Exact geodesics and shortest paths on polyhedral surfaces

Simulating human sleep spindle MEG and EEG from ion channel and circuit level dynamics

BACKGROUND

Although they form a unitary phenomenon, the relationship between extracranial M/EEG and transmembrane ion flows is understood only as a general principle rather than as a well-articulated and quantified causal chain.

METHOD

We present an integrated multiscale model, consisting of a neural simulation of thalamus and cortex during stage N2 sleep and a biophysical model projecting cortical current densities to M/EEG fields. Sleep spindles were generated through the interactions of local and distant network connections and intrinsic currents within thalamocortical circuits. 32,652 cortical neurons were mapped onto the cortical surface reconstructed from subjects' MRI, interconnected based on geodesic distances, and scaled-up to current dipole densities based on laminar recordings in humans. MRIs were used to generate a quasi-static electromagnetic model enabling simulated cortical activity to be projected to the M/EEG sensors.

RESULTS

The simulated M/EEG spindles were similar in amplitude and topography to empirical examples in the same subjects. Simulated spindles with more core-dominant activity were more MEG weighted.

COMPARISON WITH EXISTING METHODS

Previous models lacked either spindle-generating thalamic neural dynamics or whole head biophysical modeling; the framework presented here is the first to simultaneously capture these disparate scales.

CONCLUSIONS

This multiscale model provides a platform for the principled quantitative integration of existing information relevant to the generation of sleep spindles, and allows the implications of future findings to be explored. It provides a proof of principle for a methodological framework allowing large-scale integrative brain oscillations to be understood in terms of their underlying channels and synapses.

Axonal Projections From the Middle Temporal Area in the Common Marmoset

Neural activity in the middle temporal (MT) area is modulated by the direction and speed of motion of visual stimuli. The area is buried in a sulcus in the macaque, but exposed to the cortical surface in the marmoset, making the marmoset an ideal animal model for studying MT function. To better understand the details of the roles of this area in cognition, underlying anatomical connections need to be clarified. Because most anatomical tracing studies in marmosets have used retrograde tracers, the axonal projections remain uncharacterized. In order to examine axonal projections from MT, we utilized adeno-associated viral (AAV) tracers, which work as anterograde tracers by expressing either green or red fluorescent protein in infected neurons. AAV tracers were injected into three sites in MT based on retinotopy maps obtained via in vivo optical intrinsic signal imaging. Brains were sectioned and divided into three series, one for fluorescent image scanning and two for myelin and Nissl substance staining to identify specific brain areas. Overall projection patterns were similar across the injections. MT projected to occipital visual areas V1, V2, V3 (VLP) and V4 (VLA) and surrounding areas in the temporal cortex including MTC (V4T), MST, FST, FSTv (PGa/IPa) and TE3. There were also projections to the dorsal visual pathway, V3A (DA), V6 (DM) and V6A, the intraparietal areas AIP, LIP, MIP, frontal A4ab and the prefrontal cortex, A8aV and A8C. There was a visuotopic relationship with occipital visual areas. In a marmoset in which two tracer injections were made, the projection targets did not overlap in A8aV and AIP, suggesting topographic projections from different parts of MT. Most of these areas are known to send projections back to MT, suggesting that they are reciprocally connected with it.

Brain surface conformal parameterization with the Ricci flow

In brain mapping research, parameterized 3-D surface models are of great interest for statistical comparisons of anatomy, surface-based registration, and signal processing. Here, we introduce the theories of continuous and discrete surface Ricci flow, which can create Riemannian metrics on surfaces with arbitrary topologies with user-defined Gaussian curvatures. The resulting conformal parameterizations have no singularities and they are intrinsic and stable. First, we convert a cortical surface model into a multiple boundary surface by cutting along selected anatomical landmark curves. Secondly, we conformally parameterize each cortical surface to a parameter domain with a user-designed Gaussian curvature arrangement. In the parameter domain, a shape index based on conformal invariants is computed, and inter-subject cortical surface matching is performed by solving a constrained harmonic map. We illustrate various target curvature arrangements and demonstrate the stability of the method using longitudinal data. To map statistical differences in cortical morphometry, we studied brain asymmetry in 14 healthy control subjects. We used a manifold version of Hotelling's T(2) test, applied to the Jacobian matrices of the surface parameterizations. A permutation test, along with the cumulative distribution of p-values, were used to estimate the overall statistical significance of differences. The results show our algorithm's power to detect subtle group differences in cortical surfaces.

Construction of Iso-Contours, Bisectors, and Voronoi Diagrams on Triangulated Surfaces

In the research of computer vision and machine perception, 3D objects are usually represented by 2-manifold triangular meshes M. In this paper, we present practical and efficient algorithms to construct iso-contours, bisectors, and Voronoi diagrams of point sites on M, based on an exact geodesic metric. Compared to euclidean metric spaces, the Voronoi diagrams on M exhibit many special properties that fail all of the existing euclidean Voronoi algorithms. To provide practical algorithms for constructing geodesic-metric-based Voronoi diagrams on M, this paper studies the analytic structure of iso-contours, bisectors, and Voronoi diagrams on M. After a necessary preprocessing of model M, practical algorithms are proposed for quickly obtaining full information about iso--contours, bisectors, and Voronoi diagrams on M. The complexity of the construction algorithms is also analyzed. Finally, three interesting applications-surface sampling and reconstruction, 3D skeleton extraction, and point pattern analysis-are presented that show the potential power of the proposed algorithms in pattern analysis.

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.

Multivariate tensor-based morphometry on surfaces: application to mapping ventricular abnormalities in HIV/AIDS

Here we developed a new method, called multivariate tensor-based surface morphometry (TBM), and applied it to study lateral ventricular surface differences associated with HIV/AIDS. Using concepts from differential geometry and the theory of differential forms, we created mathematical structures known as holomorphic one-forms, to obtain an efficient and accurate conformal parameterization of the lateral ventricular surfaces in the brain. The new meshing approach also provides a natural way to register anatomical surfaces across subjects, and improves on prior methods as it handles surfaces that branch and join at complex 3D junctions. To analyze anatomical differences, we computed new statistics from the Riemannian surface metrics-these retain multivariate information on local surface geometry. We applied this framework to analyze lateral ventricular surface morphometry in 3D MRI data from 11 subjects with HIV/AIDS and 8 healthy controls. Our method detected a 3D profile of surface abnormalities even in this small sample. Multivariate statistics on the local tensors gave better effect sizes for detecting group differences, relative to other TBM-based methods including analysis of the Jacobian determinant, the largest and smallest eigenvalues of the surface metric, and the pair of eigenvalues of the Jacobian matrix. The resulting analysis pipeline may improve the power of surface-based morphometry studies of the brain.

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.