Research On The Theoretical Model And Capture Efficiency Of Magnetic Drug Targeting In The Permeable Microvessel Implanted A Permanent Magnetic Stent

Magnetic drug targeting (MDT) is one approach to treat cancer in which magnetic drug carrier particles (MDCPs) are delivered into the blood vessel through oral medication or injection and aggregated in the target site under the influence of magnetic devices. The key point of MDT lies in how to improve the aggregation of MDCPs in the target site so as to reduce the side effects of anti-cancer drugs on normal cells and tissues, and enhance the curative effect.Two theoretical models are established concerning MDT in the microvessel. In Model 1, the microvessel is deemed to be a rigid cylindrical straight tube and the microvascular blood is considered as a two-phase fluid composed of plasma and rigid red blood cells (RBCs). Based on two-phase mixed flow, permeation fluid mechanics and transport theory, the MDT transport under the influnce of permanent magnetic stent is explored. The following factors are considered in this model:the momentum exchange effect between the two-phase interface, the RBC distribution effect and the permeation effect of the microvessel wall as well as the elastic collision effect between the MDCP and the RBC. Furthermore, flow control equation of microvascular blood is established based on the Navier-Stokes equation of multi-phase fluid, taking account of the permeability of the microvessel wall and the influence of the tissue fluid. At the same time, the Boltzmann equation is used to describe the random motion of intravascular MDCPs. By means of non-dimensionalization, discretization and iterative solution of model equations, the flow velocity and pressure distribution of plasma, magnetic field distribution, MDCP distribution, capture efficiency (CE) under different parameters are obtained. The results show that the CE presents a nonlinear increase with the increase of magnetic induction intensity but a sharp decrease with the increase of plasma velocity, and an approximate linear increase with the increase of the particle radius; besides, the stronger permeability of the microvessel wall is of benefit to the aggregation of MDCPs.Model 2 takes account of the deformation of RBC which is regarded as a biological vesicle. The shape equation of RBC is deduced utilizing the curved surface elasticity theory. In the light of plasma flow between the RBC and permeable microvessel wall, the pressure control equation of plasma is established, adopting the lubrication theory. Combined with the pressure control equation of tissue fluid and the Boltzmann equation in Model 1, the targeting transport of MDCPs is studied under the condition of deformable RBCs. Through numerical solution of the model equations, the results are as follows:Smaller deformation of RBC and a lower CE are got in line with a larger radius of microvessel, while smaller deformation of RBC and a higher CE is gained in line with a larger permeability parameter. The increase of RBC’s velocity leads to the greater deformation and a lower CE. Besides, the greater the bending rigidity and the lower the surface tension of RBC membrane, the smaller the deformability, the higher the CE.