Anatomically informed interpolation of fMRI data on the cortical surface

Analyzing functional magnetic resonance imaging (fMRI) data restricted to the cortical surface is of particular interest for two reasons: (1) to increase detection sensitivity using anatomical constraints and (2) to compare or use fMRI results in the context of source localization from magneto/electro-encephalography (MEEG) data, which requires data to be projected on the same spatial support. Designing an optimal scheme to interpolate fMRI raw data or resulting activation maps on the cortical surface relies on a trade-off between choosing large enough interpolation kernels, because of the distributed nature of the hemodynamic response, and avoiding mixing data issued from different anatomical structures. We propose an original method that automatically adjusts the level of such a trade-off, by defining interpolation kernels around each vertex of the cortical surface using a geodesic Vorono? diagram. This Vorono?-based interpolation method was evaluated using simulated fMRI activation maps, manually generated on an anatomical MRI, and compared with a more standard approach where interpolation kernels were defined as local spheres of radius r=3 or 5 mm. Several validation parameters were considered: the spatial resolution of the simulated activation map, the spatial resolution of the cortical mesh, the level of anatomical/functional data misregistration and the location of the vertices within the gray matter ribbon. Using an activation map at the spatial resolution of standard fMRI data, robustness to misregistration errors was observed for both methods, whereas only the Vorono?-based approach was insensitive to the position of the vertices within the gray matter ribbon.     

Automated cortical projection of head-surface locations for transcranial functional brain mapping

Recent advancements in two noninvasive transcranial neuroimaging techniques, near-infrared spectroscopy (NIRS) and transcranial magnetic stimulation (TMS), signify the increasing importance of establishing structural compatibility between transcranial methods and conventional tomographic methods, such as functional magnetic resonance imaging (fMRI) and positron emission tomography (PET). The transcranial data obtained from the head surface should be projected onto the cortical surface to present the transcranial brain-mapping data on the same platform as tomographic methods. Thus, we developed two transcranial projection algorithms that project given head-surface points onto the cortical surface in structural images, and computer programs based on them. The convex-hull algorithm features geometric handling of the cortical surface, while the balloon-inflation algorithm is faster, and better reflects the local cortical structure. The automatic cortical projection methods proved to be as effective as the manual projection method described in our previous study. These methods achieved perfect correspondence between any given point on the head surface or a related nearby point in space, and its cortical projection point. Moreover, we developed a neighbor-reference method that enables transcranial cortical projection of a given head-surface point in reference to three neighboring points and one additional standard point, even when no structural image of the subject is available. We also calculated an error factor associated with these probabilistic estimations. The current study presents a close topological link between transcranial and tomographic brain-mapping modalities, which could contribute to inter-modal data standardization.     

Geometric atlas: modeling the cortex as an organized surface

Recent atlases of the cortical surface are based on a modelization of the cerebral cortex as a topological sphere. This captures effectively its organization as a regular bidimensional sheet of layers parallel to the surface and with perpendicular cortical columns. Yet, while in the vertical direction cortices are almost the same throughout phylia, in the sense of its surface the cerebral cortex is one of the most variable and distinctive parts of the nervous system. Indeed, gyri and sulci appear to have a crucial organizing role in an architectonic, connectional, and functional sense. This organization is not explicitly captured by the surface model of the cortex. We propose a geometric model of the cortical anatomy based on flat representations of principal sulci obtained from surface reconstructions of MRI data, and on neuroanatomical and theoretical considerations concerning the folding patterns of the cortex. The cortex is modeled by a sphere where primary sulci are included as axes. The arrangement of the axes is a simplification of the arrangement of principal sulci observed in flat stereographic representations of the whole cortical surface. The position of secondary and tertiary sulci is then defined by a field of orientations parallel and orthogonal to the axes. We consider the use of the geometric model as a synthetic reference cortex for addressing reconstructions of cortical surfaces. We present a method which establishes a bijection between the geometric model and a cortical surface reconstruction by using the axes of the model as boundary conditions for a set of partial differential equations solved over both surfaces. Using the geometric model as atlas provides a natural parameterization of the cortical surface that, unlike angular coordinates, allows for a localization based on the surface distance to its main organizing landmarks and folding patterns.     

