Symbol

Meaning

$\rho ,{\rho }^{\prime }$

radial distance of the (field point, source point) from the axis of the cylinder

$\varphi$

azimuthal angle

$z,z^{\prime }$

distance of the (field point, source point) along the axis of the cylinder

I₀

magnitude of the current strength at the surface of the node of Ranvier

p

radial distance from the cylindrical axis where the current magnitude vanishes

$r_1,l_1$

(starting, termination) point in time of the PWM-PPM waveform [8] of the ion channel current profile

$U(\cdot )$

Heaviside step function

$\delta (\cdot )$

Dirac delta function

${\varphi }_{LFP}\left(\overrightarrow{r},t\right)$

electric potential at spatial (field) position $\overrightarrow{r}$ and time t

$I_v\left(\overrightarrow{r},t\right),I\left(\overrightarrow{r^{\prime }}\right)$

volume source current density produced by an ion channel ring (with, without) time variation

$\overrightarrow{r^{\prime }}$

position of the source element

$\epsilon$

permittivity of free space

$\varphi ,{\varphi }^{\prime }$

azimuthal coordinates of the (field point, source point)

$\nabla$

gradient operator

$\overrightarrow{E_{\text{channel}}}$

the net electric field due to the ion channel

$\widehat{k},{\widehat{e}}_{\rho }$

two of the three unit vectors in the three-dimensional coordinate system

${{\rho }^{\prime }}_1,{{\rho }^{\prime }}_2$

two radial distances used to generate the form of the current near the node

$\Delta {\varphi }^{\prime }$

azimuthal thickness of the first ion channel in the ring of ion channels at the node of Ranvier

$c_{m\mathrm{,}k},g_{m\mathrm{,}k}$

the membrance (capacitance, conductance) of the k-th axon

$V_k\left(x\mathrm{,}t\right)$

the transmembrane potential difference of the k-th axon at spatial position x and time t

${\alpha }_N$

a parameter introduced by Reutskiy, Rossoni and Tirozzi

N

total number of axons in the tract

r

“ratio” used in the simulations which indicates the strength of the current-mediated coupling between axons

$r_f$

the resistance per unit length of the axoplasm of each axonal fiber

$G_k^{\text{axoplasm}}\mathrm{,}{G}_{m\mathrm{,}k}$

the conductance of the (axoplasm, myelin sheath) of the k-th axon

${\theta }_k,{\theta }_k\left(z\right)$

the inclination of the k-th axon (without, with) z-dependence

$K_p,K_p\left(z\right)$

a combination of parameters introduced by Chawla, Morgera and Snider (without, with) z-dependence

$I_k^{\text{injected}}$

the total injected current at the node, including contributions from ionic current, as well as external stimulation

$l\left(t\right)$

number of ion channels open at the present node at time t

$\gamma ,{\gamma }^{\prime }$

two positive real numbers less than one which determine the fraction of the field that contributes towards a nodal current

L

the total number of ion channels distributed uniformly over the nodal surface