Magnetic hyperthermia

Magnetic hyperthermia is the ever-promising "fourth leg" of cancer treatment.^[1] This thermotherapy is based on the fact that magnetic nanoparticles can transform electromagnetic energy from an external high-frequency field to heat. As a consequence, if magnetic nanoparticles are put inside a tumor and the whole patient is placed in an alternating magnetic field of well-chosen amplitude and frequency, only the tumor temperature would rise. The elevation of temperature may enhance tumor oxygenation and radio- and chemosensitivity, thus shrinking tumors.^[2] As well, this experimental cancer treatment has also been investigated for the aid of other ailments, such as bacterial infections. The technique is also of great value in many other applications from drug-delivery in medicine to the polymer industry.^[3]

Numerous clinical trials worldwide have studied hyperthermia in combination with radiation therapy and/or chemotherapy. But up to now only the company MagForce AG has received EU-wide regulatory approval for treatment of brain tumors.^[4] Active research is done to test and develop this technique further. The benefits of the application of a nanotechnological approach, as compared to conventional treatments, are expected to be accompanied by a direct health service cost reduction and improvement of the quality of life of the patients.

Generalities and definition

The different requirements composing the magnetic hyperthermia trilemma.^[5]

Many magnetic materials display a magnetic hysteresis when subjected to a magnetic field that alternates direction. The area enclosed in this hysteresis cycle represents the irreversible work, which is dissipated in the environment as thermal energy. This heat is very undesirable in many industrial applications, though it turns profitable in magnetic hyperthermia. This power is often called the "Specific Absorption Rate" (SAR) and it is usually expressed in watts per gram of nanoparticles. For a given material is then simply SAR = Af, where A is the area of the hysteresis loop and f the sweeping frequency of the magnetic field. A is expressed in J/g and is also called the "specific losses" of the material. Note that this expression for SAR is a definition; the difficulty lies in finding A. Indeed, as is explained in more detail below, A depends non-trivially on all the properties of the magnetic nanoparticles, including their effective magnetic anisotropy K (which comprises the magnetocrystalline anisotropy but also other contributions such as shape, strain, surface, etc.), their volume V, the temperature T, the frequency of the magnetic field f, its amplitude H_max, and on the concentration of the nanoparticles.^[6] Those intimately entwined ingredients can be summarized in a hyperthermia trilemma, similarly to the issues encountered in magnetic recording.^[7]

Influence of nanoparticle size on their domain structure

The size of nanoparticles influences their magnetic domains. Small enough nanoparticles are composed of a single magnetic domain. Larger particles are composed of multiple domains because this minimizes the magnetostatic energy. At intermediate sizes, they may display a magnetic structure called vortex. A rough approximation to determine the size above which a magnetic nanoparticles is not single-domain any more is when its size is above the typical domain wall dimension in the magnetic material, which ranges from a few to a few tens of nanometers.^[8][9] The nature of the domain structure has a profound influence on the hysteresis of the magnetic nanoparticles and, as a consequence, on their hyperthermia properties.

Basic mechanisms involved in the magnetization reversal of magnetic single-domain nanoparticles

Reversal by Brownian motion

In hyperthermia application, the nanoparticles are in a fluid, the blood. During in vitro hyperthermia measurements they are generally dispersed in a liquid and form a ferrofluid. They move and rotate randomly in the fluid, a phenomenon called Brownian motion. When a magnetic field is applied to them, magnetic nanoparticles rotate and progressively align with the magnetic field due to the torque generated by the interaction of the magnetic field with the magnetization. This is similar to a compass. The delay between the magnetic field reversal and the one of the magnetization leads to an hysteresis.

Reversal by thermal activation

The magnetization of tiny nanoparticles can spontaneously change of orientation under the influence of thermal energy, a phenomenon called superparamagnetism. The magnetization oscillate between its two equilibrium positions. The typical time between two orientation changes is given by the Néel relaxation time $\tau_N = \tau_0 e^{\frac{K V}{k_B T}}$, where $\tau_0$ is an attempt time with a value around 10⁻⁹–10⁻¹⁰ seconds. But when it comes to hyperthermia applications, true description of magnetic behaviour is not unique; for instance, a so-called "superparamagentic" particle at room temperature and quasi-static conditions may change into dissipation hysteresis at high frequencies.

