Far-field potentials in circular volumes: the effect of different volume sizes and intercompartmental openings

Preliminary investigations of circular volume conductors suggested that far-field potential magnitude declines progressively slower with increasing radial distance from a current source and follows a cosine function with angular displacement of the recording electrode from the electrical generator's axis. Using circular volumes of 6 differing radii, the mathematical relationship between angle, radii, and far-field potential amplitude is determined. Previous theoretical relationships of amplitude versus dipolar spacing, current, and distance from a dipole generator in a bounded volume conducting medium are verified for the near-field. Far-field potentials in circular volumes are found to become constant at radii greater than 75% of the bounded volume's radius. Additionally, an adjoining volume conductor acts simply as a passive fluid-filled electrode (wick electrode) to the circular volume containing the generator until the intercompartmental opening to the circular volume exceeds 20% of its circumference. This finding was clinically supported by recording similar P9 somatosensory-evoked far-field potentials generated caudal to the foramen magnum from various portions of the cranium, whose connections to the torso, foramen magnum, and neck, average 6.2% and 17.8%, respectively. Finally, 3 circular volume conductors were connected in series by channels less than 20% of the volume conductor's circumference. Both adjoining circular volumes were equipotential to the far-field potential present at the boundary of the first circular volume containing the dipole generator. This observation supports the clinical finding of far-field potential transmission through multiple human bodies in conductive contact.