Technical NoteProjection of fMRI data onto the cortical surface using anatomically-informed convolution kernels
Introduction
Functional magnetic resonance images (fMRI) are generally presented and analysed in their original 3D space of acquisition with little regard to the structural features of the human brain. In this context, surface-based analyses of cortical data have gained interest as they advocate for anatomical considerations of the object under study. First, as the main part of the brain activity is generated by cortical pyramidal neurons, descriptions of the cortex should respect its sheet-like structure, despite the intrinsic voxel-based nature of magnetic resonance images and the highly convoluted nature of the cortex. Moreover, distances computed in 3D voxel-based space do not take folds into account, and two points with low Euclidean distance can actually be located on the two opposite sides of a sulcus; with respect to this issue, geodesic distances, along the cortical surface, describe the anatomy better. Several papers in the literature (Clouchoux et al., 2005, Van Essen and Drury, 1997, Fischl et al., 1999, Toro and Burnod, 2003) advocate for this approach. As these works deal with visualisation, intersubjects registration or cortical localisation, little research has also been published on surface-based functional data analysis (Andrade et al., 2001, Flandin et al., 2002, Goebel and Singer, 1999, Kiebel et al., 2000). On this matter, one essential problem concerns the projection of functional data onto the anatomy, in other terms the mapping of functional voxel-based volumes onto cortical triangulated meshes. This is especially a crucial point to open the way to fMRI data analysis confined to the cortical ribbon.
Still, this problem has remained poorly studied and is rarely found in the literature. Some «geometric» simple methods do exist: some methods propose to average intensities along a normal direction or inside a sphere centered at each node of the mesh representing the cortical surface (e.g. when using free package BrainVISA), or to assign each node with the value of its containing voxel (Saad et al., 2004), or to compute trilinear interpolations (Andrade et al., 2001). Other methods try to embed some explicit anatomical information into the process: it can be done by defining each node’s influence scope through voxels distances to and along the cortical mesh (Warnking et al., 2002), or computing a geodesic Voronoï diagram so that each node is integrated within an associated set of voxels defined by the local anatomical geometry (Grova et al., 2006).
From these methods stems a common interest in delineating 3D areas, sometimes overlapping, onto which the signal emanating from the nodes would possibly be dispersed, taking local anatomical features into account. Nevertheless, the problems remains very difficult because of numerous factors such as the volumes resolution, the partial volume effects, the sensitivity to errors from previous processing steps like segmentation, mesh extraction and registration, all of this being added to the highly folded nature of the surface. Therefore, a good interpolation method should show robustness to these various parameters.
In this study, we propose an original method to produce surface-based representations of the cortical activity directly on the cortical mesh, relying on an expected distribution of the BOLD signal in EPI volumes, taking into account as much anatomical information as possible. The method itself is described in the next section. The third section presents experiments we ran to validate our process and evaluate its robustness to segmentation and registration errors. Results are presented in the fourth section and the method is discussed and compared to others in the last section.
Section snippets
Expected distribution of the signal
In order to represent the cortical activity from the whole 3D volume back to the surface where it was originated, we relied on an expected distribution of the BOLD signal around each node of the cortical mesh to address correlations between voxels and mesh nodes, with physiological and image-related motivations. Several distinct phenomena were considered: first, as a consequence of the columnar architecture of neurons inside the cortex (Mountcastle, 1978), we expect each cortical column to show
Simulated data sets
We led a series of experiments in order to assess the benefits of projecting functional data using convolution kernels, in terms of detection power, robustness to various kinds of errors and sensitivity to resolution changes. Most of these experiments were previously suggested by Grova et al. (2006) for the Voronoï-based approach. In this validation frame, several types of meshes were generated. We first extracted cortical meshes from the T1-weighted volume at three different resolution levels:
Results
We projected simulated functional data onto the cortical surfaces at three different resolutions. For each projection, we computed an AUCclose value. The results are presented in Table 1. They tend to illustrate kernel-based projection’s best accuracy in recovering, out from a simulated volume, the surface-based activation map initially taken as ground truth, in comparison to other methods, and for each resolution. With very-low resolution meshes, all the methods give results very close or
Choice of the orthogonality criterion
In order to compute geodesic and normal distances for any voxel in a node’s neighborhood, each voxel is assigned what was referred to as a normal node on the surface, from which the two distances, then the weights, were computed. These associations result from a Fast-Marching propagation algorithm. Relating voxels to surface nodes using geodesic distances is a relevant way to deal with the folded nature of cortex, rather than euclidean distances. However, the original orthogonality criterion we
Conclusion
In this paper, we propose a method allowing the projection of functional images onto the cortical surface. Relying on physiological and image-related hypotheses, it determines, for each mesh node, a specific interpolation area, strongly influenced by local anatomy, within which voxels intensities are averaged. Applying it to activation maps can serve visualisation purposes, as well as cortical localisation of activation foci through the use of a surface-based coordinate system (Clouchoux et
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