The early beginnings

The first time I encountered DCM, Dynamic Causal Modelling, was in a fMRI-methods class. The lecturer (Prof. Jansen) did a great job in explaining the gist of it. That included how it could be used to model brain networks and obtain their directed connectivity. For me this sounded very familiar to previous classes on computational neurosciene where I picked up on something that was called control theory. Thus the idea that dynamical systems could be characterized by its inputs and how these change the system wasn’t very new to me. Yet, I found DCM very intriguing, enough so to write my master thesis using this method. Back then my understanding of DCM wasn’t very profound, I got the basic concept, could apply it to the data but was lost, when facing words like “variational bayes” or “kullback-leibler divergence”. Today, I have a better idea of what DCM is about. Still, I am learning, more than once, what DCM is made of and I’m far from full comprehension. Here, I will proceed with my journey to understanding DCM, by sharing my thoughts and ideas I’ve picked up so far. With this I also want to caution the reader, for this text might contain errors and does not aim to cover all aspects of the topic discussed.

Networks

During my bachelors I decided to apply for an internship in the social sciences. They offered to conduct research trying to understand the dynamic of in-school bullying using network analysis. When I was asked, why I wanted this job, I just told them, I love networks. Unfortunatley, they didn’t take me. Later, in my masters I found a professor, who shared the same passion and who could not stop pointing out that everything is a network. Seriously, everything! From, the energy supply system, over the financial market, to the psychiatric disorders we carry. Networks come with two main properties: they have nodes (the metro stations in an underground map) and the edges (rails of the trains). If one edge connects two nodes together, then that already makes a network! Easy. And because networks are so divers, they are sometimes classified into different types. They can for example be random, small-world or scale-free (hierachical). These describe the structure of the network, how it is build up. In a random network, nodes are connected to other nodes with uniform probability (that means no connection is preferd = random). Most of the time, however the networks we encounter are not random at all, they follow certain principles. This is why we often find ourselves in our “social buble” and cannot seem to escape. The small-world network has hubs which contain many nodes connecting to eachother while only few connect to far distant nodes. Last but not least, the scale-free network, generates a hierachial architecture, where few nodes connect to more and these to even more nodes. A familiy tree for example, is such a hierachical network, whereby the edges are directed from the partents to the children. This tells us that the genetic information is passed down from generation to generation. Basically, networks are useful visualization for showing us which path information is taking. One more thing, you should know about networks is, that their edges can be weighted, making some connections possibly more prefferable than others. In case of our metro example, one line might be blocked due to a construction site. Then you’d set the edge in your underground map to zero. Or your best friend has forgotten about your birthay and now you feel more distant to them (lowering your edge weight between them and you accordingly). The great things about networks is that you can very easily write them into matrix form, making them useful for mathematical computations. Yay!