Simulation of magnetic targeted drug delivery

Targeted Magnetic Drug Delivery (TMDD) is a promising approach that is relevant to multimodal cancer therapy. Therefore, it is important to develop mathematical models of TMDD to serve as a second opinion for medical practitioners. A majority of TMDD models represent a mixture of blood and nanoparticles as a one-phase solution. Therefore, the magnetic nanoparticles (MN) and the blood follow the same streamlines. The existing two-phase models are usually one-way coupled, i.e., the blood flow has a strong impact on the MN flow. However, the inverse impact of the MN on the dynamics of the blood is not included in the models. To eliminate these drawbacks, the MN in a blood vessel is simulated by a two-phase (solid-liquid) flow in a 2D rectangular channel. The problem is governed by two-way coupled momentum and temperature equations for the blood flow and the MN. The numerical procedure invokes the stream function–vorticity formulation and an efficient numerical method on a finite-difference grid. The general formulation for the effect of the magnetic field is that of Biomagnetic fluid Dynamics (BFD) which incorporates both principles of MagnetoHydroDynamics (MHD) and FerroHydroDynamics (FHD). The model, validated by experimental results, has been applied to analyze the formation of and the zones of TMDD, where the velocity of the blood flow is low and the velocity of the MN flow is high towards the magnet. Additionally, we analyze the formation of vortices relative to the magnetic force (MFs), the drag force (DF). The model is capable of simulating the (reverse) impact of the MN on the blood flow and evaluates the corresponding changes in the vorticity. The result shows that the MHD effect causes disturbance in blood flow. It reduces blood flow and minimizes the large vortices created by FHD. Moreover, the concentration of medical drugs is another essential result. These medications have the potential to harm healthy cells. Therefore, the effects of medical drugs have been evaluated against MN size. It analyzes the impact of the size and concentration of the MN on the temperature of the blood. The preceding models cannot simulate these important scenarios.