Controlling the Kelvin Force: Basic Strategies and Applications to Magnetic Drug Targeting
This work addresses the problem of precise magnetic drug targeting for medical applications, offering a control strategy to improve targeting accuracy.
The paper proposes a method to generate a nearly constant Kelvin force in a target subdomain for magnetic drug targeting, using dipole sources with control over intensity, location, and direction. The approach effectively steers drug concentration with limited spreading, as demonstrated by drift-diffusion PDE simulations.
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.