The Brain As A Network

The brain is an enormously complicated system of interconnected cells. To give a rough estimate, Johnson and Wu suggest that the human brain has 10¹² neurons with 10¹⁵ synapses¹. To wrap your head around the magnitude of 10¹⁵ synapses, consider that it's about 222 times greater than the distance from Earth to Pluto in meters². How do you begin to understand all the madness compressed into the three pound ball of flesh? I have no idea, and I don't trust anyone who claims to know either. However, there are some clever approaches to chipping away at the problem.

At the systems-level, the brain distributes computation over multiple regions. A good analogy is a peer-to-peer network that distributes number crunching across multiple computers, where each computer is specialized to perform some specific aspect of the computation. Abstract this by simply calling the computers "nodes" (which can represent anything, for example, brain regions) and the connections "edges," and viola! you have reached the entry point of network theory, which is a quantitative and visual approach to understanding how nodes relate to one another and how networks function as a whole.

Figure: Network Graphs, (Left) Undirected cyclic graph, (Right) Undirected acyclic graph viewed as a tree. Generated using NetworkX, a Python package developed by Los Alamos National Laboratory. Notice how in this particular case there are no arrows; these graphs do not depict the effective (causal) relationship between nodes. Such a graph can be called a "structural connectivity" graph.

Olaf Sporns is a professor of Psychological and Brain Sciences at Indiana University who wrote a book entitled Networks of the Brain, where he outlines the case for using network theory to better understand the how the brain works.

Why should we take advantage of modern network approaches to study the brain? Primarily, because these approaches can provide fundamental insights into the means by which simple elements organize into dynamic patterns, thus greatly adding to the insights that can be gained by considering the individual elements in isolation. Virtually all complex systems form networks of interacting components. [...] The brain is a complex system par excellence where complex components continually create complex patterns. The collective actions of individual nerve cells linked by a dense web of intricate connectivity guide behavior, shape, thoughts, form and retrieve memories, and create consciousness. No single nerve cell can carry out any of these functions, but when large numbers are linked together in networks and organized into a nervous system, behavior, thought, memory , and consciousness become possible. Understanding these integrative functions of the brain requires an understanding of brain networks and complex and irreducible dynamic patterns they create.³

Studying the brain as a network is an advancement of the older view of brain function as a series of modular parts. This added dimension provides additinal insight to the analysis of neurological dysfunction. The 19th century Harvard neurosurgeon Henery Jacob Bigelow carefully observed Phineas Gage, the famous lesion patient who lost part of his frontal lobe when an explosion rammed a railroad spike through his skull. Bigelow writes of post-recovery Phineas:

He is fitful, irreverent, indulging at times in the grossest profanity (which was not previously his custom), manifesting but little deference for his fellows, impatient of restraint or advice when it conflicts with his desires, at times pertinaciously obstinate, yet capricious and vacillating, devising many plans of future operations, which are no sooner arranged than they are abandoned in turn for others appearing more feasible.⁴

Should one conclude that the region through which the spike penetrated possessed the sole responsibility for making an individual polite and disciplined? Such a view would argue that the region is necessary and sufficient for producing the computation underlying that specific genre of thought and behavior. However, the brain is highly interconnected and plasticity occurs following damage. Furthermore, that region would have to get information from the eyes and ears to know how to compute an appropriate response, and such information would travel through a cascade of layers where information is further processed and abstracted. At what point does the abstracted representation of information become necessary and sufficient for computing an appropriate response? To answer this question, you cannot study the process as a series of regions with fluctuating activity, but rather one must study the system as a dynamic network that processes the information in a highly parallel and distributed fashion. Professor Sporns writes:

Interestingly, science is concerned with the structure, behavior, and evolution of complex systems such as cells, brains, ecosystems, societies, or the global economy. To understand these systems, we require not only knowledge of elementary system components but also knowledge of the ways in which these components interact and the emergent properties of their interactions. [...] In all cases, the quantitative analysis of connectivity requires sophisticated mathematical and statistical techniques.³

Network Graph Method Overview: (L to R) (1) Acquire diffusion weighted image from MRI, (2) segment the MRI into labeled anatomical regions, (3) compute the magnitude of flow from each region to each region into a connectivity matrix, (4) average this matrix across individuals, (5) plot the x,y,z location of the center of each region, the number of connections as the node size (red sphere diameter), and strength of each connection as line thickness. From Heuvel & Sporns (2011)⁵

So how does one get a network graph of the brain? While the simple graph above belies the prodigious amount of physics and neuroscience behind its construction, the basic idea is to measure water molecules as they bounce from place to place and find the direction that they tend to flow most often (the fractional anisotropy). The more water molecules that flow along one tract and the more coherent the flow, the "stronger" that tract is said to be. With functional data, one can compute the functional connectivity between each region (the extent to which two areas communicate). Integrate causal estimates, such as Granger causalities, and the model begins to explore the direction through which the information flows. SiFT, written by my friend and fellow network enthusiast, Tim Mullen, is a great toolkit for exploring dynamic causal relationships.

Hopefully this brief overview hasn't been too vague or misleading-–this approach certainly does not explain how the brain works. But the application of network theory to neuroscience is a great example of how the convergence of scientific disciplines results in a deeper understanding of complex phenomena. I recommend picking up a copy of Networks of the Brain by Olaf Sporns, if not just to marvel at all of the beautiful figures, but to really soak in the complexity of it all and ask yourself just how in the heck are we going to make sense of this complex machine?

1. Johnston, D. (1995). Foundations of Cellular Neurophysiology. MIT Press.

2. Wolfram Alpha: http://www.wolframalpha.com/input/?i=distance+from+Earth+to+Pluto

3. Sporns, O. (2010). Networks of the Brain. MIT Press.

4. Harlow J. M. (1868). Recovery from the passage of an iron bar through the head. Public Massachusetts Medical Society 2, 327–347.

5. Heuvel, M. P. & Sporns, O. (2011). Rich-club organization of the human connectome. The Journal of neuroscience, 31(44), 15775-15786.

Note: 3/15/2012 The intoductory estimate was adjusted to reflect figures that acually made sense. Credit belongs to the folks on Google Plus who kindly pointed this out, without burning me to a stake. Cheers!