Reversal by the suppression of the anisotropy barrier by a magnetic field

The magnetization of the nanoparticle is also reversed when an applied magnetic field is large enough to suppress the energy barrier between the two equilibrium positions, a phenomenon which is known as the Stoner–Wohlfarth model of magnetization reversal.

Combination of the three mechanisms

In the most general case, the reversal of the magnetization is due to a combination of the three mechanisms described above. For instance, for a single domain nanoparticle is inside a fluid at room temperature and that a sweeping magnetic field is suddenly applied with a direction opposite to the one of the nanoparticle magnetization. The nanoparticle will at the same time i) rotate in the fluid ii) the barrier between the two equilibrium positions of the magnetization will decrease iii) when the energy barrier becomes of the order of the thermal energy, the magnetization will switch (if the nanoparticle is not already align with the magnetic field due to its physical rotation). There is no simple analytical expression describing this reversal and the properties of the hysteresis loop in this very general case but numerical simulations and analytical expressions can be used in some cases.^[6]

Models to be used for single-domain nanoparticles

The linear response theory

The linear response theory is only valid when the response of the magnetic material is linear with the applied magnetic field and can be thus written under the form $M=\chi H$, where $\chi$ is the complex susceptibility of the material. It is thus valid when the applied magnetic field is much smaller than the magnetic field needed to saturate the magnetization of the nanoparticle. It is able to take into account both the reversal by thermal activation and the reversal by Brownian motion.
The linear response theory uses an average relaxation time $\tau$, given by $\frac{1}{\tau} = \frac{1}{\tau_B} + \frac{1}{\tau_N}$. The out of phase component of complex susceptibility is then given by $\chi '' = \frac{\mu_0 M_S^2 V}{3 k_B T} \frac{2 \pi f \tau}{1+(2 \pi f \tau)^2}$. The hysteresis loop is then an ellipse with an area given by $A = \pi \mu_0 H^2 \chi ''$.

The Stoner–Wohlfarth model and the maximum area

The Stoner–Wohlfarth model allows one to calculate the hysteresis loop of magnetic nanoparticles at T=0 with the assumption that the nanoparticles are fixed in the magnetic field (the Brownian motion is neglected) and magnetically independent. Its main interest is to predict the maximum hysteresis area for independent nanoparticles with given properties. Indeed, the addition of thermal energy or Brownian motion only leads to a decrease of the hysteresis loop area (see below).
The Stoner–Wohlfarth model predicts that the coercive field at T=0 of an assembly of nanoparticles with randomly oriented axes is given by $H_C(0) = \frac{K}{M_S}$. The area of the hysteresis is approximatively $A = 2\mu_0 M_S H_C(0)$.

Extension of the Stoner–Wohlfarth model to include temperature and frequency

Extensions of the Stoner–Wohlfarth model have been done to include the influence of the temperature and frequency on the hysteresis loop. They allow to calculate hysteresis area in a rather large range of parameters.^[6]

Basic mechanisms involved in the magnetization of magnetic multi-domain nanoparticles

In multi-domain nanoparticles the basic ingredients to describe the magnetization reversal are the nucleation of new domains and the propagation of domain walls. Both mechanisms are strongly influenced by the structural defects at the surface or inside the nanoparticles and make difficult any quantitative prediction of the hysteresis loops shape and area from intrinsic parameters of the magnetic nanoparticles.

Models to be used for multi-domain nanoparticles

At low magnetic field, the hysteresis loop is expected to be a Rayleigh loop. In this case, the hysteresis area is $A = \frac{4}{3} \eta H^3$, where $\eta$ is the Rayleigh constant.

