consistency of the proposed method. By using our method, for the first time, we reveal several hitherto unseen properties of the dynamic and regionally heterogeneous development of the cortical surface area in the first 18months of life.

Spatial distribution and longitudinal development of deep cortical sulcal landmarks in infants

Sulcal pits, the locally deepest points in sulci of the highly convoluted and variable cerebral cortex, are found to be spatially consistent across human adult individuals. It is suggested that sulcal pits are genetically controlled and have close relationships with functional areas. To date, the existing imaging studies of sulcal pits are mainly focused on adult brains, yet little is known about the spatial distribution and temporal development of sulcal pits in the first 2 years of life, which is the most dynamic and critical period of postnatal brain development. Studying sulcal pits during this period would greatly enrich our limited understandings of the origins and developmental trajectories of sulcal pits, and would also provide important insights into many neurodevelopmental disorders associated with abnormal cortical foldings. In this paper, by using surface-based morphometry, for the first time, we systemically investigated the spatial distribution and temporal development of sulcal pits in major cortical sulci from 73 healthy infants, each with three longitudinal 3T MR scans at term birth, 1 year, and 2 years of age. Our results suggest that the spatially consistent distributions of sulcal pits in major sulci across individuals have already existed at term birth and this spatial distribution pattern keeps relatively stable in the first 2 years of life, despite that the cerebral cortex expands dramatically and the sulcal depth increases considerably during this period. Specially, the depth of sulcal pits increases regionally heterogeneously, with more rapid growth in the high-order association cortex, including the prefrontal and temporal cortices, than the sensorimotor cortex in the first 2 years of life. Meanwhile, our results also suggest that there exist hemispheric asymmetries of the spatial distributions of sulcal pits in several cortical regions, such as the central, superior temporal and postcentral sulci, consistently from birth to 2 years of age, which likely has close relationships with the lateralization of brain functions of these regions. This study provides detailed insights into the spatial distribution and temporal development of deep sulcal landmarks in infants.

Measuring the dynamic longitudinal cortex development in infants by reconstruction of temporally consistent cortical surfaces

Quantitative measurement of the dynamic longitudinal cortex development during early postnatal stages is of great importance to understand the early cortical structural and functional development. Conventional methods usually reconstruct the cortical surfaces of longitudinal images from the same subject independently, which often generate longitudinally-inconsistent cortical surfaces and thus lead to inaccurate measurement of cortical changes, especially for vertex-wise mapping of cortical development. This paper aims to address this problem by presenting a method to reconstruct temporally-consistent cortical surfaces from longitudinal infant brain MR images, for accurate and consistent measurement of the dynamic cortex development in infants. Specifically, the longitudinal development of the inner cortical surface is first modeled by a deformable growth sheet with elasto-plasticity property to establish longitudinally smooth correspondences of the inner cortical surfaces. Then, the modeled longitudinal inner cortical surfaces are jointly deformed to locate both inner and outer cortical surfaces with a spatial-temporal deformable surface method. The method has been applied to 13 healthy infants, each with 6 serial MR scans acquired at 2 weeks, 3 months, 6 months, 9 months, 12 months and 18 months of age. Experimental results showed that our method with the incorporated longitudinal constraints can reconstruct the longitudinally-dynamic cortical surfaces from serial infant MR images more consistently and accurately than the previously published methods. By using our method, for the first time, we can characterize the vertex-wise longitudinal cortical thickness development trajectory at multiple time points in the first 18 months of life. Specifically, we found the highly age-related and regionally-heterogeneous developmental trajectories of the cortical thickness during this period, with the cortical thickness increased most from 3 to 6 months (16.2%) and least from 9 to 12 months (less than 0.1%). Specifically, the central sulcus only underwent significant increase of cortical thickness from 6 to 9 months and the occipital cortex underwent significant increase from 0 to 9 months, while the frontal, temporal and parietal cortices grew continuously in this first 18 months of life. The adult-like spatial patterns of cortical thickness were generally present at 18 months of age. These results provided detailed insights into the dynamic trajectory of the cortical thickness development in infants.

