Journal of Atomic, Molecular, and Optical Physics
Volume 2012 (2012), Article ID 135708, 22 pages
An Analytic Analysis of the Diffusive-Heat-Flow Equation for Different Magnetic Field Profiles for a Single Magnetic Nanoparticle
1Department of Electrical Engineering, Faculty of Engineering, Tel-Aviv University, 69978 Tel-Aviv, Israel
2Department of Biomedical Engineering, Faculty of Engineering, Tel-Aviv University, 69978 Tel-Aviv, Israel
Received 10 February 2012; Revised 1 June 2012; Accepted 4 June 2012
Academic Editor: Yuval Garini
Copyright © 2012 Brenda Dana and Israel Gannot. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- I. M. Gescheit, M. Ben-David, and I. Gannot, “A proposed method for thermal specific bioimaging and therapy technique for diagnosis and treatment of malignant tumors by using magnetic nanoparticles,” Advances in Optical Technologies, vol. 2008, Article ID 275080, 7 pages, 2008.
- H. G. Bagaria and D. T. Johnson, “Transient solution to the bioheat equation and optimization for magnetic fluid hyperthermia treatment,” International Journal of Hyperthermia, vol. 21, no. 1, pp. 57–75, 2005.
- M. A. Giordano, G. Gutierrez, and C. Rinaldi, “Fundamental solutions to the bioheat equation and their application to magnetic fluid hyperthermia,” International Journal of Hyperthermia, vol. 26, no. 5, pp. 475–484, 2010.
- R. E. Rosensweig, “Heating magnetic fluid with alternating magnetic field,” Journal of Magnetism and Magnetic Materials, vol. 252, no. 1–3, pp. 370–374, 2002.
- J. D. Jackson, Classical Electrodynamics, John Wily & Sons, 1998.
- L. D. Landau, L. P. Pitaevskii, and E. M. Lifshitz, Electrodynamics of Continuous Media, vol. 8, 2nd edition, 1984.
- N. Guskos, E. A. Anagnostakis, V. Likodimos et al., “Ferromagnetic resonance and ac conductivity of a polymer composite of Fe3 O4 and Fe3 C nanoparticles dispersed in a graphite matrix,” Journal of Applied Physics, vol. 97, no. 2, Article ID 024304, 6 pages, 2005.
- X. Zhang, B. Q. Li, and S. S. Pang, “A perturbational approach to magneto-thermal problems of a deformed sphere levitated in a magnetic field,” Journal of Engineering Mathematics, vol. 2-3, no. 4, pp. 337–355, 1997.
- A. Jordan, P. Wust, H. Fahlin, W. John, A. Hinz, and R. Felix, “Inductive heating of ferrimagnetic particles and magnetic fluids: physical evaluation of their potential for hyperthermia,” International Journal of Hyperthermia, vol. 9, no. 1, pp. 51–68, 1993.
- P. C. Fannin, Y. L. Raikher, A. T. Giannitsis, and S. W. Charles, “Investigation of the influence which material parameters have on the signal-to-noise ratio of nanoparticles,” Journal of Magnetism and Magnetic Materials, vol. 252, no. 1–3, pp. 114–116, 2002.
- Q. A. Pankhurst, J. Connolly, S. K. Jonesand, and J. Dobson, “Applications of magnetic nanoparticles in biomedicine,” Journal of Physics D, vol. 36, no. 13, pp. 167–181, 2003.
- J. Weizenecker, B. Gleich, J. Rahmer, and J. Borgert, “Particle dynamics of mono-domain particles in magnetic particle imaging,” in Proceedings of the 1st International Workshop on Magnetic Particle Imaging, Magnetic Nanoparticles, pp. 3–15, World Scientific, 2010.
- P. C. Fannin, “Magnetic spectroscopy as an aide in understanding magnetic fluids,” Journal of Magnetism and Magnetic Materials, vol. 252, no. 1–3, pp. 59–64, 2002.
- P. C. Fannin, “Characterisation of magnetic fluids,” Journal of Alloys and Compounds, vol. 369, no. 1-2, pp. 43–51, 2004.
- P. C. Fannin and S. W. Charles, “On the calculation of the Neel relaxation time in uniaxial single-domain ferromagnetic particles,” Journal of Physics D, vol. 27, no. 2, pp. 185–188, 1994.
