Microfluidics and Nanofluidics

, Volume 13, Issue 4, pp 589–602 | Cite as

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

Research Paper


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.


Magnetic gene delivery Magnetofection Magnetic enhanced transfection Magnetophoresis Magnetic biotransport Magnetic particle transport Magnetic targeting 

List of symbols


Magnitude of the magnetic field induction (T)


Magnetic field induction (T)


Particle mobility defined as (6πηR p)−1


Initial particle volume concentration in a well


Particle volume concentration at time t


Particle diameter (m)


Brownian critical particle diameter (m)


Magnetic force field (N)


Acceleration due to gravity (m/s2)


Height above bottom of a culture well (m)


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


Applied external magnetic field (A/m)


Boltzmann constant


Height of culture well (m)


Saturation magnetization of magnet (A/m)


Saturation magnetization of particle (A/m)


Effective dipole moment of particle


Particle radius (m)


Spacing between magnet and well (m)


Temperature (K)


Particle volume (m3)


Magnetic susceptibility of fluid (dimensionless)


Particle volume-averaged susceptibility (dimensionless)


Fluid viscosity (N s/m2)


Free-space magnetic permeability (=1.257 × 10−6 N/A2)


Magnetic permeability of fluid


Fluid density (kg/m3)


Particle density (kg/m3)



