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MAGNETIC SEPARATOR DEVICE COMBINED WITH MAGNETICALLY ENHANCED. TRANSFECTION AND ELECTROPORATION OF CELLS WITH MAGNETIC.
21. – 23. 9. 2011, Brno, Czech Republic, EU

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 Department of Nuclear Physics and Biophysics, Faculty of Mathematics, Physics and Informatics, Comenius University, Mlynská dolina, 842 48, Bratislava, Slovakia; [email protected] Abstract Magnetic nanoparticles are widely used as contrast agents in MRI or mediators for cancer magnetic hyperthermia as it was reviewed in many papers [1]. Also their application as carriers for genes or other active molecules have a great potential for in vitro transfection of cells in presence of high gradient magnetic field by technique known as magnetofection [2]. Combination of this technique by any other method for permeabilization of cell membrane, like elektroporation, may increases the probability of delivery and incorporation of active molecules into the cells. In our contribution we have computationally designed and modeled flow-through device for combined magnetic separation and targeting of magnetic particles into the cells with magnetofection and electroporation. As sources of high-gradient magnetic field we have used small neodymium magnets and Maxwell coils locally modulated by presence of pure iron straps electrodes. We have evaluated threshold velocities of flowing water as fluid media for capturing of two types of magnetic particles and also the mean capture time of their motion. Simulations were done for superparamagnetic particles with parameters of commercially available nanoparticles nanomag®-D and microparticles MagSense. Keywords: magnetic magnetofection.

1.

nanoparticles;

magnetic

separation

and

targeting;

electroporation;

INTRODUCTION

Effective transfection of cells by functionalized macromolecules is one of the key problems in the field of biomedicine and biotechnology. Besides biological targeting, attention is focused also on physical techniques, when specificity is ensured by localized application of physical forces, whether mechanical, electrical or magnetic, photonic or thermic effects. Magnetofection [2], technique when superparamagnetic particles with reversibly bonded effective compound, macromolecules, are focused to the target place by magnetic field with high gradient and intensity, is promised in vivo and in vitro method for targeting of effective compounds. Magnetofection by itself supports cell transfection, but not by cell membrane permeabilization and traction compounds into the cells, but accumulation of complexes magnetic particle-effective compound to the cells surface. Its combination with other technique, like electroporation, could efficiency even increase. For pores formation during electroporation are used short high intensity electric pulses. Pores remain opened order of hundred milliseconds to several seconds. 2.

MODEL OF MAGNETIC SEPARATOR COMBINED WITH ELECTROPORATION

2.1

Basic description

Own separator consists of channel, by which carried fluid media with magnetically labeled cells by superparamagnetic microbeads and magnetically labeled functional macromolecules by superparamagnetic nanoparticles are flowing through. There are located electrodes above and below

21. – 23. 9. 2011, Brno, Czech Republic, EU

the channel, on which short high intensity electric pulses are applied, which generate electric field able to create pores in membrane of cells localized in the channel (i.e. to take place electroporation; Fig. 1). These electrodes are designed so that to modulate external magnetic field by localized increasing of magnetic field gradient on bottom Fig. 1 Electric field in the channel after application of electric pulse on part of channel in order to electrodes (side view), obtained by finite element method analysis catch first labeled cells (FEM). Inlet and outlet of channel is from left to right. presenting in media and after their electroporation also capture magnetically labeled macromolecules, which are admitted to flowing system after electroporation. This order of steps will ensure production of surface of cells on the bottom of the channel which membrane is permeabilized and subsequently their covering by the surface of functional macromolecules, so the transfection can take place. For assuring localized perturbation of magnetic field (Fig. 3) we have chosen as bottom electrode material pure iron (i.e. ferromagnet increasing magnetic field) and the bottom electrode Fig. 2 Source of magnetic field for separator and location of channel. has shape of parallel (a) two small neodymium (NdFeB) bar magnets, (b) Maxwell coils. stripes perpendicular to the direction of flow in channel (Fig. 1). By bottom electrode can pass before and after electroporation current which can induce additional localized perturbation of magnetic field. Upper electrode has plate shape parallel to upper face of channel and is made from diamagnetic copper and does not affect magnetic field in the channel. The part of separator is also source of external magnetic field with sufficient intensity and gradient, that is perturbated by bottom pure iron electrode. We have chosen as this external source firstly two small permanent magnets and secondly coils. In the first case it were two neodymium (NdFeB) magnets located parallel with magnetization in common axis, so that channel with the electrodes were parallel with upper and below faces of magnets, below their symmetry plane (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 separated by √3 times the radius and the current passes in the opposite direction (Fig. 2). Bottom face of channel with bottom electrode was tightly above upper face of bottom magnet, or in the case of coils on the upper margin of bottom coil. Reason was to ensure as high as possible intensity and gradient of magnetic field in the channel.