Longitudinal development of cortical thickness, folding, and fiber density networks in the first 2 years of life

Quantitatively characterizing the development of cortical anatomical networks during the early stage of life plays an important role in revealing the relationship between cortical structural connection and high-level functional development. The development of correlation networks of cortical-thickness, cortical folding, and fiber-density is systematically analyzed in this article to study the relationship between different anatomical properties during the first 2 years of life. Specifically, longitudinal MR images of 73 healthy subjects from birth to 2 year old are used. For each subject at each time point, its measures of cortical thickness, cortical folding, and fiber density are projected to its cortical surface that has been partitioned into 78 cortical regions. Then, the correlation matrices for cortical thickness, cortical folding, and fiber density at each time point can be constructed, respectively, by computing the inter-regional Pearson correlation coefficient (of any pair of ROIs) across all 73 subjects. Finally, the presence/absence pattern (i.e., binary pattern) of the connection network is constructed from each inter-regional correlation matrix, and its statistical and anatomical properties are adopted to analyze the longitudinal development of anatomical networks. The results show that the development of anatomical network could be characterized differently by using different anatomical properties (i.e., using cortical thickness, cortical folding, or fiber density).

Diffusion tensor imaging reveals evolution of primate brain architectures

Evolution of the brain has been an inherently interesting problem for centuries. Recent studies have indicated that neuroimaging is a powerful technique for studying brain evolution. In particular, a variety of reports have demonstrated that consistent white matter fiber connection patterns derived from diffusion tensor imaging (DTI) tractography reveal common brain architecture and are predictive of brain functions. In this paper, based on our recently discovered 358 dense individualized and common connectivity-based cortical landmarks (DICCCOL) defined by consistent fiber connection patterns in DTI datasets of human brains, we derived 65 DICCCOLs that are common in macaque monkey, chimpanzee and human brains and 175 DICCCOLs that exhibit significant discrepancies amongst these three primate species. Qualitative and quantitative evaluations not only demonstrated the consistencies of anatomical locations and structural fiber connection patterns of these 65 common DICCCOLs across three primates, suggesting an evolutionarily preserved common brain architecture but also revealed regional patterns of evolutionarily induced complexity and variability of those 175 discrepant DICCCOLs across the three species.

A functional model of cortical gyri and sulci

Diffusion tensor imaging (DTI) and high angular resolution diffusion imaging (HARDI) have been broadly used in the neuroimaging field to investigate the macro-scale fiber connection patterns in the cerebral cortex. Our recent analyses of DTI and HARDI data demonstrated that gyri are connected by denser, streamlined fibers than sulci are. Inspired by this finding and motivated by the fact that DTI-derived fibers provide the structural substrates for functional connectivity, we hypothesize that gyri are global functional connection centers and sulci are local functional units. To test this functional model of gyri and sulci, we examined the structural and functional connectivity among the landmarks on the selected gyral/sulcal areas in the frontal/parietal lobe and in the whole cerebral cortex via multimodal DTI and resting state fMRI (R-fMRI) datasets. Our results demonstrate that functional connectivity is strong among gyri, weak among sulci, and moderate between gyri and sulci. These results suggest that gyri are functional connection centers that exchange information among remote structurally connected gyri and neighboring sulci, while sulci communicate directly with their neighboring gyri and indirectly with other cortical regions through gyri. This functional model of gyri and sulci has been supported by a series of experiments, and provides novel perspectives on the functional architecture of the cerebral cortex.

Group-wise consistent parcellation of gyri via adaptive multi-view spectral clustering of fiber shapes

In-vivo parcellation of the cerebral cortex via non-invasive neuroimaging data has been in active research for years. A variety of model-driven and/or data-driven computational approaches have been proposed to parcellate the cortex. However, two fundamental common issues in these parcellation methodologies are the features or attributes used to define boundaries between cortical regions and the establishment of correspondences of the parcellated regions across different brains. This paper uses a novel DTI-derived fiber shape feature for the parcellation of cortical gyrus into fine-granularity segments. The gyral parcellation is formulated and solved as a surface vertex clustering problem, in which fiber shape feature similarity is used to define the distances between vertices. Then, we designed and applied a novel multi-view spectral clustering algorithm to group the vertices into group-wise consistent gyral segments across different brains. The experimental results showed that the precentral and postcentral gyrus, as two test-beds, can be consistently parcellated into 10 segments on both hemispheres across different subjects. Evaluation studies using benchmark task-based fMRI and cortical landmarks demonstrated the effectiveness and validity of the proposed methods.

