The human connectome is a comprehensive map of the neural connections in the brain - in other words, a graph. Coming from a background in graph algorithm development and network analysis, the field of connectome analysis seems to me a very interesting application domain. However, it is a domain I am just beginning to understand. Therefore I hope to get some feedback from both neuro- and computer scientists, starting with the following questions:
- It is my understanding that at the neural scale, the connectome is a graph of more than 10^10 nodes and 10^14 edges. If it could be comprehensively mapped at this scale - which i believe it cannot at this point due to a lack of imaging technology - would it be in the range of current computing capabilities to analyse such a network?
- Has the connectome been mapped at coarser scales? If yes, what graph sizes are we talking about?
- Are standard measures from network analysis (such as degree distribution, diameter, clustering coefficients, centrality, communities) relevant for connectome analysis? What are interpretations of such measures?
- What are other structures of interest in the connectome that could be revealed by graph algorithms? Is there a need for domain-specific algorithms to discover brain-specific graph structures?
- Are there publicly available datasets that represent the connectome as a graph?
Hi Christian - very good questions (which I stumbled upon quite by accident), and YES, connectome maps at coarser (regional) scales have indeed been compiled (many are publicly available) and have been studied extensively with graph measures and tools. Of particular interest are measures that reveal community structure and hubs - if you email me directly ([email protected]) I can send you references as well as data sets that you might find helpful. All best -- Olaf
Hi Christian,
in addition to the problems that Olaf mentioned, there are the conceptual and computational challenges of graph comparisons (are there significant network changes?), classification using graphs (diagnosis or treatment prediction for patients), and network motif (or at the larger scale: module) discovery.
There are several freely accessible connectome datasets and you can find some on my website http://www.biological-networks.org/ You can find an overview of algorithms in my 2011 Neuroimage tutorial and a discussion of using graphs as a biomarker of brain diseases in my 2013 Frontiers in Human Neuroscience article (PDFs available on that website).
Best,
Marcus
Hi Christian and Marcus!
In addition to what Marcus mentions, try www.brain-connectivity-toolbox.net for a set of Matlab tools for graph analysis (actually any network data would fit), some data sets included as well. The tutorial by Marcus would be a great first step to get started on applying graph tools to connectome data.
Hope this helps! -- Olaf
One of the key challenges that we came across when designing an intelligent processing and relay mirroring structural description of neural network; Just by imitating complex assemblies keyed in instant relay and feedback; we found that utilising multimodal methodology was helpful.
However, the test was conducted in conjunction with other enablers and integrators, such neuroimaging as suggested by Markus Axel 2012: Microscale, Mesoscale & Macroscale.
Christian,
1) for publicly available data see http://mrbrain.cs.jhu.edu/disa/download/
2) for connectome analysis see graph theory textbooks :)
Thank you for your comments. I am especially interested in where to find further large datasets.
I tested NetworKit [1] on the dataset Test.fiber.big from [2], a human connectome with 46 million edges. It's interesting to see that it is a fairly typical complex network. Features include a power-law degree distribution with an exponent of 1.6, a giant connected component, high degree assortativity, high clustering, and a distinctive modular structure with about 800 communities. A complete profile is in the attachment.
[1]: http://parco.iti.kit.edu/software/networkit.shtml
[2]: http://mrbrain.cs.jhu.edu/disa/download/
Dear Christian,
is that graph strongly connected? (I checked some smaller graphs but not this one).
There is a lot of graph theoretic invariants, you should have biological motivations.
Peteris, I treated it as an undirected graph (since NetworKit cannot yet deal with directed graphs). The graph is not connected and has 727 components - although I realize that seems strange for a brain, doesn't it?
I completely agree that such measures without a biological motivation and interpretation are not very interesting. I certainly lack the knowledge to do that. My job is to provide the algorithmic tools, but I'd love to see what domain experts could do with them.
Dear Christian,
you want to impress domain experts. You can do this either by finding a surprising fact about connectome graph structure or doing an impressive software engineering job.
I would assume that one already needs domain expert knowledge in order to know which connectome graph structures are actually surprising. Concerning the impressive software engineering job, I have some hope that NetworKit can impress in terms of performance, usability and the collection of algorithms. It might enable researchers to do analyses on a scale which was previously out of reach for them. So I am trying to assess the demand.
An example: Is it surprising that the node with the highest (approximated) betweenness in the human connectome mentioned above is the follwing one?
1.8256e+06
rh-precentral
[54, 101, 117]
n296657
[-2.85e-02, 1.00e-03, 7.50e-03, 1.98e-02, 1.85e-02, -5.39e-03, -3.08e-04, -2.82e-03, 9.19e-03, -1.37e-02, -1.28e-03, 5.05e-03, -1.84e-03, 2.35e-03, 6.79e-04, 2.25e-02, -4.40e-04, -1.54e-02, 2.41e-04, -9.27e-03, 3.36e-03, -2.46e-02, 9.37e-$
1.00571e+06
1.00098e+06
0.0897281
4724
A domain expert might be able to interpret this and deduce some relevant information. Has anyone studied betweenness in this network before? Because clearly you don't want to wait for the exact result in a 40 millon edge graph. However, getting this result took me only 5 minutes because I have implemented the approximation algorithm by Riondato & Kornaropoulos.
About the need for previous expert knowledge - not necessarily so. For example, you don't need expert knowledge to find a new motif, just search for motifs.
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