# Epilepsy mean-field model is published

Finally, the article I began working on at the University of Washington has come out. This work began as a side project, but it ultimately led to journal publication. As often happens, you never know for sure which project will work.

To give you an overview of this work, I will start from far away. There are many neurons in our brains. According to the latest estimation, there are about 100 billion of them. This is about the same number of stars in our Milky Way Galaxy. How many neurons we have exactly is unknown, but our best guess is on this order of magnitude

Many physicist (and former physicists, like me!) compare the composition of the brain to the composition of a gas. There are indeed many molecules in a gas, and the particular behavior of one gas molecular is not that important. Rather, what matters is the many molecules’ speed, energy, density, and other characteristics. All these characteristics determine the gas’ temperature and pressure. While pressure does depend on the speed of the molecules as a whole, it does not depend on the speed of one molecule in particular.

In neurobiology, we take a similar approach when describing neurons. This approach is called population modeling and it produces neural mass models. Like a gas, a large group of neurons is described by its average characteristics, such as the number of impulses the neurons generate. In this case, we do not have to look into behavior of a single cell. Instead, we describe the behavior of the whole ensemble. This approach saves substantial computational resources, simplifies the behavior of neurons, and makes our data easier to understand.

We used this approach to develop a novel population model based on human data. This model allows us to describe the behavior of epileptic seizures in the brain. Of course, real seizures can only take place in a whole brain. Still, we can learn plenty from slices of pathologic human brains. Using electric field recordings collected from slices of human hippocampus, we developed a mathematical model of epileptic seizures. In this model we argue that it is important to consider negative feedback when determining the reduction of neurons’ firing frequency. The more neural impulses are generated in the population, the stronger the negative feedback becomes.

On the level of a single neuron, this negative feedback is usually due to slow potassium currents flowing through the neuron’s membranes. It turned out that including this mechanism in the neural population model helped us describe epileptic seizures more precisely. For example, by increasing the amount of negative feedback adaptation, one could make the model’s neural population less excitable and less prone to seizures.

Of course, population models cannot give us all the answers and tell us how exactly the brain works. This is especially true because important computations take place on the level of neural impulses. These impulses are averaged in our models, meaning that their nuances are lost. These models nevertheless help us understand general principals. Ultimately, these simplified models will be incorporated into more complicated models that will produce more sophisticated data. Trying to incorporate all of the details from the start would make it impossible to see the whole picture. It is important to emphasize the crucial parts, which we did in our work by using a minimal model to explain a complex phenomenon like epilepsy. P. S. Thank you Melissa MacEwen for English corrections!