Propagation electrodynamics differential conduction of action potentials in geometrically branched squid giant axons
Abstract
Classical cable theory neglects magnetic induction, Lorentz forces, and transient electromagnetic (EM) currents, limiting its accuracy for action potential propagation in branched neuronal geometries. We develop a coupled Maxwell-cable framework that integrates finite-difference time-domain (FDTD) solutions of Maxwell's equations with extended Hodgkin-Huxley and Fitzhugh-Nagumo dynamics, including magnetic gating, EM transmembrane currents IEM, and quantum corrections for thin segments. Controlled simulations in asymmetric and symmetric axonal bifurcations show that inductive effects lower the critical branch radius for conduction failure and break symmetry in identical daughter branches under transverse magnetic fields. We introduce an EM-corrected geometric ratio GREM that revises branch-point impedance matching and captures size-dependent axial current imbalances. Parent axon conduction velocity deviates significantly from the √d scaling law when EM feedback and quantum effects are included, leading to early blockage at large diameters. Overall, quasi-static models underestimate EM corrections to speed, waveform, and transmission fidelity; our framework offers a multi-physics tool for electrodynamic signaling in complex neuronal architectures.
Related
- Symmetries and Propagation of Surface Plasmon Polaritons in Axion Electrodynamics
- Fluxoid quantization in geometrically coupled superconducting loops
- A Geometrically Parameterized Quasi-Stationary 3D Model for High-Frequency Induction Tube Welding
- Geometrically Induced Semiclassical Limit for Quasinormal Modes and Greybody Factors in Higher-Dimensional Near-Ultracold spacetimes
- Universal entanglement detection with geometrically optimal witnesses
BibTeX
@misc{liu2026propagation,
title = {{Propagation electrodynamics differential conduction of action potentials in geometrically branched squid giant axons}},
author = {Xi Liu and Wenxi Fang and Ken Perlin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.26224},
eprint = {2609.26224},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.26224},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Propagation electrodynamics differential conduction of action potentials in geometrically branched squid giant axons
AU - Xi Liu
AU - Wenxi Fang
AU - Ken Perlin
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2609.26224
UR - https://arxiv.org/abs/2609.26224
AB - Classical cable theory neglects magnetic induction, Lorentz forces, and transient electromagnetic (EM) currents, limiting its accuracy for action potential propagation in branched neuronal geometries. We develop a coupled Maxwell-cable framework that integrates finite-difference time-domain (FDTD) solutions of Maxwell's equations with extended Hodgkin-Huxley and Fitzhugh-Nagumo dynamics, including magnetic gating, EM transmembrane currents I_EM, and quantum corrections for thin segments. Controlled simulations in asymmetric and symmetric axonal bifurcations show that inductive effects lower the critical branch radius for conduction failure and break symmetry in identical daughter branches under transverse magnetic fields. We introduce an EM-corrected geometric ratio GR_EM that revises branch-point impedance matching and captures size-dependent axial current imbalances. Parent axon conduction velocity deviates significantly from the √d scaling law when EM feedback and quantum effects are included, leading to early blockage at large diameters. Overall, quasi-static models underestimate EM corrections to speed, waveform, and transmission fidelity; our framework offers a multi-physics tool for electrodynamic signaling in complex neuronal architectures.
ER -