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

The human cerebral cortex develops extremely dynamically in the first 2 years 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 18 months 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 18 months of life.     

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

The human cerebral cortex develops extremely dynamically in the first 2 years 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 18 months 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 18 months of life.     

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.     

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.     

Automatic labelling of the human cortical surface using sulcal basins

Human brain mapping aims at establishing correspondences between brain function and brain anatomy. One of the most intriguing problems in this field is the high interpersonal variability of human neuroanatomy which makes studies across many subjects very difficult. The cortical folds ('sulci') often serve as landmarks that help to establish correspondences between subjects. In this paper, we will present a method that automatically detects and attributes neuroanatomical names to the cortical folds using image analysis methods applied to magnetic resonance data of human brains. We claim that the cortical folds can be subdivided into a number of substructures which we call sulcal basins. The concept of sulcal basins allows us to establish a complete parcellation of the cortical surface into separate regions. These regions are neuroanatomically meaningful and can be identified from MR data sets across many subjects. Sulcal basins are segmented using a region growing approach. The automatic labelling is achieved by a model matching technique.     

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 1.0 mm on 10 subject images, indicating the good performance of the proposed method.     

Automatic extraction of sulcal lines on cortical surfaces based on anisotropic geodesic distance

Analyzing cortical sulci is important for studying cortical morphology and brain functions. Although sulcal lines on cortical surfaces can be defined in various ways, it is critical in a neuroimaging study to define a sulcal line along the valley of a cortical surface with a high curvature within a sulcus. To extract the sulcal lines automatically, we present a new geometric algorithm based on the computation of anisotropic skeletons of sulcal regions. Because anisotropic skeletons are highly adaptive to the anisotropic nature of the surface shape, the resulting sulcal lines lie accurately on the valleys of the sulcal areas. Our sulcal lines remain unchanged under local shape variabilities in different human brains. Through experiments, we show that the errors of the sulcal lines for both synthetic data and real cortical surfaces were nearly as constant as the function of random noise. By measuring the changes in sulcal shape in Alzheimer's disease (AD) patients, we further investigated the effectiveness of the accuracy of our sulcal lines using a large sample of MRI data. This study involved 70 normal controls (n [men/women]: 29/41, age [mean ± SD]: 71.7 ± 4.9 years), and 100 AD subjects (37/63, 72.3 ± 5.5). We observe significantly lower absolute average mean curvature and shallower sulcal depth in AD subjects, where the group difference becomes more significant if we measure the quantities along the sulcal lines rather than over the entire sulcal area. The most remarkable difference in the AD patients was the average sulcal depth (control: 11.70 and AD: 11.34).     

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.     

Group-wise consistent cortical parcellation based on connectional profiles

For decades, seeking common, consistent and corresponding anatomical/functional regions across individual brains via cortical parcellation has been a longstanding challenging problem. In our opinion, two major barriers to solve this problem are determining meaningful cortical boundaries that segregate homogeneous regions and establishing correspondences among parcellated regions of multiple brains. To establish a corresponding system across subjects, we recently developed the Dense Individualized and Common Connectivity-based Cortical Landmarks (DICCCOL) system which possesses group-wise consistent white matter fiber connection patterns across individuals and thus provides a dense map of corresponding cortical landmarks. Despite this useful property, however, the DICCCOL landmarks are still far from covering the whole cerebral cortex and do not provide clear structural/functional cortical boundaries. To address the above limitation while leveraging the advantage of DICCCOL, in this paper, we present a novel approach for group-wise consistent parcellation of the cerebral cortex via a hierarchical scheme. In each hierarchical level, DICCCOLs are used as corresponding samples to automatically determine the cluster number so that other cortical surface vertices are iteratively classified into corresponding clusters across subjects within a group-wise classification framework. Experimental results showed that this approach can achieve consistent fine-granularity cortical parcellation with intrinsically-established structural correspondences across individual brains. Besides, comparisons with resting-state and task-based fMRI datasets demonstrated that the group-wise parcellation boundaries segregate functionally homogeneous areas.     

