journal article·2021-10-15Open access

A Theoretical Analysis of Magnetic Particle Alignment in External Magnetic Fields Affected by Viscosity and Brownian Motion

Andrej Krafcik, Peter Babinec, Oliver Strbak, Ivan Frollo

Applied Sciences· Volume 11· Issue 20

Abstract

The interaction of an external magnetic field with magnetic objects affects their response and is a fundamental property for many biomedical applications, including magnetic resonance and particle imaging, electromagnetic hyperthermia, and magnetic targeting and separation. Magnetic alignment and relaxation are widely studied in the context of these applications. In this study, we theoretically investigate the alignment dynamics of a rotational magnetic particle as an inverse process to Brownian relaxation. The selected external magnetic flux density ranges from 5μT to 5T. We found that the viscous torque for arbitrary rotating particles with a history term due to the inertia and friction of the surrounding ambient water has a significant effect in strong magnetic fields (range 1–5T). In this range, oscillatory behavior due to the inertial torque of the particle also occurs, and the stochastic Brownian torque diminishes. In contrast, for weak fields (range 5–50μT), the history term of the viscous torque and the inertial torque can be neglected, and the stochastic Brownian torque induced by random collisions of the surrounding fluid molecules becomes dominant. These results contribute to a better understanding of the molecular mechanisms of magnetic particle alignment in external magnetic fields and have important implications in a variety of biomedical applications.
Source: crossref · Quality: baseline

Research context

OpenAlex topics: Characterization and Applications of Magnetic Nanoparticles · Microfluidic and Bio-sensing Technologies · Magnetic and Electromagnetic Effects

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

Affiliations

Department of Imaging Methods, Institute of Measurement Science, Slovak Academy of Sciences, Dubravska Cesta 9, 841 04 Bratislava, Slovakia

Department of Nuclear Physics and Biophysics, Faculty of Mathematics, Physics and Informatics, Comenius University, Mlynska Dolina F1, 842 48 Bratislava, Slovakia

Biomedical Center Martin, Jessenius Faculty of Medicine in Martin, Comenius University in Bratislava, Mala Hora 4, 036 01 Martin, Slovakia

Funding

Slovak Research and Development Agency · Slovak Scientific Grant Agency · Ministry of Health of the Slovak Republic

References (58)

