Scientific Understanding of Consciousness
Consciousness as an Emergent Property of Thalamocortical Activity

Geometric Structure of the Brain Fiber Pathways



Science 30 March 2012:  Vol. 335 no. 6076 pp. 1628-1634

The Geometric Structure of the Brain Fiber Pathways

Van J. Wedeen1, Douglas L. Rosene2, Ruopeng Wang1, Guangping Dai1, Farzad Mortazavi2, Patric Hagmann3, Jon H. Kaas4, Wen-Yih I. Tseng5

1Department of Radiology, Massachusetts General Hospital (MGH), Harvard Medical School and the MGH/Massachussetts Institute of Technology Athinoula A. Martinos Center for Biomedical Imaging, Building 129, 13th Street, 2nd Floor, Charlestown, MA 02129, USA.

2Department of Anatomy and Neurobiology, Boston University, Medical Campus, 700 Albany Street, W701, Boston, MA 02118, USA.

3Department of Radiology, University Hospital Center–University of Lausanne, Rue du Bugnon, 46, CH-1011 Lausanne, Switzerland.

4Department of Psychology, College of Arts and Sciences, Vanderbilt University, 301 Wilson Hall, 111 21st Avenue South, Nashville, TN 37240, USA.

5Department of Radiology, Center for Optoelectronic Biomedicine, National Taiwan University College of Medicine, 1 Jen-Ai Rd, Taipei, Sec 1, 100 Taiwan.


The structure of the brain as a product of morphogenesis is difficult to reconcile with the observed complexity of cerebral connectivity. We therefore analyzed relationships of adjacency and crossing between cerebral fiber pathways in four nonhuman primate species and in humans by using diffusion magnetic resonance imaging.


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The cerebral fiber pathways formed a rectilinear three-dimensional grid continuous with the three principal axes of development. Cortico-cortical pathways formed parallel sheets of interwoven paths in the longitudinal and medio-lateral axes, in which major pathways were local condensations. Cross-species homology was strong and showed emergence of complex gyral connectivity by continuous elaboration of this grid structure. This architecture naturally supports functional spatio-temporal coherence, developmental path-finding, and incremental rewiring with correlated adaptation of structure and function in cerebral plasticity and evolution.

The organizing principles of cerebral connectivity remain unclear. In the brainstem and spinal cord, fiber pathways are organized as parallel families derived from the three principal axes of embryonic development: the rostro-caudal, the medio-lateral (or proximo-distal), and the dorso-ventral. In the forebrain of advanced species, however, corresponding patterns of connectivity have yet to be established. Many studies of evolution, development, and gene expression point to a geometric organization of cerebral fiber pathways similar to that of the brainstem, and functional studies also suggest that connectivity is geometrically organized. Several leading theories of cerebral function propose geometric organization at multiple scales. However, high-resolution studies of cerebral connectivity with tract tracers have given only limited evidence of geometric organization.

A challenge in the investigation of cerebral structure and connectivity can be traced to the common occurrence of distinct pathways within the same small volumes of tissue, or “path crossing.” Crossing is a pervasive feature of brain structure and may be essential for efficient connectivity. Owing to crossing, the mapping of connectivity must untangle pathways from cellular to macroscopic scales simultaneously. This was accomplished with tract tracers methods, which are considered a gold standard. Tracer studies inject compounds into the live brain and allow them to disperse by means of axonal transport, marking individual axons over large distances. However, these can map only a small fraction of the pathways in any single brain and are not feasible in humans. Thus, the discovery and analysis of the structural relationships between pathways—and their context within cerebral connectivity—has remained challenging

To address these limitations, methods have been developed to map the fiber pathways of the brain through use of diffusion magnetic resonance imaging (MRI). Diffusion MRI creates multidimensional contrast that is representative of the distribution of fiber orientations at each location in the tissue. Though of lower resolution than tract tracing, diffusion MRI is noninvasive, applicable to humans and synoptic, and able to map the connectional anatomy of a single brain in its entirety, including spatial correlations between pathways. These correlations represent the mesoscale structure of connectivity, within the scope of which are the questions of whether cerebral pathways are discrete versus continuous and the detailed character of the spatial organization of connectivity.

To probe the spatial relations between the pathways of the brain, we analyzed path-adjacency and path-crossing in four nonhuman primate species and in humans. Diffusion spectrum MRI (DSI) was acquired in whole-brain specimens ex vivo in rhesus, owl monkey, marmoset, and the pro-simian galago, and in vivo in subjects (515 directions; pathways were computed with deterministic streamline integration). To demonstrate pathways’ structural relationships, we augmented interactive software to compute for any path the set of all paths with which it shares one or more voxels, termed its path neighborhood.

Strong homology of deep cerebral grid structure was found across all species studied. These included the grid systems of the callosum, sagittal stratum, and supra-Sylvian pathways, as well as the crossing of the fornix and anterior commissure in all species studied ex vivo at high resolution. In the rhesus monkey, central and subcortical grid structures, including those of the major frontal sulci (principal, arcuate, central), fit together continuously like a jigsaw puzzle. Thus, we hypothesize that the complex connectivity of the cerebral mantle represents a continuous elaboration of the simpler core.

We have found that the fiber pathways of the forebrain are organized as a highly curved 3D grid derived from the principal axes of development. This structure has a natural interpretation. By the Frobenius theorem, any three families of curves in 3D mutually cross in sheets if and only if they represent the gradients of three corresponding scalar functions. Accordingly, we hypothesize that the pathways of the brain follow a base-plan established by the three chemotactic gradients of early embryogenesis. Thus, the pathways of the mature brain presents an image of these three primordial gradients, plastically deformed by development.

A grid organization of cerebral pathways has been suggested in several contexts. Katz et al. hypothesized that a large-scale substrate of grid organization is applicable to forebrain development. Checkerboard organization of cortical Brodmann fields has been noted in visual areas of the temporal lobe and frontal motor areas in monkeys. In humans, Badre and D’Esposito have suggested hierarchic organization of the frontal cortex along a rostro-caudal axis.

The grid structure of cerebral pathways has implications for brain mapping: It suggests a simplifying framework and natural coordinate system for the description of brain structure, its pathways, and connectivity; simplifies and constrains models of cerebral white matter; and indicates that topographic organization is characteristic of cerebral connectivity and not limited to a few major pathways. Of concern, present findings suggest that existing MRI tractography may underestimate sharp turning. It also provides a means to validate MRI tractography through consistency with grid structure.

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