Extracting and Representing the Cortical Sulci

Modeling functional difference between gyri and sulci within intrinsic connectivity networks

Recently, the functional roles of the human cortical folding patterns have attracted increasing interest in the neuroimaging community. However, most existing studies have focused on the gyro-sulcal functional relationship on a whole-brain scale but possibly overlooked the localized and subtle functional differences of brain networks. Actually, accumulating evidences suggest that functional brain networks are the basic unit to realize the brain function; thus, the functional relationships between gyri and sulci still need to be further explored within different functional brain networks. Inspired by these evidences, we proposed a novel intrinsic connectivity network (ICN)-guided pooling-trimmed convolutional neural network (I-ptFCN) to revisit the functional difference between gyri and sulci. By testing the proposed model on the task functional magnetic resonance imaging (fMRI) datasets of the Human Connectome Project, we found that the classification accuracy of gyral and sulcal fMRI signals varied significantly for different ICNs, indicating functional heterogeneity of cortical folding patterns in different brain networks. The heterogeneity may be contributed by sulci, as only sulcal signals show heterogeneous frequency features across different ICNs, whereas the frequency features of gyri are homogeneous. These results offer novel insights into the functional difference between gyri and sulci and enlighten the functional roles of cortical folding patterns.

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.

Micro-probing enables fine-grained mapping of neuronal populations using fMRI

The characterization of receptive field (RF) properties is fundamental to understanding the neural basis of sensory and cognitive behaviour. The combination of non-invasive imaging, such as fMRI, with biologically inspired neural modelling has enabled the estimation of population RFs directly in humans. However, current approaches require making numerous a priori assumptions, so these cannot reveal unpredicted properties, such as fragmented RFs or subpopulations. This is a critical limitation in studies on adaptation, pathology or reorganization. Here, we introduce micro-probing (MP), a technique for fine-grained and largely assumption free characterization of multiple pRFs within a voxel. It overcomes many limitations of current approaches by enabling detection of unexpected RF shapes, properties and subpopulations, by enhancing the spatial detail with which we analyze the data. MP is based on tiny, fixed-size, Gaussian models that efficiently sample the entire visual space and create fine-grained probe maps. Subsequently, we derived population receptive fields (pRFs) from these maps. We demonstrate the scope of our method through simulations and by mapping the visual fields of healthy participants and of a patient group with highly abnormal RFs due to a congenital pathway disorder. Without using specific stimuli or adapted models, MP mapped the bilateral pRFs characteristic of observers with albinism. In healthy observers, MP revealed that voxels may capture the activity of multiple subpopulations RFs that sample distinct regions of the visual field. Thus, MP provides a versatile framework to visualize, analyze and model, without restrictions, the diverse RFs of cortical subpopulations in health and disease.

Diffusion weighted imaging-based maximum density path analysis and classification of Alzheimer's disease

Characterizing brain changes in Alzheimer's disease (AD) is important for patient prognosis and for assessing brain deterioration in clinical trials. In this diffusion weighted imaging study, we used a new fiber-tract modeling method to investigate white matter integrity in 50 elderly controls (CTL), 113 people with mild cognitive impairment, and 37 AD patients. After clustering tractography using a region-of-interest atlas, we used a shortest path graph search through each bundle's fiber density map to derive maximum density paths (MDPs), which we registered across subjects. We calculated the fractional anisotropy (FA) and mean diffusivity (MD) along all MDPs and found significant MD and FA differences between AD patients and CTL subjects, as well as MD differences between CTL and late mild cognitive impairment subjects. MD and FA were also associated with widely used clinical scores. As an MDP is a compact low-dimensional representation of white matter organization, we tested the utility of diffusion tensor imaging measures along these MDPs as features for support vector machine based classification of AD.

