Migraine sucks – understatement of the year there. Migraine is also poorly understood and it is quite difficult to come up with effective remedies if you do not understand what you are treating.
One way to understand migraines is through physics. The brain is a network of neurons that are constantly talking to each other. Speaking of physics, this is a dynamic system. Dynamic systems can have more than one stable operating point. A horrifying consequence of this particular system could be that migraine is a stable operating point of the brain.
No way back
A recent paper – one that isn’t particularly exciting – has forced me to write about oscillating brains. I’ve talked about chaotic systems, nonlinear dynamics and dynamical systems before. I won’t repeat everything written before, but I do want to emphasize the concept of transitions that cannot be easily reversed.
If you have something like a weight on a spring, then the stiffness of the spring and the mass of the weight are enough to specify the oscillation of the weight. It operates at a fixed frequency, which, if there were no friction, would last forever. If you shake the spring, the weight will shake back and forth a bit randomly before returning to its steady oscillation. This is called a stable operating point.
The stiffness of the spring, if the spring were ever overstretched, would suddenly change. So the favorite frequency of the spring only lasts as long as the oscillations of the mass remain small. If we excite the oscillator too much, the mass will travel too far and stretch the spring. That will suddenly change the vibrational frequency of the mass. Criticism, it will never change back. The spring has a new stiffness and that determines the new oscillation frequency.
This analogy is a bit stretched, as we’ll see below, but it’s a good starting point for understanding irreversible transitions. The stiffness of the spring is irreversibly changed by large oscillations, changing the frequency of the oscillation.
Your brain is strangely attractive
Although the brain is not a simple mass on a spring, the network of neurons does create a dynamic system. Each neuron excites or suppresses the neurons it is connected to. The firing order, overall activity, and measurable mean electromagnetic activity all oscillate within certain limits, even when they respond to external stimuli.
Unlike our mass on a spring, which has a single stable point, the brain operates on a multidimensional surface. That surface has remarkable properties: it is infinite in size, meaning the brain has access to an infinite number of possible states. But the infinite surface occupies a finite volume, which means that there are also an infinite number of states that the brain cannot access because they are not on the surface.
The surface is called a strange attractor. The presence, absence and shape of this surface depends on the physics of the brain. In a strange way, the brain is completely unpredictable, yet in some ways it is predictable.
Migraine studies suggest that an unknown stimulus alters the brain in a way that changes the shape of the surface of available states. The brain then moves to the new surface and travels from state to state along this surface. Unfortunately, these new states all bring pain.
Watch the pain spread
The article that started me writing modifies an existing model. In fact, the model links the change in activity of a local part of the network of neurons to the activity of neighboring regions, adding a driving factor of external stimulus and a damping factor that causes the activity to die out. That means there are a few buttons to play with: the amount of external stimuli, the sensitivity of the local activity to neighboring activity, and the rate at which the activity dies out.
Because previous research showed that migraines spread outward from one location of the brain, the researchers were particularly interested in how the model behavior was influenced by changing the sensitivity of adjacent brain regions to each other. To do this, one region was chosen as the starting point for the migraine. The sensitivity of that area was adjusted to see how it changed the behavior of the whole brain.
The researcher’s model shows transitions from a normal brain to a migraine (“prodromal”) state and from there to a pain state, as the sensitivity of a single region gradually changes. Importantly, the prodromal state does not appear to be a strange attraction – neural activity becomes periodic and predictable, rather than wandering over a surface of possible states.
The transition to and from the prodromal state is preceded by greater variability in local peaks in brain activity. The pain state looks like another stable area (and is also a strange pull), so once you get there, it takes a significant change to return the brain to its normal state.
Does the model make a difference?
To create a treatment based on this, electrodes are needed in the brain to kick it out of this state. Many experimental systems where electrodes are placed in the brain have problems. Most notably, the body recognizes the invading electrodes and wraps them in scar tissue. This reduces their ability to sense and modify brain activity.
That leaves medicine, which is another step between the brain’s model description and how the treatment is applied. The more steps we take, the smaller the chance that we can extract insights from the model that can be linked to the treatment.
I think I’m trying to say that I really love these models as a way of understanding in a general sense why the brain does what it does. But I don’t believe that this global understanding can be directly used to create treatments.
European physics letters, 2018, DOI: 10.1209/0295-5075/123/10006. (About DOIs).