Mathematical Model on 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 micro vascular 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 noninvasive magnetic targeting of therapeutic carrier particles in a micro vessel. The flow of blood in the micro vessel is described by a two phase Herschel-Bulkley fluid model. The Brinkmann model is used to characterize the permeable nature of the inner wall of the micro-vessel. The fluidic force on the carrier traversing the micro-vessel and the magnetic force due to the external magnetic field is taken into account. The model enables rapid parametric analysis of magnetic targeting as a function of key variables including the size of the carrier particle, the properties and volume fraction of the imbedded magnetic nanoparticles, the properties of the magnet, the micro vessel and the permeability of the micro vessel.