- W. J. Atkinson, I. A. Brezovich, and D. P. Chakraborty, “Usable frequencies in hyperthermia with thermal seeds,” IEEE Transactions on Biomedical Engineering, vol. 31, no. 1, pp. 70–75, 1984.
- S. Mornet, S. Vasseur, F. Grasset, and E. Duguet, “Magnetic nanoparticle design for medical diagnosis and therapy,” Journal of Materials Chemistry, vol. 14, no. 14, pp. 2161–2175, 2004.
- C. H. Moran, S. M. Wainerdi, T. K. Cherukuri et al., “Size-dependent joule heating of gold nanoparticles using capacitively coupled radiofrequency fields,” Nano Research, vol. 2, no. 5, pp. 400–405, 2009.
- V. P. Torchilin, “Targeted pharmaceutical nanocarriers for cancer therapy and imaging,” The AAPS Journal, vol. 9, no. 2, pp. E128–E147, 2007.
- T. R. Sathe, Integrated magnetic and optical nanotechnology for early cancer detection and monitoring [Ph.D. thesis], Georgia Institute of Technology, 2007.
- N. Gigel, “Magnetic nanoparticles impact on tumoral cells in the treatment by magnetic fluid hyperthermia,” Digest Journal of Nanomaterials and Biostructures, vol. 3, no. 3, pp. 103–107, 2008.
- F. Matsuoka, M. Shinkai, H. Honda, T. Kubo, T. Sugita, and T. Kobayashi, “Hyperthermia using magnetite cationic liposomes for hamster osteosarcoma,” BioMagnetic Research and Technology, vol. 2, no. 3, pp. 1–6, 2004.
- Q. A. Pankhurst, “Nanomagnetic medical sensors and treatment methodologies,” BT Technology Journal, vol. 24, no. 3, pp. 33–38, 2006.
- E. Kita, T. Oda, T. Kayano et al., “Ferromagnetic nanoparticles for magnetic hyperthermia and thermoablation therapy,” Journal of Physics D, vol. 43, no. 47, Article ID 474011, 9 pages, 2010.
- L. Pilon and K. M. Katika, “Modified method of characteristics for simulating microscale energy transport,” Journal of Heat Transfer, vol. 126, no. 5, pp. 735–743, 2004.
- G. Chen, R. Yang, and X. Chen, “Nanoscale heat transfer and thermal-electric energy conversion,” Journal de Physique IV, vol. 125, no. 1, pp. 499–504, 2005.
- G. Chen, “Non local and nonequilibrium heat conduction in the vicinity of nanoparticles,” Journal of Heat Transfer, vol. 118, no. 3, pp. 539–546, 1996.
- C. Kittel, Introduction to Solid-State Physics, John Wiley & Sons, New York, NY, USA, 1996.
- R. Röhlsberger, W. Sturhahn, T. S. Toellner et al., “Phonon damping in thin films of Fe,” Journal of Applied Physics, vol. 86, no. 1, pp. 584–592, 1999.
- K. E. Goodson and M. I. Flik, “Electron and phonon thermal conduction in epitaxial high-Tc superconducting films,” Journal of Heat Transfer, vol. 115, no. 1, pp. 17–25, 1993.
- Y. Rabin, “Is intracellular hyperthermia superior to extracellular hyperthermia in the thermal sense?” International Journal of Hyperthermia, vol. 18, no. 3, pp. 194–202, 2002.
- G. Chen, “Ballistic-diffusive heat-conduction equations,” Physical Review Letters, vol. 86, no. 11, pp. 1197–2300, 2000.
- E. H. Wissler, “Pennes' 1948 paper revisited,” Journal of Applied Physiology, vol. 85, no. 1, pp. 35–41, 1998.
- T. C. Shih, P. Yuan, W. L. Lin, and H. S. Kou, “Analytical analysis of the Pennes bioheat transfer equation with sinusoidal heat flux condition on skin surface,” Medical Engineering & Physics, vol. 29, no. 9, pp. 946–953, 2007.
- P. Yuan, H. E. Liu, C. W. Chen, and H. S. Kou, “Temperature response in biological tissue by alternating heating and cooling modalities with sinusoidal temperature oscillation on the skin,” International Communications in Heat and Mass Transfer, vol. 35, no. 9, pp. 1091–1096, 2008.
