Positive definite symmetric matrices (so-called tensors in this article) are nowadays a common source of geometric information. In this paper, we propose to provide the tensor space with an affine-invariant Riemannian metric. We demonstrate that it leads to strong theoretical properties: the cone of positive definite symmetric matrices is replaced by a regular manifold of constant curvature without boundaries (null eigenvalues are at the infinity), the geodesic between two tensors and the mean of a set of tensors are uniquely defined, etc. We have

The anatomical connectivity pattern of a brain region determines its function 1 . Although invasive tracer studies have produced a large body of evidence concerning connectivity patterns in non-human animals 2-4 , direct information concerning brain connections in humans is very limited. Injection of fluorescent dyes post mortem allows tracing of tracts, but only for distances of tens of millimeters 5 . Longer-distance connections can be investigated by dissection of major tracts or histological studies of remote degeneration following a focal lesion 6 , but such work is based on a relatively small number of informative patients. A specific, important focus for investigation is the thalamus because nearly all incoming information to the cortex is routed through this deep gray-matter structure. The thalamus is subdivided into cytoarchitectonically distinct nuclei which have different patterns of anatomical connectivity that are well characterized for non-human animals Diffusion imaging characterizes the apparent diffusion properties of water Here, using a probabilistic tractography algorithm, we were able to infer anatomical connectivity that progresses fully into gray matter. We thus provide a comprehensive description of the connections between thalamus and cortex in the human brain in vivo. An additional result of this approach is the discrimination of human thalamic subregions on the basis of their connections with the cortex. RESULTS We used a fully automated probabilistic tractography algorithm (see Methods) to form connectivity distributions from individual voxels within the thalamus of a single subject. From these distributions, we traced pathways all the way to the cortex Commonly connected thalamic subregions We segmented the cortex into large, anatomically defined regions (see Methods) corresponding to known connection areas of the major thalamic nuclear groups in non-human primates

REVIEWS Behavioural research on ageing has mapped contrasting patterns of decline and stability in cognition across the adult lifespan. Both cross-sectional and longitudinal studies find robust declines in abilities such as encoding new memories of episodes or facts, working memory (the simultaneous short-term maintenance and manipulation of information involving EXECUTIVE PROCESSES) and processing speed (the speed with which information can be processed). By contrast, short-term memory (a component process of working memory), autobiographical memory, semantic knowledge and emotional processing remain relatively stable. This variable vulnerability of human abilities across the adult lifespan indicates that ageing has distinctive effects on the neural systems that subserve various abilities. Understanding age-associated changes in cognition is challenging for several reasons. First, it is often difficult to separate the effects of normal ageing from those of pathological processes that compromise cognition. Most older adults experience some form of age-related neural pathology, because ageing is associated strongly with risk for Alzheimer's disease, Parkinson's disease, diabetes, hypertension and arteriosclerosis. However, research involving highly select and healthy older adults indicates that even in the best case, normal ageing is associated with changes in the neural basis of cognition. Second, because age cannot be experimentally manipulated, conclusions regarding the effects of ageing are necessarily correlational. Third, studies of ageing are often based on cross-sectional comparisons between age groups, to avoid the time and expense of longitudinal research. Few studies have followed individuals from young adulthood into old age, although an increasing number of studies have examined longitudinal changes above the age of 60. Fourth, many brain and mental changes occur in parallel during ageing, and correlational approaches make it challenging to relate particular changes in the brain with particular mental changes. In an effort to infer causal relationships with ageing, researchers attempt to show that age is related to some, but not other, neurocognitive functions. Even with these challenges, advances in brain imaging methods have allowed unprecedented insights into the neural correlates of healthy ageing. This review summarizes recent work in the cognitive neuroscience of ageing, with an emphasis on human neuropsychological and neuroimaging research, that demonstrates the varied nature of age-related neural and psychological changes. We discuss several of the most pressing issues in the cognitive neuroscience of ageing in an attempt to sketch a research agenda for the future. INSIGHTS INTO THE AGEING MIND: A VIEW FROM COGNITIVE NEUROSCIENCE Trey Hedden and John D. E. Gabrieli As we grow older, we may grow wiser, but we can also experience memory loss and cognitive slowing that can interfere with our daily routines. The cognitive neuroscience of human ageing, which relies largely on neuroimaging techniques, relates these cognitive changes to their neural substrates, including structural and functional changes in the prefrontal cortex, medial temporal lobe regions and white matter tracts. Much remains unknown about how normal ageing affects the neural basis of cognition, but recent research on individual differences in the trajectory of ageing effects is helping to distinguish normal from pathological origins of agerelated cognitive changes. EXECUTIVE PROCESSES General purpose cognitive mechanisms for goal-oriented organization and manipulation of information stored in working memory, and for switching among several tasks and sources of information. NATURE REVIEWS | NEUROSCIENCE

