Russian Physics Journal, Vol. 50, No. 9, 2007
MAGNETIC INDUCTION HYPERTHERMIA UDC 621.318
V. N. Nikiforov
A review of physical principles and experimental data on magnetic hyperthermia are presented. The main principles of magnetic hyperthermia are considered. Results of its application in the therapy of oncology diseases are presented. 1. PHYSICAL PRINCIPLES OF HYPERTHERMIA
Two components of ac electromagnetic fields E and H can cause heating of tissues. Based on the Maxwell equations and thermodynamic relations, not only the electrocaloric effect, namely, the heat absorption in substance caused by the electric field component E [6], but also the magnetocaloric effect caused by variations in H can be calculated. These effects are mainly determined by the dielectric (ε and δε/δТ) and magnetic (μ) properties of substances, respectively. Because magnetism of biological objects is negligibly small, biologically compatible nontoxic magnetic nanoparticles (based on magnetite and so on) are used to strengthen the influence of an external magnetic field. Thermodynamic relations for a magnet in a magnetic field are similar to those for a dielectric in an electric field [6]. However, an essential difference is that the magnetic field, unlike the electric field, does no work on charges moving in it, because the Lorentz force is perpendicular to the velocity vector of the moving charge. To calculate a change in the energy of the medium when the magnetic field is switched on, electric fields induced by magnetic field variations should be considered. In their turn, high-frequency electromagnetic fields cause heating due to the electric field component. At low frequencies, this effect is insignificant. At the same time, the role of the magnetic field component in magnet heating is significant only at low frequencies [6]. Therefore, inclusion of electromagnetic induction hyperthermia in a separate class of high-frequency phenomena [1], on the one hand, and of magnetic hyperthermia as a low-frequency influence, on the other hand, though relative, is justified. Low-frequency (less than 100 kHz) electromagnetic fields can cause heating of magnetic nanoparticles at the expense of the magnetocaloric effect [7], magnetic reversal in the presence of a hysteresis loop, and magnetic crystal anisotropy of superparamagnetic particles. Physics of the magnetocaloric effect of this phenomenon is the following: elementary magnetic moments are directed chaotically without magnetic field, and hence the magnetic contribution to the entropy is significant. As the magnetic field increases, the magnetic moments are ordered along the field. As a result, the magnetic entropy component SM decreases. Because the magnetization process is close to adiabatic one, the total entropy S does not change, but the entropy component caused by thermal motion increases. Thus, the ferromagnet temperature increases with the magnetic field. Quantitatively, the temperature change is calculated from the formula T ΔT = −ΔH
( dM dT ) S
CH
H
.
From the above formula it follows that the temperature can raise when the magnetic moment МS changes with temperature, since the heat capacity C is always positive. The magnetocaloric effect of ferrites weakens significantly at
M. V. Lomonosov Moscow State University; e-mail:
[email protected]. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 60–72, September, 2007. Original article submitted December 28, 2006. 1064-8887/07/5009-0913 ©2007 Springer Science+Business Media, Inc.
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temperatures above the Curie point TC because the magnetic moment sharply decreases. It is well known that a ferromagnet placed in an ac magnetic field is heated. The thermal effect during magnetic reversal of the magnet is proportional to the area of the hysteresis loop in B, Н coordinates. Superparamagnetic gels based on single-domain particles with sizes less than 8–10 nm have recently been used for hyperthermia. The thermal effect of magnetic reversal of particles is not connected with the hysteresis phenomena, because no domain system is present; it is caused by the energy change accompanying the magnetic moment rotation, that is, by the magnetic crystal anisotropy. Induction heating of tumors in vivo in an ac magnetic field is performed at frequencies, as a rule, below 200 kHz [8] with the help of preliminary implanted ferrite nanoparticles. The choice of the working frequency is determined by physiological properties of the electromagnetic field of this frequency, magnetic susceptibility, and ferrite particle sizes. Heating occurs due to losses in the hysteresis loop [9]. It should be noted that when sizes of ferromagnetic particles decrease, they transform to the superparamagnetic state; in this case, the heating mechanisms are caused by the magnetic crystal anisotropy. Ferromagnetic materials are heated well at rather low frequencies
