Propagation electrodynamics and differential conduction of action potentials in geometrically branched squid giant axons and neurons

<jats:p>Classical neuronal cable theory relies on quasi-static electric field approximations and neglects magnetic induction, Lorentz force coupling, and transient electromagnetic currents, limiting its ability to fully characterize action potential propagation within geometrically branched axons and dendrites. This work develops a coupled Maxwell-electromagnetic cable framework by integrating finite-difference time-domain (FDTD) solutions of Maxwell’s equations with extended Hodgkin-Huxley and Fitzhugh-Nagumo membrane dynamics, incorporating magnetic gating perturbations, electromagnetic trans-membrane currents 𝐼EM, and nanoscale quantum corrections for thin neural segments. Controlled propagation experiments are designed to quantify deviations from standard cable predictions across asymmetric and symmetric axonal bifurcation geometries. Numerical results demonstrate that inductive magnetic effects lower the critical branch radius for junction conduction failure and break symmetric action potential invasion in geometrically identical child branches under external transverse magnetic fields. An electromagnetic corrected geometric ratio 𝐺𝑅EM is proposed to revise impedance-matching conditions at branch points, accounting for size-dependent axial current imbalance induced by magnetic and displacement currents. Parent axon conduction velocity deviates substantially from the canonical √𝑑 scaling law when electromagnetic feedback and quantum charge distributions are included, triggering early signal blockage at large cable diameters. Collectively, this study establishes that quasi-static cable models underestimate electromagnetic corrections to propagation speed, waveform shape, and bifurcation transmission fidelity; the coupled Maxwell-cable framework provides a comprehensive multi-physics tool for modeling electrodynamic signal behavior in complex neuronal architectures.</jats:p>