Effects of mindful-attention and compassion meditation training on amygdala response to emotional stimuli in an ordinary, non-meditative state.

The amygdala has been repeatedly implicated in emotional processing of both positive and negative-valence stimuli. Previous studies suggest that the amygdala response to emotional stimuli is lower when the subject is in a meditative state of mindful-attention, both in beginner meditators after an 8-week meditation intervention and in expert meditators. However, the longitudinal effects of meditation training on amygdala responses have not been reported when participants are in an ordinary, non-meditative state. In this study, we investigated how 8 weeks of training in meditation affects amygdala responses to emotional stimuli in subjects when in a non-meditative state. Healthy adults with no prior meditation experience took part in 8 weeks of either Mindful Attention Training (MAT), Cognitively-Based Compassion Training (CBCT; a program based on Tibetan Buddhist compassion meditation practices), or an active control intervention. Before and after the intervention, participants underwent an fMRI experiment during which they were presented images with positive, negative, and neutral emotional valences from the IAPS database while remaining in an ordinary, non-meditative state. Using a region-of-interest analysis, we found a longitudinal decrease in right amygdala activation in the Mindful Attention group in response to positive images, and in response to images of all valences overall. In the CBCT group, we found a trend increase in right amygdala response to negative images, which was significantly correlated with a decrease in depression score. No effects or trends were observed in the control group. This finding suggests that the effects of meditation training on emotional processing might transfer to non-meditative states. This is consistent with the hypothesis that meditation training may induce learning that is not stimulus- or task-specific, but process-specific, and thereby may result in enduring changes in mental function.

Near-isometric flattening of brain surfaces.

Flattened representations of brain surfaces are often used to visualize and analyze spatial patterns of structural organization and functional activity. Here, we present a set of rigorous criteria and accompanying test cases with which to evaluate flattening algorithms that attempt to preserve shortest-path distances on the original surface. We also introduce a novel flattening algorithm that is the first to satisfy all of these criteria and demonstrate its ability to produce accurate flat maps of human and macaque visual cortex. Using this algorithm, we have recently obtained results showing a remarkable, unexpected degree of consistency in the shape and topographic structure of visual cortical areas within humans and macaques, as well as between these two species.

Exact geodesics and shortest paths on polyhedral surfaces.

We present two algorithms for computing distances along convex and non-convex polyhedral surfaces. The first algorithm computes exact minimal-geodesic distances and the second algorithm combines these distances to compute exact shortest-path distances along the surface. Both algorithms have been extended to compute the exact minimal-geodesic paths and shortest paths. These algorithms have been implemented and validated on surfaces for which the correct solutions are known, in order to verify the accuracy and to measure the run-time performance, which is cubic or less for each algorithm. The exact-distance computations carried out by these algorithms are feasible for large-scale surfaces containing tens of thousands of vertices, and are a necessary component of near-isometric surface flattening methods that accurately transform curved manifolds into flat representations.

Locating the functional and anatomical boundaries of human primary visual cortex.

The primary visual cortex (V1) can be delineated both functionally by its topographic map of the visual field and anatomically by its distinct pattern of laminar myelination. Although it is commonly assumed that the specialized anatomy V1 exhibits corresponds in location with functionally defined V1, demonstrating this in human has not been possible thus far due to the difficulty of determining the location of V1 both functionally and anatomically in the same individual. In this study we use MRI to measure the anatomical and functional V1 boundaries in the same individual and demonstrate close agreement between them. Functional V1 location was measured by parcellating occipital cortex of 10 living humans into visual cortical areas based on the topographic map of the visual field measured using functional MRI. Anatomical V1 location was estimated for these same subjects using a surface-based probabilistic atlas derived from high-resolution structural MRI of the stria of Gennari in 10 intact ex vivo human hemispheres. To ensure that the atlas prediction was correct, it was validated against V1 location measured using an observer-independent cortical parcellation based on the laminar pattern of cell density in serial brain sections from 10 separate individuals. The close agreement between the independent anatomically and functionally derived V1 boundaries indicates that the whole extent of V1 can be accurately predicted based on cortical surface reconstructions computed from structural MRI scans, eliminating the need for functional localizers of V1. In addition, that the primary cortical folds predict the location of functional V1 suggests that the mechanism giving rise to V1 location is tied to the development of the cortical folds.

