Mukund Balasubramanian

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 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.

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.

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.

On the lorentzian versus Gaussian character of time-domain spin-echo signals from the brain as sampled by means of gradient-echoes: Implications for quantitative transverse relaxation studies.

To determine whether Lorentzian or Gaussian intra‐voxel frequency distributions are better suited for modeling data acquired with gradient‐echo sampling of single spin‐echoes for the simultaneous characterization of irreversible and reversible relaxation rates. Clinical studies (e.g., of brain iron deposition) using such acquisition schemes have typically assumed Lorentzian distributions.

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.

Incorporating reversible and irreversible transverse relaxation effects into Steady State Free Precession (SSFP) signal intensity expressions for fMRI considerations

Among the multiple sequences available for functional magnetic resonance imaging (fMRI), the Steady State Free Precession (SSFP) sequence offers the highest signal-to-noise ratio (SNR) per unit time as well as distortion free images not feasible with the more commonly employed single-shot echo planar imaging (EPI) approaches. Signal changes occurring with activation in SSFP sequences reflect underlying changes in both irreversible and reversible transverse relaxation processes. The latter are characterized by changes in the central frequencies and widths of the inherent frequency distribution present within a voxel. In this work, the well-known frequency response of the SSFP signal intensity is generalized to include the widths and central frequencies of some common frequency distributions on SSFP signal intensities. The approach, using a previously unnoted series expansion, allows for a separation of reversible from irreversible transverse relaxation effects on SSFP signal intensity changes. The formalism described here should prove useful for identifying and modeling mechanisms associated with SSFP signal changes accompanying neural activation.

On the perils of multiexponential fitting of diffusion MR data.

We read with interest the recent article by Ohno et al in which diffusion measurements in the human brain over an extended bfactor range were analyzed with a modified triexponential fitting procedure. The primary purpose of the study was to extract information regarding the small, very fast decaying (>10 3 10 mm/s), and somewhat controversial, “pseudo-perfusion” component along with two other components: the (less) fast ( 1 3 10 mm/s) and slow ( 0.1 3 10 mm/s) decaying diffusion components as previously characterized using unconstrained biexponential fits. Of particular interest were the relative fractions of these latter two components reported by Ohno et al, which were approximately 0.2 and 0.8, respectively, apparently resolving a major issue encountered when we and others first attempted to interpret these fractional amplitudes. Namely, the attractively simple interpretation of the fast and slow diffusion components as corresponding to extraand intracellular water compartments was thwarted by the biological fact that extraand intracellular volume fractions in the brain are on the order of 0.2 and 0.8, respectively, whereas unconstrained biexponential fits consistently revealed the fast and slow diffusion component fractions to be closer to 0.8 and 0.2, in opposite proportion to the extraand intracellular water fractions in the brain. The remarkable finding by Ohno et al of fractions more in line with extraand intracellular water was not commented upon by the authors, despite the implication that, if correct, the simplest interpretation for the fast and slow diffusion components could be resurrected. Although this finding would be an exciting development, we have unfortunately come to the conclusion that the specific fitting method employed by Ohno et al has most probably led to incorrect estimates of the relative proportions of these fractions. In particular, Ohno et al fixed the fast diffusion coefficient to be 3 3 10 mm/s, i.e., that of pure water at 378C. Using simulated decay curves we show that such a constrained fitting procedure dramatically influences the relative fractions of the fast and slow diffusion components, explaining the peculiar findings regarding the fast and slow fractional amplitudes. From a purely physical standpoint as well, the tortuosity of the extracellular space in brain tissue guarantees that, over the typical diffusion times used for high-b diffusion imaging, water molecules

Fast myelin water fraction estimation using 2D multislice CPMG

T2 relaxometry based on multiexponential fitting to a single slice multiecho sequence has been the most common MRI technique for myelin water fraction mapping, where the short T2 is associated with myelin water. However, very long acquisition times and physically unrealistic models for T2 distribution are limitations of this approach. We present a novel framework for myelin imaging which substantially increases the imaging speed and myelin water fraction estimation accuracy.

RF Heating of Gold Cup and Conductive Plastic Electrodes during Simultaneous EEG and MRI

ABSTRACT Purpose: To investigate the heating of EEG electrodes during magnetic resonance imaging (MRI) scans and to better understand the underlying physical mechanisms with a focus on the antenna effect. Materials and Methods: Gold cup and conductive plastic electrodes were placed on small watermelons with fiberoptic probes used to measure electrode temperature changes during a variety of 1.5T and 3T MRI scans. A subset of these experiments was repeated on a healthy human volunteer. Results: The differences between gold and plastic electrodes did not appear to be practically significant. For both electrode types, we observed heating below 4°C for straight wires whose lengths were multiples of ½ the radiofrequency (RF) wavelength and stronger heating (over 15°C) for wire lengths that were odd multiples of ¼ RF wavelength, consistent with the antenna effect. Conclusions: The antenna effect, which has received little attention so far in the context of EEG-MRI safety, can play as significant a role as the loop effect (from electromagnetic induction) in the heating of EEG electrodes, and therefore wire lengths that are odd multiples of ¼ RF wavelength should be avoided. These results have important implications for the design of EEG electrodes and MRI studies as they help to minimize the risk to patients undergoing MRI with EEG electrodes in place.