Highly accurate surface models of the cerebral cortex are becoming increasingly important as tools in the investigation of the functional organization of the human brain. The construction of such models is difficult using current neuroimaging technology due to the high degree of cortical folding. Even single voxel misclassifications can result in erroneous connections being created between adjacent banks of a sulcus, resulting in a topologically inaccurate model. These topological defects cause the cortical model to no longer be homeomorphic to a sheet, preventing the accurate inflation, flattening, or spherical morphing of the reconstructed cortex. Surface deformation techniques can guarantee the topological correctness of a model, but are time-consuming and may result in geometrically inaccurate models. In order to address this need we have developed a technique for taking a model of the cortex, detecting and fixing the topological defects while leaving that majority of the model intact, resulting in a surface that is both geometrically accurate and topologically correct.

We present a novel approach to creating flat maps of the brain. Our approach attempts to preserve the conformal structure between the original cortical surface in 3-space and the flattened surface. We demonstrate this with data from the human cerebellum. Our maps exhibit quasiconformal behavior and offer several advantages over existing approaches. Introduction l The convoluted surface of the brain, fold complexity and anatomical variability make it difficult to compare anatomical and functional information within and between subjects. l Current visualization techniques (such as projecting functional data onto a rendered cortical surface) make it difficult to compare the location and extent of activated foci. For example, foci buried in deep sulci may appear on the cortical surface and widely separated foci on opposite walls of a sulcus may appear to be close together. Surface Flattening l The surface representing the cortical grey matter is topologically equivalent to a two-dimensi...

We present a novel data smoothing and analysis framework for cortical thickness data defined on the brain cortical manifold. Gaussian kernel smoothing, which weights neighboring observations according to their 3D Euclidean distance, has been widely used in 3D brain images to increase the signal-to-noise ratio. When the observations lie on a convoluted brain surface, however, it is more natural to assign the weights based on the geodesic distance along the surface. We therefore develop a framework for geodesic distance-based kernel smoothing and statistical analysis on the cortical manifolds. As an illustration, we apply our methods in detecting the regions of abnormal cortical thickness in 16 high functioning autistic children via random field based multiple comparison correction that utilizes the new smoothing technique.

Dynamic programming algorithms are presented for automated generation of length minimizing geodesics and curves of extremal curvature on the neocortex of the macaque and the Visible Human. Probabilistic models of curve variation are constructed in terms of the variability in speed, curvature and torsion in the Frenet representation. The work was supported by NSF BIR-9424264 grant to Michael. I. Miller and the Brain Mapping Grant NIH 50567 to David Van Essen and Michael. I. Miller. This paper was submitted February 1 1997 to Pattern Analysis and Machine Intelligence , and resubmitted February 1998. We would like to thank the anonymous referees for their input to the paper, and David Van Essen and Heather Drury for their contribution to constructing the Visible Human cortical surface. y Department of Electrical Engineering, Center for Imaging Science, Washington University St. Louis, MO. 63130 z Division of Applied Mathematics, Brown University, Providence, Rhode Island 1 1 In...

Computational anatomy (CA) is the mathematical study of anatomy I a I = I a BG, an orbit under groups of diffeomorphisms (i.e., smooth invertible mappings) g a G of anatomical exemplars Iaa I. The observable images are the output of medical imaging devices. There are three components that CA examines: (i) constructions of the anatomical submanifolds, (ii) comparison of the anatomical manifolds via estimation of the underlying diffeomorphisms g a G defining the shape or geometry of the anatomical manifolds, and (iii) generation of probability laws of anatomical variation P(d) on the images I for inference and disease testing within anatomical models. This paper reviews recent advances in these three areas applied to shape, growth, and atrophy.

We present a population registration framework that acts on large collections or populations of data volumes. The data alignment procedure runs in a simultaneous fashion, with every member of the population approaching the central tendency of the collection at the same time. Such a mechanism eliminates the need for selecting a particular reference frame a priori, resulting in a non-biased estimate of a digital atlas. Our algorithm adopts an affine congealing framework with an information theoretic objective function and is optimized via a gradientbased stochastic approximation process embedded in a multi-resolution setting. We present experimental results on both synthetic and real images. 1.

We apply nine analytic methods employed currently in imaging neuroscience to simulated and actual BOLD fMRI signals and compare their performances under each signal type. Starting with baseline time series generated by a resting subject during a null hypothesis study, we compare method performance with embedded focal activity in these series of three different types whose magnitudes and time courses are simple, convolved with spatially varying hemodynamic responses, and highly spatially interactive. We then apply these same nine methods to BOLD fMRI time series from contralateral primary motor cortex and ipsilateral cerebellum collected during a sequential finger opposition study. Paired comparisons of results across methods include a voxel-specific concordance correlation

Much of the human cortical surface is obscured from view by the complex pattern of folds, making the spatial relationship between different surface locations hard to interpret. Methods for viewing large portions of the brain's surface in a single flattened representation are described. The flattened representation preserves several key spatial relationships between regions on the cortical surface. The principles used in the implementations and evaluations of the implemen-tation using artificial test surfaces are provided. Results of applying the methods to structural magnetic resonance measurements of the human brain are also shown. The implementation details are available in the source code which is freely available on the Internet. Wandell et al. Cortical Visualization January 2000 2 Introduction The rapid growth of functional magnetic resonance imaging (fMRI) has served to motivate the development of new methods for analyzing and visualizing neuroimaging data. In this p...

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

We present the Spherical Demons algorithm for registering two spherical images. By exploiting spherical vector spline interpolation theory, we show that a large class of regularizors for the modified Demons objective function can be efficiently approximated on the sphere using iterative smoothing. Based on one parameter subgroups of diffeomorphisms, the resulting registration is diffeomorphic and fast. The Spherical Demons algorithm can also be modified to register a given spherical image to a probabilistic atlas. We demonstrate two variants of the algorithm corresponding to warping the atlas or warping the subject. Registration of a cortical surface mesh to an atlas mesh, both with more than 160k nodes requires less than 5 minutes when warping the atlas and less than 3 minutes when warping the subject on a Xeon 3.2GHz single processor machine. This is comparable to the fastest non-diffeomorphic landmarkfree surface registration algorithms. Furthermore, the accuracy of our method compares favorably to the popular FreeSurfer registration algorithm. We validate the technique in two different applications that use registration to transfer segmentation labels onto a new image: (1) parcellation of in-vivo cortical surfaces and (2) Brodmann area localization in ex-vivo cortical surfaces.