Near-isometric flattening of brain surfaces

Adaptive smoothing of retinotopic maps based on Teichmüller parametrization

Retinotopic mapping, the mapping between visual inputs on the retina and neural responses on the cortical surface, is one of the fundamental topics in visual neuroscience. In human studies, retinotopic maps are conventionally constructed and processed by decoding blood oxygenation-level dependent (BOLD) functional magnetic resonance imaging (fMRI) responses to designed visual stimuli on the cortical surface. However, these methods frequently generate retinotopic maps that do not preserve topology, contradicting a fundamental property of retinotopic maps observed in neurophysiology. To address this problem, we propose an integrated approach to simultaneously refine the flattening from the 3D cortical surface to the 2D parametric space and adaptively smooth retinotopic perception centers in the visual space to make the retinotopic maps topological. One key element of the approach is the enhanced error tolerant Teichmüller mapping, which refines the parametrization by minimizing angle distortions and maximizing alignment to noisy landmarks. We validated our overall approach with synthetic and real retinotopic mapping datasets and applied it to compute cortical magnification factor (CMF). The results showed that the proposed approach was superior to other conventional retinotopic mapping methods in predicting BOLD fMRI time series and preserving topology.

Quantitative characterization of the human retinotopic map based on quasiconformal mapping

The retinotopic map depicts the cortical neurons' response to visual stimuli on the retina and has contributed significantly to our understanding of human visual system. Although recent advances in high field functional magnetic resonance imaging (fMRI) have made it possible to generate the in vivo retinotopic map with great detail, quantifying the map remains challenging. Existing quantification methods do not preserve surface topology and often introduce large geometric distortions to the map. In this study, we developed a new framework based on computational conformal geometry and quasiconformal Teichmüller theory to quantify the retinotopic map. Specifically, we introduced a general pipeline, consisting of cortical surface conformal parameterization, surface-spline-based cortical activation signal smoothing, and vertex-wise Beltrami coefficient-based map description. After correcting most of the violations of the topological conditions, the result was a "Beltrami coefficient map" (BCM) that rigorously and completely characterizes the retinotopic map by quantifying the local quasiconformal mapping distortion at each visual field location. The BCM provided topological and fully reconstructable retinotopic maps. We successfully applied the new framework to analyze the V1 retinotopic maps from the Human Connectome Project (n=181), the largest state of the art retinotopy dataset currently available. With unprecedented precision, we found that the V1 retinotopic map was quasiconformal and the local mapping distortions were similar across observers. The new framework can be applied to other visual areas and retinotopic maps of individuals with and without eye diseases, and improve our understanding of visual cortical organization in normal and clinical populations.

Optimizing Visual Cortex Parameterization with Error-Tolerant Teichmüller Map in Retinotopic Mapping

The mapping between the visual input on the retina to the cortical surface, i.e., retinotopic mapping, is an important topic in vision science and neuroscience. Human retinotopic mapping can be revealed by analyzing cortex functional magnetic resonance imaging (fMRI) signals when the subject is under specific visual stimuli. Conventional methods process, smooth, and analyze the retinotopic mapping based on the parametrization of the (partial) cortical surface. However, the retinotopic maps generated by this approach frequently contradict neuropsychology results. To address this problem, we propose an integrated approach that parameterizes the cortical surface, such that the parametric coordinates linearly relates the visual coordinate. The proposed method helps the smoothing of noisy retinotopic maps and obtains neurophysiological insights in human vision systems. One key element of the approach is the Error-Tolerant Teichmüller Map, which uniforms the angle distortion and maximizes the alignments to self-contradicting landmarks. We validated our overall approach with synthetic and real retinotopic mapping datasets. The experimental results show the proposed approach is superior in accuracy and compatibility. Although we focus on retinotopic mapping, the proposed framework is general and can be applied to process other human sensory maps.

Intracortical smoothing of small-voxel fMRI data can provide increased detection power without spatial resolution losses compared to conventional large-voxel fMRI data

Continued improvement in MRI acquisition technology has made functional MRI (fMRI) with small isotropic voxel sizes down to 1 mm and below more commonly available. Although many conventional fMRI studies seek to investigate regional patterns of cortical activation for which conventional voxel sizes of 3 mm and larger provide sufficient spatial resolution, smaller voxels can help avoid contamination from adjacent white matter (WM) and cerebrospinal fluid (CSF), and thereby increase the specificity of fMRI to signal changes within the gray matter. Unfortunately, temporal signal-to-noise ratio (tSNR), a metric of fMRI sensitivity, is reduced in high-resolution acquisitions, which offsets the benefits of small voxels. Here we introduce a framework that combines small, isotropic fMRI voxels acquired at 7 T field strength with a novel anatomically-informed, surface mesh-navigated spatial smoothing that can provide both higher detection power and higher resolution than conventional voxel sizes. Our smoothing approach uses a family of intracortical surface meshes and allows for kernels of various shapes and sizes, including curved 3D kernels that adapt to and track the cortical folding pattern. Our goal is to restrict smoothing to the cortical gray matter ribbon and avoid noise contamination from CSF and signal dilution from WM via partial volume effects. We found that the intracortical kernel that maximizes tSNR does not maximize percent signal change (ΔS/S), and therefore the kernel configuration that optimizes detection power cannot be determined from tSNR considerations alone. However, several kernel configurations provided a favorable balance between boosting tSNR and ΔS/S, and allowed a 1.1-mm isotropic fMRI acquisition to have higher performance after smoothing (in terms of both detection power and spatial resolution) compared to an unsmoothed 3.0-mm isotropic fMRI acquisition. Overall, the results of this study support the strategy of acquiring voxels smaller than the cortical thickness, even for studies not requiring high spatial resolution, and smoothing them down within the cortical ribbon with a kernel of an appropriate shape to achieve the best performance-thus decoupling the choice of fMRI voxel size from the spatial resolution requirements of the particular study. The improvement of this new intracortical smoothing approach over conventional surface-based smoothing is expected to be modest for conventional resolutions, however the improvement is expected to increase with higher resolutions. This framework can also be applied to anatomically-informed intracortical smoothing of higher-resolution data (e.g. along columns and layers) in studies with prior information about the spatial structure of activation.