Comparing surface-based and volume-based analyses of functional neuroimaging data in patients with schizophrenia

A major challenge in functional neuroimaging is to cope with individual variability in cortical structure and function. Most analyses of cortical function compensate for variability using affine or low-dimensional nonlinear volume-based registration (VBR) of individual subjects to an atlas, which does not explicitly take into account the geometry of cortical convolutions. A promising alternative is to use surface-based registration (SBR), which capitalizes on explicit surface representations of cortical folding patterns in individual subjects. In this study, we directly compare results from SBR and affine VBR in a study of working memory in healthy controls and patients with schizophrenia (SCZ). Each subject's structural scan was used for cortical surface reconstruction using the SureFit method. fMRI data were mapped directly onto individual cortical surface models, and each hemisphere was registered to the population-average PALS-B12 atlas using landmark-constrained SBR. The precision with which cortical sulci were aligned was much greater for SBR than VBR. SBR produced superior alignment precision across the entire cortex, and this benefit was greater in patients with schizophrenia. We demonstrate that spatial smoothing on the surface provides better resolution and signal preservation than a comparable degree of smoothing in the volume domain. Lastly, the statistical power of functional activation in the working memory task was greater for SBR than for VBR. These results indicate that SBR provides significant advantages over affine VBR when analyzing cortical fMRI activations. Furthermore, these improvements can be even greater in disorders that have associated structural abnormalities.     

Cortical surface-based analysis of 18F-FDG PET: measured metabolic abnormalities in schizophrenia are affected by cortical structural abnormalities

The purpose of the study is to propose a new framework for surface-based statistical parametric mapping of PET images using MRI-based cortical surface analysis, including partial volume correction, intensity normalization and spatial normalization on the cortical surface. Maximum PET intensities along the path between inner and outer layer of the cortical gray matter are mapped onto the cortical surface to generate a metabolic activity surface map. For the partial volume correction, the metabolic activity surface map was divided by the partial volume effect map. The regional metabolic activity was normalized by the global activity iteratively calculated at the surface nodes, statistically independent of the group, as measured by F statistics. After surface-based spatial normalization, a statistical evaluation of both cortical thickness and cortical metabolic activity was conducted on the normalized surfaces of 16 patients with schizophrenia and 16 age- and gender-matched healthy controls. The patients with schizophrenia were found to have significant cortical thinning in the temporal and inferior frontal cortices. Accordingly, their PET imaging was significantly affected by the partial volume effect, indicating that partial volume correction could change the statistical results. After correction of the partial volume effects, the patients showed hyperactivity in the temporal cortex, whereas hypoactivity in the prefrontal cortex, predominantly in the left hemisphere. Our results demonstrate that anatomical factors affect an analysis for functional data from the PET, and therefore the importance of combining anatomy and function in the analysis of imaging data for schizophrenia should be considered.     

An empirical comparison of surface-based and volume-based group studies in neuroimaging

Being able to detect reliably functional activity in a population of subjects is crucial in human brain mapping, both for the understanding of cognitive functions in normal subjects and for the analysis of patient data. The usual approach proceeds by normalizing brain volumes to a common three-dimensional template. However, a large part of the data acquired in fMRI aims at localizing cortical activity, and methods working on the cortical surface may provide better inter-subject registration than the standard procedures that process the data in the volume. Nevertheless, few assessments of the performance of surface-based (2D) versus volume-based (3D) procedures have been shown so far, mostly because inter-subject cortical surface maps are not easily obtained. In this paper we present a systematic comparison of 2D versus 3D group-level inference procedures, by using cluster-level and voxel-level statistics assessed by permutation, in random effects (RFX) and mixed-effects analyses (MFX). We consider different schemes to perform meaningful comparisons between thresholded statistical maps in the volume and on the cortical surface. We find that surface-based multi-subject statistical analyses are generally more sensitive than their volume-based counterpart, in the sense that they detect slightly denser networks of regions when performing peak-level detection; this effect is less clear for cluster-level inference and is reduced by smoothing. Surface-based inference also increases the reliability of the activation maps.     

Reconstruction of central cortical surface from brain MRI images: method and application

Reconstruction of the central surface representation of the cerebral cortex is an important means to study the structure and function of the human brain. In this paper, we propose a novel method based on an elastic transform vector field to drive a deformable model for the reconstruction of the central cortical surface. Both simulated brain cortexes and real brain images are used to evaluate this approach. We applied the surface reconstruction method and a hybrid volumetric and surface registration algorithm to detect simulated brain atrophy. Experimental results show that the central cortical surface representation has better performance in detecting simulated atrophy than the traditionally used inner or outer cortical surface representations.     