Measuring hyperthermia: in vitro experiments

Producing a high frequency magnetic field

Two basic means to produce the high frequency field necessary to study hyperthermia can be used: the coil and the electromagnet. For the "coil" way, a very simple method to get the high frequency magnetic field is to use an induction furnace, which precisely used a high-frequency magnetic field to heat materials. It is however conceived to work at a single frequency and requires a water cooling system. It is also possible to build electromagnets or coils able to work at various frequencies at the condition to use variable capacitors.^[10] It is also possible to get rid of the cooling system in coils at the condition to build them with Litz wire.^[10]

Measuring the temperature and artefacts

A platinum or semi-conductor resistance thermometer in a high-frequency magnetic field is self-heated and leads to erroneous temperature measurements. Temperature measurements in hyperthermia can be made using alcohol thermometer, optic fiber thermometers, infrared cameras, or differential heating measurements using traditional semiconductor-based sensing elements.
A colloidal solution heated by an external magnetic field will be subject to convection phenomena so the temperature inside the calorimeter is not homogeneous. Shaking of the colloidal solutions at the end of a measurement or average on several temperature probes can ensure a more accurate temperature measurement.

Materials for magnetic hyperthermia

Iron oxide nanoparticles

The most widely used magnetic nanoparticles for hyperthermia consists in iron oxide nanoparticles. Similar nanoparticles are used as MRI contrast agent. They are in the context of MRI called "Superparamagnetic Iron Oxide Nanoparticles", or SPION. The main interest of these nanoparticles are their biocompatibility and their stability with respect to oxidation. The nanoparticles displaying the largest hysteresis area so far are the ones synthesized by magnetotactic bacteria,^[11] with A = 2.3 mJ/g although man-made particles are reaching values above A = 1.5 mJ/g.^[12]

The continuous efforts to increase SAR and to reduce the dose of nanoparticles to be administered, treatment duration as well as side-effects, lead to a plethora of research on the nanoparticle nature (stoichiometry, morphology, size,...)^[13] As mentioned above, the SAR depends on the area of the hysteresis loop. Thus, naively the magnetic hysteresis losses scale with the so-called magnetic anisotropy constant, K. Therefore, increasing the K of the ferrite particles leads to an increase of the SAR, as exemplified by Lee et al.^[14] in exchange-biased core-shell nanoparticles. Efforts to enhance the heating performance of iron oxides may draw inspiration from the success of nature; for instance, another approach is the tuning of the effective K by the assembling of particles into chains replicating magnetosomes.^[15] Though, the large anisotropy implies that very large fields are required to switch the particles’ magnetization, which leads again to the trilemma mentioned above. In this regard, a limit for the product of H x f was discussed in the 80’s based on patient discomfort.^[16] Therefore, most of the times pre-clinical research has been limited to the kHz range, although the seminal results by Gilchrist et al.^[17] in the 1950s where reported at the microwave region, and that promising protocols are being conducted at industrial, scientific and medical (ISM) radio bands, specially the 13.56 MHz.^[18]

Metallic nanoparticles

Alternatively, the higher magnetization of metallic nanoparticles of Co, Fe or FeCo compared to iron oxides increases the maximum SAR values which can be reached using them in hyperthermia applications. A = 1.5 mJ/g has been reported for FeCo nanoparticles,^[19] A = 3.25 mJ/g for Co nanoparticles^[20] and A=5.6 mJ/g for Fe nanoparticles.^[21] The main issue with respect to metallic nanoparticles concerns their protection against oxidation and their eventual toxicity. Thus, new synthetic approaches include the formation of biocompatible core-shell type particles, comprising multilayered carbon,^[22] oxides,^[23] or even noble metals.^[24]

Ex vivo experiments

Ex vivo experiments in hyperthermia require to make tumor cells absorb magnetic nanoparticles, to place them into an alternative magnetic field and to test their survival rate compared to tumor cells which would follow the same protocol but would not absorb magnetic nanoparticles.

