Computational Simulations of Magnetic Particle Capture in Arterial Flows

The aim of Magnetic Drug Targeting (MDT) is to concentrate drugs, attached to magnetic particles, in a specific part of the human body by applying a magnetic field. Computational simulations are performed of blood flow and magnetic particle motion in a left coronary artery and a carotid artery, using the properties of presently available magnetic carriers and strong superconducting magnets (up to B ≈ 2 T). For simple tube geometries it is deduced theoretically that the particle capture efficiency scales as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\eta \sim \sqrt{{Mn}_{\rm p}}$$\end{document}, with Mnp the characteristic ratio of the particle magnetization force and the drag force. This relation is found to hold quite well for the carotid artery. For the coronary artery, the presence of side branches and domain curvature causes deviations from this scaling rule, viz. η ∼ Mnpβ, with β > 1/2. The simulations demonstrate that approximately a quarter of the inserted 4 μm particles can be captured from the bloodstream of the left coronary artery, when the magnet is placed at a distance of 4.25 cm. When the same magnet is placed at a distance of 1 cm from a carotid artery, almost all of the inserted 4 μm particles are captured. The performed simulations, therefore, reveal significant potential for the application of MDT to the treatment of atherosclerosis

Explicit and Implicit Finite -Volume Methods for Depth Averaged Free-Surface Flows

In recent years, much progress has been made in solving free-surface flow variation problems in order to prevent flood environmental problems in natural rivers. Computational results and convergence acceleration of two different (explicit and implicit numerical techniques) finite-volume based numerical algorithms, for depth-averaged subcritical and/or supercritical, free-surface, steady flows in channels, are presented. The implicit computational model is a bi-diagonal, finite-volume numerical scheme, based on MacCormack's predictor-corrector technique and uses the semi-linearization matrices for the governing Navier- Stokes equations which are expressed in terms of diagonalization. This implicit numerical scheme puts primary emphasis to solution convergence using non-orthogonal local coordinate system. The explicit formulation uses volume integrals to solve the governing flow equations. Computational results and convergence performance between the implicit and the explicit finite-volume numerical schemes, for incompressible, viscous, depth-averaged free-surface, steady flows are presented. Implicit and explicit computational results are satisfactorily compared with available measurements. The implicit bi-diagonal technique yields fast convergence compared to the explicit one at the expense of programming effort. Iterations require to achieve convergence solution error of less than 10-5can be reduced down to 90.0 % in comparison to analogous flows with using explicit numerical technique. © 2020. The American Society of Hematology. All Rights Reserved