Using fundamental graph theory analysis to deconstruct the human brain as a..network!
Although science has made great progress in countless fields of study, it still falls a bit short with understanding the one rudimentary thing behind scientific progress: Science still does not fully understand the human brain.
When we try to scientifically understand and breakdown something, we break the subject down into measurements, scientific meta data, mathematical structures, molecular building blocks, or ,simply put, anything quantifiable to make a large concept easier to understand. This same methodology can be used to understand the human brain and the many interactions within the human brain. When we look closely at the brain’s structure we see that it shares many similarities with complex networks and that it can be analyzed the same way using fundamental rules of graph theory. Before we dive into this analysis first we have to understand a couple of definitions which will also let us see how relevant this analysis actually is to the graph theory we learned at the beginning of the course.
We understand a network to be a group of nodes, which we label as vertices, connected to each other by a group of lines which we label as edges. A complex network is a more nuanced version of this used largely to group the sort of networks associated with real world systems. These complex networks are characterized by topological features such as small-worldness, modularity, the existence of high degree nodes, etc. Ultimately this form of complex network can be used to describe the human brain and the way the human brain sends information throughout its structure. These topological features that the article mentions are quite relevant in our course discussion of graphs especially in the context of real world networks. For example small-worldness, which is a property the article cites as being a common property found in new empirical studies of brain networks (in animals and in humans), is something that we cover in nearly all of our discussions of networks. Small-worldness describes a network where most of the nodes are close to each other in terms of edge distance but are not neighbors of each other. This is the exact sort of structure that Facebook uses for friend suggestions and the structure used in homework one since suggested friend nodes aren’t direct neighbors of the node representing you but are still close through mutual friends. Small-worldness in the context of the human brain is becoming more and more prominent in recent studies of human brain structures.
Now let’s talk about the brain. The brain is extremely complex but with a certain approach we can break down its structure into a network and analyze it using the fundamentals of graph theory. There are a couple of steps to this approach.
In order to construct a graph of the brain we need to follow four distinct steps. These steps can be found in their original text in the article but for our purposes I have simplified them a bit and reformatted them for this blog post.
- 1. First we have to pick what we want to define as the nodes of the graph. In the context of the brain we can either pick large sections of the brain characterized by their function, or more effectively we can zoom in closer and pick electroencephalography or multielectrode-array electrodes which detail the movement of data in the brain. And in medical applications the nodes could be anatomical regions of an MRI imaging result.
- 2. Measure roughly how close these nodes are in terms of how often and frequent they interact with each other. This is done through either the spectral coherence or something we call a Granger causality measure between two sensors.
- 3. Now we create an association matrix based on the associations between nodes we made in step 2.
- 4. We finalize and calculate the network parameters of the graph we have constructed.
In a very deconstructed sense we have just constructed a graph of the human brain that allows us to study its anatomical patterns. The nodes are simple neural elements(neurons or entire brain regions) and the edges are connectivity structures such as synapses or axonal projections. Then using the different graph analysis tools we’ve discussed in the course we can sufficiently describe and interrogate the structure of the brain.
Although being able to see the brain through the lens of a graph seems like a very simple application of graph/network theory onto neurology it is the most powerful. There are also more complicated and immediately practical uses of projecting graph theory onto the brain. Using graph construction to construct a brain can also help us to understand how certain mental conditions/illnesses can affect the structure of the brain. This is a very clear example:
Here we can clearly see the effects that Schizophrenia has on a brain structure by constructing it as a graph. It exhibits huge structural differences in its anatomical formation and it is quite easy to make the distinction between it and a healthy brain. Applications like this are quite remarkable and can keep us highly optimistic about the future of brain study.
Studying the brain is certainly not an easy task and while looking at the brain through the construction of a graph might not be the easiest approach either, it is certainly an approach worth committing to. Being able to see the brain as a construction of its most functional parts(neurons) will allow us to learn every detail about the brain. This application will lead to breakthroughs in countless fields including AI, medicine, sociology, criminology, epidemiology, etc. And all of this is made possible through networks and graph theory.
Source and pictures:
http://www.indiana.edu/~cortex/networks_nrn.pdf
Complex brain networks: graph
theoretical analysis of structural and
functional systems
Ed Bullmore*‡ and Olaf Sporns§