Dynamic inversion enables external magnets to concentrate ferromagnetic rods to a central target.

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.

Shaping magnetic fields to direct therapy to ears and eyes.

Magnetic fields have the potential to noninvasively direct and focus therapy to disease targets. External magnets can apply forces on drug-coated magnetic nanoparticles, or on living cells that contain particles, and can be used to manipulate them in vivo. Significant progress has been made in developing and testing safe and therapeutic magnetic constructs that can be manipulated by magnetic fields. However, we do not yet have the magnet systems that can then direct those constructs to the right places, in vivo, over human patient distances. We do not yet know where to put the external magnets, how to shape them, or when to turn them on and off to direct particles or magnetized cells-in blood, through tissue, and across barriers-to disease locations. In this article, we consider ear and eye disease targets. Ear and eye targets are too deep and complex to be targeted by a single external magnet, but they are shallow enough that a combination of magnets may be able to direct therapy to them. We focus on how magnetic fields should be shaped (in space and time) to direct magnetic constructs to ear and eye targets.

The Behaviors of Ferro-Magnetic Nano-Particles In and Around Blood Vessels under Applied Magnetic Fields.

In magnetic drug delivery, therapeutic magnetizable particles are typically injected into the blood stream and magnets are then used to concentrate them to disease locations. The behavior of such particles in-vivo is complex and is governed by blood convection, diffusion (in blood and in tissue), extravasation, and the applied magnetic fields. Using physical first-principles and a sophisticated vessel-membrane-tissue (VMT) numerical solver, we comprehensively analyze in detail the behavior of magnetic particles in blood vessels and surrounding tissue. For any blood vessel (of any size, depth, and blood velocity) and tissue properties, particle size and applied magnetic fields, we consider a Krogh tissue cylinder geometry and solve for the resulting spatial distribution of particles. We find that there are three prototypical behaviors (blood velocity dominated, magnetic force dominated, and boundary-layer formation) and that the type of behavior observed is uniquely determined by three non-dimensional numbers (the magnetic-Richardson number, mass Péclet number, and Renkin reduced diffusion coefficient). Plots and equations are provided to easily read out which behavior is found under which circumstances (Figures 5, 6, 7, and 8). We compare our results to previously published in-vitro and in-vivo magnetic drug delivery experiments. Not only do we find excellent agreement between our predictions and prior experimental observations, but we are also able to qualitatively and quantitatively explain behavior that was previously not understood.

Planar Steering of a Single Ferrofluid Drop by Optimal Minimum Power Dynamic Feedback Control of Four Electromagnets at a Distance.

Any single permanent or electro magnet will always attract a magnetic fluid. For this reason it is difficult to precisely position and manipulate ferrofluid at a distance from magnets. We develop and experimentally demonstrate optimal (minimum electrical power) 2-dimensional manipulation of a single droplet of ferrofluid by feedback control of 4 external electromagnets. The control algorithm we have developed takes into account, and is explicitly designed for, the nonlinear (fast decay in space, quadratic in magnet strength) nature of how the magnets actuate the ferrofluid, and it also corrects for electro-magnet charging time delays. With this control, we show that dynamic actuation of electro-magnets held outside a domain can be used to position a droplet of ferrofluid to any desired location and steer it along any desired path within that domain - an example of precision control of a ferrofluid by magnets acting at a distance.

Toxicology study for magnetic injection of prednisolone into the rat cochlea.

This paper investigates the safety of a novel 'magnetic injection' method of delivering therapy to the cochlea, in a rodent model. In this method of administration, a magnetic field is employed to actively transport drug-eluting superparamagnetic iron-oxide core nanoparticles into the cochlea, where they then release their drug payload (we delivered the steroid prednisolone). Our study design and selection of control groups was based on published regulatory guidance for safety studies that involve local drug delivery. We tested for both single and multiple delivery doses to the cochlea, and found that magnetic delivery did not harm hearing. There was no statistical difference in hearing between magnetically treated ears versus ears that received intra-tympanic steroid (a mimic of a standard-of-care for sudden sensorineural hearing loss), both 2 and 30 days after treatment. Since our treatment is local to the ear, the levels of steroid and iron circulating systemically after our treatment were low, below mass-spectrometry detection limits for the steroid and no different from normal for iron. No adverse findings were observed in ear tissue histopathology or in animal gross behavior. At 2 and 30 days after treatment, inflammatory changes examined in the ear were limited to the middle ear, were very mild in severity, and by day 90 there was ongoing and almost complete reversibility of these changes. There were no ear tissue scarring or hemorrhage trends associated with magnetic delivery. In summary, after conducting a pre-clinical safety study, no adverse safety issues were observed.

Magnetic microkayaks: propulsion of microrods precessing near a surface by kilohertz frequency, rotating magnetic fields.

Surface-swimming nano- and micromotors hold significant potential for on-chip mixing, flow generation, sample manipulation, and microrobotics. Here we describe rotating microrods magnetized nearly orthogonally to their long axes. When actuated near a solid surface, these microrods demonstrate precessing motion, with rods describing a double cone similar to the motion of a kayaker's paddle. The precessing motion induces translation. At 1 kHz, these "microkayaks" move at translational velocities of ≈14 µm s-1 and generate advective flows up to 10 µm s-1.

Magnetic nanoparticle transport within flowing blood and into surrounding tissue.

Magnetic drug delivery refers to the physical confinement of therapeutic magnetic nanoparticles to regions of disease, tumors, infections and blood clots. Predicting the effectiveness of magnetic focusing in vivo is critical for the design and use of magnetic drug delivery systems. However, current simple back-of-the-envelope estimates have proven insufficient for this task. In this article, we present an analysis of nanoparticle distribution, in and around a single blood vessel (a Krogh tissue cylinder), located at any depth in the body, with any physiologically relevant blood flow velocity, diffusion and extravasation properties, and with any applied magnetic force on the particles. For any such blood vessel our analysis predicts one of three distinct types of particle behavior (velocity dominated, magnetic dominated or boundary-layer formation), which can be uniquely determined by looking up the values of three nondimensional numbers we define. We compare our predictions to previously published magnetic-focusing in vitro and in vivo studies. Not only do we find agreement between our predictions and prior observations, but we are also able to quantitatively explain behavior that was not understood previously.