Each nanoelectrode is modelled as a point current source in a homogeneous conductive tissue of conductivity σ. The electric field magnitude it produces at distance r is:
E(r) = I / (4πσr²)
Fields from every active electrode add by superposition at each nerve fibre's position. A fibre fires only if the local field exceeds its activation threshold — and that threshold itself depends on pulse width via Lapicque's strength-duration law:
E_th(PW) = E_rheobase · (1 + τ_chronaxie / PW)
Shorter pulses need a disproportionately stronger field to trigger a response (rheobase = the threshold at infinitely long pulses; chronaxie ≈ 200 µs here, typical of a myelinated peripheral fibre). Every fibre in the bundle has its own randomised rheobase, so recruitment grows gradually rather than as an all-or-nothing switch — exactly the tunable "how much of the nerve did we reach" behaviour a real neurorehabilitation nanoelectrode array is tuned for.
- Current amplitude — scales the field from every active electrode linearly.
- Pulse width — shorter pulses raise every fibre's threshold (right side of the strength-duration curve).
- Electrode spacing — widens or tightens the implanted grid, changing which fibres sit closest to an active contact.
- Pattern — single/cross/full-array selects how many contacts are simultaneously driven, directly changing the superposed field.
- Current for 50% recruitment — the amplitude at which the median fibre in the bundle would just reach threshold at the current pulse width, computed by inverting the linear field-vs-current relationship for every fibre and taking the median.