So welcome everyone. Today we have a very fruitful workshop on one-eyed dynamics. We

have two invited speakers both from the TU Berlin, so we have Moritz Kessler who is

now in Leipzig. So we actually changed our affiliation to MPI Leipzig now and then we

have Professor Tilo Schwalke from the Institute of Mathematics, TU Berlin and myself who gave

three talks in Neural Dynamics and I think that the talks are kind of expanding a little bit,

not all but various research directions in Neural Dynamics. So today we will start with

Moritz Kessler and then we will have Professor Schwalke and then we'll have a short coffee

bread depending on how we succeed with time and then I will also have to give a talk afterward.

So without taking much time we will start with Moritz Kessler. So maybe you can try

sharing your slides. We can hear you very well. Please you have the floor.

Okay great. Well yeah thank you very much for inviting me. I'm very happy to give a talk today

and I will present the results of my master thesis which were obtained at the TU Berlin

and collaboration with Viko Berner, Jakub Zabitsky, Anna Zaragova and then Antonin Skoch and Jaroslav

Linka from Prague and Klaus Lenat from the Department of Epileptology in Bonn and Eke Hatschel

and I will talk about neural synchronization during epileptic seizures. First I will briefly

define what epileptic seizures and epilepsy is. Then I will introduce the model that I use to

simulate the seizures and the network. I will show my simulation results and compare them to

the empirical results and finally I will address the question whether our brain is a small world

network. So what is epilepsy? Epilepsy is a group of neurological disorders involving seizures.

It affects 1% of the world population so it's quite common and a person is diagnosed with

epilepsy if they have at least two seizures in their life. And this brings us to the next

question. What is an epileptic seizure? Before I will give you the official definition I will

show you a video of an epileptic seizure so that you can get some feeling for what is happening

in the brain. Here we see a young girl who is reading in a book and she has EEG electrodes

attached to her head and you can see the signal of these electrodes on the left side and the time

series are quite flat indicating desynchronization. But now a seizure starts, the girl starts to tilt

her head and she stopped reading and now the EEG electrodes they all basically show the very same

signal. They show this characteristic three hertz spike wave discharges. Now the seizure is over

and the girl returned back to normal. So what just happened here? The official definition says

an epileptic seizure is a transient occurrence of signs and or symptoms due to abnormal excessive

or synchronous neuronal activity in the brain. The seizure we have just seen is an absent seizure

and absent seizures are nonconvulsive. That means they don't involve muscle cramping. They have

characteristic three hertz spike wave discharges which will become important later. And compared

to other types of seizures they are more subtle, involve no falling and usually last only around 10 seconds.

So now with this definition in mind I will show you briefly another seizure of the same girl.

So now again the girl is in the healthy brain state and the electrodes show desynchronized behavior

and now she starts drinking and here again the seizure starts. And you can see that these big

spikes that you can see we have three of these spikes passing my red laser pointer on each second.

This is the characteristic three hertz spike wave discharge and you can see that all electrodes show

the same behavior indicating that this is a global brain phenomenon that impacts the entire brain.

And now the seizure is over and again the girl returned back to normal.

So my goal was to model what is happening during such seizures. In my model I used the

Fitsunagumo oscillator which consists of two differential equations which are shown here.

In these equations we have two variables the activator variable u and the inhibitor variable v.

In front of the activator variable we have the time scale separation epsilon which is chosen very

small such that we observe these characteristics low-fast dynamics of neural spiking.

We also have the threshold parameter a when the absolute value of a is larger than one

we are in the excitatory regime and when the absolute value of a is smaller than one

we are in the oscillatory regime. We want to model epileptic oscillations so we chose

a equals 0.5 that means we are in the oscillatory regime.