Show source-provided references
1. Targeted delivery of magnetic aerosol droplets to the lung10.1038/nnano.2007.217 ↗
2. Computational analysis of magnetic field induced deposition of magnetic particles in lung alveolus in comparison to deposition produced with viscous drag and gravitational force10.1016/j.jmmm.2014.10.018 ↗
3. Microfluidic Devices for Magnetic Separation of Biological Particles: A Review10.1115/1.4048912 ↗
4. Dynamics of magnetic particles in cylindrical Halbach array: Implications for magnetic cell separation and drug targeting10.1007/s11517-010-0636-8 ↗
5. High gradient magnetic separation with involved Basset history force: Configuration with single axial wire10.1016/j.powtec.2019.02.044 ↗
6. Fundamentals and advances in magnetic hyperthermia10.1063/1.4935688 ↗
7. Applications of magnetoliposomes with encapsulated doxorubicin for integrated chemotherapy and hyperthermia of rat C6 glioma10.1515/znc-2017-0110 ↗
8. Magnetic particle imaging (MPI) for NMR and MRI researchers10.1016/j.jmr.2012.11.029 ↗
9. Strbak, O., Antal, I., Khmara, I., Koneracka, M., Kubovcikova, M., Zavisova, V., Molcan, M., Jurikova, A., Hnilicova, P., and Gombos, J. (2020). Influence of dextran molecular weight on the physical properties of magnetic nanoparticles for hyperthermia and MRI applications. Nanomaterials, 10.10.3390/nano10122468 ↗
10. Strbak, O., Balejcikova, L., Kmetova, M., Gombos, J., Kovac, J., Dobrota, D., and Kopcansky, P. (2021). Longitudinal and transverse relaxivity analysis of native ferritin and magnetoferritin at 7 T MRI. Int. J. Mol. Sci., 22.10.3390/ijms22168487 ↗
11. Gubin, S.P. (2009). Magnetism of Nanoparticles: Effects of Size, Shape, and Interactions. Magnetic Nanoparticles, John Wiley & Sons, Ltd.. Chapter 6.10.1002/9783527627561 ↗
12. Magnetic-field dependence of Brownian and Néel relaxation times10.1063/1.4940724 ↗
13. Relaxation in x-space magnetic particle imaging10.1007/978-3-642-24133-8_24 ↗
14. Nanoparticles in magnetic resonance imaging: From simple to dual contrast agents
15. Imaging and quantification of magnetic nanoparticles: Comparison of magnetic resonance imaging and magnetic particle imaging10.1016/j.jmmm.2018.10.082 ↗
16. High intrinsic loss power of multicore magnetic nanoparticles with blood-pooling property for hyperthermia10.1063/1.5079875 ↗
17. From Micromagnetic to In Silico Modeling of Magnetic Nanodisks for Hyperthermia Applications10.1002/adts.202100013 ↗
18. Using magnetic particle imaging systems to localize and guide magnetic hyperthermia treatment: Tracers, hardware, and future medical applications10.7150/thno.40858 ↗
19. Theranostics Based on Magnetic Nanoparticles and Polymers: Intelligent Design for Efficient Diagnostics and Therapy10.3389/fchem.2020.00561 ↗
20. Combining magnetic particle imaging and magnetic fluid hyperthermia in a theranostic platform10.1088/1361-6560/aa5601 ↗
21. Magnetorelaxometry—A new binding specific detection method based on magnetic nanoparticles10.1016/S0304-8853(02)00657-1 ↗
22. OPM magnetorelaxometry in the presence of a DC bias field10.1140/epjqt/s40507-020-00087-3 ↗
23. Quantifying the magnetic advantage in magnetotaxis10.1529/biophysj.106.085167 ↗
24. Faivre, D. (2016). Magnetoreception and Magnetotaxis. Iron Oxides: From Nature to Applications, John Wiley & Sons, Ltd.. Chapter 22.10.1002/9783527691395 ↗
25. Orientational dynamics of magnetotactic bacteria in Earth’s magnetic field—A simulation study10.1007/s10867-021-09566-9 ↗
26. Dynamics of magnetotactic bacteria in a rotating magnetic field10.1529/biophysj.107.107474 ↗
27. QA: Animal behaviour: Magnetic-field perception10.1038/4641140a ↗
28. Jackson, J.D. (1999). Classical Electrodynamics, Wiley. [3rd ed.].10.1119/1.19136 ↗
29. Torsional oscillations of a sphere in a Stokes flow10.1007/s00348-015-2075-7 ↗
30. Viscous torque on a sphere under arbitrary rotation10.1063/1.2372704 ↗
31. On the motion of a sphere in a viscous liquid
32. Atypical non-Basset particle dynamics due to hydrodynamic slip10.1063/5.0021986 ↗
33. Detection of Brownian Torque in a Magnetically-Driven Rotating Microsystem10.1038/srep21212 ↗
34. Nonlinear phenomena in systems of magnetic holes10.1103/PhysRevLett.64.1425 ↗
35. Physiochemical microparticle sensors based on nonlinear magnetic oscillations10.1016/j.snb.2006.09.043 ↗
36. Overdamped dynamics of paramagnetic ellipsoids in a precessing magnetic field10.1103/PhysRevE.79.021501 ↗
37. Lamb, H. (1932). Hydrodynamics, Cambridge University Press. [6th ed.].
38. Rotational diffusion model of magnetic alignment10.1143/JJAP.48.063001 ↗
39. Characterization of three-dimensional magnetic alignment for magnetically biaxial particles10.7567/JJAP.52.013003 ↗
40. Stochastic processes crossing from ballistic to fractional diffusion with memory: Exact results10.5488/CMP.13.23001 ↗
41. Jones, R.B. (2003). Rotational Diffusion in Dispersive Media, Centre of Excellence for Advanced Materials and Structures.
42. Simulation of a Brownian particle in an optical trap10.1119/1.4772632 ↗
43. Langevin theory of anomalous Brownian motion made simple10.1088/0143-0807/32/3/002 ↗
44. A note on ‘Langevin theory of anomalous Brownian motion made simple’
45. Generalized Langevin theory of the Brownian motion and the dynamics of polymers in solution
46. Øksendal, B. (2014). Stochastic Differential Equations: An Introduction with Applications (Universitext), Springer. [6th ed.].
47. Stokes versus Basset: Comparison of forces governing motion of small bodies with high acceleration10.1088/1361-6404/aaabc7 ↗
48. Importance of Basset history force for the description of magnetically driven motion of magnetic particles in air10.2478/msr-2020-0007 ↗
49. Butcher, J.C. (2003). Numerical Methods for Ordinary Differential Equations, John Wiley & Sons, Ltd.10.1002/0470868279 ↗
50. Advection of inertial particles in the presence of the history force: Higher order numerical schemes10.1016/j.jcp.2013.07.024 ↗
51. Resonances arising from hydrodynamic memory in Brownian motion10.1038/nature10498 ↗
52. Direct observation of the full transition from ballistic to diffusive Brownian motion in a liquid10.1038/nphys1953 ↗
53. Zwanzig, R. (2001). Nonequilibrium Statistical Mechanics, Oxford University Press.10.1093/oso/9780195140187.001.0001 ↗
54. Generalized Langevin equation and the fluctuation-dissipation theorem for particle-bath systems in a harmonic field10.1016/j.rinp.2019.01.003 ↗
55. Brownian motion of charged particles in a bath responding to an external magnetic field10.12693/APhysPolA.137.657 ↗
56. Brownian motion in a bath responding to external electric fields10.1016/j.molliq.2020.113920 ↗
57. Brownian motion in a gas of charged particles under the influence of a magnetic field10.1016/j.physa.2020.125110 ↗
58. Brownian motion in a bath affected by an external harmonic potential