E. Kurgan, and P. Gas, “Magnetophoretic Placement of Ferromagnetic Nanoparticles in RF Hyperthermia”, 2017 Progress in Applied Electrical Engineering (PAEE), IEEE Xplore, 2017, art. no. 8009003, [pp. 1-4]. Available at: http://dx.doi.org/10.1109/PAEE.2017.8009003 978-1-5386-1528-7/17/$31.00 ©2017 IEEE Magnetophoretic Placement of Ferromagnetic Nanoparticles in RF Hyperthermia Eugeniusz Kurgan, Piotr Gas AGH University of Science and Technology Department of Electrical and Power Engineering al. Mickiewicza 30, 30-059 Krakow, Poland e-mails: kurgan@agh.edu.pl, piotr.gas@agh.edu.pl Abstract — This article presents a method of permanently placing ferromagnetic particles in the tumor region for the duration of the treatment. It is based on the phenomenon of magnetophoresis, that is, the influence of a magnetic field with a strongly variable gradient on magnetically induced magnetic moment of particle. The presented approach has a great impor- tance in particle separation industry as well as in nanoparticle tumor targeting. Keywords — hyperthermia; magnetophoresis; FEM; magnetic particles placement; tumor targeting; drug delivery I. INTRODUCTION On magnetic particles in a nonuniform magnetic field acts a force, which results from the mutual reaction between the induced magnetic moment in a particle and applied external magnetic field. This phenomenon is named magnetophoresis [1], and is used in a various commercial as well as industrial processes for, among others, separation of solid magnetic particles suspended in fluids. Magnetophoresis can also be used to distinguish and separate biological cells for bio- chemical analysis based on internal and external magnetic properties of biomolecules [2]. Suspension of ferromagnetic nanoparticles that are stably spread in a carrier fluid, also called ferrofluid, has been recently used for the magnetic induction hyperthermia treatment of cancers [3]. It consists in placing in the tumor or nearby, the ferromagnetic or super- paramagnetic particles and interacting with them thought high frequency electromagnetic field. In this process magnetic particles produce heat which causes the tissue temperature rising to 42 ÷ 44°C, which causes tumor destruction [4], [5]. There are two methods for embedding magnetic nano- particles in the vicinity of tumors. The first consists of direct insertion of the aqueous suspension together with these mole- cules directly into the tumor and the other relays on injection particles into the artery where the blood is transported into the tumor with the blood [6]. The time needed to heat the tissue to right temperature can be as high as several dozen minutes. At this time, some or even all of the particles, can leave their place in the tumor and flow along with the blood to other parts of the body. In this case the hyperthermia process will be ineffective. It seems therefore necessary to develop a method that can keep ferromagnetic particles at their proper place in the tumor during the treatment procedure [7]. This article presents a method of permanently placing ferromagnetic nanoparticles in the tumor region for the dura- tion of the medical treatment. It is based on the phenomenon of magnetophoresis, that is influenced by magnetic field with a strongly variable gradient on magnetically induced magnetic moment of ferromagnetic particles. The presented approach has a great importance in nanoparticle tumor targeting [6], [7] as well as in particle separation industry [8]. II. MAGNETHOPHORETIC FORCE Let us consider two dimensional problem of homogenous particle (cylinder) with radius r 0 and permeability μ 1 immersed inside fluid with permeability μ 2 . The external magnetic field B 0 in which the cylinder is located, is directed perpendicular to the cylinder and parallel to the x-axis as showed in Fig. 1. Fig. 1. Particle in external magnetic field B0 Let us estimate the magnetic field outside and inside the cylinder, and then substitute dipole moment of the cylinder. The magnetic vector potential, of which one should calculate the value first, must satisfy the equation [1], [4]: 0 r 1 0             A M  where M is magnetization vector in magnets (see Fig. 2). Since the vector A is parallel to the cylinder axis, components of the magnetic potential A 2x = A 2y = 0. Therefore equation (1) will depend only on one A z component and assume the form: 2 2 2 1 1 0 A A r r r r r                