Optimization method of a magnetic field generating a magnetic force field for magnetic nanoparticle control

Abstract

We present a novel method for estimating the magnetic field that can generate the desired magnetic force to move magnetic nanoparticles in a region of interest. The magnetic field is expanded using vector spherical harmonics, and the optimal multipole moments are estimated. The multipole moments are included in quadratic form because the magnetic force is defined as the product of the magnetic field and its gradient. We transform the system of quadratic equations into a rank-one-matrix estimation problem to construct a convex numerical algorithm based on a well-established proximal operation. The proposed method was validated using numerical simulations and can be used to design magnetic force patterns that cannot be generated using a simple coil pair.