Mapping longitudinal hemispheric structural asymmetries of the human cerebral cortex from birth to 2 years of age

Mapping cortical hemispheric asymmetries in infants would increase our understanding of the origins and developmental trajectories of hemispheric asymmetries. We analyze longitudinal cortical hemispheric asymmetries in 73 healthy subjects at birth, 1, and 2 years of age using surface-based morphometry of magnetic resonance images with a specific focus on the vertex position, sulcal depth, mean curvature, and local surface area. Prominent cortical asymmetries are found around the peri-Sylvian region and superior temporal sulcus (STS) at birth that evolve modestly from birth to 2 years of age. Sexual dimorphisms of cortical asymmetries are present at birth, with males having the larger magnitudes and sizes of the clusters of asymmetries than females that persist from birth to 2 years of age. The left supramarginal gyrus (SMG) is significantly posterior to the right SMG, and the maximum position difference increases from 10.2 mm for males (6.9 mm for females) at birth to 12.0 mm for males (8.4 mm for females) by 2 years of age. The right STS and parieto-occipital sulcus are significantly larger and deeper than those in the left hemisphere, and the left planum temporale is significantly larger and deeper than that in the right hemisphere at all 3 ages. Our results indicate that early hemispheric structural asymmetries are inherent and gender related.

Individual functional ROI optimization via maximization of group-wise consistency of structural and functional profiles

Studying connectivities among functional brain regions and the functional dynamics on brain networks has drawn increasing interest. A fundamental issue that affects functional connectivity and dynamics studies is how to determine the best possible functional brain regions or ROIs (regions of interest) for a group of individuals, since the connectivity measurements are heavily dependent on ROI locations. Essentially, identification of accurate, reliable and consistent corresponding ROIs is challenging due to the unclear boundaries between brain regions, variability across individuals, and nonlinearity of the ROIs. In response to these challenges, this paper presents a novel methodology to computationally optimize ROIs locations derived from task-based fMRI data for individuals so that the optimized ROIs are more consistent, reproducible and predictable across brains. Our computational strategy is to formulate the individual ROI location optimization as a group variance minimization problem, in which group-wise consistencies in functional/structural connectivity patterns and anatomic profiles are defined as optimization constraints. Our experimental results from multimodal fMRI and DTI data show that the optimized ROIs have significantly improved consistency in structural and functional profiles across individuals. These improved functional ROIs with better consistency could contribute to further study of functional interaction and dynamics in the human brain.

Consistent reconstruction of cortical surfaces from longitudinal brain MR images

Accurate and consistent reconstruction of cortical surfaces from longitudinal human brain MR images is of great importance in studying longitudinal subtle change of the cerebral cortex. This paper presents a novel deformable surface method for consistent and accurate reconstruction of inner, central and outer cortical surfaces from longitudinal brain MR images. Specifically, the cortical surfaces of the group-mean image of all aligned longitudinal images of the same subject are first reconstructed by a deformable surface method, which is driven by a force derived from the Laplace's equation. And then the longitudinal cortical surfaces are consistently reconstructed by jointly deforming the cortical surfaces of the group-mean image to all longitudinal images. The proposed method has been successfully applied to two sets of longitudinal human brain MR images. Both qualitative and quantitative experimental results demonstrate the accuracy and consistency of the proposed method. Furthermore, the reconstructed longitudinal cortical surfaces are used to measure the longitudinal changes of cortical thickness in both normal and diseased groups, where the overall decline trend of cortical thickness has been clearly observed. Meanwhile, the longitudinal cortical thickness also shows its potential in distinguishing different clinical groups.

