Far-field potentials in circular volumes: evidence to support the leading/trailing dipole model

Far-field potentials in the compound muscle action potential

It has long been believed that the compound muscle action potential (CMAP) in motor-nerve conduction studies (MCSs) records the action potential beneath the active electrode over the muscle belly. However, recent studies have revealed the contribution of the reference electrode to the CMAP, most prominent in the tibial nerve, followed by the ulnar nerve. This "reference electrode potential" is recorded when the conventional reference electrode distal to the muscle belly is connected to a proximal reference. It must be a far-field potential (FFP) considering its distribution, although the precise mechanism of its generation has not been clarified. The conventional theory of termination of the action potential at the muscle-tendon junction is insufficient. Regarding the ulnar CMAP, interosseous muscles mostly contribute to the FFPs. New understanding of CMAP based on the FFP theory may provide new insights into the interpretation of MCSs and related techniques, including motor unit number estimation.

Classification of the extracellular fields produced by activated neural structures

BACKGROUND

Classifying the types of extracellular potentials recorded when neural structures are activated is an important component in understanding nerve pathophysiology. Varying definitions and approaches to understanding the factors that influence the potentials recorded during neural activity have made this issue complex.

METHODS

In this article, many of the factors which influence the distribution of electric potential produced by a traveling action potential are discussed from a theoretical standpoint with illustrative simulations.

RESULTS

For an axon of arbitrary shape, it is shown that a quadrupolar potential is generated by action potentials traveling along a straight axon. However, a dipole moment is generated at any point where an axon bends or its diameter changes. Next, it is shown how asymmetric disturbances in the conductivity of the medium surrounding an axon produce dipolar potentials, even during propagation along a straight axon. Next, by studying the electric fields generated by a dipole source in an insulating cylinder, it is shown that in finite volume conductors, the extracellular potentials can be very different from those in infinite volume conductors. Finally, the effects of impulses propagating along axons with inhomogeneous cable properties are analyzed.

CONCLUSION

Because of the well-defined factors affecting extracellular potentials, the vague terms far-field and near-field potentials should be abandoned in favor of more accurate descriptions of the potentials.

Anatomic origin of P13 and P14 scalp far-field potentials

After median nerve stimulation, noncephalic or earlobe reference montages enable one to record over the scalp a well-defined, positive far-field response, which has been labeled the P14 or P13-P14 complex. It has been ascertained that this wave is generated in the caudal brainstem. Its use is reliable and sometimes mandatory in assessing a number of diseases that affect primarily the brainstem, such as multiple sclerosis or coma. Because of its complex shape as well as discrepant findings in the literature, it is still debated whether this potential is produced by a single or by multiple serial generators. The authors present these different views and summarize the different recording methods, while bearing in mind that some recording techniques are more suitable for routine purposes and others are preferred in selected cases, when more information regarding caudal brainstem function is required.

Concentric and single fiber electrode spatial recording characteristics

A better appreciation of the specific spatial recording characteristics of the single fiber and concentric needle electrode can result in more accurate physiologic and theoretical interpretations of single fiber and quantitative motor unit action potential analysis. We demonstrate by physical modeling that the 90% and 99% amplitude sensitivity envelopes are not simple hemispherical shapes. The 90% sensitivity concentric electrode volume does not extend beyond the insulated portion of the 15 degree beveled surface between the core and cannula and extends only 280 microm perpendicularly from the center of the core's surface. The 99% envelope extends approximately 830 microm perpendicularly from the core's center. This is a much smaller volume of sensitivity than exists for a similarly modeled monopolar electrode. The 90% and 99% envelopes extend to 110 and 320 microm perpendicularly from the exposed single fiber core. Both the single fiber and concentric needle volumes of sensitivity have specific asymmetries described.

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.

Far-field potentials in cylindrical and rectangular volume conductors

The occurrence of a transient dipole is one method of producing a far-field potential. This investigation qualitatively defines the characteristics of the near-field and far-field electrical potentials produced by a transient dipole in both cylindrical and rectangular volume conductors. Most body segments of electrophysiologic interest such as arms, legs, thorax, and neck are roughly cylindrical in shape. A centrally located dipole generator produces a nonzero equipotential region which is found to occur along the cylindrical wall at a distance from the dipole of approximately 1.4 times the cylinder's radius and 1.9 times the cylinder's radius for the center of the cylinder. This distance to the equi-potential zone along the surface wall expands but remains less than 3.0 times the cylindrical radius when the dipole is eccentrically placed. The magnitude of the equipotential region resulting from an asymmetrically placed dipole remains identical to that when the dipole is centrally located. This behavior is found to be very similar in rectangular shallow conducting volumes that model a longitudinal slice of the cylinder, thus allowing a simple experimental model of the cylinder to be utilized. Amplitudes of the equipotential region are inversely proportional to the cylindrical or rectangular volume's cross-sectional area at the location of dipolar imbalance. This study predicts that referential electrode montages, when placed at 3.0 times the radius or greater from a dipolar axially aligned far-field generator in cylindrical homogeneous volume conductors, will record only equipotential far-field effects.

Far-field potentials

Far-field potentials are produced by neural generators located at a distance from the recording electrodes. These potentials were initially characterized incorrectly as being of positive polarity, widespread distribution, and constant latency; however, recent advances have clearly demonstrated that far-field potentials may be either positive or negative depending upon the location of the electrodes with respect to the orientation of the dipole generator. Additionally, peak latencies in the far-field can vary with alterations in body position and the spatial distribution of far-field potentials, while widespread, is not uniform. Recent studies of far-field potentials suggest how such waveforms are produced when the symmetry of an action potential, as recorded by distant electrodes, is broken by such factors as differing conductivities of volume conductor compartments, direction of action potential propagation, size differentials in adjoining body segments, or the termination of action potential propagation in excitable tissue. Human, animal, and computer experiments support the preceding generalizations. These new explanations are directly applicable to such far-field potentials as the short latency somatosensory-evoked potential. Furthermore, since far-field potentials can also occur in muscle tissue, one should expect that these generalizations will hold with respect to electromyographic potentials.