Cortical sulci recognition and spatial normalization

Brain mapping techniques pair similar anatomical information across individuals. In this context, spatial normalization is mainly used to reduce inter-subject differences to improve comparisons. These techniques may benefit from anatomically identified landmarks useful to drive the registration. Automatic labeling, classification or segmentation techniques provide such labels. Most of these approaches depend strongly on normalization, as much as normalization depends on landmark accuracy. We propose in this paper a coherent Bayesian framework to automatically identify approximately 60 sulcal labels per hemisphere based on a probabilistic atlas (a mixture of spam models: Statistical Probabilistic Anatomy Map) estimating simultaneously normalization parameters. This way, the labelization method provides also with no extra computational costs a new automatically constrained registration of sulcal structures. We have limited our study to global affine and piecewise affine registration. The suggested global affine approach outperforms significantly standard affine intensity-based normalization techniques in term of sulci alignments. Further, by combining global and local joint labeling, a final mean recognition rate of 86% has been obtained with much more reliable labeling posterior probabilities. The different methods described in this paper have been integrated since the release version 3.2.1 of the BrainVISA software platform (Riviére et al., 2009).

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.

Image-guided intraoperative cortical deformation recovery using game theory: application to neocortical epilepsy surgery

During neurosurgery, nonrigid brain deformation prevents preoperatively-acquired images from accurately depicting the intraoperative brain. Stereo vision systems can be used to track intraoperative cortical surface deformation and update preoperative brain images in conjunction with a biomechanical model. However, these stereo systems are often plagued with calibration error, which can corrupt the deformation estimation. In order to decouple the effects of camera calibration from the surface deformation estimation, a framework that can solve for disparate and often competing variables is needed. Game theory, which was developed to handle decision making in this type of competitive environment, has been applied to various fields from economics to biology. In this paper, game theory is applied to cortical surface tracking during neocortical epilepsy surgery and used to infer information about the physical processes of brain surface deformation and image acquisition. The method is successfully applied to eight in vivo cases, resulting in an 81% decrease in mean surface displacement error. This includes a case in which some of the initial camera calibration parameters had errors of 70%. Additionally, the advantages of using a game theoretic approach in neocortical epilepsy surgery are clearly demonstrated in its robustness to initial conditions.

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

The human cerebral cortex is a highly convoluted structure composed of sulci and gyri, corresponding to the valleys and ridges of the cortical surface respectively. Automatic parcellation of the cortical surface into sulcal regions is of great importance in structural and functional mapping of the human brain. In this paper, a novel method is proposed for automatic cortical sulcal parcellation based on the geometric characteristics of cortical surface including its principal curvatures and principal directions. This method is composed of two major steps: 1) employing the hidden Markov random field model (HMRF) and the expectation maximization (EM) algorithm on the maximum principal curvatures of the cortical surface for sulcal region segmentation, and 2) using a principal direction flow field tracking method on the cortical surface for sulcal basin segmentation. The flow field is obtained by diffusing the principal direction field on the cortical surface mesh. A unique feature of this method is that the automatic sulcal parcellation process is quite robust and efficient, and is independent of any external guidance such as atlas-based warping. The method has been successfully applied to the inner cortical surfaces of twelve healthy human brain MR images. Both quantitative and qualitative evaluation results demonstrate the validity and efficiency of the proposed method.

Joint sulcal detection on cortical surfaces with graphical models and boosted priors

In this paper, we propose an automated approach for the joint detection of major sulci on cortical surfaces. By representing sulci as nodes in a graphical model, we incorporate Markovian relations between sulci and formulate their detection as a maximum a posteriori (MAP) estimation problem over the joint space of major sulci. To make the inference tractable, a sample space with a finite number of candidate curves is automatically generated at each node based on the Hamilton-Jacobi skeleton of sulcal regions. Using the AdaBoost algorithm, we learn both individual and pairwise shape priors of sulcal curves from training data, which are then used to define potential functions in the graphical model based on the connection between AdaBoost and logistic regression. Finally belief propagation is used to perform the MAP inference and select the joint detection results from the sample spaces of candidate curves. In our experiments, we quantitatively validate our algorithm with manually traced curves and demonstrate the automatically detected curves can capture the main body of sulci very accurately. A comparison with independently detected results is also conducted to illustrate the advantage of the joint detection approach.

