A four sphere model for calculating the magnetic field associated with spreading cortical depression

In our previous model, we ascertained that the large amplitude waves (LAWs), reported by Barkley and coworkers (1990) in time series magnetoencephalography (MEG) recordings from migraine patients, could be simulated and compared with the recorded signals using a simple plane volume conductor model (Tepley and Wijesinghe 1996). In this paper, we model LAWs using the help of more complicated yet reliable four-sphere model. This mathematical model furthermore assumes that the LAWs arise from propagation of Spreading Cortical Depression (SCD) across a sulcus and these simulated signals are more similar to the recorded signals than the ones we obtained from our previous model. SCD propagates slowly across the cortex in all species in which it has been observed. In our model, current dipoles represent the excitable neurons in the cortex and magnetic fields created by these individual dipoles are calculated using a four-sphere model. The magnetic field arising from the excited area of cortex is obtained by summing the fields due to these individual dipoles. Sulci shapes are represented by simple mathematical formulae.