Semiautomatic brain region extraction: a method of parcellating brain regions from structural magnetic resonance images

Structural MR imaging has become essential to the evaluation of regional brain changes in both healthy aging and disease-related processes. Several methods have been developed to measure structure size and regional brain volumes, but many of these methods involve substantial manual tracing and/or landmark identification. We present a new technique, semiautomatic brain region extraction (SABRE), for the rapid and reliable parcellation of cortical and subcortical brain regions. We combine the SABRE parcellation with tissue compartment segmentation [NeuroImage 17 (2002) 1087] to produce measures of gray matter (GM), white matter (WM), ventricular CSF, and sulcal CSF for 26 brain regions. Because SABRE restricts user input to a few easily identified landmarks, inter-rater reliability is high for all volumes, with all coefficients between 0.91 and 0.99. To assess construct validity, we contrasted SABRE-derived volumetric data from healthy young and older adults. Results from the SABRE parcellation and tissue segmentation showed significant differences in multiple brain regions in keeping with regional atrophy described in the literature by researchers using lengthy manual tracing methods. Our findings show that SABRE is a reliable semiautomatic method for assessing regional tissue volumes that provides significant timesavings over purely manual methods, yet maintains information about individual cortical landmarks.     

Mapping techniques for aligning sulci across multiple brains

Visualization and mapping of function on the cortical surface is difficult because of its sulcal and gyral convolutions. Methods to unfold and flatten the cortical surface for visualization and measurement have been described in the literature. This makes visualization and measurement possible, but comparison across multiple subjects is still difficult because of the lack of a standard mapping technique. In this paper, we describe two methods that map each hemisphere of the cortex to a portion of a sphere in a standard way. To quantify how accurately the geometric features of the cortex -- i.e., sulci and gyri -- are mapped into the same location, sulcal alignment across multiple brains is analyzed, and probabilistic maps for different sulcal regions are generated to be used in automatic labelling of segmented sulcal regions.     

Comparison of landmark-based and automatic methods for cortical surface registration

Group analysis of structure or function in cerebral cortex typically involves, as a first step, the alignment of cortices. A surface-based approach to this problem treats the cortex as a convoluted surface and coregisters across subjects so that cortical landmarks or features are aligned. This registration can be performed using curves representing sulcal fundi and gyral crowns to constrain the mapping. Alternatively, registration can be based on the alignment of curvature metrics computed over the entire cortical surface. The former approach typically involves some degree of user interaction in defining the sulcal and gyral landmarks while the latter methods can be completely automated. Here we introduce a cortical delineation protocol consisting of 26 consistent landmarks spanning the entire cortical surface. We then compare the performance of a landmark-based registration method that uses this protocol with that of two automatic methods implemented in the software packages FreeSurfer and BrainVoyager. We compare performance in terms of discrepancy maps between the different methods, the accuracy with which regions of interest are aligned, and the ability of the automated methods to correctly align standard cortical landmarks. Our results show similar performance for ROIs in the perisylvian region for the landmark-based method and FreeSurfer. However, the discrepancy maps showed larger variability between methods in occipital and frontal cortex and automated methods often produce misalignment of standard cortical landmarks. Consequently, selection of the registration approach should consider the importance of accurate sulcal alignment for the specific task for which coregistration is being performed. When automatic methods are used, the users should ensure that sulci in regions of interest in their studies are adequately aligned before proceeding with subsequent analysis.     

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.     

Quantitative comparison and analysis of sulcal patterns using sulcal graph matching: a twin study

The global pattern of cortical sulci provides important information on brain development and functional compartmentalization. Sulcal patterns are routinely used to determine fetal brain health and detect cerebral malformations. We present a quantitative method for automatically comparing and analyzing the sulcal pattern between individuals using a graph matching approach. White matter surfaces were reconstructed from volumetric T1 MRI data and sulcal pits, the deepest points in local sulci, were identified on this surface. The sulcal pattern was then represented as a graph structure with sulcal pits as nodes. The similarity between graphs was computed with a spectral-based matching algorithm by using the geometric features of nodes (3D position, depth and area) and their relationship. In particular, we exploited the feature of graph topology (the number of edges and the paths between nodes) to highlight the interrelated arrangement and patterning of sulcal folds. We applied this methodology to 48 monozygotic twins and showed that the similarity of the sulcal graphs in twin pairs was significantly higher than in unrelated pairs for all hemispheres and lobar regions, consistent with a genetic influence on sulcal patterning. This novel approach has the potential to provide a quantitative and reliable means to compare sulcal patterns.     

