Mechanism of conduction block in amphibian myelinated axon induced by biphasic electrical current at ultra-high frequency

Abstract

The mechanism of axonal conduction block induced by ultra-high frequency (≥20 kHz) biphasic electrical current was investigated using a lumped circuit model of the amphibian myelinated axon based on Frankenhaeuser-Huxley (FH) equations. The ultra-high frequency stimulation produces constant activation of both sodium and potassium channels at the axonal node under the block electrode causing the axonal conduction block. This blocking mechanism is different from the mechanism when the stimulation frequency is between 4 kHz and 10 kHz, where only the potassium channel is constantly activated. The minimal stimulation intensity required to induce a conduction block increases as the stimulation frequency increases. The results from this simulation study are useful to guide future animal experiments to reveal the different mechanisms underlying nerve conduction block induced by high-frequency biphasic electrical current.

Appendix

The ionic current I _i,j at j^th node is described as:

$$ \begin{array}{*{20}{c}} {{I_{{i,j}}} = {i_{{Na}}} + {i_K} + {i_P} + {i_L}} \\ {{i_{{Na}}} = {P_{{Na}}}{m^2}h\frac{{E{F^2}}}{{RT}}\frac{{{{[Na]}_0} - {{[Na]}_i}{e^{{EF/RT}}}}}{{1 - {e^{{EF/RT}}}}}} \\ {{i_K} = {P_K}{n^2}\frac{{E{F^2}}}{{RT}}\frac{{{{[K]}_0} - {{[K]}_i}{e^{{EF/RT}}}}}{{1 - {e^{{EF/RT}}}}}} \\ {{i_P} = {P_P}{p^2}\frac{{E{F^2}}}{{RT}}\frac{{{{[Na]}_0} - {{[Na]}_i}{e^{{EF/RT}}}}}{{1 - {e^{{EF/RT}}}}}} \\ {{i_L} = {g_L}\left( {{V_j} - {V_L}} \right)} \\ {E = {V_j} + {V_{{rest}}}} \\ \end{array} $$

where P _Na (0.008 cm/s), P _K (0.0012 cm/s) and P _P (0.00054 cm/s) are the ionic permeabilities for sodium, potassium and nonspecific currents respectively; ${g_L}$ (30.3 kΩ⁻¹ cm⁻²) is the maximum conductance for leakage current. V_L (0.026 mV) is reduced equilibrium membrane potential for leakage ions, in which the resting membrane potential ${V_{{rest}}}$ (−70 mV) has been subtracted. [Na]_i (13.7 mmole/l) and [Na]_o (114.5 mmole/l) are sodium concentrations inside and outside the axon membrane. [K]_i (120 mmole/l) and [K]_o (2.5 mmole/l) are potassium concentrations inside and outside the axon membrane. F (96,485 c/mole) is Faraday constant. R (8314.4 mJ/K/mole) is gas constant. m, h, n and p are dimensionless variables, whose values always change between 0 and 1. m and h represent activation and inactivation of sodium channels, whereas n represents activation of potassium channels. p represents activation of non-specific ion channels. The evolution equations for m, h, n and p are the following:

$$ \begin{array}{*{20}{c}} {dm/dt = [{\alpha_m}(1 - m) - {\beta_m}m]{k_m}} \\ {dh/dt = [{\alpha_h}(1 - h) - {\beta_h}h]k} \\ {dn/dt = [{\alpha_n}(1 - n) - {\beta_n}n]k} \\ {dp/dt = [{\alpha_p}(1 - p) - {\beta_p}p]{k}} \\ \end{array} $$

and

$$ \begin{array}{*{20}{c}} {{\alpha_m} = \frac{{0.36({V_j} - 22)}}{{1 - \exp (\frac{{22 - {V_j}}}{3})}}} \\ {{\beta_m} = \frac{{0.4(13 - {V_j})}}{{1 - \exp (\frac{{{V_j} - 13}}{{20}})}}} \\ {{\alpha_h} = - \frac{{0.1({V_j} + 10)}}{{1 - \exp (\frac{{{V_j} + 10}}{6})}}} \\ {{\beta_h} = \frac{{4.5}}{{1 + \exp (\frac{{45 - {V_j}}}{{10}})}}} \\ {{\alpha_n} = \frac{{0.02({V_j} - 35)}}{{1 - \exp (\frac{{35 - {V_j}}}{{10}})}}} \\ {{\beta_n} = \frac{{0.05(10 - {V_j})}}{{1 - \exp (\frac{{{V_j} - 10}}{{10}})}}} \\ {{\alpha_p} = \frac{{0.006({V_j} - 40)}}{{1 - \exp (\frac{{40 - {V_j}}}{{10}})}}} \\ {{\beta_p} = - \frac{{0.09({V_j} + 25)}}{{1 - \exp (\frac{{{V_j} + 25}}{{20}})}}} \\ {{k_m} = {{1.8}^{{(T - 293)/10}}}} \\ {k = {3^{{(T - 293)/10}}}} \\ \end{array} $$

where T is the temperature in °Kelvin. The initial values for m, h, n and p (when V_j = 0 mV) are 0.0005, 0.0268, 0.8249 and 0.0049 respectively.