Conference Dates

June 22-27, 2014


We present a mathematical model for targeting a drug at malignant tissue cells in a permeable microvessel. The drug molecules are transported in carrier particles which are assumed to be porous spheres. This mode of drug delivery is non-invasive and has less toxic effects on healthy cells and tissues. The microvessel tube (see Figure 1) is subdivided into three regions, the outer endothelial glycocalyx layer where the blood has a Newtonian character, and a core and plug regions where the blood flow is described using a non-Newtonian Casson fluid model which is suitable for microvessels of radius 5mμ. Targeting is achieved through a locally applied magnetic field using a cylindrical magnet positioned outside the body near the tumour position so that the carrier particles, bound with nanoparticles and drug molecules are captured at the tumour site. The study seeks to understand, inter alia, the effects of the size and permeability of the carrier particle, the volume fraction of embedded magnetic nanoparticles and the placement of the external magnetic field on the magnetic targeting of the carrier particles.