Coupled Maxwell-Cable Framework for Action Potential Propagation in Branched Squid Giant Axons

This paper addresses limitations in classical cable theory for modeling action potential propagation in geometrically branched squid giant axons. The authors 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, incorporating magnetic gating and electromagnetic transmembrane currents. The approach captures magnetic induction and Lorentz forces that are neglected in traditional cable theory.