Andrej KRAFČÍK, Peter BABINEC, and Melánia BABINCOVÁ

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1 MAGNETIC SEPARATOR DEVICE COMBINED WITH MAGNETICALLY ENHANCED TRANSFECTION AND ELECTROPORATION OF CELLS WITH MAGNETIC NANOPARTICLES AS FUNCTIONALIZED CARRIERS: COMPUTATIONAL DESIGN Andrej KRAFČÍK, Peter BABINEC, and Melánia BABINCOVÁ Deartment of Nuclear Physics and Biohysics, Faculty of Mathematics, Physics and Informatics, Comenius University, Mlynská dolina, , Bratislava, Slovakia; Abstract Magnetic nanoarticles are widely used as contrast agents in MRI or mediators for cancer magnetic hyerthermia as it was reviewed in many aers [1]. Also their alication as carriers for genes or other active molecules have a great otential for in vitro transfection of cells in resence of high gradient magnetic field by technique known as magnetofection [2]. Combination of this technique by any other method for ermeabilization of cell membrane, like elektrooration, may increases the robability of delivery and incororation of active molecules into the cells. In our contribution we have comutationally designed and modeled flow-through device for combined magnetic searation and targeting of magnetic articles into the cells with magnetofection and electrooration. As sources of high-gradient magnetic field we have used small neodymium magnets and Maxwell coils locally modulated by resence of ure iron stras electrodes. We have evaluated threshold velocities of flowing water as fluid media for caturing of two tyes of magnetic articles and also the mean cature time of their motion. Simulations were done for sueraramagnetic articles with arameters of commercially available nanoarticles nanomag -D and microarticles MagSense. Keywords: magnetic nanoarticles; magnetic searation and targeting; electrooration; magnetofection. 1. INTRODUCTION Effective transfection of cells by functionalized macromolecules is one of the key roblems in the field of biomedicine and biotechnology. Besides biological targeting, attention is focused also on hysical techniques, when secificity is ensured by localized alication of hysical forces, whether mechanical, electrical or magnetic, hotonic or thermic effects. Magnetofection [2], technique when sueraramagnetic articles with reversibly bonded effective comound, macromolecules, are focused to the target lace by magnetic field with high gradient and intensity, is romised in vivo and in vitro method for targeting of effective comounds. Magnetofection by itself suorts cell transfection, but not by cell membrane ermeabilization and traction comounds into the cells, but accumulation of comlexes magnetic article-effective comound to the cells surface. Its combination with other technique, like electrooration, could efficiency even increase. For ores formation during electrooration are used short high intensity electric ulses. Pores remain oened order of hundred milliseconds to several seconds. 2. MODEL OF MAGNETIC SEPARATOR COMBINED WITH ELECTROPORATION 2.1 Basic descrition Own searator consists of channel, by which carried fluid media with magnetically labeled cells by sueraramagnetic microbeads and magnetically labeled functional macromolecules by sueraramagnetic nanoarticles are flowing through. There are located electrodes above and below

2 the channel, on which short high intensity electric ulses are alied, which generate electric field able to create ores in membrane of cells localized in the channel (i.e. to take lace electrooration; Fig. 1). These electrodes are designed so that to modulate external Fig. 1 Electric field in the channel after alication of electric ulse on electrodes (side view), obtained by finite element method analysis (FEM). Inlet and outlet of channel is from left to right. magnetic field by localized increasing of magnetic field gradient on bottom art of channel in order to catch first labeled cells resenting in media and Fig. 2 Source of magnetic field for searator and location of channel. (a) two small neodymium (NdFeB) bar magnets, (b) Maxwell coils. after their electrooration also cature magnetically labeled macromolecules, which are admitted to flowing system after electrooration. This order of stes will ensure roduction of surface of cells on the bottom of the channel which membrane is ermeabilized and subsequently their covering by the surface of functional macromolecules, so the transfection can take lace. For assuring localized erturbation of magnetic field (Fig. 3) we have chosen as bottom electrode material ure iron (i.e. ferromagnet increasing magnetic field) and the bottom electrode has shae of arallel stries erendicular to the direction of flow in channel (Fig. 1). By bottom electrode can ass before and after electrooration current which can induce additional localized erturbation of magnetic field. Uer electrode has late shae arallel to uer face of channel and is made from diamagnetic coer and does not affect magnetic field in the channel. The art of searator is also source of external magnetic field with sufficient intensity and gradient, that is erturbated by bottom ure iron electrode. We have chosen as this external source firstly two small ermanent magnets and secondly coils. In the first case it were two neodymium (NdFeB) magnets located arallel with magnetization in common axis, so that channel with the electrodes were arallel with uer and below faces of magnets, below their symmetry lane (Fig. 2). In the second case we use two coils known as Maxwell coil, which can generate uniform gradient near the center when the coils are searated by 3 times the radius and the current asses in the oosite direction (Fig. 2). Bottom face of channel with bottom electrode was tightly above uer face of bottom magnet, or in the case of coils on the uer margin of bottom coil. Reason was to ensure as high as ossible intensity and gradient of magnetic field in the channel.

