Mathematical Modelling of Drug Targeting Using Computational Methods

Abstract

Magnetic nanoparticles play a crucial role as drug carriers in the human body. In this investigation the particle movement is analysed knowing the local flow condition and using appropriate magnets. The particles are injected into the vascular system upstream from malignant tissue and captured at the tumor using an applied magnetic field. The applied field was obtained by using a quadrupole magnet that couples to the magnetic nanoparticles inside the carrier particle and produces a force that attracts the particle to the tumor. The flux density components of the quadrupole magnet is calculated using Scilab. This study also provides a mathematical model (I) needed for the development of drug targeting to the lungs in comparison with experimental results. The trajectories of magnetite particles of different sizes in the field of permanent quadrupole in the air and water were traced in different times with the help of numerical solver. It was found that the tendency of the particle to be captured by the magnet increases when air is chosen as the medium. In the Investigation of model (II) the behavior of blood was considered as Hershel-bulkley fluid which is suitable for the micro vessel of radius 50 nm. Analytical expression was derived for predicting the volume fraction of embedded magnetic nanoparticles required to capture the carrier particle at the tumor. A parametric analysis of magnetic targeting as a function of key variables including the size of the carrier particle and volume fraction is made. The assumptions to the model was made by comparing with the theoretical model done earlier [9] and implemented using mathematical software scilab 5.4.