Dynamic Inversion Enables External Magnets To Concentrate Ferromagnetic Rods to a Central Target

TLDR

External magnets have struggled to focus ferromagnetic therapeutics deep within the body because Earnshaw’s theorem precludes stable potential wells between static magnets. The study proposes that rapid magnetic pulses can act on ferromagnetic rods before they reorient, potentially overcoming this limitation. By effectively reversing the sign of the potential energy term in Earnshaw’s theorem, the pulses create a quasi‑static stable trap between the magnets. In vitro experiments confirm that shaped magnetic pulses generate inward forces that concentrate ferromagnetic rods at a central target.

Abstract

The ability to use magnets external to the body to focus therapy to deep tissue targets has remained an elusive goal in magnetic drug targeting. Researchers have hitherto been able to manipulate magnetic nanotherapeutics in vivo with nearby magnets but have remained unable to focus these therapies to targets deep within the body using magnets external to the body. One of the factors that has made focusing of therapy to central targets between magnets challenging is Samuel Earnshaw's theorem as applied to Maxwell's equations. These mathematical formulations imply that external static magnets cannot create a stable potential energy well between them. We posited that fast magnetic pulses could act on ferromagnetic rods before they could realign with the magnetic field. Mathematically, this is equivalent to reversing the sign of the potential energy term in Earnshaw's theorem, thus enabling a quasi-static stable trap between magnets. With in vitro experiments, we demonstrated that quick, shaped magnetic pulses can be successfully used to create inward pointing magnetic forces that, on average, enable external magnets to concentrate ferromagnetic rods to a central location.