21. – 23. 9. 2011, Brno, Czech Republic, EU

2.2

Simulation of motion of superparamagnetic particles in magnetic field

A calculated trajectory of particle 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, Vp and D are mass, volume and dv p diameter of magnetic particle, respectively. vp and m  V p M p   B  3 f D v p  v f vf are particle and fluid media velocity, ηf is dt dynamical viscosity of fluid media ambient, and Mp is magnetization of superparamagnetic particle. In our model we suppose that external magnetic field B is zero in the z-dimension, so it is a planar magnetostatic problem. Another simplification is that we assume fully magnetically saturated superparamagnetic particles, i.e. magnitude of Mp 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 product 40 MG.Oe, and magnetization on common axis and spacing 1 cm. In the second case, Maxwell coils had inner diameter 2 cm and spacing 1.73 cm. Each one consisted of 10,000 turns of copper wire with diameter 0.125 mm with current 0.1 A passing by each turn.

Fig. 3 Magnetic field in the channel of separator in the field of two NdFeB magnets.

Parameters for particles were set from the specifications of commercially available nanoparticles nanomag®-D (micromod Partikeltechnologie GmbH, Germany) and microparticles MagSense

(MagSense Life Sciences, USA), which are shown in the Table 1.. Trajectory calculations for each type of superparamgnetic particle and magnetic source in our separator were done numerically using MATLAB (The MathWorks, 2007) [3, 4]. Table 1 Specifications of used particles Particle

Diameter

Density -3 [g∙cm ] 3.0 2.5

Saturation Magnetization -1 a -1 b [emu∙g ] [A∙m ] 5 67 2.01 × 10 5 50 1.25 × 10

Nanomag®-D 130 nm MagSense 1 μm a In cgs emu quoted by manufacturer. b Estimated as product of quoted Saturation Magnetization and Density, in SI.

21. – 23. 9. 2011, Brno, Czech Republic, EU

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 rapidly as the object gets smaller. For example, the required field gradients to generate a 1 pN force on a spherical superparamagnetc particle fully 5 -1 magnetically saturated with saturation magnetization 2.01 × 10 A∙m are 10 and 4300 T/m for spheres of diameter 1 μm and 130 nm, respectively. Another important outcome is that, whereas magnetic force is volumetric, the fluid drag forces are dependent on the cross-sectional area (or in the case of a sphere in laminar flow, on the diameter) For this reason, as the size of the particles gets smaller, the required magnetic field gradient to control the position of the particle inside a flowing fluid media becomes larger. For comparison, the drag forces on spherical particles with diameter 1 μm and -3 -1 130 nm in water as laminar flowing fluid media with relative velocity 10 m∙s are 9.5 and 1.2 pN, respectively. For another comparison, gradients inside modeled channel on major part of channel height in direction perpendicular to the bottom face of channel were 50 and 2.3 T/m in the case of NdFeB magnets (Fig. 3) and Maxwell coils, respectively, as the sources of external magnetic field, so the magnetic forces acting on the spherical superparamagnetic nanoparticles and microparticles were relatively small in comparison with drag forces, depending on size of particles and external magnetic field source. But gradient in close neighborhood of bottom pure iron electrodes in the channel reached levels of 900 and 130 T/m in the cases of permanent magnets and Maxwell coils, respectively, and have reaching distance from 50 to 100 μm (Fig. 3) what allowed to hold tightly particles, that have already been captured by the bottom electrodes to the bottom surface of the channel.

