On the parameters used in finite element modeling of compound peripheral nerves

. Author manuscript; available in PMC: 2020 Jun 23.

Published in final edited form as: J Neural Eng. 2018 Dec 3;16(1):016007. doi: 10.1088/1741-2552/aaeb0c

$\vec{J} = σ \vec{E}$	Ohm’s law (constitutive relation)
$\vec{J} = - σ \nabla ϕ$	Substitute scalar potential for electric field
$\vec{n} \cdot \vec{J} = \vec{n} \cdot (- σ \nabla ϕ)$	Normal component
$\vec{n} \cdot \vec{J} = - σ (\frac{\partial ϕ}{\partial r})$	Assuming that the unit normal vector is pointed radially
$\vec{n} \cdot \vec{J} = - σ (\frac{Δ ϕ}{Δ r}) = - \frac{σ}{d} Δ ϕ$	Assuming d is small, such that the electric field is constant
$\vec{n} \cdot \vec{J_{2}} = - \frac{σ}{d} (V_{1} - V_{2}) = \frac{σ}{d} (V_{2} - V_{1})$	Unit normal vector points outward from medium 2
$\vec{n} \cdot \vec{J_{2}} = (\frac{1}{R_{S}}) (V_{2} - V_{1})$	Specify sheet resistance, Rs, in Ω-m² (“contact impedance” boundary condition in COMSOL)