The intrinsic shape of human and macaque primary visual cortex.

Previous studies have reported considerable variability in primary visual cortex (V1) shape in both humans and macaques. Here, we demonstrate that much of this variability is due to the pattern of cortical folds particular to an individual and that V1 shape is similar among individual humans and macaques as well as between these 2 species. Human V1 was imaged ex vivo using high-resolution (200 microm) magnetic resonance imaging at 7 T. Macaque V1 was identified in published histological serial section data. Manual tracings of the stria of Gennari were used to construct a V1 surface, which was computationally flattened with minimal metric distortion of the cortical surface. Accurate flattening allowed investigation of intrinsic geometric features of cortex, which are largely independent of the highly variable cortical folds. The intrinsic shape of V1 was found to be similar across human subjects using both nonparametric boundary matching and a simple elliptical shape model fit to the data and is very close to that of the macaque monkey. This result agrees with predictions derived from current models of V1 topography. In addition, V1 shape similarity suggests that similar developmental mechanisms are responsible for establishing V1 shape in these 2 species.

Accurate prediction of V1 location from cortical folds in a surface coordinate system.

Previous studies demonstrated substantial variability of the location of primary visual cortex (V1) in stereotaxic coordinates when linear volume-based registration is used to match volumetric image intensities [Amunts, K., Malikovic, A., Mohlberg, H., Schormann, T., and Zilles, K. (2000). Brodmann's areas 17 and 18 brought into stereotaxic space-where and how variable? Neuroimage, 11(1):66-84]. However, other qualitative reports of V1 location [Smith, G. (1904). The morphology of the occipital region of the cerebral hemisphere in man and the apes. Anatomischer Anzeiger, 24:436-451; Stensaas, S.S., Eddington, D.K., and Dobelle, W.H. (1974). The topography and variability of the primary visual cortex in man. J Neurosurg, 40(6):747-755; Rademacher, J., Caviness, V.S., Steinmetz, H., and Galaburda, A.M. (1993). Topographical variation of the human primary cortices: implications for neuroimaging, brain mapping, and neurobiology. Cereb Cortex, 3(4):313-329] suggested a consistent relationship between V1 and the surrounding cortical folds. Here, the relationship between folds and the location of V1 is quantified using surface-based analysis to generate a probabilistic atlas of human V1. High-resolution (about 200 microm) magnetic resonance imaging (MRI) at 7 T of ex vivo human cerebral hemispheres allowed identification of the full area via the stria of Gennari: a myeloarchitectonic feature specific to V1. Separate, whole-brain scans were acquired using MRI at 1.5 T to allow segmentation and mesh reconstruction of the cortical gray matter. For each individual, V1 was manually identified in the high-resolution volume and projected onto the cortical surface. Surface-based intersubject registration [Fischl, B., Sereno, M.I., Tootell, R.B., and Dale, A.M. (1999b). High-resolution intersubject averaging and a coordinate system for the cortical surface. Hum Brain Mapp, 8(4):272-84] was performed to align the primary cortical folds of individual hemispheres to those of a reference template representing the average folding pattern. An atlas of V1 location was constructed by computing the probability of V1 inclusion for each cortical location in the template space. This probabilistic atlas of V1 exhibits low prediction error compared to previous V1 probabilistic atlases built in volumetric coordinates. The increased predictability observed under surface-based registration suggests that the location of V1 is more accurately predicted by the cortical folds than by the shape of the brain embedded in the volume of the skull. In addition, the high quality of this atlas provides direct evidence that surface-based intersubject registration methods are superior to volume-based methods at superimposing functional areas of cortex and therefore are better suited to support multisubject averaging for functional imaging experiments targeting the cerebral cortex.

Isoperimetric graph partitioning for image segmentation.

Spectral graph partitioning provides a powerful approach to image segmentation. We introduce an alternate idea that finds partitions with a small isoperimetric constant, requiring solution to a linear system rather than an eigenvector problem. This approach produces the high quality segmentations of spectral methods, but with improved speed and stability.

Physical limits to spatial resolution of optical recording: clarifying the spatial structure of cortical hypercolumns.

