The brain contains about 10^11 neurons, electrically excitable
cells that are characterized by a transmembrane electric potential
whose perturbations propagate along the axons. When reaching the
synaptic cleft, the signal is passed from the presynaptic neuron to
the postsynaptic neuron chemically by neurotransmitters. The
postsynaptic neuron may remain activated for a relatively long time,
about a millisecond, and when thousands of postsynaptic neurons are
activated simultaneously in a neuron bundle, the local electromagnetic
activity is strong enough to create an observable magnetic field
outside the head.
Magnetoencephalography (MEG) is a technique for mapping brain activity
by measuring outside the head the weak magnetic fields induced by the
neuronal activity. Unlike more widely used brain imaging techniques
such as fMRI or PET, MEG imaging does not rely on secondary effects of
neuronal activity such as increased metabolic rate or increased blood
flow, but registers directly the neuron firing. Also, the time
resolution of the method is in the millisecond range. The drawback of
MEG is that signals are weak and difficult to measure, the
signal-to-noise ratio is low and the interpretation of data requires
sophisticated mathematical tools.
This project is an introduction to the mathematics of MEG. Some of the
standard models and inversion algorithms are reviewed, and students
get a hands-on experience on simulating and interpreting MEG
data. Real MEG data will be provided by the MEG laboratory of the
Epilepsy Center of the Cleveland Clinic, where methods are developed
and tested for localizing the focus of the onset of epileptic
seizures.
The project will be conducted at the Department of Mathematics under
the supervision of Dr. Erkki Somersalo, in collaboration with Dr. John
Mosher from the Epilepsy Center of the Cleveland Clinic. The
programming is based on Matlab.
|
