|Network||#av. sim.||Tot. #av.||#sim.||Seizure Frequency|
Welcome to the Resector
The Resector is an app (interactive website), illustrating how mathematical models can advance epilepsy research.
About 1% of the world population suffers from epilepsy. In about two-thirds of cases, medication helps to suppress seizures. In other cases, when drugs are ineffective, epilepsy surgery might offer a solution. The aim of epilepsy surgery is to stop the seizures, or at least reduce the seizure frequency substantially by resecting a specific part of the brain. The resection area differs between patients. For the determination of the resection area analysis methods are being improved continuously.
One such new technique is the use of mathematical models. These models simulate the spontaneous activity of interconnected brain areas, just as in the real brain. Within such a model, we can remove one or more nodes, i.e. perform virtual resection. Studying the effect of this resection, we can determine what area(s) are the best to remove. In this app, you can experiment yourself with a small-scale model consisting of four regions.
- A Simple Network
- Simulating Activity
- Inspecting the Activity
Select the option 'ex1' for the example network. The picture to the left represents this network. Within this network, nodes 1 and 2 are unconnected, and there is a connection from node 3 to node 4. Node 2 is grey meaning that this node is more excitable. That is, it more easily shows epileptiform activity. We will see the implications when simulating the model.
Click on the button 'Perform Simulation'. A bar appears indicating the progress of the simulation. When the simulation is ready after a few seconds, the figure in the lower left is filled with four graphs (or signals). Each graph corresponds to the activity of a node showing either peaks or low amplitude fluctuations. The peaks correspond to epileptiform activity of a particular node. The little fluctuations during the remaining time represent regular physiological activity. Compare the number of peaks for nodes 1 and 2. As node 2 is more pathological, it will have display more peaks.
Move the cursor over the graph. The figure on the right shows a magnification of this part. You may observe that nodes 3 and 4 exhibit epileptiform activity simultaneously. The magnification shows that this activity starts at node 3. Through the connection, this activity also spreads to node 4. This simple network has just one connection; it is time to explore networks with more connections.
Now select the second example network 'ex2' and perform a simulation. If all is well, nodes 2, 3 and 4 will show no (or very little) epileptiform activity. This is due to the different network structure. The new reciprocal connection from node 4 to 3, allows making a loop from node 3 to 4 and back. Such a loop is referred to as a cycle. In this model, such a cycle inhibits the epileptiform activity. Also, the new connection from node 4 to 2 keeps even the more epileptic node 2 under control.
Let us involve node 1 by adding a connection from node 1 to node 3. Select the third example network 'ex3' and perform a simulation. The new connection dramatically increases the amount of epileptiform activity. This surge is due to the special position of node 1 within the network. This node has only outgoing and no incoming connections. Such a node we call a driver. Drivers play a crucial role in this model and often initiate epileptiform activity. Let's see if we can do something about that.
- Seizure Frequency
In this model, a seizure is a period in which three nodes show epileptiform activity simultaneously. These periods are marked with a * in the graph. The table with simulation statistics shows the total number of seizures under '#av. sim.'. Next, the column '#sim.' indicates the number of simulations for this network, and 'Tot. #av.' the total number of seizures. The seizure frequency is the average number of seizures over all simulations. Now, perform (at least) five simulations to determine the mean seizure frequency with sufficient accuracy.
Next, we want to emulate epilepsy surgery within our model and lower the seizure frequency. We do this by removing a node from the network. Let's first remove the more pathological node 2. At 'Removed Node' specify node 2, and perform five simulations. As you will see in the graph or the statistics, this removal does not help to decrease the seizure frequency. Next, try removing one of the other nodes, perform five simulations each time. Removal of node 1, which is the driver, will display the best suppression. This result implies that not just the properties of a node, but also its place within a network are crucial to predict successful epilepsy surgery.
The model used in this app consists of just four areas, yet it provides interesting insights. Adding more areas and using recordings of patients' brain activity to create a network, we can construct an individual model for a single patient. In further research, we want to explore in similar ways what areas could best be resected. Even then, such a model remains an abstraction of reality and comes with limitations.About this research
This is app has been developed as part of the project "From computational models of epilepsy to clinical protocols". This project is a collaboration of chair Applied Analysis at the University of Twente and the group Clinical Neurophysiology at the University Medical Centre Utrecht. The project was funded by the Dutch Epilepsy Fund and ZonMW.