Neurons in macaque primary visual cortex are spatially arranged by their global topographic position and in at least three overlapping local modular systems: ocular dominance columns, orientation pinwheels, and cytochrome oxidase (CO) blobs. Individual neurons in the blobs are not tuned to orientation, and populations of neurons in the pinwheel center regions show weak orientation tuning, suggesting a close relation between pinwheel centers and CO blobs. However, this hypothesis has been challenged by a series of optical recording experiments. In this report, we show that the statistical error associated with photon scatter and absorption in brain tissue combined with the blurring introduced by the optics of the imaging system has typically been in the range of 250 microm. These physical limitations cause a systematic error in the location of pinwheel centers because of the vectorial nature of these patterns, such that the apparent location of a pinwheel center measured by optical recording is never (on average) in the correct in vivo location. The systematic positional offset is approximately 116 microm, which is large enough to account for the claimed misalignment of CO blobs and pinwheel centers. Thus, optical recording, as it has been used to date, has insufficient spatial resolution to accurately locate pinwheel centers. The earlier hypothesis that CO blobs and pinwheel centers are coterminous remains the only hypothesis currently supported by reliable observation.

The V1 -V2-V3 complex: quasiconformal dipole maps in primate striate and extra-striate cortex.

The mapping function w = k log(z + a) is a widely accepted approximation to the topographic structure of primate V1 foveal and parafoveal regions. A better model, at the cost of an additional parameter, captures the full field topographic map in terms of the dipole map function w = k log[(z + a)/(z + b)]. However, neither model describes topographic shear since they are both explicitly complex-analytic or conformal. In this paper, we adopt a simple ansatz for topographic shear in V1, V2, and V3 that assumes that cortical topographic shear is rotational, i.e. a compression along iso-eccentricity contours. We model the constant rotational shear with a quasiconformal mapping, the wedge mapping. Composing this wedge mapping with the dipole mapping provides an approximation to V1, V2, and V3 topographic structure, effectively unifying all three areas into a single V1-V2-V3 complex using five independent parameters. This work represents the first full-field, multi-area, quasiconformal model of striate and extra-striate topographic map structure.

Topographic shear and the relation of ocular dominance columns to orientation columns in primate and cat visual cortex.

Shear has been known to exist for many years in the topographic structure of the primary visual cortex, but has received little attention in the modeling literature. Although the topographic map of V1 is largely conformal (i.e. zero shear), several groups have observed topographic shear in the region of the V1/V2 border. Furthermore, shear has also been revealed by anisotropy of cortical magnification factor within a single ocular dominance column. In the present paper, we make a functional hypothesis: the major axis of the topographic shear tensor provides cortical neurons with a preferred direction of orientation tuning. We demonstrate that isotropic neuronal summation of a sheared topographic map, in the presence of additional random shear, can provide the major features of cortical functional architecture with the ocular dominance column system acting as the principal source of the shear tensor. The major principal axis of the shear tensor determines the direction and its eigenvalues the relative strength of cortical orientation preference. This hypothesis is then shown to be qualitatively consistent with a variety of experimental results on cat and monkey orientation column properties obtained from optical recording and from other anatomical and physiological techniques. In addition, we show that a recent result of Das and Gilbert (Das, A., & Gilbert, C. D., 1997. Distortions of visuotopic map match orientation singularities in primary visual cortex. Nature, 387, 594-598) is consistent with an infinite set of parameterized solutions for the cortical map. We exploit this freedom to choose a particular instance of the Das-Gilbert solution set which is consistent with the full range of local spatial structure in V1. These results suggest that further relationships between ocular dominance columns, orientation columns, and local topography may be revealed by experimental testing.

The Local Structure of Space-variant Images.

Local image structure is widely used in theories of both machine and biological vision. The form of the differential operators describing this structure for space-invariant images has been well documented. Although space-variant coordinates are universally used in mammalian visual systems, the form of the operators in the space-variant coordinate system has received little attention. In this report we derive the form of the most common differential operators and surface characteristics in the space-variant domain and show examples of their use. The operators include the Laplacian, the gradient and the divergence, as well as the fundamental forms of the image treated as a surface. We illustrate the use of these results by deriving the space-variant form of corner detection and image enhancement algorithms. The latter is shown to have interesting properties in the complex log domain, implicitly encoding a variable grid-size integration of the underlying PDE, allowing rapid enhancement of large scale peripheral features while preserving high spatial frequencies in the fovea. Copyright 1997 Elsevier Science Ltd.