Direct cortical mapping via solving partial differential equations on implicit surfaces

In this paper, we propose a novel approach for cortical mapping that computes a direct map between two cortical surfaces while satisfying constraints on sulcal landmark curves. By computing the map directly, we can avoid conventional intermediate parameterizations and help simplify the cortical mapping process. The direct map in our method is formulated as the minimizer of a flexible variational energy under landmark constraints. The energy can include both a harmonic term to ensure smoothness of the map and general data terms for the matching of geometric features. Starting from a properly designed initial map, we compute the map iteratively by solving a partial differential equation (PDE) defined on the source cortical surface. For numerical implementation, a set of adaptive numerical schemes are developed to extend the technique of solving PDEs on implicit surfaces such that landmark constraints are enforced. In our experiments, we show the flexibility of the direct mapping approach by computing smooth maps following landmark constraints from two different energies. We also quantitatively compare the metric preserving property of the direct mapping method with a parametric mapping method on a group of 30 subjects. Finally, we demonstrate the direct mapping method in the brain mapping applications of atlas construction and variability analysis.     

Automatic segmentation of human brain sulci

The neocortical surface has a rich and complex structure comprised of folds (gyri) and fissures (sulci). Sulci are important macroscopic landmarks for orientation on the cortex. A precise segmentation and labeling of sulci is helpful in human brain mapping studies relating brain anatomy and function. Due to their structural complexity and inter-subject variability, this is considered as a non-trivial task. An automatic algorithm is proposed to accurately segment neocortical sulci: vertices of a white/gray matter interface mesh are classified under a Bayesian framework as belonging to gyral and sulcal compartments using information about their geodesic depth and local curvature. Then, vertices are collected into sulcal regions by a watershed-like growing method. Experimental results demonstrate that the method is accurate and robust.     

Automatic sulcal line extraction on cortical surfaces using geodesic path density maps

We present here a method that is designed to automatically extract sulcal lines on the mesh of any cortical surface. The method is based on the definition of a new function, the Geodesic Path Density Map (GPDM), within each sulcal basin (i.e. regions with a negative mean curvature). GPDM indicates at each vertex the likelihood that a shortest path between any two points of the basins boundary goes through that vertex. If the distance used to compute shortest path is anisotropic and constrained by a geometric information such as the depth, the GPDM indicates the likelihood that a vertex belongs to the sulcal line in the basin. An automatic GPDM adaptive thresholding procedure is proposed and sulcal lines are then defined. The process has been validated on a set of 25 subjects by comparing results to the manual segmentation from an expert and showed an average error below 2mm. It is also compared to our previous reference method in the context of inter-subject cortical surface registration and shows an significant improvement in performance.     

Symmetric abnormalities in sulcal patterning in schizophrenia

To compare the morphology of the cerebral cortex and its characteristic pattern of gyri and sulci in individuals with and without schizophrenia, T1-weighted magnetic resonance scans were collected, along with clinical and cognitive information, from 33 individuals with schizophrenia and 30 healthy individuals group-matched for age, gender, race and parental socioeconomic status. Sulcal depth was measured across the entire cerebral cortex by reconstructing surfaces of cortical mid-thickness (layer 4) in each hemisphere and registering them to the human PALS cortical atlas. Group differences in sulcal depth were tested using methods for cluster size analysis and interhemispheric symmetry analysis. A significant group difference was found bilaterally in the parietal operculum, where the average sulcal depth was shallower in individuals with schizophrenia. In addition, group differences in sulcal depth showed significant bilateral symmetry across much of the occipital, parietal, and temporal cortices. In individuals with schizophrenia, sulcal depth in the left hemisphere was correlated with the severity of impaired performance on tests of working memory and executive function.     

Cortical reconstruction using implicit surface evolution: accuracy and precision analysis

Two different studies were conducted to assess the accuracy and precision of an algorithm developed for automatic reconstruction of the cerebral cortex from T1-weighted magnetic resonance (MR) brain images. Repeated scans of three different brains were used to quantify the precision of the algorithm, and manually selected landmarks on different sulcal regions throughout the cortex were used to analyze the accuracy of the three reconstructed surfaces: inner, central, and pial. We conclude that the algorithm can find these surfaces in a robust fashion and with subvoxel accuracy, typically with an accuracy of one third of a voxel, although this varies with brain region and cortical geometry. Parameters were adjusted on the basis of this analysis in order to improve the algorithm's overall performance.