Background: In magnetic drug targeting (MDT), micro- or nanoparticles are injected into the human body to locally deliver therapeutics. These magnetic particles can be guided from a distance by external magnetic fields and gradients from electromagnets.
Purpose: During the particles' movement through the vascular network, they are affected by magnetic forces, fluid (drag) forces, particle interactions, diffusion, etc. Adequate targeting is hindered when drag forces overcome the magnetic forces and particles present in vessels are carried away from the targeted region. Moreover, the magnetic force directions and diffusion mechanisms can cause particles to scatter, while they should remain together for an effective targeting performance. In this work, these adverse effects are tackled using optimization methods.
Methods: We formulate an optimization problem with respect to the currents in surrounding electromagnets that aims to maximize the magnetic force on a particle along a predefined direction. A boundary on the magnetic force divergence is introduced as a constraint to limit particle spreading. We also consider particles to be moved from an initial to a target location in a finite-time interval. To this end dynamic optimization is applied.
Results: Simulations for particles in a bifurcated vessel show an increase of particle speed by 20% and a successful movement towards the targeted regions without spreading. For the dynamic optimization, simulation results demonstrate that particle collections are accurately guided with 10 times less scattering and 10 times more particles at the target than without the divergence constraint.
Conclusions: The proposed methods significantly improve the steering and capturing of particles in a region of interest. They are applicable to any magnetic drug targeting configuration with electromagnets.
Keywords: dynamic optimization; magnetic drug targeting; magnetic nanoparticles; modelling & optimization.
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