Geometrical analysis of human three-channel Lissajous' trajectory of auditory brain-stem evoked potentials

Three-channel Lissajous' trajectories (3CLTs) of auditory brain-stem evoked potentials (ABEPs) were obtained for a group of 15 normal humans. 3CLTs were studied using geometric spatial descriptors of rate of bending (curvature), local planarity (torsion), as well as the parameters of best fit planes along the trajectory. Point-by-point analysis enabled objective determination of apices (curvature maxima) which divided the trajectory to curvilinear segments. Consecutive apices defined planar segments (each consisting of two curvilinear segments) along the trajectory. Of the two possibilities of arranging apices in the middle of planar segments only one yielded consistently planar segments. The alternative set of apex triads represented transitions between truly planar segments. The variability of position and orientation measures of planar segments was greater than that of apex latencies and plane limits. The significance of planes, as well as their generation, in 3CLT of ABEP, remains to be studied.