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authors, the question prompts reflection on the range and adequacy of the method-
ological tools actually available for work in this area. One sticks with improper tools
only when the other options appear even worse. And while there are indeed more
sophisticated tools for cooperation-sensitive investigations of neuroscientific data,
those techniques are typically highly complex, hard to master, and - most impor-
tantly - produce results that can be difficult to interpret.
To help address these related problems, this chapter will describe a very sim-
ple analytical technique that we have been using in our lab to make cooperation-
sensitive investigations tractable. In this chapter, we will outline that method, report
some preliminary results of its application, and illustrate some of the many future
projects in which we expect this technique (and the underlying database of brain
imaging studies) will be of considerable use.
2.2 Graph Theory and Neuroscience
A graph is a set of objects called points, vertices, or nodes connected by links
called lines or edges. Graphs have proven to be a convenient format to represent
relationships in very many different areas, including computer networks, telephone
calls, airline route maps, and social interactions [18, 19]. In neuroscience, graphs
have been used for such purposes as investigating neural connectivity patterns [27],
correcting brain images [17], and analyzing the patterns of neural activations in
epilepsy [32]. Nevertheless graphs and graph theory - the branch of mathematics
concerned with exploring the topological properties of graphs [15] - remain at this
time underutilized tools with enormous potential to advance our understanding of
the operations of the brain.
Our approach to investigating functional cooperation in the cortex involves build-
ing co-activation graphs, based on applying some simple data analysis techniques
to large numbers of brain imaging studies. The method consists of two steps: first,
choosing a spatial segmentation of the cortex to represent as nodes (current work
uses Brodmann areas, but alternate segmentation schemes could easily be used; see
below); and second, performing some simple analyses to discover which regions -
which nodes - are statistically likely to be co-active. These relationships are repre-
sented as edges in our graphs.
For this second step we proceed in the following way. Given a database of brain
imaging studies containing information about brain activations in various contexts
(we describe the particular database we have been using in the next section), we
first determine the chance likelihood of activation for each region by dividing the
number of experiments in which it is reported to be active by the total number of
experiments in the database. Then, for each pair of regions, we use a
2
measure
to determine if the regions are more (or less) likely to be co-active than would be
predicted by chance. We also perform a binomial analysis, since a binomial measure
can provide directional information. (It is sometimes the case that, while area A and
area B are co-active more (or less) often than would be predicted by chance, the
χ
