Threshold variability in fibers with field stimulation of excitable membranes

The central focus of this report is the evolution of transmembrane potentials following initiation of a point-source field stimulus, particularly when the stimulus is short and the stimulating electrode is close to the fiber. The transmembrane voltage threshold in response to a point-source field stimulus was determined in a numerical model of a single unmyelinated fiber. Both nerve (Hodgkin-Huxley) and cardiac (Ebihara-Johnson [1]) models of the fiber membrane were evaluated. A central question is whether it is possible to know in advance whether a stimulus of specific magnitude, duration, and location will result in a subsequent action potential. Such determination can be based on the membrane's "voltage threshold." In contrast to the commonly held view, the voltage threshold was found to vary markedly depending on the duration and location of the field stimulus. Voltage thresholds ranged from about 8 mV above baseline to more than 100 mV above baseline, the higher thresholds occurring with shorter stimuli and electrode locations closer to the membrane. A related question is whether the passive membrane response can be used as a tool in determining whether a subsequent action potential is elicited. If the answer is affirmative, this finding can be very useful, since passive properties are linear and thereby much simpler to evaluate than active ones. The results show that the passive response tracks active responses long enough to be a good estimator of subsequent action potential development. Examples show that the evaluation of Vm at 0.2-0.5 msec after stimulus initiation, times chosen on the basis of membrane characteristics, was a better predictor of subsequent excitation than was either initial transmembrane current or Vm at the time when the stimulus ends. Most of the circumstances analyzed here with electric field stimulation also appear likely to be valid with magnetic field stimulation.