In vivo experiments

Clinical trials

The only hyperthermia setup suitable to treat humans has been developed at the Charité Medical School, Clinic of Radiation Therapy in Berlin.^[25] Andreas Jordan's team in this hospital has performed clinical trials on patients with prostate cancers.^[26] The clinical trial showed that hyperthermia followed by radiotherapy provided a median survival time of 13.4 months in 59 patients with glioblastoma, which is very high compared with 6.2 months survival for patients in a control group.^[27]

See also

• Experimental cancer treatment
• Magnetic nanoparticles
• Ferrofluid

References

1. Roussakow, Sergey (2013-07-28). "The History of Hyperthermia Rise and Decline". Conference Papers in Medicine 2013: 1–40. doi:10.1155/2013/428027.
2. Kumar, Challa S. S. R.; Mohammad, Faruq (2011-08-14). "Magnetic nanomaterials for hyperthermia-based therapy and controlled drug delivery". Advanced Drug Delivery Reviews. Layer-by-Layer Self-Assembled Nanoshells for Drug Delivery 63 (9): 789–808. doi:10.1016/j.addr.2011.03.008. PMC 3138885. PMID 21447363.
3. Mohr, R.; Kratz, K.; Weigel, T.; Lucka-Gabor, M.; Moneke, M.; Lendlein, A. (2006-03-07). "Initiation of shape-memory effect by inductive heating of magnetic nanoparticles in thermoplastic polymers". Proceedings of the National Academy of Sciences of the United States of America 103 (10): 3540–3545. doi:10.1073/pnas.0600079103. ISSN 0027-8424. PMC 1383650. PMID 16537442.
4. "MagForce AG – Home". www.magforce.de. Retrieved 2015-11-12.
5. Conde-Leboran, Ivan; Baldomir, Daniel; Martinez-Boubeta, Carlos; Chubykalo-Fesenko, Oksana; del Puerto Morales, María; Salas, Gorka; Cabrera, David; Camarero, Julio; Teran, Francisco J. (2015-07-09). "A Single Picture Explains Diversity of Hyperthermia Response of Magnetic Nanoparticles". The Journal of Physical Chemistry C 119 (27): 15698–15706. doi:10.1021/acs.jpcc.5b02555. ISSN 1932-7447.
6. J. Carrey, B. Mehdaoui, M. Respaud, J. Appl. Phys. 109, 083921 (2011).
7. Weller, D.; Moser, Andreas (1999-11-01). "Thermal effect limits in ultrahigh-density magnetic recording". IEEE Transactions on Magnetics 35 (6): 4423–4439. doi:10.1109/20.809134. ISSN 0018-9464.
8. Levi, Shaul; Merrill, Ronald T. (1978-01-10). "Properties of single-domain, pseudo-single-domain, and multidomain magnetite". Journal of Geophysical Research: Solid Earth 83 (B1): 309–323. doi:10.1029/JB083iB01p00309. ISSN 2156-2202.
9. Peddis, Davide; Cannas, Carla; Musinu, Anna; Piccaluga, Giorgio (2009-08-10). "Magnetism in Nanoparticles: Beyond the Effect of Particle Size". Chemistry – A European Journal 15 (32): 7822–7829. doi:10.1002/chem.200802513. ISSN 1521-3765.
10. L.-M. Lacroix, J. Carrey and M. Respaud, Rev. Sci. Instr. 79, 093909 (2008). http://arxiv.org/abs/0806.3005
11. R. Hergt, R. Hiergeist, M. Zeisberger, D. Schüler, U. Heyen, I. Hilger and W. A. Kaiser, J. Magn. Magn. Mater. 293, 80 (2005).
12. R. Hergt, R. Hiergeist, I. Hilger, W. A. Kaiser, Y. Lapatnikov, S. Margel and U. Richter, J. Magn. Magn. Mater. 270, 345 (2004).
13. Armijo, L.M.; Brandt, Y.I.; Mathew, D.; Yadav, S.; Maestas, S.; Rivera, A.C.; Cook, N.C.; Withers, N.J.; Smolyakov, G.A.; Adolphi, N.L.; Monson, T.C.; Huber, D.L.; Smyth, H.D.C.; Osiński, M. Iron Oxide Nanocrystals for Magnetic Hyperthermia Applications. Nanomaterials 2012, 2, 134-146
