What tube maps tell us about adhd and the brain

Most people consider the tube maps of big cities e.g. London’s tube map complex and irritating.

On the other hand, people immediately spot patterns in most tube maps. Most often, you recognize a limited number of hubs e.g. the central station. If the central station is left out, traveling gets much harder. A tube map is a compromise between a completely random net between nodes (or call it stations) and a simple, extremely hierarchical one.tube-map

Mathematicians call this a small network and developed a whole theory for better characterization of the lines and nodes (vertices and edges, in the mathematicians’ slang).

So, what has this to do with ADHD? If brain connectivity plays a role for attention and better organization of your behavior, maybe the “tube map” of an ADHD patient is not efficiently organized. This could be analyzed by measuring the brain’s activity in several regions over time and then correlating these timecourses to look which regions are tightly linked (form connections) and which regions are not (no “subway connection available between these regions”). Than one could use this theory for characterizing the brain network. That’s exactly what Robert Cary and colleagues report in the Journal Cerebral Cortex (2016;1–10; doi: 10.1093/cercor/bhw209).

They investigated 22 patients with ADHD with and without their medication and compared it to the network pattern of 31 controls.

For this, they calculated for each point in the resting-state data of the brain (so-called “voxel”) a measure they termed “node dissociation index” (NDI). The basic idea is that for a part of the brain nodes, we can define a “module”. A module for a given node is its number of links to different nodes in relation to the sum of all links (a bit more complicated, but that’s the basic idea). The Modularity in a region is the sum of the modularity of all nodes in this region. The node dissociation index is the sum of all modules in relation to the number of connections (in the specific node i and across all nodes).

When we look at the nodes number 1,5 and six, we see two highly interconnected networks in green and blue. These form two different “modules”. While node 1 has three connections to 2,3, and 4, it does not connect to the blue module, therefore its NDI is zero. Node number six is highly connected within the blue module but not to the green module, its NDI is zero. Node number 5 has four connections and one connection to the green module, therefore its NDI is 0.25.


In the analysis by Cary et al. the NDI (summed for specific networks like “visual”, “default mode” or “salience” ) takes values between 0.1 (visual) or almost 0.7 (salience). These measures give us a clue how tightly these networks are linked to nodes within their own communities (low dissociation indices) or whether they “dissolve” their connections and have connections to nodes which are not grouped into their own node community.

What was the effect when patients were scanned after having had a short medication wash-out? And how does this compare to the healthy controls?

The controls had lower values of the dissociation index than the patients. In patients, the visual system was not affected (very plausible!), but a variety of networks showed a decrease of the dissociation index when patients were on medication. The largest differences in networks were found in the visual attention network, the salience network and the fronto-parietal network. These networks are involved in higher order cognitive functioning and mediate psychological functions which are implicated in ADHD. The interesting take home message is, that by giving stimulant medications to patients a confuse and badly organized “tube map” (or brain network) gets a more concise structure. Graph theory offers an interesting perspective on brain networks. Future work might look in detail at how clinical phenomena are connected to brain networks or how specific comorbidities (e.g. additional addiction disorders) influence brain networks.