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


  1. Ahn CH, Allen MG, Trimmer W et al (1996) A fully integrated micromachined magnetic particle separator. J Microelectromech Syst 5:151–158CrossRefGoogle Scholar
  2. Arfken G (1985) Mathematical methods for physics, 3rd edn. Academic Press, CaliforniaGoogle Scholar
  3. Arrueboa M, Fernández-Pachecoa R, Ibarraa RM et al (2007) Magnetic nanoparticles for drug delivery. Nanotoday 2(3):22–32Google Scholar
  4. Berry CC (2009) Progress in functionalization of magnetic nanoparticles for applications in biomedicine. J Phys D Appl Phys 42(3):9Google Scholar
  5. Choi J-W, Ahn CH, Bhansali S, Henderson HT (2000) A new magnetic bead-based, filterless bio-separator with planar electromagnet surfaces for integrated bio-detection systems. Sens Actuators, B 68:34–39CrossRefGoogle Scholar
  6. Choi J-W, Liakopoulos TM, Ahn CH (2001) An on-chip magnetic bead separator using spiral electromagnets with semi-encapsulated permalloy. Biosens Bioelectron 16:409–416CrossRefGoogle Scholar
  7. Dobson J (2006a) Magnetic micro- and nano-particle-based targeting for drug and gene delivery. Nanomedicine 1(1):31–37CrossRefGoogle Scholar
  8. Dobson J (2006b) Gene therapy progress and prospects: magnetic nanoparticle-based gene delivery. Gene Ther 13:283–287MathSciNetCrossRefGoogle Scholar
  9. Fletcher D (1991) Fine particle high gradient magnetic entrapment. IEEE Trans Magn 27:3655–3677CrossRefGoogle Scholar
  10. Furlani EP (1992) A method for computing the field in permanent-magnet axial-field motors. IEEE Trans Magn 28(5):2061–2066CrossRefGoogle Scholar
  11. Furlani EP (1994) Computing the field in permanent-magnet axial-field motors. IEEE Trans Magn 30(5):3660–3663CrossRefGoogle Scholar
  12. Furlani EP (1997) Field analysis and optimization of NdFeB axial field permanent magnet motors. IEEE Trans Magn 33(5):3883–3885CrossRefGoogle Scholar
  13. Furlani EP (2001) Permanent magnet and electromechanical devices; materials, analysis and applications. Academic Press, New YorkGoogle Scholar
  14. Furlani EP (2006) Analysis of particle transport in a magnetophoretic microsystem. J Appl Phys 99(2):11 (024912)CrossRefGoogle Scholar
  15. Furlani EP (2007) Magnetophoretic separation of blood cells at the microscale. J Phys D Appl Phys 40:1313–1319CrossRefGoogle Scholar
  16. Furlani EP (2010a) Magnetic biotransport: analysis and applications. Materials 3(4):2412–2446CrossRefGoogle Scholar
  17. Furlani EP (2010b) Particle transport in magnetophoretic microsystems. In: Kumar CSSR (ed) Microfluidic devices in nanotechnology: fundamental concepts. Wiley, New York, pp 215–262CrossRefGoogle Scholar
  18. Furlani EP (2010c) Nanoscale magnetic biotransport. In: Sattler K (ed) Handbook of nanophysics. CRC Press, Boca RatonGoogle Scholar
  19. Furlani EJ, Furlani EP (2007) A model for predicting magnetic targeting of multifunctional particles in the microvasculature. J Magn Magn Mat 312(1):187–193CrossRefGoogle Scholar
  20. Furlani EP, Knewtson MA (1997) A three-dimensional field solution for permanent-magnet axial-field motors. IEEE Trans Magn 33(3):2322–2325CrossRefGoogle Scholar
  21. Furlani EP, Ng KC (2006) Analytical model of magnetic nanoparticle capture in the microvasculature. Phys Rev E 73(6) (061919, part 1)Google Scholar
  22. Furlani EP, Ng KC (2008) Nanoscale magnetic biotransport with application to magnetofection. Phys Rev E 77 (061914)Google Scholar
  23. Furlani EP, Sahoo Y (2006) Analytical model for the magnetic field and force in a magnetophoretic microsystem. J Phys D Appl Phys 39:1724–1732CrossRefGoogle Scholar
  24. Furlani EP, Xue X (2012) A model for predicting field-directed particle transport in the magnetofection process. Pharm Res. doi: 10.1007/s11095-012-0681-0
  25. Furlani EP, Sahoo Y, Ng KC, Wortman JC, Monk TE (2007) A model for predicting magnetic particle capture in a microfluidic bioseparator. Biomed Microdevices 9(4):451–463CrossRefGoogle Scholar
  26. Ganguly R, Puri IK (2010) Microfluidic transport in magnetic MEMS and bioMEMS. Nanomed Nanobiotechnol 2(4):382–399CrossRefGoogle Scholar
  27. Geraldes CF, Laurent S (2009) Classification and basic properties of contrast agents for magnetic resonance imaging. Contrast Media Mol Imaging 4(1):1–23CrossRefGoogle Scholar
  28. Gerber R, Briss R (1983) High gradient magnetic separation (magnetic materials and their applications). Research Studies Press Div. of Wiley, New YorkGoogle Scholar
  29. Gerber R, Takayasu M, Friedlander FJ (1983) Generalization of HGMS theory: the capture of ultrafine particles. IEEE Trans Magn 19(5):2115–2117CrossRefGoogle Scholar
  30. Gijs MAM (2004) Magnetic bead handling on-chip: new opportunities for analytical applications. Microfluid Nanofluid 1(1):22–40Google Scholar
