Cortex-Based Alignment of Sulci and Gyri
A good match between corresponding brain regions is important for many applications including group-level statistical data analysis. Group analysis in Talairach or MNI space suffers, however, from a coarse alignment between subjects' brains producing suboptimal, and sometimes even misleading group maps due to extensive spatial smoothing. While functional areas are not precisely predictable from macroanatomical landmarks, it has been shown for areas V1 and motor cortex (Fischl et al., 1999) and for many other areas (Frost & Goebel, 2012) that a cortical matching approach substantially improves statistical group results by reducing anatomical variability. BrainVoyager offers an advanced, high-resolution, approach to align brains using macro-anatomical (curvature) and optionally functional information of the cortex (Goebel et al., 2002, 2004, 2006; Frost & Goebel, 2012, 2013). Since the curvature of the cortex reflects the gyral/sulcal folding pattern of the brain, this brain matching approach essentially aligns gyri and sulci across brains when initialized with an approximate (e.g. MNI or Talairach-based) pre-alignment step. The figure above, for example, shows the average brain (folded cortex) of a group of 19 left and right hemipspheres after curvature-driven cortex-based alignment (Rosenke et al., in preparation).
Curvature-driven cortex-based alignment (CBA) operates in several stages. The reconstructed folded cortical representations of each subject and hemisphere constitute the input of the alignment procedure. In the first step, these folded representations are morphed into a spherical representation, which provides a parameterizable surface well-suited for across-subject non-rigid alignment. Each vertex on the sphere (spherical coordinate system) corresponds to a vertex of the folded cortex (Cartesian coordinate system) and vice versa. The curvature information computed in the folded representation is preserved as a curvature map on the spherical representation. The curvature information (macroanatomical folding pattern) is produced in several versions with minimal and more extensive smoothing along the surface in order to provide spatially extended gradient information driving intercortex alignment. Alignment proceeds by moving vertices to minimize the mean squared differences between the curvature of a source and a target sphere. The essential step of the alignment is an iterative procedure following a coarse-to-fine matching strategy. Alignment starts with highly smoothed curvature maps and progresses to only slightly smoothed representations. Starting with a coarse alignment as provided by MNI or Talairach space and optionally a rigid spherical alignment step, this method ensures that the smoothed curvature of the cortices possess enough curvature overlap for a locally operating gradient-descent procedure to converge without user intervention (Goebel et al., 2002, 2004, 2006; Frost & Goebel, 2012). Visual inspection and a measure of the averaged mean squared curvature difference reveal that the alignment of major gyri and sulci can be achieved reliably by this method. Smaller structures, visible in the curvature maps with minimal smoothing, may not be completely aligned since they often reflect idiosyncratic differences between the subject's brains, such as continuous versus broken sulci.
Note that the alignment requires the specification of a target brain to which source brains are aligned. The program offers two approaches to define the target brain. In the explicit target approach, one sphere is selected as a target to which all other spheres are subsequently aligned. The target sphere can be derived from one of the brains of the investigated group or from a special reference brain, such as the MNI template brain. Although tests have shown that alignment results are very similar when using different target spheres, the selection of a specific target brain might lead to results that are dependent partially on the chosen target brain, especially in case that the selected brain contains many regions with a non-typical folding pattern. In the moving target group averaging approach, the selection of a target sphere is not required. In this approach, the goal function is specified as a moving target computed repeatedly during the alignment process as the average curvature across all hemispheres at a given alignment stage. The procedure starts with the most coarse curvature maps. Then the next finer curvature maps are used and averaged with the obtained alignment result of the previous level.
The established correspondence mapping between vertices of the cortices can be subsequently used to align the subject's functional data (mesh time courses). The fixed and random-effects GLM calculations in BrainVoyager used for volume data are also able to process cortically aligned mesh time course data. Furthermore, surface maps (SMPs) and Patches-Of-Interest (POIs) defined on cortex meshes of individual subjects can be transformed into group-aligned cortex space.
Curvature-driven CBA is performed using the Cortex-Based Alignment dialog (see screenshot above) that contains several tabs for the various stages of this process. The dialog can be opened via the Cortex-Based Alignment item in the Meshes menu. To use the curvature-driven cortex-based approach for inter-subject alignment, follow these steps:
- Prepare a cortex mesh
- Morph a prepared cortex hemisphere mesh into a sphere
- Map vertices of standard sphere to those of morphed sphere
- Create curvature maps for each resampled cortex mesh at different resolutions
- Align source spheres to a moving target group average or to a selected target sphere
After these essential steps, you can perform further procedures to quantify and visualize the achieved alignment. You can also proceed with cortex-based statistical data analyses using the created alignment files with created mesh time course (MTC) files.
In case that information about corresponding regions is available from independent functional localizer runs, it is possible to integrate that information. For more details, see topic Functionally Informed Cortex-Based Alignment.
Resolution of Aligned SpaceThe curvature-driven inter-subject alignment is performed using generic spherical meshes that are used to sample the original subject-specific (morphed to sphere) meshes in a common space. The options in the Resolution field in the first (Curvature) tab of the Cortex-Based Alignment dialog allow to select one of 3 resolution levels determining the number of vertices used for generated spherical representations. In most cases, the Standard resolution option (default) should be used that will create sphere meshes with 40962 vertices and 81920 trianges. In case that one works with high-resolution (sub-millimeter) anatomical data, one might consider using the High resolution option that will create sphere meshes with 163842 vertices and 327680 triangles. The Low resolution option is recommended in case one wants to perform EEG / MEG source imaging in multi-subject aligned cortex space (10242 vertices, 20480 triangles).
A non-standard resolution should be chosen prior to starting the first subject and it should be checked again before processing another subject to avoid incompatible sphere resolution for different hemispheres. The chosen setting not only influences the resolution of the generated shpere meshes but also sets parameters to optimize speed and robustness for the non-linear alignment process.
Fischl B, Sereno, M.I., Tootel, R.B.H., and Dale, A.M. (1999). High-resolution intersubject averaging and a coordinate system for the cortical surface. Human Brain Mapping, 8, 272-284.
Goebel, R., Staedtler, E., Munk, M.H.J., Muckli, L. (2002). Cortex-based alignment using functional and structural constraints. NeuroImage Supplement.
Goebel, R., Hasson, U., Harel, M., Levy, I., Malach, R. (2004). Statistical analyses across aligned cortical hemispheres reveal high-resolution population maps of human visual cortex. NeuroImage Supplement (Human Brain Mapping, Budapest).
Goebel, R., Esposito, F. & Formisano, E. (2006). Analysis of functional image analysis contest (FIAC) data with Brainvoyager QX: From single-subject to cortically aligned group general linear model analysis and self-organizing group independent component analysis. Human Brain Mapping, 27, 392-401.
Frost, M. & Goebel, R. (2012). Measuring structural-functional correspondence: Spatial variability of specialised brain regions after macro-anatomical alignment. NeuroImage, 59, 1369-1381.
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