Calculation of electric fields in a multiple cylindrical volume conductor induced by magnetic coils

Tripolar-cuff deviation from ideal model: Assessment by bioelectric field simulations and saline-bath experiments

Ideally, interference in neural measurements due to signals from nearby muscles can be completely eliminated with the use of tripolar cuffs, in combination with appropriate amplifier configurations, such as the quasi-tripole (QT) and the true-tripole (TT). The operation of these amplifiers, is based on the theoretical property of the nerve cuff to produce a linear relationship of potential versus distance along its length, internally, when external potentials appear between its ends. Thus, in principle, electroneurogram (ENG) recordings from an ideal tripolar cuff would be free from electromyogram (EMG) interference generated by nearby muscles. However, in practice the cuff exhibits non-ideal behaviour leading to "cuff imbalance". The main focus of this paper is to investigate the causes of cuff imbalance, to demonstrate that it should be incorporated as a main parameter in the theoretical ENG-recording cuff electrode model. In addition to cuff asymmetry and tissue growth, the proximity of the interference source to the cuff is shown to result in cuff imbalance. The influence of proximity imbalance on the performance of the QT and TT amplifiers is also considered. Proximity imbalance is studied using bioelectric field simulations and saline-bath experiments. Variation is observed with both distance (40 mm and 70 mm was examined) and orientation (0-180 degrees), with the latter causing a more severe effect especially when the source dipole and the cuff are vertical to each other. The simulations and measurements are in close agreement. Tissue growth imbalance and asymmetry imbalance are also investigated in vitro. Finally, the signal-to-interference ratio (SIR; ENG/EMG) of the QT and TT amplifiers is examined in the presence of cuff imbalance. It is shown that proximity imbalance results in their SIR to peak only at certain cuff orientation values. This important finding offers an insight as to why in practice ENG recordings using these amplifiers have been widely reported to be degraded by EMG interference.

Rigorous Green's function formulation for transmembrane potential induced along a 3-D infinite cylindrical cell

The quasi-static electromagnetic field interaction with three-dimensional infinite-cylindrical cell is investigated for both intracellular (IPS) and extracellular (EPS) current point-source excitation. The induced transmembrane potential (TMP), expressed conventionally via Green's function, may alternatively be expanded into a faster-converging representation using a complex contour integration, consisting of an infinite-discrete set of exponentially decaying oscillating modes (corresponding to complex eigenvalues) and a continuous source-mode convolution integral. The dominant contributions for both the IPS and EPS problems are obtained in simple closed-form expressions, including well documented special mathematical functions. In the IPS case, the dominant modal contribution (of order zero)--an exact solution of the well-known cable equation--is explicitly and analytically corrected by the imaginary part of its eigenvalue and the source-mode convolution contribution. However, the TMP along a fiber was shown to decay at infinity algebraically and not exponentially, as predicted by the classic cable equation solution. In the EPS case, the dominant contribution is expressed as a source-mode convolution integral. However, for a long EPS distance (e.g., >10 cable length constant) the order-one-modes involved in the convolution is not a solution of the cable equation. Only for shorter EPS distance should the cable equation solution (i.e., the order zero dominant mode) be included in addition to the modes of order one. For on-membrane EPS location, additional modes should be included as well. In view of our EPS result, we suggest that the cable equation modeling existing in the literature and related to functional electrical stimulation for EPS problems, should be critically reviewed and corrected.