Hamilton-Jacobi skeleton on cortical surfaces

In this paper, we propose a new method to construct graphical representations of cortical folding patterns by computing skeletons on triangulated cortical surfaces. In our approach, a cortical surface is first partitioned into sulcal and gyral regions via the solution of a variational problem using graph cuts, which can guarantee global optimality. After that, we extend the method of Hamilton-Jacobi skeleton [1] to subsets of triangulated surfaces, together with a geometrically intuitive pruning process that can trade off between skeleton complexity and the completeness of representing folding patterns. Compared with previous work that uses skeletons of 3-D volumes to represent sulcal patterns, the skeletons on cortical surfaces can be easily decomposed into branches and provide a simpler way to construct graphical representations of cortical morphometry. In our experiments, we demonstrate our method on two different cortical surface models, its ability of capturing major sulcal patterns and its application to compute skeletons of gyral regions.

Brain functional localization: a survey of image registration techniques

Functional localization is a concept which involves the application of a sequence of geometrical and statistical image processing operations in order to define the location of brain activity or to produce functional/parametric maps with respect to the brain structure or anatomy. Considering that functional brain images do not normally convey detailed structural information and, thus, do not present an anatomically specific localization of functional activity, various image registration techniques are introduced in the literature for the purpose of mapping functional activity into an anatomical image or a brain atlas. The problems addressed by these techniques differ depending on the application and the type of analysis, i.e., single-subject versus group analysis. Functional to anatomical brain image registration is the core part of functional localization in most applications and is accompanied by intersubject and subject-to-atlas registration for group analysis studies. Cortical surface registration and automatic brain labeling are some of the other tools towards establishing a fully automatic functional localization procedure. While several previous survey papers have reviewed and classified general-purpose medical image registration techniques, this paper provides an overview of brain functional localization along with a survey and classification of the image registration techniques related to this problem.

Joint Sulci Detection Using Graphical Models and Boosted Priors

In this paper we propose an automated approach for joint sulci detection on cortical surfaces by using graphical models and boosting techniques to incorporate shape priors of major sulci and their Markovian relations. For each sulcus, we represent it as a node in the graphical model and associate it with a sample space of candidate curves, which is generated automatically using the Hamilton-Jacobi skeleton of sulcal regions. To take into account individual as well as joint priors about the shape of major sulci, we learn the potential functions of the graphical model using AdaBoost algorithm to select and fuse information from a large set of features. This discriminative approach is especially powerful in capturing the neighboring relations between sulcal lines, which are otherwise hard to be captured by generative models. Using belief propagation, efficient inferencing is then performed on the graphical model to estimate each sulcus as the maximizer of its final belief. On a data set of 40 cortical surfaces, we demonstrate the advantage of joint detection on four major sulci: central, precentral, postcentral and the sylvian fissure.

Abnormal cortical complexity and thickness profiles mapped in Williams syndrome

We identified and mapped an anatomically localized failure of cortical maturation in Williams syndrome (WS), a genetic condition associated with deletion of approximately 20 contiguous genes on chromosome 7. Detailed three-dimensional (3D) maps of cortical thickness, based on magnetic resonance imaging (MRI) scans of 164 brain hemispheres, identified a delimited zone of right hemisphere perisylvian cortex that was thicker in WS than in matched controls, despite pervasive gray and white matter deficits and reduced total cerebral volumes. 3D cortical surface models were extracted from 82 T1-weighted brain MRI scans (256 x 192 x 124 volumes) of 42 subjects with genetically confirmed WS (mean +/- SD, 29.2 +/- 9.0 years of age; 19 males, 23 females) and 40 age-matched healthy controls (27.5 +/- 7.4 years of age; 16 males, 24 females). A cortical pattern-matching technique used 72 sulcal landmarks traced on each brain as anchors to align cortical thickness maps across subjects, build group average maps, and identify regions with altered cortical thickness in WS. Cortical models were remeshed in frequency space to compute their fractal dimension (surface complexity) for each hemisphere and lobe. Surface complexity was significantly increased in WS (p < 0.0015 and p < 0.0014 for left and right hemispheres, respectively) and correlated with temporoparietal gyrification differences, classified via Steinmetz criteria. In WS, cortical thickness was increased by 5-10% in a circumscribed right hemisphere perisylvian and inferior temporal zone (p < 0.002). Spatially extended cortical regions were identified with increased complexity and thickness; cortical thickness and complexity were also positively correlated in controls (p < 0.03). These findings visualize cortical zones with altered anatomy in WS, which merit additional study with techniques to assess function and connectivity.

