# Field, force and transport analysis for magnetic particle-based gene delivery

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## Abstract

Magnetic particles are used to deliver gene vectors to target cells for uptake in a process known as magnetofection. Magnetic particle-based gene delivery has been successfully demonstrated for all types of nucleic acids and across a broad range of cell lines. It is well suited for multiwell culture plate systems wherein magnetic particles with surface-bound gene vectors are introduced into culture wells, and a magnetic force provided by rare-earth magnets beneath and aligned with the wells attracts the particles to the cells for uptake. In this paper, models are presented for analyzing and optimizing this process. These include closed-form equations for predicting the magnetic field and force and a drift–diffusion equation for predicting the transport and accumulation of particles in a well. The closed-form equations enable rapid parametric analysis of the spatial distribution of the field and force in a well as a function of key parameters including its dimensions, the magnet-to-well spacing, the strength of the magnet, the influence of neighboring magnets and the properties of the particles. The particle transport equation accounts for the field-induced drift of particles as well as fluidic drag and Brownian diffusion. It is solved numerically using the finite volume method. The theory is demonstrated via application to a multiwall plate magnetofection system and the impact of various factors that govern gene delivery is assessed. The models provide insight into gene delivery and are well suited for parametric analysis of particle accumulation in the wells. They enable the rational design of novel magnetofection systems.

## Keywords

Magnetic gene delivery Magnetofection Magnetic enhanced transfection Magnetophoresis Magnetic biotransport Magnetic particle transport Magnetic targeting## List of symbols

*B*Magnitude of the magnetic field induction (T)

**B**Magnetic field induction (T)

*β*Particle mobility defined as (6

*πηR*_{p})^{−1}*c*_{0}Initial particle volume concentration in a well

*c*(*t*)Particle volume concentration at time

*t**D*_{p}Particle diameter (m)

*D*_{c,p}Brownian critical particle diameter (m)

**F**_{m}Magnetic force field (N)

**g**Acceleration due to gravity (m/s

^{2})*h*Height above bottom of a culture well (m)

*H*Magnitude of the applied external magnetic field (A/m)

**H**Applied external magnetic field (A/m)

*k*Boltzmann constant

*L*_{c}Height of culture well (m)

*M*_{s}Saturation magnetization of magnet (A/m)

*M*_{sp}Saturation magnetization of particle (A/m)

**m**_{p,eff}Effective dipole moment of particle

*R*_{p}Particle radius (m)

*s*Spacing between magnet and well (m)

*T*Temperature (K)

*V*_{p}Particle volume (m

^{3})*χ*_{f}Magnetic susceptibility of fluid (dimensionless)

*χ*_{p}Particle volume-averaged susceptibility (dimensionless)

*η*Fluid viscosity (N s/m

^{2})*μ*_{o}Free-space magnetic permeability (=1.257 × 10

^{−6}N/A^{2})*μ*_{f}Magnetic permeability of fluid

*ρ*_{f}Fluid density (kg/m

^{3})*ρ*_{p}Particle density (kg/m

^{3})

## Notes

### Acknowledgments

The authors are grateful to Professor Christian Plank and Dr. Olga Mykhaylyk for many useful technical discussions.

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