The role of long-range connectivity for the characterization of the functional-anatomical organization of the cortex

Abstract

This review focuses on the role of long-range connectivity as one element of brain structure that is of key importance for the functional-anatomical organization of the cortex. In this context, we discuss the putative guiding principles for mapping brain function and structure onto the cortical surface. Such mappings reveal a high degree of functional-anatomical segregation. Given that brain regions frequently maintain characteristic connectivity profiles and the functional repertoire of a cortical area is closely related to its anatomical connections, long-range connectivity may be used to define segregated cortical areas. This methodology is called connectivity-based parcellation. Within this framework, we investigate different techniques to estimate connectivity profiles with emphasis given to non-invasive methods based on diffusion magnetic resonance imaging (dMRI) and diffusion tractography. Cortical parcellation is then defined based on similarity between diffusion tractograms, and different clustering approaches are discussed. We conclude that the use of non-invasively acquired connectivity estimates to characterize the functional-anatomical organization of the brain is a valid, relevant, and necessary endeavor. Current and future developments in dMRI technology, tractography algorithms, and models of the similarity structure hold great potential for a substantial improvement and enrichment of the results of the technique.

Keywords: anatomical connectivity; connectivity-based parcellation; cortex area; diffusion tractography; functional connectivity.

Figure 1

Schematic drawing of the mappings between functional features space (e. g., stimulus features, movement parameters, cognitive operations, etc.), structural feature space (cell morphology, connectivity, neurotransmitter type, etc.), and cerebral cortex, modeled as two-dimensional sheet (R²) or three-dimensional volume (R³).

Figure 2

Contributing factors for anatomical connectivity. One possible quantitative definition of anatomical connectivity is the potential influence of the mean membrane potential in one brain area onto the mean membrane potential of another area (Yo et al., 2009). In this line, the anatomical connectivity from area A to area B depends on: (1) the number of cells in the presynaptic area A, the local circuitry there and the number of axons leaving this area for the respective target area B (= number of projection neurons in A); (2) the distribution of axonal diameter and myelination of the axons as well as the distance between A and B and the exact course of the fibers – all these factors determine the distribution of transmission speeds; (3) the number of synapses made with cells in area B, their distribution over the target cells and the synaptic efficacies, which depend on numerous factors, including abundance of neurotransmitters and receptors, (4) the number of cells in area B and the local circuitry there.

Figure 3

Schematic overview of the main operations involved in connectivity-based gray matter parcellation. (A) Definition of seed points. The seed points discretize the region of interest to be parcellated. This may, for example, be the cortical mantle or a section thereof, represented by the points at the gray–white matter interface (red dots, e.g., Anwander et al., 2007), or a sub-cortical structure like the caudate. As such sub-cortical structures are penetrated by fibers much more than the cortex, the use of all voxels as seed points is warranted (green dots, e.g., Behrens et al., 2003). (B) Definition of the target space. The target space determines to which voxels or regions the connectivity from the seed voxels will be computed. For example, one may simply use the entire brain (top, e.g., Johansen-Berg et al., 2004), or just a certain part of the brain (e.g., Bach et al., 2011), such as the cortex or all gray matter (middle) or a collection of predefined regions (e.g., Behrens et al., 2003b), e.g., based on macroscopic landmarks (bottom). (C) Connectional fingerprints: the fingerprints comprise the connectivity of each seed voxel with all target voxels or regions. They can be estimated in various ways. Here, as an example, probabilistic tractograms connecting the seed voxel with all other voxels of the brain are depicted. (D) Similarity structure: similarity between different connectional fingerprints can be measured in different ways, for example, as correlation, as Euclidean distance (after normalization) or as mutual information. It can be represented as similarity matrix (top) or hierarchical cluster tree (bottom). (E) Parcellation mapped on the brain: clustering or partitioning algorithms extract sensible parcellations from the similarity structure, which can then be mapped on the brain. Here, we show a cortical parcellation computed with an agglomerative clustering method (Gorbach et al., 2010).