3 2.2 Simulation of motion of sueraramagnetic articles in magnetic field A calculated trajectory of article submerged in fluid media in the channel and external magnetic field can be deduced from the equation of motion involving a magnetic force and a viscous-drag force: where m, V and D are mass, volume and dv diameter of magnetic article, resectively. v and m V M B 3 f D v vf dt v f are article and fluid media velocity, η f is dynamical viscosity of fluid media ambient, and M is magnetization of sueraramagnetic article. In our model we suose that external magnetic field B is zero in the z-dimension, so it is a lanar magnetostatic roblem. Another simlification is that we assume fully magnetically saturated sueraramagnetic articles, i.e. magnitude of M equals saturation magnetization and has direction of external magnetic field in every moment. Sources of magnetic field in our simulations were modeled by finite element method (FEM) using FEMM (David Meeker, 2008). In first case we use two 1cm 1cm bar NdFeB magnets with magnetic energy roduct 40 MG.Oe, and magnetization on common axis and sacing 1 cm. In the second case, Maxwell coils had inner diameter 2 cm and sacing 1.73 cm. Each one consisted of 10,000 turns of coer wire with diameter mm with current 0.1 A assing by each turn. Fig. 3 Magnetic field in the channel of searator in the field of two NdFeB magnets. (MagSense Life Sciences, USA), which are shown in the Table 1.. Parameters for articles were set from the secifications of commercially available nanoarticles nanomag -D (micromod Partikeltechnologie GmbH, Germany) and microarticles MagSense Trajectory calculations for each tye of sueraramgnetic article and magnetic source in our searator were done numerically using MATLAB (The MathWorks, 2007) [3, 4]. Table 1 Secifications of used articles Density Saturation Magnetization Particle Diameter [g cm -3 ] [emu g -1 ] a [A m -1 ] b Nanomag -D 130 nm MagSense 1 μm a In cgs emu quoted by manufacturer. b Estimated as roduct of quoted Saturation Magnetization and Density, in SI.

