Research Interests

For my dissertation, I am working on solutions to the Inverse EEG problem. The goal is to non-invasively determine which regions of an individual's brain are electrically active at a particular instant in time based solely on scalp EEG recordings and measured anatomic data (MRI and/or CT). Neuro-pathologies ranging from epilepsy to schizophrenia stand to benefit from an accurate solution to this problem; if scientists can determine which regions of a particular patient's brain are being used for specific tasks, more accurate diagnoses can be made, ultimately enabling better treatment.

Model Construction

We solve the Inverse EEG problem using a finite element approach. The first step in setting up a finite element problem is to construct a finite element mesh that fills the volume of interest. For our problem, we discretize the cranial volume into small tetrahedral elements. To run our physical simulation, it is necessary for each tetrahedral element to be assigned an appropriate conductivity tensor based on the anatomy. For this reason, it is important that the elements conform to the anatomic boundaries of the volume. We describe the major components of our model construction pipeline in detail in our 2000 ISCG paper, as well as in our 2000 IEEE Visualization paper.

After constructing the finite element mesh, we coregister the EEG measurement sites to the finite element model. This can be accomplished by a geometric coordinate transformation, as described in this 1998 Tech Report.

We have also evaluated techniques for reducing the complexity of the measured EEG signals. One particularly interesting method we recently applied was Independent Component Analysis (ICA). With this technique we were able to separate the measurements into statistically independent signals. (For more information, please see our 1999 IEEE EMB paper.)

Simulation

After the geometry has been discretized, we can use the tetrahedral elements to mathematically support approximations to the governing physics. Maxwell's Laws define how electric fields set up in a volume conductor, and it is these equations that we seek to locally satisfy throughout our domain. Globally grouping together all of the local equations, we build a large stiffness matrix that defines the relationship between current sources and the potentials they induce through the domain. For a particular stiffness matrix, A, and a particular set of current sources, b, we can derive the voltages, phi, through the domain by solving the linear system, A x phi = b.

For the inverse EEG problem, the problem is turned upside down: we have a limited set of voltages measured from the scalp surface, and from those measurements we attempt to recover the corresponding current sources within the brain. To solve this problem, we have developed lead-field techniques (described in our 2000 Annals of Biomedical Engineering paper, our 2000 Human Brain Mapping poster, and our 1999 Technical Report).

Another approach to solving the inverse EEG problem is via the surface-to-surface formulation. With this method, we can solve for the potentials on the cortical surface directly based on potentials measured on the scalp. This technique is based on the assumption that there are no current sources located between the two surfaces; for our problem, this assumption holds. Unfortunately, though the solution is guaranteed to exist, the problem is exceedingly ill-conditioned. In order to restore continuity onto the solution, we have developed local regularization techniques, as described in our 1995 SPIE paper.

Visualization

Visualizing the results of our simulations, or even of our models, is always a challenge when dealing with large, complex datasets. Most recently, we have been investigating way of visualizing the underlying tensor data (as described in our 1999 IEEE Visualization papers).