MULTICHANNEL EVOKED-POTENTIALS AS VOLTAGE SPACE TRAJECTORIES

Multichannel brain evoked potentials can be represented as trajectorie s V(t) in n-dimensional voltage space, analogous to three-channel Liss ajous trajectories (3-CLT). Equations of motion are developed based on an arbitrary number of dipole generators at arbitrary locations withi n the brain, and the properties of 3-CLT are generalized to the higher dimensional case. The trajectory is shown to be limited to k < n dime nsions, and k channels are found to be sufficient for predicting the p otential difference between any two points on the head, provided that an empirically determined set of linear functionals is known. A method for choosing the ''best'' m-channel montage (m less than or equal to k) is described, by associating with each montage an alternating m-ten sor on R(k). Planar analysis of the voltage trajectories is generalize d to the k-dimensional case, in which m-planes are compared using a ma pping between the Grassman manifold and real projective space.