Towards a theory of magnetic hyperthermia: effect of immobilized chain-like aggregates
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part of Springer Nature, 2020 https://doi.org/10.1140/epjst/e2020-000054-1
THE EUROPEAN PHYSICAL JOURNAL SPECIAL TOPICS
Regular Article
Towards a theory of magnetic hyperthermia: effect of immobilized chain-like aggregates A.F. Abu-Bakr1,2,a , and A.Yu. Zubarev2,3 1
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Mathematics and Computer Science Department, Faculty of Science, Menoufia University, Shebin El-Kom 32511, Egypt Theoretical and Mathematical Physics Department, Institute of Natural Sciences and Mathematics, Ural Federal University, Lenin Avenue 51, Ekaterinburg 620083, Russia M.N. Mikheev Institute of Metal Physics of the Ural Branch of the Russian Academy of Sciences, Ekaterinburg, Russia Received 2 April 2020 / Accepted 9 September 2020 Published online 19 November 2020 Abstract. We present results of theoretical approach and mathematical modeling of magnetic hyperthermia produced by aggregates of ferromagnetic nanoparticles immobilized in a non-liquid carrier medium. It is supposed that the particles, due to their magnetic either disperse interaction, can form linear chain-like clusters. The mathematical model of kinetics of the particles remagnetization is formulated and solved for the cases of the single particles as well as for two- and threeparticles chains. The limiting cases of the strong and weak internal magnetic anisotropy of the nanoparticles are considered. The results show that the chain-like aggregates reduce the heat production in the case of the strong magnetic anisotropy of the particles and enhances that in the opposite case of the weak anisotropy.
1 Introduction Magnetic hyperthermia (MH) plays a vital role in the cancer therapy [1–7]. The key idea of this method is injection of a magnetic fluid, consisting of ferro- or ferrimagnetic nanoparticles, covered by special bio-active layers, into a region with the tumor. Due to these layers, the particles are captured be the tumor cells. Applied alternating magnetic field induces heating of the particles, therefore, of the cells. If the tumor cell temperature exceeds some threshold value, usually estimated as 42 ◦ C, the cell dies because of protein denaturation. At the same time, the health cells are more temperature resistable and survive up to temperature about ten degree higher. This is the point of the therapy effect. As a rule, the iron-oxide (magnetite or maghemite) nanoparticle is utilized at the medical application of the magnetic hyperthermia [8,9]. First of all, they are not toxic. Secondly, they are relatively cheap and have magnetic moment sufficient for the necessary reaction to applied magnetic fields of quite moderate strength, easily a
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The European Physical Journal Special Topics
Fig. 1. Sketch of the ferro-nanoparticles: (a) single ferro-nanoparticles; (b) two ferronanoparticles clusters; (c) chain-like clusters of the three ferro-nanoparticles. Hex is applied field. Solid arrows show the moments of ferro-nanoparticles.
achievable in clinical conditions and acceptable from the viewpoint of the human physiology. This is wel
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