A computational growth model for measuring dynamic cortical development in the first year of life

Human cerebral cortex develops extremely fast in the first year of life. Quantitative measurement of cortical development during this early stage plays an important role in revealing the relationship between cortical structural and high-level functional development. This paper presents a computational growth model to simulate the dynamic development of the cerebral cortex from birth to 1 year old by modeling the cerebral cortex as a deformable elastoplasticity surface driven via a growth model. To achieve a high accuracy, a guidance model is also incorporated to estimate the growth parameters and cortical shapes at later developmental stages. The proposed growth model has been applied to 10 healthy subjects with longitudinal brain MR images acquired at every 3 months from birth to 1 year old. The experimental results show that our proposed method can capture the dynamic developmental process of the cortex, with the average surface distance error smaller than 0.6 mm compared with the ground truth surfaces, and the results also show that 1) the curvedness and sharpness decrease from 2 weeks to 12 months and 2) the frontal lobe shows rapidly increasing cortical folding during this period, with relatively slower increase of the cortical folding in the occipital and parietal lobes.

Template-free detection of macromolecular complexes in cryo electron tomograms

Motivation: Cryo electron tomography (CryoET) produces 3D density maps of biological specimen in its near native states. Applied to small cells, cryoET produces 3D snapshots of the cellular distributions of large complexes. However, retrieving this information is non-trivial due to the low resolution and low signal-to-noise ratio in tomograms. Current pattern recognition methods identify complexes by matching known structures to the cryo electron tomogram. However, so far only a small fraction of all protein complexes have been structurally resolved. It is, therefore, of great importance to develop template-free methods for the discovery of previously unknown protein complexes in cryo electron tomograms.

Results: Here, we have developed an inference method for the template-free discovery of frequently occurring protein complexes in cryo electron tomograms. We provide a first proof-of-principle of the approach and assess its applicability using realistically simulated tomograms, allowing for the inclusion of noise and distortions due to missing wedge and electron optical factors. Our method is a step toward the template-free discovery of the shapes, abundance and spatial distributions of previously unknown macromolecular complexes in whole cell tomograms.

Contact:alber@usc.edu

Supplementary information:Supplementary data are available at Bioinformatics online.

A few thoughts on brain ROIs

Quantitative mapping of structural and functional connectivities in the human brain via non-invasive neuroimaging offers an exciting and unique opportunity to understand brain architecture. Because connectivity alterations are widely reported in a variety of brain diseases, assessment of structural and functional connectivities has emerged as a fundamental research area in clinical neuroscience. A fundamental question arises when attempting to map structural and functional connectivities: how to define and localize the best possible Regions of Interests (ROIs) for brain connectivity mapping? Essentially, when mapping brain connectivities, ROIs provide the structural substrates for measuring connectivities within individual brains and for pooling data across populations. Thus, identification of reliable, reproducible and accurate ROIs is critically important for the success of brain connectivity mapping. This paper discusses several major challenges in defining optimal brain ROIs from our perspective and presents a few thoughts on how to deal with those challenges based on recent research work done in our group.

Consistent sulcal parcellation of longitudinal cortical surfaces

Automated accurate and consistent sulcal parcellation of longitudinal cortical surfaces is of great importance in studying longitudinal morphological and functional changes of human brains, since longitudinal cortical changes are normally very subtle, especially in aging brains. However, applying the existing methods (which were typically developed for cortical sulcal parcellation of a single cortical surface) independently to longitudinal cortical surfaces might generate longitudinally-inconsistent results. To overcome this limitation, this paper presents a novel energy function based method for accurate and consistent sulcal parcellation of longitudinal cortical surfaces. Specifically, both spatial and temporal smoothness are imposed in the energy function to obtain consistent longitudinal sulcal parcellation results. The energy function is efficiently minimized by a graph cut method. The proposed method has been successfully applied to sulcal parcellation of both real and simulated longitudinal inner cortical surfaces of human brain MR images. Both qualitative and quantitative evaluation results demonstrate the validity of the proposed method.