A Population-Average, Landmark- and Surface-based (PALS) atlas of human cerebral cortex

This report describes a new electronic atlas of human cerebral cortex that provides a substrate for a wide variety of brain-mapping analyses. The Population-Average, Landmark- and Surface-based (PALS) atlas approach involves surface-based and volume-based representations of cortical shape, each available as population averages and as individual subject data. The specific PALS-B12 atlas introduced here is derived from structural MRI volumes of 12 normal young adults. Accurate cortical surface reconstructions were generated for each hemisphere, and the surfaces were inflated, flattened, and mapped to standard spherical configurations using SureFit and Caret software. A target atlas sphere was generated by averaging selected landmark contours from each of the 24 contributing hemispheres. Each individual hemisphere was deformed to this target using landmark-constrained surface registration. The utility of the resultant PALS-B12 atlas was demonstrated using a variety of analyses. (i) Probabilistic maps of sulcal identity were generated using both surface-based registration (SBR) and conventional volume-based registration (VBR). The SBR approach achieved markedly better consistency of sulcal alignment than did VBR. (ii) A method is introduced for 'multi-fiducial mapping' of volume-averaged group data (e.g., fMRI data, probabilistic architectonic maps) onto each individual hemisphere in the atlas, followed by spatial averaging across the individual maps. This yielded a population-average surface representation that circumvents the biases inherent in choosing any single hemisphere as a target. (iii) Surface-based and volume-based morphometry applied to maps of sulcal depth and sulcal identity demonstrated prominent left-right asymmetries in and near the superior temporal sulcus and Sylvian fissure. Moreover, shape variability in the temporal lobe is significantly greater in the left than the right hemisphere. The PALS-B12 atlas has been registered to other surface-based atlases to facilitate interchange of data and comparison across atlases. All data sets in the PALS-B12 atlas are accessible via the SumsDB database for online and offline visualization and analysis.     

Whole brain diffeomorphic metric mapping via integration of sulcal and gyral curves, cortical surfaces, and images

This paper introduces a novel large deformation diffeomorphic metric mapping algorithm for whole brain registration where sulcal and gyral curves, cortical surfaces, and intensity images are simultaneously carried from one subject to another through a flow of diffeomorphisms. To the best of our knowledge, this is the first time that the diffeomorphic metric from one brain to another is derived in a shape space of intensity images and point sets (such as curves and surfaces) in a unified manner. We describe the Euler-Lagrange equation associated with this algorithm with respect to momentum, a linear transformation of the velocity vector field of the diffeomorphic flow. The numerical implementation for solving this variational problem, which involves large-scale kernel convolution in an irregular grid, is made feasible by introducing a class of computationally friendly kernels. We apply this algorithm to align magnetic resonance brain data. Our whole brain mapping results show that our algorithm outperforms the image-based LDDMM algorithm in terms of the mapping accuracy of gyral/sulcal curves, sulcal regions, and cortical and subcortical segmentation. Moreover, our algorithm provides better whole brain alignment than combined volumetric and surface registration (Postelnicu et al., 2009) and hierarchical attribute matching mechanism for elastic registration (HAMMER) (Shen and Davatzikos, 2002) in terms of cortical and subcortical volume segmentation.     

BrainSuite: an automated cortical surface identification tool

We describe a new magnetic resonance (MR) image analysis tool that produces cortical surface representations with spherical topology from MR images of the human brain. The tool provides a sequence of low-level operations in a single package that can produce accurate brain segmentations in clinical time. The tools include skull and scalp removal, image nonuniformity compensation, voxel-based tissue classification, topological correction, rendering, and editing functions. The collection of tools is designed to require minimal user interaction to produce cortical representations. In this paper we describe the theory of each stage of the cortical surface identification process. We then present classification validation results using real and phantom data. We also present a study of interoperator variability.     

Measuring and comparing brain cortical surface area and other areal quantities

Structural analysis of MRI data on the cortical surface usually focuses on cortical thickness. Cortical surface area, when considered, has been measured only over gross regions or approached indirectly via comparisons with a standard brain. Here we demonstrate that direct measurement and comparison of the surface area of the cerebral cortex at a fine scale is possible using mass conservative interpolation methods. We present a framework for analyses of the cortical surface area, as well as for any other measurement distributed across the cortex that is areal by nature. The method consists of the construction of a mesh representation of the cortex, registration to a common coordinate system and, crucially, interpolation using a pycnophylactic method. Statistical analysis of surface area is done with power-transformed data to address lognormality, and inference is done with permutation methods. We introduce the concept of facewise analysis, discuss its interpretation and potential applications.     