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.

Surface fluid registration of conformal representation: application to detect disease burden and genetic influence on hippocampus

In this paper, we develop a new automated surface registration system based on surface conformal parameterization by holomorphic 1-forms, inverse consistent surface fluid registration, and multivariate tensor-based morphometry (mTBM). First, we conformally map a surface onto a planar rectangle space with holomorphic 1-forms. Second, we compute surface conformal representation by combining its local conformal factor and mean curvature and linearly scale the dynamic range of the conformal representation to form the feature image of the surface. Third, we align the feature image with a chosen template image via the fluid image registration algorithm, which has been extended into the curvilinear coordinates to adjust for the distortion introduced by surface parameterization. The inverse consistent image registration algorithm is also incorporated in the system to jointly estimate the forward and inverse transformations between the study and template images. This alignment induces a corresponding deformation on the surface. We tested the system on Alzheimer's Disease Neuroimaging Initiative (ADNI) baseline dataset to study AD symptoms on hippocampus. In our system, by modeling a hippocampus as a 3D parametric surface, we nonlinearly registered each surface with a selected template surface. Then we used mTBM to analyze the morphometry difference between diagnostic groups. Experimental results show that the new system has better performance than two publicly available subcortical surface registration tools: FIRST and SPHARM. We also analyzed the genetic influence of the Apolipoprotein E[element of]4 allele (ApoE4), which is considered as the most prevalent risk factor for AD. Our work successfully detected statistically significant difference between ApoE4 carriers and non-carriers in both patients of mild cognitive impairment (MCI) and healthy control subjects. The results show evidence that the ApoE genotype may be associated with accelerated brain atrophy so that our work provides a new MRI analysis tool that may help presymptomatic AD research.

Hemispherically-unified surface maps of human cerebral cortex: reliability and hemispheric asymmetries

Understanding the anatomical and structural organization of the cerebral cortex is facilitated by surface-based analysis enabled by FreeSurfer, Caret, and related tools. Here, we examine the precision of FreeSurfer parcellation of the cortex and introduce a method to align FreeSurfer-registered left and right hemispheres onto a common template in order to characterize hemispheric asymmetries. The results are visualized using Mollweide projections, an area-preserving map. The regional distribution, inter-hemispheric asymmetries and intersubject variability in cortical curvature, sulcal depth, cortical thickness, and cortical surface area of 138 young, right handed subjects were analyzed on the Mollweide projection map of the common spherical space. The results show that gyral and sulcal structures are aligned with high but variable accuracy in different cortical regions and show consistent hemispheric asymmetries that are maximal in posterior temporal regions.

Laminar analysis of 7T BOLD using an imposed spatial activation pattern in human V1

With sufficient image encoding, high-resolution fMRI studies are limited by the biological point-spread of the hemodynamic signal. The extent of this spread is determined by the local vascular distribution and by the spatial specificity of blood flow regulation, as well as by measurement parameters that (i) alter the relative sensitivity of the acquisition to activation-induced hemodynamic changes and (ii) determine the image contrast as a function of vessel size. In particular, large draining vessels on the cortical surface are a major contributor to both the BOLD signal change and to the spatial bias of the BOLD activation away from the site of neuronal activity. In this work, we introduce a laminar surface-based analysis method and study the relationship between spatial localization and activation strength as a function of laminar depth by acquiring 1mm isotropic, single-shot EPI at 7 T and sampling the BOLD signal exclusively from the superficial, middle, or deep cortical laminae. We show that highly-accelerated EPI can limit image distortions to the point where a boundary-based registration algorithm accurately aligns the EPI data to the surface reconstruction. The spatial spread of the BOLD response tangential to the cortical surface was analyzed as a function of cortical depth using our surface-based analysis. Although sampling near the pial surface provided the highest signal strength, it also introduced the most spatial error. Thus, avoiding surface laminae improved spatial localization by about 40% at a cost of 36% in z-statistic, implying that optimal spatial resolution in functional imaging of the cortex can be achieved using anatomically-informed spatial sampling to avoid large pial vessels.