Statistical Mechanics Transport Model of Magnetic Drug Targeting in Permeable Microvessel

Abstract

A transport model of magnetic drug carrier particles (MDCPs) in permeable microvessel based on statistical mechanics has been developed to investigate capture efficiency (CE) of MDCPs at the tumor position. Casson-Newton two-fluid model is used to describe the flow of blood in permeable microvessel and the Darcy model is used to characterize the permeable nature of the microvessel. Coupling effect between the interstitial fluid flow and blood flow is considered by using the Starling assumptions in the model. The Boltzmann equation is used to depict the transport of MDCPs in microvessel. The elastic collision effect between MDCPs and red blood cell is incorporated. The distribution of blood flow velocity, blood pressure, interstitial fluid pressure, and MDCPs has been obtained through the coupling solutions of the model. Based on these, the CE of the MDCPs is obtained. Present results show that the CE of the MDCPs will increase with the enhancement of the size of the MDCPs and the external magnetic field intensity. In addition, when the permeability of the inner wall is better and the inlet blood flow velocity is slow, the CE of the MDCPs will increase as well. Close agreements between the predictions and experimental results demonstrate the capability of the model in modeling transport of MDCPs in permeable microvessel.