Fig. 4 Trajectories of superparamagnetic particles: (a) nano- nanomag®-D and (b) microparticles MagSense; in the channel with flowing fluid media (water) in the x-axis direction with mean flow velocity in the magnetic field of two NdFeB magnets. × marks initial position and ○ final position. tmean – mean capture time of 100 particles and tmax - movement time of the slowest particle. External magnetic field can be used to induce forces on magnetized object and control its orientation and position. In our simulations we have tried to use magnetic field to capture magnetic particles moving in flowing fluid media on the surface of the channel. Efficiency of this process depends on the size of used magnetic particles. Particles are in fluid media dragged by the flow and fact that they will be captured in the channel or taken away depends 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 -3 -1 -4 -1 the flow for effective capturing of microparticles 5 × 10 m∙s and nanoparticles 10 m∙s , when the particles were captured along the whole channel. Trajectories in the channel of both types of particles

21. – 23. 9. 2011, Brno, Czech Republic, EU

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 capturing less effective due to less magnitude of gradient of magnetic field. -4 -1 Then threshold velocity of the flow for capturing of microparticles and nanoparticles was 10 m∙s and -6 -1 5 × 10 m∙s , respectively. We have described efficiency of particles capturing by time needed to move of particle from its random initial position in the channel and flowing media to its bottom surface (by capturing) or out area of channel (due to drift). Mean capture time for 100 particles and movement time of the slowest particle are shown for both types of particles and both cases of external magnetic field sources together with threshold velocities of fluid media flow in the Table 2.. Table 2 Capturing of superparamagnetic particles in the channel External Magnetic Field Sources NdFeB Magnets Maxwell Coils Particle a a vf,t tmean tmax vf,t tmean tmax -1 -1 [m∙s ] [s] [s] [m∙s ] [s] [s] -4 -6 Nanomag 1 ×10 21.80 63.70 5 ×10 572.0 1520.0 -3 -4 MagSense 5 ×10 0.54 1.49 1 ×10 22.9 55.5 1 cm long channel between two parallel plates, with above copper electrode and bottom pure iron parallel strap electrodes located in the external magnetic field source. Through the channel flows carried fluid media with magnetic particles. a Threshold velocity of fluid media flow (water) for effective magnetic capturing of particles. In our work we have computationally designed and modeled flow-through device for combined magnetic separation and targeting of magnetic particles into the cells with magnetofection and electroporation. ACKNOWLEDGEMENTS This work was supported by VEGA grant No. 1/0642/11. LITERATURE [1]

MORNET, S., VASSEUR, S., GRASSET, F., DUGUET, E. Magnetic nanoparticle design for medical diagnosis and therapy.Journal of Materials Chemistry, 2004, vol. 14(14), 2161-2175.

[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 Therapy, 2002, vol. 9(2), 102-109.

[3]

KRAFČÍK, A., M. BABINCOVÁ, P. BABINEC. Theoretical analysis of magnetic particle trajectory in high-current pulsed quadrupole: Implications for magnetic cell separation, drug targeting, and gene therapy. Optoelectronics and Advanced Materials, Rapid Communications, 2009, vol. 3(3): 226-230.

[4]

BABINEC, P., A. KRAFČÍK, M. BABINCOVÁ, J. ROSENECKER. (2010). Dynamics of magnetic particles in cylindrical halbach array: Implications for magnetic cell separation and drug targeting. Medical and Biological Engineering and Computing 2010, vol. 48(8): 745-753.