Dynamic Inversion Enables External Magnets To Concentrate Ferromagnetic Rods to 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.

Biodistribution, biocompatibility and targeted accumulation of magnetic nanoporous silica nanoparticles as drug carrier in orthopedics

“…The relatively small geometry of the implant could likely drastically lower the usually higher permeability. In the case that the electromagnetic field is the dominating magnetic force, it is conceivable that MNPSNPs align themselves in this field [112] instead of being attracted by a point source and leave the region of interest after field removal. Compensating, the distance between the used ferritic implant and a blood vessel in muscle tissue or skin is about a few micrometers or less, so very small [105].…”

In-situ particles reorientation during magnetic hyperthermia application: Shape matters twice

“…The details of the synthesis procedure can be found in the Experimental Details section. The magnetic characterization (see M(H) curves displayed in the Supporting Information, Figure S1) shows that the particles do not undergo the superparamagnetic transition at high temperature (possessing at 250 K, H C  = 180 Oe and M r  = 0.3 M S ), thus being adequate driving vectors for deep targeting with respect to their large magnetic moment31. We have evaluated the hyperthermia performance of the synthesized nanorods (Fig.…”

A Combined Magnetic‐Acoustic Device for Simultaneous, Coaligned Application of Magnetic and Ultrasonic Fields

“…Typically, the force from a solid magnetic volume decays almost exponentially with distance, but the recess in the front face of the magnet compromises the magnetic force at short range, and even produces a small on‐axis push force ( F pull < 0) within 2 mm of the magnet. It should be noted that the position along the axis where the pull force crosses to zero coincides with a saddle point in the field profile, and a local maximum in the magnetic potential energy ( U = − V M · B ), as no arrangement of static permanent magnets can produce a stable potential energy well at range (i.e., Earnshaw's principle). The normalized force (or force per moment) at the position of interest, z opt is 15.8 T m −1 , which compares well with the force expected from a magnet optimized for the same parameters without the excluded volume (about 18 T m −1 ).…”