# Controlling the Kelvin Force: Basic Strategies and Applications to Magnetic Drug Targeting

## TL;DR

This paper presents a control strategy to generate a nearly constant Kelvin magnetic force for targeted drug delivery, using optimization of magnetic sources to steer drug concentration effectively along prescribed paths.

## Contribution

It introduces a novel optimization-based approach to control magnetic fields for precise drug targeting, considering realistic dipole sources and PDE-governed drug dynamics.

## Key findings

- Effective steering of drug concentration demonstrated
- Magnetic field control achieves limited spreading
- Optimization approach adapts to prescribed trajectories

## Abstract

Motivated by problems arising in magnetic drug targeting, we propose to generate an almost constant Kelvin (magnetic) force in a target subdomain, moving along a prescribed trajectory. This is carried out by solving a minimization problem with a tracking type cost functional. The magnetic sources are assumed to be dipoles and the control variables are the magnetic field intensity, the source location and the magnetic field direction. The resulting magnetic field is shown to effectively steer the drug concentration, governed by a drift-diffusion PDE, from an initial to a desired location with limited spreading.