Three-dimensional probabilistic anatomical cranio-cerebral correlation via the international 10-20 system oriented for transcranial functional brain mapping

The recent advent of multichannel near-infrared spectroscopy (NIRS) has expanded its technical potential for human brain mapping. However, NIRS measurement has a technical drawback in that it measures cortical activities from the head surface without anatomical information of the object to be measured. This problem is also found in transcranial magnetic stimulation (TMS) that transcranially activates or inactivates the cortical surface. To overcome this drawback, we examined cranio-cerebral correlation using magnetic resonance imaging (MRI) via the guidance of the international 10-20 system for electrode placement, which had originally been developed for electroencephalography. We projected the 10-20 standard cranial positions over the cerebral cortical surface. After examining the cranio-cerebral correspondence for 17 healthy adults, we normalized the 10-20 cortical projection points of the subjects to the standard Montreal Neurological Institute (MNI) and Talairach stereotactic coordinates and obtained their probabilistic distributions. We also expressed the anatomical structures for the 10-20 cortical projection points probabilistically. Next, we examined the distance between the cortical surface and the head surface along the scalp and created a cortical surface depth map. We found that the locations of 10-20 cortical projection points in the standard MNI or Talairach space could be estimated with an average standard deviation of 8 mm. This study provided an initial step toward establishing a three-dimensional probabilistic anatomical platform that enables intra- and intermodal comparisons of NIRS and TMS brain imaging data.     

A multiple-plane approach to measure the structural properties of functionally active regions in the human cortex

Advanced magnetic resonance imaging (MRI) techniques provide the means of studying both the structural and the functional properties of various brain regions, allowing us to address the relationship between the structural changes in human brain regions and the activity of these regions. However, analytical approaches combining functional (fMRI) and structural (sMRI) information are still far from optimal. In order to improve the accuracy of measurement of structural properties in active regions, the current study tested a new analytical approach that repeated a surface-based analysis at multiple planes crossing different depths of cortex. Twelve subjects underwent a fear conditioning study. During these tasks, fMRI and sMRI scans were acquired. The fMRI images were carefully registered to the sMRI images with an additional correction for cortical borders. The fMRI images were then analyzed with the new multiple-plane surface-based approach as compared to the volume-based approach, and the cortical thickness and volume of an active region were measured. The results suggested (1) using an additional correction for cortical borders and an intermediate template image produced an acceptable registration of fMRI and sMRI images; (2) surface-based analysis at multiple depths of cortex revealed more activity than the same analysis at any single depth; (3) projection of active surface vertices in a ribbon fashion improved active volume estimates; and (4) correction with gray matter segmentation removed non-cortical regions from the volumetric measurement of active regions. In conclusion, the new multiple-plane surface-based analysis approaches produce improved measurement of cortical thickness and volume of active brain regions. These results support the use of novel approaches for combined analysis of functional and structural neuroimaging.     

Robust subdivision of the thalamus in children based on probability distribution functions calculated from probabilistic tractography

Virtually all information that enters the cortex must first pass through the thalamus. This prominent role has made the human thalamus a target for detailed imaging studies. It has previously been shown that probabilistic tractography together with cortical parcellation allowed subdivision of the thalamus into its constituent substructures. A new method is presented that allows the subdivision of the thalamus according to its cortical projection targets based on the assumption that any cortical region receives input from the thalamus and calculates the probability of connectivity distribution functions based on probabilistic tractography. The feasibility of the method was tested in a data set of 43 healthy children aged between 8 and 13 years. A thalamic parcellation pattern similar to that previously found in adults and children below the age of 2 years was obtained. However, no evidence for an age related change in cortical parcellation volumes were found in line with previously reported studies of thalamic volumes during development. Lower standard deviations were found for the two smallest projections, the sensory and occipital projection using the new method. Furthermore it was found, through comparison with a published thalamic atlas, that the method allowed the localization of the center of the different thalamic projection areas within an accuracy of 2 mm.     

A novel quantitative cross-validation of different cortical surface reconstruction algorithms using MRI phantom

Cortical surface reconstruction is important for functional brain mapping and morphometric analysis of the brain cortex. Several methods have been developed for the faithful reconstruction of surface models which represent the true cortical surface in both geometry and topology. However, there has been no explicit comparison study among those methods because each method has its own procedures, file formats, coordinate systems, and use of the reconstructed surface. There has also been no explicit evaluation method except visual inspection to validate the whole-cortical surface models quantitatively. In this study, we presented a novel phantom-based validation method of the cortical surface reconstruction algorithm and quantitatively cross-validated the three most prominent cortical surface reconstruction algorithms which are used in Freesurfer, BrainVISA, and CLASP, respectively. The validation included geometrical accuracy and mesh characteristics such as Euler number, fractal dimension (FD), total surface area, and local density of points. CLASP showed the best geometric/topologic accuracy and mesh characteristics such as FD and total surface area compared to Freesurfer and BrainVISA. In the validation of local density of points, Freesurfer and BrainVISA showed more even distribution of points on the cortical surface compared to CLASP.     