- J. Liu and L. X. Xu, “Estimation of blood perfusion using phase shift in temperature response to sinusoidal heating at the skin surface,” IEEE Transactions on Biomedical Engineering, vol. 46, no. 9, pp. 1037–1043, 1999.
- I. K. Tjahjono, An analytical model for near-infrared light heating of a slab by embedded gold nanoshells [Ph.D. thesis], Rice University, 2006.
- P. Keblinski, D. G. Cahill, A. Bodapati, C. R. Sullivan, and T. A. Taton, “Limits of localized heating by electromagnetically excited nanoparticles,” Journal of Applied Physics, vol. 100, no. 5, Article ID 054305, 5 pages, 2006.
- E. Gescheidtova, R. Kubásek, and K. Bartušek, “Quality of gradient magnetic fields estimation,” Journal of EE, vol. 57, no. 8, pp. 54–57, 2006.
- M. Squibb, “A guide to experimental exposure of biological tissue to pulsed magnetic fields,” PEMF Usage Guide, 2007.
- G. C. Goats, “Pulsed electromagnetic (short-wave) energy therapy,” British Journal of Sports Medicine, vol. 23, no. 4, pp. 213–216, 1989.
- T. Niwa, Y. Takemura, N. Aida, H. Kurihara, and T. Hisa, “Implant hyperthermia resonant circuit produces heat in response to MRI unit radiofrequency pulses,” The British Journal of Radiology, vol. 81, no. 961, pp. 69–72, 2008.
- P. Cantillon-Murphy, L. L. Wald, M. Zahn, and E. Adalsteinsson, “Proposing magnetic nanoparticle hyperthermia in low-field MRI,” Concepts in Magnetic Resonance A, vol. 36, no. 1, pp. 36–47, 2010.
- S. M. Morgan and R. H. Victora, “Use of square waves incident on magnetic nanoparticles to induce magnetic hyperthermia for therapeutic cancer treatment,” Applied Physics Letters, vol. 97, no. 9, Article ID 093705, 3 pages, 2010.
- K. E. Oughstun, Electromagnetic and Optical Pulse Propagation, Springer, 2006.
- L. R. Squire and J. A. Zouzounis, “ECT and memory: brief pulse versus sine wave,” The American Journal of Psychiatry, vol. 143, no. 5, pp. 596–601, 1986.
- R. Kappiyoor, M. Liangruksa, R. Ganguly, and I. K. Puri, “The effects of magnetic nanoparticle properties on magnetic fluid hyperthermia,” Journal of Applied Physics, vol. 108, no. 9, Article ID 094702, 8 pages, 2010.
- A. Trakic, F. Liu, and S. Crozier, “Transient temperature rise in a mouse due to low-frequency regional hyperthermia,” Physics in Medicine and Biology, vol. 51, no. 7, pp. 1673–1691, 2006.
- A. O. Govorov, W. Zhang, T. Skeini, H. Richardson, E. J. Lee, and N. A. Kotov, “Gold nanoparticle ensembles as heaters and actuators: melting and collective plasmon resonances,” Nanoscale Research Letters, vol. 1, no. 1, pp. 84–90, 2006.
- O. N. Strand, “A method for the computation of the error function of a complex variable,” Mathematics of Computation, vol. 19, pp. 127–129, 1965.
- J. Kestin and L. N. Persen, “On the error function of a complex argument,” Zeitschrift für Angewandte Mathematik und Physik, vol. 7, no. 1, pp. 33–40, 1956.
- M. Kettering, J. Winter, M. Zeisberger et al., “Magnetic nanoparticles as bimodal tools in magnetically induced labelling and magnetic heating of tumour cells: an in vitro study,” Nanotechnology, vol. 18, no. 17, Article ID 175101, 9 pages, 2007.
- R. Hergt, S. Dutz, R. Müller, and M. Zeisberger, “Magnetic particle hyperthermia: nanoparticle magnetism and materials development for cancer therapy,” Journal of Physics, vol. 18, no. 38, pp. S2919–S2934, 2006.
- I. Hilger, R. Hergt, and W. A. Kaiser, “Use of magnetic nanoparticle heating in the treatment of breast cancer,” IEE Proceedings-Nanobiotechnology, vol. 152, no. 1, pp. 33–39, 2005.
