Effect of non-symmetric waveform on conduction block induced by high-frequency (kHz) biphasic stimulation in unmyelinated axon

Abstract

The effect of a non-symmetric waveform on nerve conduction block induced by high-frequency biphasic stimulation is investigated using a lumped circuit model of the unmyelinated axon based on Hodgkin-Huxley equations. The simulation results reveal that the block threshold monotonically increases with the stimulation frequency for the symmetric stimulation waveform. However, a non-monotonic relationship between block threshold and stimulation frequency is observed when the stimulation waveform is non-symmetric. Constant activation of potassium channels by the high-frequency stimulation results in the increase of block threshold with increasing frequency. The non-symmetric waveform with a positive pulse 0.4–0.8 µs longer than the negative pulse blocks axonal conduction by hyperpolarizing the membrane and causes a decrease in block threshold as the frequency increases above 12–16 kHz. On the other hand, the non-symmetric waveform with a negative pulse 0.4–0.8 µs longer than the positive pulse blocks axonal conduction by depolarizing the membrane and causes a decrease in block threshold as the frequency increases above 40–53 kHz. This simulation study is important for understanding the potential mechanisms underlying the nerve block observed in animal studies, and may also help to design new animal experiments to further improve the nerve block method for clinical applications.

Conduction block in myelinated axons induced by high-frequency (kHz) non-symmetric biphasic stimulation

“…This study predicts in myelinated axons that the block threshold will reach a peak and then gradually decrease when the stimulation frequency increases above approximately 50 kHz for non-symmetric waveforms (Figure 3 ). A similar non-monotonic block response has been observed in unmyelinated axons of sea slugs and frogs with the block threshold peaks ranging between 12 and 15 kHz (Joseph and Butera, 2009 , 2011 ) and in our recent simulation study of unmyelinated axons (Zhao et al, 2014 ). Previous animal studies that examined block of myelinated axons (Bhadra and Kilgore, 2005 ; Gaunt and Prochazka, 2009 ; Joseph and Butera, 2011 ) only tested frequencies up to 50 kHz and showed a monotonic increase in block threshold as the frequency increases same as our simulation results at frequencies below 50 kHz (Figure 3 ).…”

“…These simulation studies have been successful in reproducing many phenomena observed in animal experiments, for example the minimal block frequency, the influence of temperature on minimal block frequency, and the relationship between axon diameter and block threshold (Tai et al, 2005a , b , 2009a , b , 2011 ; Zhang et al, 2006 ; Bhadra et al, 2007 ; Liu et al, 2009 ; Ackermann et al, 2011 ). The newly discovered non-monotonic relationship between block threshold and stimulation frequency was also successfully reproduced in our recent simulation study of unmyelinated axons (Zhao et al, 2014 ). This study indicates that the monotonic decrease in block threshold in unmyelinated axons at frequencies above 15 kHz is probably caused by a slightly (<1 μs in pulse width) non-symmetric waveform of the high-frequency stimulation, which constantly hyperpolarizes or depolarizes the axon as the frequency increases above 15 kHz.…”

“…Although our previous simulation study (Tai et al, 2011 ) of large (10–20 μm diameter) myelinated axons showed a monotonic increase in block threshold with stimulation frequency up to 100 kHz, the effect of a non-symmetric waveform on the block threshold was not investigated. Based on our recent simulation study of unmyelinated axons (Zhao et al, 2014 ), we hypothesize that a non-symmetric waveform can also cause a decrease in block threshold as the frequency increases above a certain level in myelinated axons. It is known that the ion channel kinetics of myelinated axons is faster than unmyelinated axons (Hodgkin and Huxley, 1952 ; Frankenhaeuser, 1960 ).…”

Dependence of excitability indices on membrane channel dynamics, myelin impedance, electrode location and stimulus waveforms in myelinated and unmyelinated fibre models

“…These membrane models (summarized in Table 2) are selected, because they are the "classical" models of membrane dynamics, that are often used for applications in which no specialized model exists or is accepted. Because of their widespread use in computational neuroscience (e.g., in computational studies of the cochlear nerve [5,6,23] or for modeling conduction block [39,42,43]), these membrane models are especially interesting for this study, which aims to determine the influence of membrane dynamics on neuronal excitability. The first multi-compartmental model (SENN-MA) listed in Table 1, describes a myelinated axon and is an implementation of the spatially extended nonlinear node (SENN) model [30].…”

“…Finally, a model for unmyelinated fibres (termed "C-FIBRE" in Table 1) is obtained by carefully altering the geometrical and electrophysiological parameters of the SENN-M model. Models of unmyelinated fibres, similar to the C-FIBRE model used in this study, have been used by researchers to study the excitation properties of C-fibres [39,43,11]. Model equations for the different fibre and membrane models (Table 1-2) used in this study are summarized in Appendix A.…”