From sMRI to task-fMRI: A unified geometric deep learning framework for cross-modal brain anatomo-functional mapping

Achieving predictions of brain functional activation patterns/task-fMRI maps from its underlying anatomy is an important yet challenging problem. Once successful, it will not only open up new ways to understand how brain anatomy influences functional organization of the brain, but also provide new technical support for the clinical use of anatomical information to guide the localization of cortical functional areas. However, due to the non-Euclidean complex architecture of brain anatomy and the inherent low signal-to-noise ratio (SNR) properties of fMRI signals, the key challenge in building such a cross-modal brain anatomo-functional mapping is how to effectively learn the context-aware information of brain anatomy and overcome the interference of noise-containing task-fMRI labels on the learning process. In this work, we propose a Unified Geometric Deep Learning framework (BrainUGDL) to perform the cross-modal brain anatomo-functional mapping task. Considering that both global and local structures of brain anatomy have an impact on brain functions from their respective perspectives, we innovatively propose the novel Global Graph Encoding (GGE) unit and Local Graph Attention (LGA) unit embedded into two parallel branches, focusing on learning the high-level global and local context information, respectively. Specifically, GGE learns the global context information of each mesh vertex by building and encoding global interactions, and LGA learns the local context information of each mesh vertex by selectively aggregating patch structure enhanced features from its spatial neighbors. The information learnt from the two branches is then fused to form a comprehensive representation of brain anatomical features for final brain function predictions. To address the inevitable measurement noise in task-fMRI labels, we further elaborate a novel uncertainty-filtered learning mechanism, which enables BrainUGDL to realize revised learning from the noise-containing labels through the estimated uncertainty. Experiments across seven open task-fMRI datasets from human connectome project (HCP) demonstrate the superiority of BrainUGDL. To our best knowledge, our proposed BrainUGDL is the first to achieve the prediction of individual task-fMRI maps solely based on brain sMRI data.     

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.     

A multi-resolution scheme for distortion-minimizing mapping between human subcortical structures based on geodesic construction on Riemannian manifolds

In this paper, we deal with a subcortical surface registration problem. Subcortical structures including hippocampi and caudates have a small number of salient features such as heads and tails unlike cortical surfaces. Therefore, it is hard, if not impossible, to perform subcortical surface registration with only such features. It is also non-trivial for neuroanatomical experts to select landmarks consistently for subcortical surfaces of different subjects. We therefore present a landmark-free approach for subcortical surface registration by measuring the amount of mesh distortion between subcortical surfaces assuming that the surfaces are represented by meshes. The input meshes can be constructed using any surface modeling tool available in the public domain since our registration method is independent of a surface modeling process. Given the source and target surfaces together with their representing meshes, the vertex positions of the source mesh are iteratively displaced while preserving the underlying surface shape in order to minimize the distortion to the target mesh. By representing each surface mesh as a point on a high-dimensional Riemannian manifold, we define a distance metric on the manifold that measures the amount of distortion from a given source mesh to the target mesh, based on the notion of isometry while penalizing triangle flipping. Under this metric, we reduce the distortion minimization problem to the problem of constructing a geodesic curve from the moving source point to the fixed target point on the manifold while satisfying the shape-preserving constraint. We adopt a multi-resolution framework to solve the problem for distortion-minimizing mapping between the source and target meshes. We validate our registration scheme through several experiments: distance metric comparison, visual validation using real data, robustness test to mesh variations, feature alignment using anatomic landmarks, consistency with previous clinical findings, and comparison with a surface-based registration method, LDDMM-surface.     

Shape-based cortical surface segmentation for visualization brain mapping

We describe a knowledge-based approach to cortical surface segmentation that uses learned knowledge of the overall shape and range of variation of the cortex (excluding the detailed gyri and sulci) to guide the search for the grey-CSF boundary in a structural MRI image volume. The shape knowledge is represented by a radial surface model, which is a type of geometric constraint network (GCN) that we hypothesize can represent shape by networks of locally interacting constraints. The shape model is used in a protocol for visualization-based mapping of cortical stimulation mapping (CSM) sites onto the brain surface, prior to integration with other mapping modalities or as input to existing surface analysis and reconfiguration programs. Example results are presented for CSM data related to language organization in the cortex, but the methods should be applicable to other situations where a realistic visualization of the brain surface, as seen at neurosurgery, is desired.