Program for Assisted Labeling of Sulcal Regions (PALS): description and reliability

With the improvements in techniques for generating surface models from magnetic resonance (MR) images, it has recently become feasible to study the morphological characteristics of the human brain cortex in vivo. Studies of the entire surface are important for measuring global features, but analysis of specific cortical regions of interest provides a more detailed understanding of structure. We have previously developed a method for automatically segmenting regions of interest from the cortical surface using a watershed transform. Each segmented region corresponds to a cortical sulcus and is thus termed a "sulcal region." In this work, we describe two important augmentations of this methodology. First, we describe a user interface that allows for the efficient labeling of the segmented sulcal regions called the Program for Assisted Labeling of Sulcal Regions (PALS). An additional augmentation allows for even finer divisions on the cortex with a methodology that employs the fast marching technique to track a curve on the cortical surface that is then used to separate segmented regions. After regions of interest have been identified, we compute both the cortical surface area and gray matter volume. Reliability experiments are performed to assess both the long-term stability and short-term repeatability of the proposed techniques. These experiments indicate the proposed methodology gives both highly stable and repeatable results.

ROC-based assessments of 3D cortical surface-matching algorithms

Algorithms for the semi-automated analysis of brain surfaces have recently received considerable attention, and yet, they rarely receive a rigorous assessment of their performance. We present a method for the quantitative assessment of performance across differing surface analysis algorithms and across various modifications of a single algorithm. The sensitivity and specificity of an algorithm for detecting known deformations added synthetically to the brains being studied are assessed using curves for Receiver Operating Characteristics (ROC). We also present a method for the isolation of sources of variance in MRI data sets that can contribute to degradation in performance of surface-matching algorithms. Isolation of these sources of variance allows determination of whether degradation in performance of surface-matching algorithms derives primarily from errors in registration of brains to a common coordinate space, from errors in placement of the known deformation, or from interindividual or between-group variability in morphology of the cortical surface. We apply these methods to the study of surface-matching algorithms that are based on fluid flow (FF) deformation, geodesic (GD) interpolation, or nearest neighbor (NN) proximity. We show that the performances of surface-matching algorithms depend on the presence of interindividual and between-group variability in the surfaces surrounding the cortical deformation. We also show that, in general, the FF algorithm performs as well as or better than the GD and NN algorithms. The large variance in identifying point correspondences across brain surfaces using the GD and the NN algorithms suggests strongly that these point correspondences are less valid than those determined by the FF algorithm. The GD and NN algorithms, moreover, are both vulnerable to detecting false-positive activations at points of high curvature, particularly along large fissures, cisterns, and cortical sulci.

"Sulcal Root" Generic Model: a Hypothesis to Overcome the Variability of the Human Cortex Folding Patterns

The great variability of cerebral cortical folding patterns raises major problems for the systematic study of functional-structural relationships. This paper describes a novel perspective for explaining this variability, a perspective that relies on gyri buried in the depth of the sulci. From this perspective we propose a generic model of folding, based on indivisible units, called sulcal roots, which correspond to the first folding locations during antenatal life. These units are organized according to a basic scheme allowing us to describe the cortical surface using a system of meridians and parallels. This scheme is thought to be stable across individuals at the fetal stage, and may be related to the protomap model. Variability at the adult stage is thought to result from the chaotic behavior of the folding process: inter-individual differences in cortical areas can lead to qualitatively different folding patterns. We have tested the capacity of this model to match actual cortical anatomy with a database of magnetic resonance images of 20 normal subjects, using new three-dimensional visualization tools giving access to shapes buried in the cortex.