- A. A. Velayati, P. Farnia, and T. A. Ibrahim, “Differences in cell wall thickness between resistant and nonresistant strains of Mycobacterium tuberculosis: using transmission electron microscopy,” Chemotherapy, vol. 55, no. 5, pp. 303–307, 2009.
- V. Dupres, Y. F. Dufreěne, and J. J. Heinisch, “Measuring cell wall thickness in living yeast cells using single molecular rulers,” American Chemical Society Nano, vol. 4, no. 9, pp. 5498–5504, 2010.
- “What is the thickness of the cell membrane?” http://www.weizmann.ac.il/plants/Milo/images/membraneThickness110109RM.pdf.
- M. Kaiser, J. Heintz, I. Kandela, and R. Albrecht, “Tumor cell death induced by membrane melting via immunotargeted, inductively heated core/shell nanoparticles,” Microscopy and Microanalysis, vol. 13, supplement 2, pp. 18–19, 2007.
- J. Vera and Y. Bayazitoglu, “Gold nanoshell density variation with laser power for induced hyperthermia,” International Journal of Heat and Mass Transfer, vol. 52, no. 3-4, pp. 564–573, 2009.
- E. I. Gabrielle, Biology The Easy Way, Barron's Educational Series, New York, NY, USA, 1990.
- B. Chan, B. D. Chithrani, A. A. Ghazani, and C. W. Warren, “Determining the size and shape dependence of gold nanoparticle uptake into mammalian cells,” Nano Letters, vol. 6, no. 4, pp. 662–668, 2006.
- Z. Yang, Z. W. Liu, R. P. Allaker et al., “A review of nanoparticle functionality and toxicity on the central nervous system,” Journal of the Royal Society Interface, vol. 7, no. 4, pp. S411–S422, 2010.
- N. Singha, G. J. S. Jenkinsa, R. Asadib, and S. H. Doaka, “Potential toxicity of superparamagnetic iron oxide nanoparticles,” Nano Reviews, vol. 1, pp. 1–15, 2010.
- H. Huang, Magnetic nanoparticles based magnetophresis for efficient separation of foodborne pathogenes [M.S. thesis], University of Arkansa, 2009.
- M. P. Melancon, W. Lu, Z. Yang et al., “In vitro and in vivo targeting of hollow gold nanoshells directed at epidermal growth factor receptor for photothermal ablation therapy,” Molecular Cancer Therapeutics, vol. 7, no. 6, pp. 1730–1739, 2008.
- P. H. Linh, N. C. Thuan, N. A. Tuan et al., “Invitro toxicity test and searching the possibility of cancer cell line extermination by magnetic heating with using Fe3O4 magnetic fluid,” Journal of Physics, vol. 187, no. 1, Article ID 012008, 9 pages, 2009.
- S. Balivada, R. S. Rachakatla, H. Wang et al., “A/C magnetic hyperthermia of melanoma mediated by iron(0)/iron oxide core/shell magnetic nanoparticles: a mouse study,” Bio Med Centeral Cancer, vol. 10, article 119, 9 pages, 2010.
- S. Bedanta and W. Kleemann, “Supermagnetism,” Journal of Physics D, vol. 42, no. 1, Article ID 013001, 28 pages, 2009.
- M. Lewin, N. Carlesso, C. H. Tung et al., “Tat peptide-derivatized magnetic nanoparticles allow in vivo tracking and recovery of progenitor cells,” Nature Biotechnology, vol. 18, no. 4, pp. 410–414, 2000.
- S. Purushotham and R. V. Ramanujan, “Modeling the performance of magnetic nanoparticles in multimodal cancer therapy,” Journal of Applied Physics, vol. 107, no. 11, Article ID 114701, 9 pages, 2010.
- J. S. Walker, Encyclopedia of Physical Science and Technology, Elsevier Science, 3th edition, 2003.
- S. W. Smith, The Scientist and Engineer's Guide to Digital Signal Processing, chapter 13, California Technical Publishing, 1997.
- J. Pellicer-Porres, R. Lacomba-Perales, J. Ruiz-Fuertes, D. Martínez-García, and M. V. Andrés, “Force characterization of eddy currents,” American Journal of Physics, vol. 74, no. 4, pp. 267–271, 2006.