Application of the three-channel lissajous trajectory of auditory brainstem-evoked potentials to the question of generators.

In studies of generators of auditory brainstem-evoked potentials (ABEP), depth recordings and clinical correlates may not reflect all the activity involved. Although the 'inverse problem' is mathematically ill-posed, a synthesis of physico-anatomical data with a three-channel Lissajous trajectory (3CLT) may indicate the actual number and identity of generators. A 3CLT of ABEP in three-dimensional voltage space, is isomorphic with the vector tip representing the momentary centrally located dipole in a uniform, spherical volume conductor. This isomorphism enables approximations of ABEP dipole equivalents to be made. 3CLT summarizes the surface activity in a single plot. It accentuates correlations within the orthogonal records, such as planarity of segments, allowing segmentation of the analysis epoch into components. These properties of 3CLT simplify the analysis of parametric effects on the surface distribution of ABEP components. The results of applying this technique indicate the experimental conditions under which the assumptions for the approximation of generators are closest to being fulfilled. Of all the points along the trajectory, apices (points with maximum absolute amplitude and curvature) have the most unique generators. The 3CLT to low-intensity and high-rate clicks, indicate more unique generators than the customarily used high-intensity slow-rate clicks, in which considerable temporal overlap of generator activity exists.

Geometrical principal component analysis of planar-segments of the three-channel Lissajous' trajectory of human auditory brain stem evoked potentials.

Three-Channel Lissajous' Trajectories (3CLTs) of Auditory Brain Stem Evoked Potentials (ABEP) were obtained from 15 normal humans. Planar-segments of 3CLT were identified and the orientations of the first two geometrical principal components, which interact to produce the planar-segments, were calculated. Each principal component's orientation in voltage space was quantified by its coefficients (A, B and C). Intersubject variability of these orientations was comparable to the variability of plane orientations. The principal components of planar-segments can indicate the type of generator activity that is involved in the formation of planar-segments. The results of this analysis indicate that planarity of each 3CLT component is produced by the interaction of simultaneous multiple generators, or by a single synchronous generator which changes its orientation. The coefficients of these principal components may complement plane coefficients as quantitative indices of 3CLT of ABEP.

Three-channel Lissajous' trajectory of the human short latency visual evoked potentials.

Three orthogonally derived voltage-time records, when plotted simultaneously on three-dimensional voltage-voltage-voltage coordinates, produce a 3-Channel Lissajous' Trajectory (3CLT). 3CLTs of short latency visual evoked potentials (SVEP) were obtained for 8 adult humans (16 eyes) in response to monocular flash stimulation. Intersubject variability of 3CLT of SVEP was small enough to enable identification along the trajectory of comparable planar-segments of approx. 3-5 ms duration across subjects. In each planar-segment, the point at which the trajectory exhibited marked bending was noted. These points were called apices and they corresponded to maxima in the trajectory's distance from the origin (Trajectory Amplitude). Intersubject variability in apex latencies was comparable to, or smaller than, peak latency variability of single-channel records. 3CLT of SVEP consisted of 8 planar-segments in each of the latency ranges of 0-40, 40-70 and 70-100 ms. Analysis of 3CLT, combining the criteria of segment planarity, apices and trajectory amplitude peaks, enabled differentiation between components that had been considered the same in surface distribution studies. 3CLT of SVEP seemed to be influenced by the direction of propagation along the visual pathway.

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.

Three-channel Lissajous' trajectory of human auditory brain stem evoked potentials.

By simultaneously recording from 3 orthogonal electrode montages, and plotting the 3 voltage-time records on three-dimensional voltage-voltage-voltage coordinates, a spatial Lissajous' trajectory is obtained. This 3-Channel Lissajous' Trajectory (3CLT) represents the simultaneous voltage values from 3 independent montages and, assuming a uniform volume conductor, it includes all the information required for calculation of the dipole equivalent of surface-recorded activity. In 3CLT time is not explicitly graphed, but is implied as motion along the trajectory. Thanks to the small distribution of the generators of BAEPs, relative to their distance from the recording electrodes, 3CLT of BAEPs holds the promise of summarizing all activity from the surface. Comparing 3CLT of BAEPs to left vs. right ear stimulation has confirmed the lateralization of components I and III, but has also shown lateralization for the other components, which detailed surface mapping studies had overlooked. 3CLT may offer a more sensitive, yet less cumbersome, alternative to detailed surface mapping of BAEPs. The full promise of 3CLT can only be evaluated after quantitative indices of the trajectory are developed.