Magnetic Drug Targeting in the Permeable Blood Vessel—The Effect of Blood Rheology

The present investigation deals with finding the trajectories of the drug dosed magnetic carrier particle in a microvessel, which is subjected to the external magnetic field. We consider the physical model that was given in the work of Furlani and Furlani (2007, “A Model for Predicting Magnetic Targeting of Multifunctional Particles in the Microvasculature,” J. Magn. Magn. Mater., 312, pp. 187–193), but deviating by taking the non-Newtonian fluid model for the blood in the permeable microvessel. Both the Herschel–Bulkley fluid and Casson models are considered to analyze the present problem. The expression for the fluid velocity in the permeable microvessel is obtained using the analogy given by Decuzzi et al. (2006, “The Effective Dispersion of Nanovectors Within the Tumor Microvasculature,” Ann. Biomed. Eng., 34, pp. 633–641) first. Then the expression for the fluidic force for the carrier particle traversing in the non-Newtonian fluid is obtained. Several factors that influence the magnetic targeting of the carrier particles in the microvasculature, such as the permeability of the inner wall, size of the carrier particle, the volume fraction of embedded nanoparticles, and the diameter of the microvessel are considered in the present problem. The trajectories of the carrier particles are found in both invasive and noninvasive targeting systems. A comparison is made between the trajectories in these cases in both the Casson and Herschel–Bulkley fluid models. The present results for the permeable microvessel are compared with the impermeable inner wall trajectories given by Shaw et al. (2010, “Effect of Non-Newtonian Characteristics of Blood on Magnetic Targeting in the Impermeable Micro Vessel,” J. Magn. Magn. Mater., 322, pp. 1037–1043). Also, a prediction of the capture of therapeutic magnetic nanoparticle in the human permeable microvasculature is made for different radii and volume fractions in both the invasive and noninvasive cases.