Optimal Halbach permanent magnet designs for maximally pulling and pushing nanoparticles

Abstract

Optimization methods are presented to design Halbach arrays to maximize the forces applied on magnetic nanoparticles at deep tissue locations. In magnetic drug targeting, where magnets are used to focus therapeutic nanoparticles to disease locations, the sharp fall off of magnetic fields and forces with distances from magnets has limited the depth of targeting. Creating stronger forces at depth by optimally designed Halbach arrays would allow treatment of a wider class of patients, e.g. patients with deeper tumors. The presented optimization methods are based on semi-definite quadratic programming, yield provably globally optimal Halbach designs in 2 and 3-dimensions, for maximal pull or push magnetic forces (stronger pull forces can collect nano-particles against blood forces in deeper vessels; push forces can be used to inject particles into precise locations, e.g. into the inner ear). These Halbach designs, here tested in simulations of Maxwell’s equations, significantly outperform benchmark magnets of the same size and strength. For example, a 3-dimensional 36 element 2000 cm3 volume optimal Halbach design yields a ×5 greater force at a 10 cm depth compared to a uniformly magnetized magnet of the same size and strength. The designed arrays should be feasible to construct, as they have a similar strength (≤ 1 Tesla), size (≤ 2000 cm3), and number of elements (≤ 36) as previously demonstrated arrays, and retain good performance for reasonable manufacturing errors (element magnetization direction errors ≤ 5°), thus yielding practical designs to improve magnetic drug targeting treatment depths.

Remote magnetic targeting of iron oxide nanoparticles for cardiovascular diagnosis and therapeutic drug delivery: where are we now?

“…To overcome this problem, various technical setups have been proposed that (among others) include custom-made electromagnets, the use of an arrangement of permanent magnets, the implantation of a magnetizable material, or the design of special gradient coils for conventional MRI scanners. [32][33][34][35][36] In general, the attractive force exerted on a particle by a magnetic targeting system should equal the hydrodynamic …”

“…Using numerical optimization, Sarwar et al simulated a 36-element array that creates five times greater magnetic forces at 10 cm depth than a benchmark magnet of the same volume and material. 33 If this arrangement could be designed with a light weight and as a mobile solution to enable longer magnet exposure times, for example, at bedside, long circulating ION formulations could be attracted more efficiently to the desired tissue/organ. A more sophisticated method that relies on a dynamic feedback control scheme of eight electromagnets positioned around the patient was proposed in 2012 by Nacev et al 74 During the course of simulation, however, perfect real-time imaging was assumed to assess the current position of a SPION assembly, which in turn was fed back into the control algorithm that orchestrates the magnets.…”

Simulation studies of a novel electromagnetic actuation scheme for focusing magnetic micro/nano-carriers into a deep target region

“…[6][7][8] Hence, the majority of previous systems have been designed to attract therapeutic particles to target regions. [9][10][11][12][13][14][15] Because two or more magnets can be utilized to push particles, 16 the method can be applied to therapies directed toward the back of the eye 6,7 and the inner ear.…”

Fabrication of Multipole Magnets with Enhanced Flux Density Using Anisotropic Bond Magnets for Miniature Optical Pickup Devices

“…2,3) In recent years, HAMs have been widely used for highly efficient electromagnetic devices, in addition to mechanical devices such as electric motors, tape recorders and undulators at synchrotron radiation facilities. [4][5][6][7][8][9] However, HAMs are still subject to serious problems in mass production, because HAMs require bonding processes using adhesives and/or fixtures. Such processes increase both the difficulty in precise assembly and the mass production costs, which make it impossible to produce a number of miniature or large sized HAMs.…”