4 3. RESULTS AND DISCUSION The magnetic forces are volumetric, therefore, the required fields and field gradients to exert a certain torque and force on magnetized object increase raidly as the object gets smaller. For examle, the required field gradients to generate a 1 N force on a sherical sueraramagnetc article fully magnetically saturated with saturation magnetization A m -1 are 10 and 4300 T/m for sheres of diameter 1 μm and 130 nm, resectively. Another imortant outcome is that, whereas magnetic force is volumetric, the fluid drag forces are deendent on the cross-sectional area (or in the case of a shere in laminar flow, on the diameter) For this reason, as the size of the articles gets smaller, the required magnetic field gradient to control the osition of the article inside a flowing fluid media becomes larger. For comarison, the drag forces on sherical articles with diameter 1 μm and 130 nm in water as laminar flowing fluid media with relative velocity 10-3 m s -1 are 9.5 and 1.2 N, resectively. For another comarison, gradients inside modeled channel on major art of channel height in direction erendicular to the bottom face of channel were 50 and 2.3 T/m in the case of NdFeB magnets (Fig. 3) and Maxwell coils, resectively, as the sources of external magnetic field, so the magnetic forces acting on the sherical sueraramagnetic nanoarticles and microarticles were relatively small in comarison with drag forces, deending on size of articles and external magnetic field source. But gradient in close neighborhood of bottom ure iron electrodes in the channel reached levels of 900 and 130 T/m in the cases of ermanent magnets and Maxwell coils, resectively, and have reaching distance from 50 to 100 μm (Fig. 3) what allowed to hold tightly articles, that have already been catured by the bottom electrodes to the bottom surface of the channel. Fig. 4 Trajectories of sueraramagnetic articles: (a) nano- nanomag -D and (b) microarticles MagSense; in the channel with flowing fluid media (water) in the x-axis direction with mean flow velocity <vf> in the magnetic field of two NdFeB magnets. marks initial osition and final osition. t mean mean cature time of 100 articles and t max - movement time of the slowest article. External magnetic field can be used to induce forces on magnetized object and control its orientation and osition. In our simulations we have tried to use magnetic field to cature magnetic articles moving in flowing fluid media on the surface of the channel. Efficiency of this rocess deends on the size of used magnetic articles. Particles are in fluid media dragged by the flow and fact that they will be catured in the channel or taken away deends also on the velocity of the flow and intensity and gradient of used external magnetic field. In the case of used NdFeB magnets was threshold velocity of the flow for effective caturing of microarticles m s -1 and nanoarticles 10-4 m s -1, when the articles were catured along the whole channel. Trajectories in the channel of both tyes of articles

5 in the case of NdFeB magnets as the external magnetic field source are shown on Fig. 4. In the case of using Maxwell coils was caturing less effective due to less magnitude of gradient of magnetic field. Then threshold velocity of the flow for caturing of microarticles and nanoarticles was 10-4 m s -1 and m s -1, resectively. We have described efficiency of articles caturing by time needed to move of article from its random initial osition in the channel and flowing media to its bottom surface (by caturing) or out area of channel (due to drift). Mean cature time for 100 articles and movement time of the slowest article are shown for both tyes of articles and both cases of external magnetic field sources together with threshold velocities of fluid media flow in the Table 2.. Table 2 Caturing of sueraramagnetic articles in the channel Particle a v f,t External Magnetic Field Sources NdFeB Magnets Maxwell Coils t mean t max a v f,t t mean t max [m s -1 ] [s] [s] [m s -1 ] [s] [s] Nanomag MagSense cm long channel between two arallel lates, with above coer electrode and bottom ure iron arallel stra electrodes located in the external magnetic field source. Through the channel flows carried fluid media with magnetic articles. a Threshold velocity of fluid media flow (water) for effective magnetic caturing of articles. In our work we have comutationally designed and modeled flow-through device for combined magnetic searation and targeting of magnetic articles into the cells with magnetofection and electrooration. ACKNOWLEDGEMENTS This work was suorted by VEGA grant No. 1/0642/11. LITERATURE [1] MORNET, S., VASSEUR, S., GRASSET, F., DUGUET, E. Magnetic nanoarticle design for medical diagnosis and theray.journal of Materials Chemistry, 2004, vol. 14(14), [2] SCHERER, F., ANTON, M., SCHILLINGER, U., HENKE, J., BERGEMANN, C., KRÜGER, A., et al. Magnetofection: Enhancing and targeting gene delivery by magnetic force in vitro and in vivo. Gene Theray, 2002, vol. 9(2), [3] KRAFČÍK, A., M. BABINCOVÁ, P. BABINEC. Theoretical analysis of magnetic article trajectory in high-current ulsed quadruole: Imlications for magnetic cell searation, drug targeting, and gene theray. Otoelectronics and Advanced Materials, Raid Communications, 2009, vol. 3(3): [4] BABINEC, P., A. KRAFČÍK, M. BABINCOVÁ, J. ROSENECKER. (2010). Dynamics of magnetic articles in cylindrical halbach array: Imlications for magnetic cell searation and drug targeting. Medical and Biological Engineering and Comuting 2010, vol. 48(8):