Investigations on a Branched Tube Model in Magnetic Drug Targeting—Systematic Measurements and Simulation

Due to its high targeting efficiency magnetic drug targeting has been proposed as a promising technique for tumor treatment. Since drug-loaded nanoparticles are concentrated within a target region due to the influence of a magnetic field unwanted side effects are considerably reduced. In a first step to contribute to the understanding of basic phenomena experiments on a half-Y-branched glass tube model as a model-system for a blood vessel supplying a tumor were performed. The results of those systematic quantitative measurements were summarized in novel drug-targeting maps. Based on the considered setup and artery-model the current focus is a theoretical approach with a finite-element simulation. The fluid flow is described by the Navier-Stokes equations, the mass flux is given by the advection-diffusion equation and the magnetic field is derived from Maxwell´s equations. The magnetic volume force acting on a volume of magnetic fluid combines the magnet and the ferrofluid data and is proportional to the field dependent magnetisation and the gradient of the field strength. The diffusion equation additionally allows the implementation of a concentration-dependent magnetic volume force. Our experimental investigations have shown that the miscibility of even the water-based ferrofluid and water is low. Since in medical applications the ferrofluid will be injected close to an appropriate junction one cannot necessarily assume a homogeneous mixture approaching the branch-region. Therefore, the characteristic focus of the presented simulation is a model where at the point of injection the ferrofluid and the carrier-fluid are initially separated and further mixture occurs due to the velocity field, diffusion, volume forces and magnetophoresis.