This article examines functional and anatomical connectivity in healthy human subjects measured with magnetic resonance imaging methods. Anatomical connectivity in white matter is obtained from measurements of the diffusion tensor. A Monte-Carlo simulation determines the probability that a particle diffuses between two points, with the probability of a jump in a particular direction from a given voxel being based on the local value of the diffusion tensor components. Functional connectivity between grey matter pixels is assessed without recourse to a specific activation paradigm, by calculating the correlation coefficient between random fluctuations in the blood oxygenation level-dependent signal time course in different pixels. The methods are used to examine the

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Abstract — We propose a new white matter atlas creation method that learns a model of the common white matter structures present in a group of subjects. We demonstrate that our atlas creation method, which is based on group spectral clustering of tractography, discovers structures corresponding to expected white matter anatomy such as the corpus callosum, uncinate fasciculus, cingulum bundles, arcuate fasciculus, and corona radiata. The white matter clusters are augmented with expert anatomical labels and stored in a new type of atlas that we call a high-dimensional white matter atlas. We then show how to perform automatic segmentation of tractography from novel subjects by extending the spectral clustering solution, stored in the atlas, using the Nystrom method. We present results regarding the stability of our method and parameter choices. Finally we give results from an atlas creation and automatic segmentation experiment. We demonstrate that our automatic tractography segmentation identifies corresponding white matter regions across hemispheres and across subjects, enabling group comparison of white matter anatomy. Index Terms — diffusion MRI, tractography, white matter, atlas, clustering

Figure 1: Human brain pathways recovered from DT-MRI data using the oriented tensor reconstruction algorithm In this paper we develop a new technique for tracing anatomical fibers from 3D tensor fields. The technique extracts salient tensor features using a local regularization technique that allows the algo-rithm to cross noisy regions and bridge gaps in the data. We applied the method to human brain DT-MRI data and recovered identifiable anatomical structures that correspond to the white matter brain-fiber pathways. The images in this paper are derived from a dataset hav-ing 121x88x60 resolution. We were able to recover fibers with less than the voxel size resolution by applying the regularization tech-nique, i.e., using a priori assumptions about fiber smoothness. The regularization procedure is done through a moving least squares fil-ter directly incorporated in the tracing algorithm.

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White matter is the brain region underlying the gray matter cortex, composed of neuronal fibers coated with electrical insulation called myelin. Previously of interest in demyelinating diseases such as multiple sclerosis, myelin is attracting new interest as an unexpected contributor to a wide range of psychiatric disorders, including depression and schizophrenia. This is stimulating research into myelin involvement in normal cognitive function, learning and IQ. Myelination continues for decades in the human brain; it is modifiable by experience, and it affects information processing by regulating the velocity and synchrony of impulse conduction between distant cortical regions. Cell-culture studies have identified molecular mechanisms regulating myelination by electrical activity, and myelin also limits the critical period for learning through inhibitory proteins that suppress axon sprouting and synaptogenesis. Introduction New findings together with experiments spanning 40 years are forcing a pivotal shift in views of white matter in the brain. White matter comprises over half the human brain, a far greater proportion than in other animals This article considers evidence that white matter is involved in learning, information-processing, neurological and psychological disorders. It examines historical evidence and information from new techniques indicating that white matter changes with functional experience, and it explores the molecular mechanisms. It presents possible mechanisms for white matter effects on synaptic function and cognition, and it outlines unanswered questions and directions for future research.