It’s impossible to create an universal map of the functional organization of the brain


New research conducted by Professor Itamar Kahn, director of the Brain Systems Organization in Health and Disease Lab in the Technion’s Rappaport Faculty of Medicine, in collaboration with scientists from France and the U.S., demonstrates the importance of personalized brain models.

The research team’s findings show that individual variations in the brain’s structural connectome (map of neural connections) define a specific structural fingerprint with a direct impact on the functional organization of individual brains.

The groundbreaking research, “Individual structural features constrain the mouse functional connectome,” was published in PNAS, the official journal of the National Academy of Sciences of the United States. Technion MD/Ph.D. candidate Eyal Bergmann and Université d’Aix-Marseille doctoral student Francesca Melozzi were lead co-authors.

By using a connectome-based model approach, Prof. Kahn and his partners aimed to understand the functional organization of the brain by modeling the brain as a dynamic system, then studying how the functional architecture rises from the underlying structural skeleton.

Taking advantage of mice studies, they systematically investigated the informative content of different structural features in explaining the emergence of the functional ones.

Whole brain dynamics intuitively depend upon the internal wiring of the brain; but to which extent the individual structural connectome constrains the corresponding functional connectome is unknown, even though its importance is uncontested.

After acquiring structural MRI data from individual mice, the researchers virtualized their brain networks and simulated in silico functional MRI data.

Theoretical results were validated against empirical awake functional MRI data obtained from the same mice.

As a result, the researchers were able to demonstrate that individual structural connectomes predict the functional organization of individual brains.

Whole brain dynamics intuitively depend upon the internal wiring of the brain; but to which extent the individual structural connectome constrains the corresponding functional connectome is unknown, even though its importance is uncontested.

While structural MRI is a common non-invasive method that can estimate structural connectivity in individual humans and rodents, it is not as precise as the gold standard connectivity mapping possible in the mouse.

Utilizing precise mapping available in mice, the authors identified which missing connections (not measurable with structural MRI) are important for whole brain dynamics in the mouse.

The researchers identified that individual variations thus define a specific structural fingerprint with a direct impact upon the functional organization of individual brains, a key feature for personalized medicine.

uman psychology and behaviour are determined by functional brain connectivity among neurons, neural assemblies, or entire regions, making the patterns of circuitry that can be detected by brain imaging1. Recent large-scale research into the brain imaging data within the Human Connectome Project (HCP)24 aims to uncover, describe and understand the functional structure of human connectome; the connectome is visualised as a network consisting of different brain regions (grey matter) and paths between them (white-matter fibre bundles) that can be determined by mapping the diffusion-MRI and tractography data.

The network nodes are identified as distinct brain regions that are functionally similar and spatially close as well as equally connected to the other regions47. The connections between these regions are inferred from brain imaging data.

Recent studies provided insight into the developmental trajectory, elucidating that the architecture of connections in the brain develops over time to support the function8. Thus the inferred structure of edges may vary among different subjects, performed tasks and conditions.

In this context, the sex-related differences in brain connectivity evolve across the development to accompany all functional and behavioural dimensions8,9. Therefore, the consensus between the pipelines in the structural connectome can be mapped from a large population tractography data10 and depends on many parameters.

Based on the data from HCP2 and the brain mapper developed in11, the Budapest connectome server12 provides the possibilities to infer the consensus networks at a variety of the relevant parameters, as described in13.

The mapping of imaging data to the brain networks enables an objective analysis based on graph theory methods14,15.

Recently, different studies of brain imaging data revealed the strong evidences for sex-related differences in the structural connectome1622. This subject was not well researched, but already it brought some controversial debates9.

The exact origin of these differences and their potentials and impact on the level of individual and social behaviour are still to be investigated23. On the other hand, the current degree of reliability of the connectome data provides an opportunity for a mathematical analysis of structural differences at all levels. For example, a recent study22 has shown that the consensus female connectome has superior connectivity than the consensus male connectome in many graph-theoretic measures.

Recent investigations of geometrical properties of various complex systems2433 show the relevance of the higher-order connectivity beyond standardly considered pairways interactions. Mathematically, the impact of these higher order interactions is adequately described by the simplicial complexes in the algebraic topology of graphs3437.

In these complexes, elementary geometrical shapes (triangles, tetrahedra, and simplexes of higher order) are combined through shared substructures of various orders. These geometrical structures directly influence dynamic processes that the complex system in question performs, such as transport, diffusion, or synchronisation among the involved nodes.

In the case of brain networks, the main dynamic function pertains to maintaining an optimal balance between the processes of integration and segregation where different regions of the brain can be simultaneously involved and the present modular structure of the brain plays an important role3841.

Anatomical modules of the brain, which are recognized as different mesoscopic communities in the network4245, are based on spatial topography and coexpression of genes in the brain cells46. It has been suggested that each module performs a discrete cognitive function while specific connector nodes take on communication between modules40. However, the fine functional organisation inside these modules remains unexplored.

Besides, the occurrence of simplicial complexes causes the emergent hyperbolicity or a negative curvature47 in the structure of the graph, which affects its functional properties. In this sense, the complete graph and associated tree are ideally hyperbolic, characterised by the hyperbolicity parameter δ=0.

The graphs with small values of δ are subject to intensive investigations for their ubiquity in natural and social systems, as well as in technology applications24,25,30,33,48. Moreover, current theoretical studies reveal that Gromov hyperbolic graphs with a small hyperbolicity parameter have specific mathematical properties48.

In particular, the bounds for the δ-parameter of the whole graph can be derived from subjacent simpler graphs, for example, induced cycles or clique separators of a given length4954. Therefore, the study of the hyperbolicity of brain graphs can reveal the presence of typical local structures that are potentially decomposable into some known forms, which underlie the brain’s dynamic complexity.

In this work, we considerably expand the analysis of human connectome beyond the simple pairwise connectivity. Using the mathematical techniques of algebraic topology of graphs, we identify hierarchically organised complexes that encode higher-order relationships between regions of the brain and explore the hyperbolic geometry of brain graphs. We consider the consensus connectomes mapped from 100 female (F-connectome) and 100 male (M-connectome) subjects, using the brain mapper and imaging data from the Human Connectome Project, which is provided by the Budapest server 3.012.

The weighted edges are inferred according to the electrical connectivity criteria, which are most sensitive to the number of fibres observed in the tractography data. We analyse the connectomes that correspond to the significant variation in the number of fibres launched (see Methods). With the appropriate topology measures, our objectives are to determine the hidden structure of human connectome endowed with the relationships between groups of nodes and express the possible gender differences in this context.

To this end, we construct and investigate a common F&M-connectome at different numbers of fibres and determine its structure, parametrised by simplicial complexes, and the graph’s hyperbolicity parameter. Furthermore, by comparing edges in the F- and M-connectomes, we identify the excess edges that appear consistently in the F-connectome with an increased number of fibres. Our mathematical analysis reveals a rich structure of simplicial complexes that are common to the F&M-connectome and belong to different brain anatomical communities and cycles that connect them inside and across the two brain hemispheres.

It further confirms the higher connectivity of the F-connectome and demonstrates that the excess edges have a well-organised structure that includes a particular set of paths and brain regions.

Technion-Israel Institute of Technology
Media Contacts:
Itamar Kahn – Technion-Israel Institute of Technology

Original Research: Open access
“Individual structural features constrain the mouse functional connectome”. Francesca Melozzi, Eyal Bergmann, Julie A. Harris, Itamar Kahn, Viktor Jirsa, and Christophe Bernard.
PNAS doi:10.1073/pnas.1906694116.


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