Modelling of magnetic bead transport in a microvascular network

In in vivo applications of magnetic particles one crucial aspect is the control of their transport in the tissue microvasculature and their release to target areas. These mechanisms can be driven and influenced by external magnetic fields with large gradients. Experimental results can be elucidated with the aid of in silico models that can also be employed to design optimized multifunctional particles and magnetic field sources. In this framework, we have developed a numerical model that enables us to calculate the trajectory of an ensemble of magnetic nano/microbeads injected in a blood vessel and manipulated by an applied magnetic field. The model combines Navier-Stokes equations for the fluid dynamics simulation of blood flow with classical Newtonian mechanics for bead motion, performing the analysis in a 3D vessel segment reconstructed from a computed tomography scan. The numerical model is applied to study the influence of bead properties (size and magnetic moment) on both transport and adhesion rate, taking into account the interplay of magnetic and viscous drag forces, as well as magnetic dipole–dipole and steric interactions. We also consider different configurations of the external magnetic field source, in order to optimize bead accumulation and adhesion to the vessel wall in a specific target region, processes that can be driven by magnetic forces.