Diffusion tensor-based fast marching for modeling human brain connectivity network

Diffusion tensor imaging (DTI) is an effective modality in studying the connectivity of the brain. To eliminate possible biases caused by fiber extraction approaches due to low spatial resolution of DTI and the number of fibers obtained, the fast marching (FM) algorithm based on the whole diffusion tensor information is proposed to model and study the brain connectivity network. Our observation is that the connectivity extracted from the whole tensor field would be more robust and reliable for constructing brain connectivity network using DTI data. To construct the connectivity network, in this paper, the arrival time map and the velocity map generated by the FM algorithm are combined to define the connectivity strength among different brain regions. The conventional fiber tracking-based and the proposed tensor-based FM connectivity methods are compared, and the results indicate that the connectivity features obtained using the FM-based method agree better with the neuromorphical studies of the human brain.

In-vivo measurement of cortical morphology: means and meanings

PURPOSE OF REVIEW

Study of the variability of the cortical mantle thickness is now a key issue in neuroimaging. Here we describe a more recent trend aiming at the study of the variability of the cortical folding morphology.

RECENT FINDINGS

Computerized three-dimensional versions of gyrification index and other morphometric features dedicated to the folding patterns are modified in psychiatric syndromes and neurologic disorders. These observations provide new insights into the mechanisms involved in abnormal development or abnormal aging.

SUMMARY

Quantification of the folding morphology will contribute to the global endeavor aiming at building biomarkers from neuroimaging data, with a specific focus on developmental diseases.

Parametric representation of cortical surface folding based on polynomials

The development of folding descriptors as an effective approach for describing geometrical complexity and variation of the human cerebral cortex has been of great interests. This paper presents a parametric representation of cortical surface patches using polynomials, that is, the primitive cortical patch is compactly and effectively described by four parametric coefficients. By this parametric representation, the patterns of cortical patches can be classified by either model-driven approach or data-driven clustering approach. In the model-driven approach, any patch of the cortical surface is classified into one of eight primitive shape patterns including peak, pit, ridge, valley, saddle ridge, saddle valley, flat and inflection; corresponding to eight sub-spaces of the four parameters. The major advantage of this polynomial representation of cortical folding pattern is its compactness and effectiveness, while being rich in shape information. We have applied this parametric representation for segmentation of cortical surface and promising results are obtained.

A computational model of cerebral cortex folding

The geometric complexity and variability of the human cerebral cortex have long intrigued the scientific community. As a result, quantitative description of cortical folding patterns and the understanding of underlying folding mechanisms have emerged as important research goals. This paper presents a computational 3D geometric model of cerebral cortex folding initialized by MRI data of a human fetal brain and deformed under the governance of a partial differential equation modeling cortical growth. By applying different simulation parameters, our model is able to generate folding convolutions and shape dynamics of the cerebral cortex. The simulations of this 3D geometric model provide computational experimental support to the following hypotheses: (1) Mechanical constraints of the skull regulate the cortical folding process. (2) The cortical folding pattern is dependent on the global cell growth rate of the whole cortex. (3) The cortical folding pattern is dependent on relative rates of cell growth in different cortical areas. (4) The cortical folding pattern is dependent on the initial geometry of the cortex.

An automated pipeline for cortical sulcal fundi extraction

In this paper, we propose a novel automated pipeline for extraction of sulcal fundi from triangulated cortical surfaces. This method consists of four consecutive steps. Firstly, we adopt a finite difference method to estimate principal curvatures, principal directions and curvature derivatives, along the principal directions, for each vertex. Then, we detect the sulcal fundi segment in each triangle of the cortical surface based on curvatures and curvature derivatives. Afterwards, we link the sulcal fundi segments into continuous curves. Finally, we connect breaking sulcal fundi and smooth bumping sulcal fundi by using the fast marching method on the cortical surface. The proposed method can find the accurate sulcal fundi using curvatures and curvature derivatives without any manual interaction. The method was applied to 10 normal brain MR images on inner cortical surfaces. We quantitatively evaluated the accuracy of the sulcal fundi extraction method using manually labeled sulcal fundi by experts. The average difference between automatically extracted major sulcal fundi and the expert labeled results is consistently around 1.0mm on 10 subject images, indicating the good performance of the proposed method.