14. Lee, Jae-Hyun; Jang, Jung-tak; Choi, Jin-sil; Moon, Seung Ho; Noh, Seung-hyun; Kim, Ji-wook; Kim, Jin-Gyu; Kim, Il-Sun; Park, Kook In. "Exchange-coupled magnetic nanoparticles for efficient heat induction". Nature Nanotechnology 6 (7): 418–422. doi:10.1038/nnano.2011.95.
15. Martinez-Boubeta, Carlos; Simeonidis, Konstantinos; Makridis, Antonios; Angelakeris, Makis; Iglesias, Oscar; Guardia, Pablo; Cabot, Andreu; Yedra, Lluis; Estradé, Sonia (2013-04-11). "Learning from Nature to Improve the Heat Generation of Iron-Oxide Nanoparticles for Magnetic Hyperthermia Applications". Scientific Reports 3. doi:10.1038/srep01652. PMC 3622918. PMID 23576006.
16. Atkinson, William J.; Brezovich, Ivan A.; Chakraborty, Dev P. (1984-01-01). "Usable Frequencies in Hyperthermia with Thermal Seeds". IEEE Transactions on Biomedical Engineering. BME-31 (1): 70–75. doi:10.1109/TBME.1984.325372. ISSN 0018-9294.
17. Gilchrist, R. K.; Medal, Richard; Shorey, William D.; Hanselman, Russell C.; Parrott, John C.; Taylor, C. Bruce (1957-10-01). "Selective Inductive Heating of Lymph Nodes". Annals of Surgery 146 (4): 596–606. ISSN 0003-4932. PMC 1450524. PMID 13470751.
18. Postnikov, Andrei; Moldosanov, Kamil (2015-08-04). "Phonon-assisted radiofrequency absorption by gold nanoparticles resulting in hyperthermia". arXiv:1508.00735.
19. L.-M. Lacroix, R. Bel Malaki,J. Carrey, S. Lachaize, M. Respaud, G. F. Goya and B. Chaudret, J. Appl. Phys. 105, 023911 (2009), http://arxiv.org/abs/0810.4109
20. M. Zeisberger, S. Dutz, R. Müller, R. Hergt, N. Matoussevitch, and H.Bönneman, J. Magn. Magn. Mater. 311, 224 (2005)
21. B. Mehdaoui, A. Meffre, L.-M. Lacroix, J. Carrey, S. Lachaize, M. Respaud, M. Gougeon, B. Chaudret, http://arxiv.org/abs/0907.4063
22. Seo, Won Seok; Lee, Jin Hyung; Sun, Xiaoming; Suzuki, Yoriyasu; Mann, David; Liu, Zhuang; Terashima, Masahiro; Yang, Philip C.; McConnell, Michael V. "FeCo/graphitic-shell nanocrystals as advanced magnetic-resonance-imaging and near-infrared agents". Nature Materials 5 (12): 971–976. doi:10.1038/nmat1775.
23. Martinez-Boubeta, Carlos; Balcells, Lluis; Cristòfol, Rosa; Sanfeliu, Coral; Rodríguez, Elisenda; Weissleder, Ralph; Lope-Piedrafita, Silvia; Simeonidis, Konstantinos; Angelakeris, Makis. "Self-assembled multifunctional Fe/MgO nanospheres for magnetic resonance imaging and hyperthermia". Nanomedicine: Nanotechnology, Biology and Medicine 6 (2): 362–370. doi:10.1016/j.nano.2009.09.003.
24. Xu, Yun-Hao; Wang, Jian-Ping (2007-12-03). "FeCo–Au core-shell nanocrystals". Applied Physics Letters 91 (23): 233107. doi:10.1063/1.2823574. ISSN 0003-6951.
25. A. Jordan et al., J. Magn. Magn. Mater. 225, 118 (2001). http://vpd.ms.northwestern.edu/Publications_files/Lei/JMMM_225_118_2001.pdf
26. M. Johannsen et al., Int. J. of Hyperthermia 21, 637 (2005). http://www.anamacap.fr/telechargement/hyperthermie-vo.pdf
27. Maier-Hauff, K. (2011). "Efficacy and safety of intratumoral thermotherapy using magnetic iron-oxide nanoparticles combined with external beam radiotherapy on patients with recurrent glioblastoma multiforme". J. Neurooncol 103: 317–324. doi:10.1007/s11060-010-0389-0.

External links

• Hyperthermia - Cancer therapy hots up article on physics.org