  31. Khashan SA, Furlani EP (2011) Effects of particle–fluid coupling on particle transport and capture in a magnetophoretic microsystem. Microfluid Nanofluid. doi: 10.1007/s10404-011-0898-y MATHGoogle Scholar
  32. Khashan SA, Haik Y (2006) Numerical simulation of bio-magnetic fluid downstream an eccentric stenotic orifice. Phys Fluids 18(11) (113601)Google Scholar
  33. Khashan SA, Elnajjar E, Haik Y (2011a) Numerical simulation of the continuous biomagnetic separation in a two-dimensional channel. Int J Multiph Flow 37(8):947–955CrossRefGoogle Scholar
  34. Khashan SA, Elnajjar E, Haik Y (2011b) Numerical simulation of the continuous biomagnetic separation in a two-dimensional channel. J Magn Magn Mat 323(23):2960–2967CrossRefGoogle Scholar
  35. Majewski P, Thierry B (2007) Functionalized magnetite nanoparticles—synthesis, properties, and bio-applications. Crit Rev Solid State Mater Sci 32:203–215CrossRefGoogle Scholar
  36. Modak N, Datta A, Ganguly R (2009) Cell separation in a microfluidic channel using magnetic microspheres. J Microfluid Nanofluid 6:647–660CrossRefGoogle Scholar
  37. Modak N, Datta A, Ganguly R (2010) Numerical analysis of transport and binding of a target analyte and functionalized magnetic microspheres in a microfluidic immunoassay. J Phys D Appl Phys 43:12 (485002)CrossRefGoogle Scholar
  38. Mohanty S, Baierb T, Schönfeld F (2010) Three-dimensional CFD modelling of a continuous immunomagnetophoretic cell capture in BioMEMs. Biochem Eng J 51:110–116CrossRefGoogle Scholar
  39. Moroz P, Jones SK, Gray BN (2002) Magnetically mediated hyperthermia: current status and future directions. Int J Hyperth 18:267–284CrossRefGoogle Scholar
  40. Moser Y, Lehnert T, Gijs MAM (2009) On-chip immuno-agglutination assay with analyte capture by dynamic manipulation of superparamagnetic beads. Lab Chip 9:3261–3267CrossRefGoogle Scholar
  41. Mykhaylyk O, Antequera YS, Vlaskou D, Plank C (2007) Generation of magnetic nonviral gene transfer agents and magnetofection in vitro. Nat Protoc 2:2391–2411CrossRefGoogle Scholar
  42. Pamme N (2006) Magnetism and microfluidics. Lab Chip 6:24–38CrossRefGoogle Scholar
  43. Pamme N (2007) Continuous flow separations in microfluidic devices. Lab Chip 7:1644–1659CrossRefGoogle Scholar
  44. Pamme N, Wilhelm C (2006) Continuous sorting of magnetic cells via on-chip free flow magnetophoresis. Lab Chip 6:974–980CrossRefGoogle Scholar
  45. Pankhurst QA, Connolly J, Jones SK et al (2003) Applications of magnetic nanoparticles in biomedicine. J Phys D Appl Phys 36:R167–R181CrossRefGoogle Scholar
  46. Pankhurst QA, Thanh NKT, Jones SK, Dobson J (2009) Progress in applications of magnetic nanoparticles in biomedicine. J Phys D Appl Phys 42 (224001)Google Scholar
  47. Pedro T, Morales MP, Veintemillas-Verdaguer S et al (2003) The preparation of magnetic nanoparticles for applications in biomedicine. J Phys D Appl Phys 36:R182–R197CrossRefGoogle Scholar
  48. Plank C, Scherer F, Schillinger U et al (2002) Magnetofection: enhancing and targeting gene delivery by magnetic force. Eur Cells Mater 3(Suppl 2):79–80Google Scholar
  49. Plank C, Zelphati OF, Mykhaylyk O (2011) Magnetically enhanced nucleic acid delivery. Ten years of magnetofection: progress and prospects. Adv Drug Deliv Rev 63(14–15):1300–1331CrossRefGoogle Scholar
  50. Safarik I, Safarikova M (2002) Magnetic nanoparticles and biosciences. Monatshefte fur Chemie 133:737–759CrossRefGoogle Scholar
  51. Smistrup K, Hansen O, Bruus H, Hansen MF (2005) Magnetic separation in microfluidic systems using microfabricated electromagnets: experiments and simulations. J Magn Magn Mater 293:597–604CrossRefGoogle Scholar
  52. Smistrup K, Lund-Olesen T, Hansen MF, Tang PT (2006) Microfluidic magnetic separator using an array of soft magnetic elements. J Appl Phys 99:3Google Scholar
  53. Smistrup K, Bu MQ, Wolff A, Bruus H, Hansen MF (2008) Theoretical analysis of a new, efficient microfluidic magnetic bead separator based on magnetic structures on multiple length scales. Microfluid Nanofluid 4(6):565–573CrossRefGoogle Scholar
  54. Stratton JA (1941) Electromagnetic theory. McGraw-Hill, New YorkMATHGoogle Scholar
  55. Berry CC, Curtis ASG (2003) Functionalization of magnetic nanoparticles for applications in biomedicine. J Phys D Appl Phys 36:R198–R206CrossRefGoogle Scholar
  56. Zborowski M, Chalmers JJ (2007) Magnetic cell separation, vol 32 (Laboratory techniques in biochemistry and molecular biology). Elsevier Science, New YorkGoogle Scholar

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Department of Chemical and Biological EngineeringUniversity at Buffalo, SUNYBuffaloUSA
  2. 2.Department of Electrical EngineeringUniversity at Buffalo, SUNYBuffaloUSA

Personalised recommendations