Magnetic drug targeting in a permeable microvessel

A mathematical model is presented for predicting magnetic targeting of multifunctional carrier particles that deliver therapeutic agents to malignant tissue in vivo. These particles consist of a nonmagnetic core material that contains embedded magnetic nanoparticles and therapeutic agents such as photodynamic sensitizers. For in vivo therapy, the particles are injected into the microvascular system upstream from malignant tissue, and captured at the tumor using an applied magnetic field. In this paper, a mathematical model is developed for predicting non-invasive magnetic targeting of therapeutic carrier particles in a microvessel. The flow of blood in the microvessel is described by a two-phase Casson fluid model. The Darcy model is used to characterize the permeable nature of the inner wall of the microvessel. The fluidic force on the carrier traversing the microvessel and the magnetic force due to the external magnetic field is taken into account. We solved the system of coupled equations to obtain the capture condition for the carrier particle in the non-invasive case. The model enables rapid parametric analysis of magnetic targeting as a function of key variables including the size and shape of the carrier particle, the properties and volume fraction of the imbedded magnetic nanoparticles, the properties of the magnet, the microvessel and the permeability of the microvessel.