Simulation of the magnetization dynamics of diluted ferrofluids in medical applications

Henrik Rogge 1 , Marlitt Erbe 1 , Thorsten M. Buzug 1 ,  and Kerstin Lüdtke-Buzug 1
  • 1 Institute of Medical Engineering, University of Lübeck, Ratzeburger Allee 160, 23538 Lübeck, Germany
Henrik Rogge, Marlitt Erbe, Thorsten M. Buzug and Kerstin Lüdtke-Buzug


Ferrofluids, which are stable, colloidal suspensions of single-domain magnetic nanoparticles, have a large impact on medical technologies like magnetic particle imaging (MPI), magnetic resonance imaging (MRI) and hyperthermia. Here, computer simulations promise to improve our understanding of the versatile magnetization dynamics of diluted ferrofluids. A detailed algorithmic introduction into the simulation of diluted ferrofluids will be presented. The algorithm is based on Langevin equations and resolves the internal and the external rotation of the magnetic moment of the nanoparticles, i.e., the Néel and Brown diffusion. The derived set of stochastic differential equations are solved by a combination of an Euler and a Heun integrator and tested with respect to Boltzmann statistics.

  • [1]

    Arruebo M, Fernández-Pacheco R, Ibarra MR, Santamaría J. Magnetic nanoparticles for drug delivery. Nano Today 2007; 2: 22–32.

    • Crossref
  • [2]

    Berkov DV, Gorn NL, Schmitz R, Stock D. Langevin dynamic simulations of fast remagnetization processes in ferrofluids with internal magnetic degrees of freedom. J Phys Cond Matter 2006; 18: S2595.

    • Crossref
  • [3]

    Bertotti G, Mayergoyz I, Serpico C. Nonlinear magnetization dynamics in nanosystems. UK: Elsevier, 2009.

    • Crossref
  • [4]

    Coffey WT, Kalmykov YP, Waldron JT. The Langevin equation. 2nd ed. USA: World Scientific, 2004.

    • Crossref
  • [5]

    Garca-Palacios JL, Luis J, Lázaro FJ. Langevin-dynamics study of the dynamical properties of small magnetic particles. Phys Rev B 1998; 58: 14937–14958.

    • Crossref
  • [6]

    Gardiner GW. Handbook of stochastic methods. 3rd ed. Germany: Springer, 2004.

    • Crossref
  • [7]

    Guimaraes AP. Principles of nanomagnetism. Nanoscience and Technology. Germany: Springer, 2009.

    • Crossref
  • [8]

    Gleich B, Weizenecker J. Tomographic imaging using the nonlinear response of magnetic particles. Nature 2005; 435: 1214–1217.

    • Crossref
  • [9]

    Kloeden PE, Platen E. Numerical solution of stochastic differential equation. 2nd ed. Germany: Springer, 1995.

    • Crossref
  • [10]

    Raible M, Engel A. Langevin equation for the rotation of a magnetic particle. Appl Organometal Chem 2004; 18: 536–541.

    • Crossref
  • [11]

    Rosensweig RE. Heating magnetic fluid with alternating magnetic field. J Magn Magn Mater 2002; 252: 370–374.

    • Crossref
  • [12]

    Scherer C. Computer simulation of the stochastic dynamics of super-paramagnetic particles in ferrofluids. Brazilian J Phys 2006; 36: S0103.

    • Crossref
  • [13]

    Van Kampen NG. Stochastic processes in physics and chemistry. Netherlands: North Holland, 2007.

    • Crossref
  • [14]

    Weizenecker J, Gleich B, Rahmera J, Bogert J. Particle dynamics of mono-domain particles in magnetic particle imaging. Magnetic Nanoperticless, USA: World Scientific, 2010.

    • Crossref
  • [15]

    Wong E, Zakai M. On the convergence of ordinary integrals to stochastic integrals. Ann Math Stat 1965; 36: 1560–1564.

    • Crossref
  • [16]

    Yasumuri, I Reinen D, Selwood PW. Anisotropic behaviour in superparamagnetic systems. J Appl Phys 1963; 34: 3544–3549.

    • Crossref
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