A Two-Magnet System to Push Therapeutic Nanoparticles

Abstract

Magnetic fields can be used to direct magnetically susceptible nanoparticles to disease locations: to infections, blood clots, or tumors. Any single magnet always attracts (pulls) ferro- or para-magnetic particles towards it. External magnets have been used to pull therapeutics into tumors near the skin in animals and human clinical trials. Implanting magnetic materials into patients (a feasible approach in some cases) has been envisioned as a means of reaching deeper targets. Yet there are a number of clinical needs, ranging from treatments of the inner ear, to antibiotic-resistant skin infections and cardiac arrhythmias, which would benefit from an ability to magnetically "inject", or push in, nanomedicines. We develop, analyze, and experimentally demonstrate a novel, simple, and effective arrangement of just two permanent magnets that can magnetically push particles. Such a system might treat diseases of the inner ear; diseases which intravenously injected or orally administered treatments cannot reach due to the blood-brain barrier.

Figure 1

The inner ear is behind the blood brain barrier: micro-circulation vessels that supply blood to the cochlea have tight capillary junctions that prevent therapies from reaching many inner ear diseases. An ability to push magnetizable therapeutic nanoparticles particles through the round window membrane would allow us to bypass the blood-brain barrier and transport therapy directly into the inner ear. The envisioned treatment is shown above, from left to right: the magnetic push system; human ear anatomy; a gel filled with magnetic nanoparticles that has been injected into the middle ear (light blue with black dots, in the tympanic cavity); the round window membrane (black oval); and a magnetic push force (yellow arrow) to deliver therapeutic particles through the RWM into the inner ear (cochlea).

Figure 2

The key concept: two permanent magnets can push particles away. A) Schematic field lines around a single magnet magnetized along its width. B) Two magnets. We tilt the top magnet down till the magnetic field $\stackrel{\rightharpoonup }{H}$ is along the y axis at the desired node location (green dot). We flip and tilt the other magnet up. C) When these two magnets are correctly overlaid their magnetic fields add to exactly cancel at the node point C (big dot) but they do not cancel around that point (orange annulus) thus forces go outwards from $\stackrel{\rightharpoonup }{H}=0$ at the node to $\overrightarrow{H}\ne 0$ surrounding it (the pink force arrow). An alternate arrangement: D) A single magnet magnetized along its length. E) Here the bottom magnet is both tilted up and its polarity is reversed. This flips the sign of the magnetic field at point B and cancels the horizontal magnetic field at point A for the top magnet (panel F). In both cases, the magnets’ orientations and their separation can be varied to position the outward-force region as needed. (Note that the magnetic fields, not magnetic field lines, add together. The gray curves in panel C and F are only meant as a guide for the eye. See also Figure 3.)

Figure 3

The magnetic field and forces around two magnets magnetized across their width and rotated inward at 30 degrees, matching the experimental configuration shown in Figure 8. A) Magnetic field lines are illustrated by the gray curves, the direction of the magnetic field is shown by the green arrows. B) The strength of the magnetic field is shown by a logarithmic color scale from 10⁻¹ Tesla (white) to 10⁻⁴ Tesla (black, at the node); 20 contour of constant magnetic field strength are also marked. Black arrows show the resulting force directions that will be created on magnetic particles at each location. The maximum push force occurs just beyond the (x,y) = (0.033, 0) cancellation node. This node would have to be placed on the left of the gel shown in Figure 1 to push particles to the right through the round window membrane. Length units are marked in meters.

Figure 4

The magnetic field strength in a vertical and horizontal slice around our magnet push system. Regions of high magnetic field are shown in white and yellow, regions of smallest magnetic field strength are in black, and the right magnet is shown by a green wire frame (the left magnet is hidden behind the vertical slice). The push node is visible as a small black egg shape that is tight in the horizontal direction and has a larger extent vertically. Forces on the particles go outwards, from black to red. A second node is visible inside the magnet system (the yellow dot with the red center inside the high-field white region). Length units are marked in meters.

Figure 5

The magnetic field directions around a single permanent magnet magnetized through its width. A) Magnetic field lines (gray) and the direction of the magnetic field (green arrows). B) Each colored contour shows the location of all points that have a magnetic field at that angle. The +120° curve is bolded in pink: the node point for our 30° push system lies along this curve. (The multicolored curve marked ‘jump’ shows where the angle convention changes from +180° back down to −180°. Green magnetic field arrows are repeated for clarity.)

Figure 6

The predicted magnetic field strength in front of the two-magnet push system for A) the nominal magnet configuration, B) when the right magnet is rotated 10° degrees out of the horizontal plane, and C) when it is misaligned by 25° degrees. The color and contours corresponds to the log of the magnetic field strength $\log \mid \stackrel{\rightharpoonup }{H}\mid$; closed contours around a black region show the push node in the first two panels. The large 25° degrees misalignment of the third panel eliminates the node.

Figure 7

The first magnetic push device prototype: two magnets attached to wooden strips by glue and black tape. A) Side view of a magnet attached to a single shim. B) Top view of the two angled magnets. C) The system in use against the side of a Petri dish.

Figure 8

The second magnetic push prototype. A) Top and side view schematic. B) View from the back showing the angle adjustment mechanism. C) View from the front. D) Zoomed top view of the front and working region. The configuration and size of the magnets is shown, along with the location of the null point that they create in the Petri dish.

Figure 9

Experimental validation of the magnetic push system. A) Photograph of the first simple experiment: two magnets held on a wood wedge. B) The series shows a nanopure water solution with initially uniformly dispersed magnetite nanoparticles at the initial time (i) and at times 5 seconds (ii), 10 seconds (iii), and several minutes (iv) after introduction of the magnetic push system on the left. Circles at top of images i) – iv) indicate particles collecting at the dish edge due to the magnets pulling them in behind the node, white lines delineate the plume of nano-particles, and arrows show its pushing motion away from the magnets in front of the node. Series C i)-iii) shows a micro liter drop of ferrofluid being moved away from the magnet system. The Petri dish is resting flat on a table, the view is from the above, and the ends of the magnetic push system can be seen at the left edge of the three images. As the droplet moved to the right, the relative position between the magnets and the drop was kept “constant” to keep the ferrofluid in the maximum push region of the system, i.e. the angle of the system and its distance to the edge of the Petri dish was adjusted to keep the drop moving forward on a relatively straight path. This series took place over a ~90 s interval and the drop was pushed ~ 4 mm from its starting point. The ruler red grid lines are spaced 3.2 mm apart.