Evidence for hubs in human functional brain networks
Jonathan Power, Brad Schlaggar, Christina Lessov-Schlaggar, Steve Petersen
Neuron 2013 Aug 21; 79(4):798-813
Files (nii, xls)
This article is really two shorter articles joined at the hip. The first segment is about interpreting network properties in correlation networks, and how such interpretations may differ in correlation versus non-correlation networks. The second segment is about finding potentially important locations in the brain using resting state data.
All papers have backstories, but this paper took a more tortuous path than most for me. I originally wrote a commentary on the 2009 hubs paper from Randy Buckner's group. Just a few paragraphs making the conceptual point, no figures. Then Brad suggested that I flesh out the arguments with data from real-life networks, turning it into a small paper. At the same time I was developing ideas about potentially important locations in the brain, but that also was a small paper. So I stuck them together as related but semi-independent points. The article was written and submitted by late 2011, after I had published my first paper on brain organization, but before we had established the collaboration with Iowa (that would happen during a winter road trip to Iowa City a few months later). So the paper made predictions that hadn't yet been tested. In the first submission, an editor asked to publish only the first half of the paper. The suggestion was tempting, but I declined because I wanted the critical message (of the first half) paired with a (potentially) constructive message. As the review process lengthened I sometimes regretted this decision. And certainly once the Iowa results emerged other groupings of analyses became possible. But we were well into the review process at that point and I was happy that the paper was intact when it emerged.
In talking to people about this paper, I've come to believe I did a poor job of explaining my arguments in the first half of the paper. And if you don't buy the first half of the paper the second part is not as well motivated. So I'm going to try to explain myself again, but differently, and hopefully better.
First, a bit about resting state fMRI signals. These signals are present in everyone, and signals in groups of a few dozen people look much like signals in another few dozen people. In individual subjects, though data are very noisy with only 5-10 minutes of data, similar signals are seen, and if you get 30+ minutes of data from individuals, they often look quite like group average data. The signals are seen in primates, mice, and birds, and there are notable similarities in the organization of the signals across primates. The signals are seen in humans, with similar organization, in some stages of sleep and under light anesthesia. My supposition is that these signals are doing some basic function for the brain. When I see correlated signals, I suppose, without much elaboration, that the correlated signals indicate either direct communication or indirect co-involvement in some process. Mainly I suspect the latter case. In my view, the unifying thing is the process. It matters little to me whether 100 mm3 or 10,000 mm3 of cortex are involved in the process, the important thing is that a process is linking tissue across the brain. We know from decades of functional neuroimaging that the resting state signals tend to pull together regions that are generally coactive. The default regions are a prime example: regions often deactivate during goal-oriented tasks, i.e., that have similar co(de)activation profiles in study after study, have highly and selectively correlated resting state signals. So I view correlated activity among these default regions not as activity among X nodes or Y mm3 of tissue, but principally as activity among a set of regions that frequently coordinate activity in the service of some constrained set of processes.
So when I see a correlation matrix of resting state signals, I am not very interested in how many regions (or nodes, or voxels) are in the default module, or the visual module, or any module. When I see that matrix, if I think about what I might be able to say about more-important or less-important nodes, my first thought is about the diversity of processes a node appears to participate in. If a node only correlates strongly within its module, it must display mainly a single major signal, and I suspect that node is involved in a relatively constrained set of processes. If a node correlates strongly to multiple modules, it must display a signal correlated with several major signals, and correspondingly I suspect that this node might be involved in several "classes" of processes.
The paper is just an elaboration of the previous paragraph. Put strongly, the paper argues that 1) degree does not necessarily indicate node importance in correlation networks, 2) important brain nodes may be mis-identified by degree and related measures in resting state correlation networks, and 3) signal diversity seems an interpretable property of nodes in resting state correlation networks.
Point 1: The number of strong correlations a node has, in a correlation network, is strongly linked to the modular structure of the network. If this is not clear on reflection, consider this example. Let's take a string quartet, a chamber orchestra, and a full symphony, with perhaps 4, 15, and 50 members respectively. If you examine practice schedules (a proxy of communication among the members), you'll find that each group (module) has its own practice schedule. These schedules are highly correlated within a group, but are less or uncorrelated between the groups. For a given member (node), the number of strongly correlated schedules is directly proportional to the group size. So node degree or strength, for a given member, is mainly a function of whether they are in the quartet, the chamber group, or the symphony. This tight link between group size and the number of strong connections a node makes is a feature of many real-world correlation networks, but is not a feature of many real-world non-correlation networks. When such a link exists, it cannot be stated whether a node has high degree because it has many important connections, or whether the node has high degree because it has many connections because it is in a large module.
Point 2: Modules in resting state data are of various sizes, some being considerably larger than others. The default module is largest (~20% of the brain/network), the visual and several other modules are next-largest (~10% of the brain/network). Each of these modules has a "main signal" that binds them together and causes them to be identified as modules in the data. Connection-counting methods, like degree, are highest in default regions like the PCC/precuneus, vmPFC, and the angular gyrus. This can be explained purely as a function of the default module bring the largest in the brain. As I view things, high degree at a node is indexing that a lot of tissue displays a similar signal, but that doesn't necessarily translate to being an especially important node. Note that I'm not saying that the PCC or other high-degree nodes are unimportant (other factors, for other reasons, may indicate that these nodes are important), but that high degree isn't strong evidence that a node is important.
Point 3: Signal diversity of a node in resting state correlation networks is an interesting property. I think I explained why adequately above, so let me talk about the measures used in the paper. The germ of this part of the paper came from staring at the modules (communities) from my 2011 paper. I noticed that in certain places, a lot of modules were in close spatial proximity and I thought "I don't want a stroke there". The obvious places were the anterior insula, the anterior cingulate, portions of the anterior bank of the prefrontal gyrus, and lateral occipito-temporal cortex. I made up an index, "community density", to identify these locations. I also wondered whether any well-known network properties could help identify nodes with high signal diversity. Participation coefficient was the most obvious candidate, so I calculated that as well and overlaid the results. Participation coefficient was high, mainly, at or near places where community density was high. We termed such co-occurences "articulation complexes", which is awkward to say. We don't really use that term anymore. But what we identified are a few parts of the brain where especially many major signals are represented in close spatial proximity, and where signal at nearby nodes correlates strongly to multiple major signals. These two factors may be inter-dependent (the latter property stemming from the former), but even if it were so, it doesn't matter for the purposes of the paper. You would still have the prediction that where signal diversity is high lesions will have consequences for a broader set of processes than where signal diversity is low. Loosely speaking, this should translate to broad versus narrow cognitive impairment after lesions, a topic we take up in the 2014 PNAS paper.
One thing I like about this paper is that it makes predictions that can be falsified. Any resting state paper is open to numerous criticisms about techniques, parameters, conclusions and so forth. It's not possible to satisfy all the criticisms or alternative explanations in a single publication. But if a paper has predictive power, the criticisms do lose some force. The predictions of this paper have been largely fulfilled in our first follow-up study (the 2014 PNAS paper). It's possible to be right for the wrong reasons, but at the moment no alternative explanation of our findings seems more plausible than the one we proposed in the current paper. We are of course working to expand this promising line of inquiry, and will be better positioned to refine and/or refute our own findings as time goes on.