A NEW NEUROSURGICAL TOOL INCORPORATING DIFFERENTIAL GEOMETRY AND CELLULAR AUTOMATA TECHNIQUES
This work is supported by the Marshall Aid Commemoration Commission.
Using optical coherence imaging, it is possible to visualize seizure progression intraoperatively. However, it is difficult to pinpoint an exact epileptic focus. This is crucial in attempts to minimize the amount of resection necessary during surgical therapeutic interventions for epilepsy and is typically done approximately from visual inspection of optical coherence imaging stills. In this paper, we create an algorithm with the potential to pinpoint the source of a seizure from an optical coherence imaging still. To accomplish this, a grid is overlaid on optical coherence imaging stills. This then serves as a grid for a two-dimensional cellular automation. Each cell is associated with a Riemannian curvature tensor representing the curvature of the brain's surface in all directions for a cell. Cells which overlay portions of the image which show neurons that are firing are considered "depolarized". The cellular automation is then run with the following rules:
(1) At each step all squares in contact with a depolarized square become depolarized if | ∇uv| * t ≤ c. ∇u is the covariant derivative in the direction of vector u. The vector u is a unit vector in the direction the depolarization from the original depolarized square. v is a tangent vector to the brain manifold at a touching square. t is the total time in terms of time steps that has been spent at a square. c is a constant given by the speed of the propagation of the wavefront.
(2) If a square depolarizes its neighboring squares, it becomes repolarized.
(3) A repolarized square cannot be depolarized again for tr time steps, given by a the neuronal refractory period.
While the simulation is running, the depolarizing "wavefront" of cells converges on to a few specific cells which we hypothesis correspond to the epileptic focus. Simulations on several parts of the brain are run, comparisons are made to actual optical coherence imaging visualizations, and a tool is proposed for use intraoperatively during therapeutic epilepsy surgery.