Analysis of the hemispheric asymmetry using fractal dimension of a skeletonized cerebral surface

We investigated hemispheric asymmetry using the fractal dimension (FD) of the skeletonized cerebral surface. Sixty-two T1-weighted magnetic resonance imaging volumes from normal Korean adults were used. The skeletonization of binary volume data, which corresponded to the union of the gray matter and cerebrospinal flow classified by fuzzy clustering, was performed slice by slice in the sagittal direction, and then skeletonized slices were integrated into the three-dimensional (3-D) hemisphere. Finally, the FD of the 3-D skeletonized cerebral surface was calculated using the box-counting method. We measured the FD of the skeletonized cerebral surface and the volumes of intracranial gray matter and white matter for the whole hemispheres and obtained the hemispheric asymmetries of each measurement. The FD, the gray matter, and the white matter volumes for the whole hemispheres decreased in the old group. The asymmetry of the FD revealed a significant right-greater-than-left asymmetry showed rightward, but did not change according to age and gender. None of the intracranial gray matter or white matter volumes showed any significant asymmetric changes. It could be said that the FD of the skeletonized cerebral surface is a novel measure of cerebral asymmetry.

Automated sulcal segmentation using watersheds on the cortical surface

The human cortical surface is a highly complex, folded structure. Sulci, the spaces between the folds, define location on the cortex and provide a parcellation into anatomically distinct areas. A topic that has recently received increased attention is the segmentation of these sulci from magnetic resonance images, with most work focusing on extracting either the sulcal spaces between the folds or curve representations of sulci. Unlike these methods, we propose a technique that extracts actual regions of the cortical surface that surround sulci, which we call "sulcal regions." The method is based on a watershed algorithm applied to a geodesic depth measure on the cortical surface. A well-known problem with the watershed algorithm is a tendency toward oversegmentation, meaning that a single region is segmented as several pieces. To address this problem, we propose a postprocessing algorithm that merges appropriate segments from the watershed algorithm. The sulcal regions are then manually labeled by simply selecting the appropriate regions with a mouse click and a preliminary study of sulcal depth is reported. Finally, a scheme is presented for computing a complete parcellation of the cortical surface.

Turning Unorganized Points into Contours

There are a variety of research applications that require reconstruction of objects from unorganized points. In our implementation, we accomplish this task in two steps: first by connecting points to contours and then contours to objects. We focus on the first step in this paper. We present a Voxel-coding algorithm which assembles unorganized points into contours in a straightforward and efficient way. First the points are converted into a binary volumetric object using simple 3D Voxel-coding starting with voxels that include the sample points. Then contours are interpreted as centerlines of cross-sections. The centerlines are obtained by using a series of2D Voxel-coding operations.Input points are sampled from an unknown object satisfying certain sampling criteria. No additional details about the input data are needed. Output contours pass through or approximate sample points. The algorithm is tested with several data sets, showing its efficiency.

Efficient Skeletonization of Volumetric Objects

Skeletonization promises to become a powerful tool for compact shape description, path planning, and other applications. However, current techniques can seldom efficiently process real, complicated 3D data sets, such as MRI and CT data of human organs. In this paper, we present an efficient voxel-coding based algorithm for Skeletonization of 3D voxelized objects. The skeletons are interpreted as connected centerlines. consisting of sequences of medial points of consecutive clusters. These centerlines are initially extracted as paths of voxels, followed by medial point replacement, refinement, smoothness, and connection operations. The voxel-coding techniques have been proposed for each of these operations in a uniform and systematic fashion. In addition to preserving basic connectivity and centeredness, the algorithm is characterized by straightforward computation, no sensitivity to object boundary complexity, explicit extraction of ready-to-parameterize and branch-controlled skeletons, and efficient object hole detection. These issues are rarely discussed in traditional methods. A range of 3D medical MRI and CT data sets were used for testing the algorithm, demonstrating its utility.