Far-field potential production by quadrupole generators in cylindrical volume conductors

Far-field potentials have been observed clinically and recognized as such for approximately 30 years. Unfortunately a complete understanding of far-field potential generation is not yet at hand. An attractive model is the representation of an action potential by a quadrupole consisting of a leading and trailing dipole with respect to the direction of propagation. This investigation physically models an action potential by using a quadrupole constant current source and substantiates the concept that an action potential as modeled by two dipoles back-to-back is capable of producing far-field potentials in cylindrical volume conductors. The 4 postulated mechanisms of generating far-field potentials are validated, i.e., an action potential encountering (1) different size volume conductors, (2) the termination of excitable tissue, (3) a change in conducting medium conductivity, and (4) a bend in the nerve. A fifth postulated but previously not demonstrated method of far-field production, neural branching, is shown by the quadrupole model to also be capable of yielding far-field potentials. The termination of a volume conductor is also shown to be capable of generating a voltage difference across the quadrupole. Any of the above 6 conditions create an alteration in the symmetry of the leading and trailing dipole moments resulting in a transient potential difference across the quadrupole as recorded with a far-field recording montage. The potential difference produced by the asymmetric electric field between the leading and trailing dipoles recorded distantly in areas of low potential gradient is the so-called far-field potential. This investigation substantiates the utility of the leading/trailing dipole model of far-field production and offers a simple model of passive voltage distributions secondary to dipolar moment imbalances to better understand the generation of far-field potentials in cylindrical volume conductors.