| Summary: | <b> </b>The cancer therapy with the lowest possible toxicity is today an issue that raises major difficulties in treating malignant tumors because chemo- and radiotherapy currently used in this field have a high degree of toxicity and in many cases are ineffective. Therefore, alternative solutions are rapidly being sought in cancer therapy, in order to increase efficacy and a reduce or even eliminate toxicity to the body. One of the alternative methods that researchers believe may be the method of the future in cancer therapy is superparamagnetic hyperthermia (SPMHT), because it can be effective in completely destroying tumors while maintaining low toxicity or even without toxicity on the healthy tissues. Superparamagnetic hyperthermia uses the natural thermal effect in the destruction of cancer cells, obtained as a result of the phenomenon of superparamagnetic relaxation of the magnetic nanoparticles (SPMNPs) introduced into the tumor; SPMNPs can heat the cancer cells to 42–43 °C under the action of an external alternating magnetic field with frequency in the range of hundreds of kHz. However, the effectiveness of this alternative method depends very much on finding the optimal conditions in which this method must be applied during the treatment of cancer. In addition to the type of magnetic nanoparticles, and the biocompatibility with the biological tissue or nanoparticles biofunctionalization that must be appropriate for the intended purpose, a key parameter is the size of the nanoparticles. Also, establishing the appropriate parameters for the external alternating magnetic field (AMF), respectively the amplitude and frequency of the magnetic field are very important in the efficiency and effectiveness of the magnetic hyperthermia method. This paper presents a 3D computational study on specific loss power (Ps) and heating temperature (∆T) which allows establishing the optimal conditions that lead to efficient heating of Fe<sub>3</sub>O<sub>4</sub> nanoparticles, which were found to be the most suitable for use in superparamagnetic hyperthermia (SPMHT), as a non-invasive and alternative technique to chemo- and radiotherapy. The size (diameter) of the nanoparticles (D), the amplitude of the magnetic field (H) and the frequency (f) of AMF were established in order to obtain maximum efficiency in SPMHT and rapid heating of magnetic nanoparticles at the required temperature of 42–43 °C for irreversible destruction of tumors, without affecting healthy tissues. Also, an analysis on the amplitude of the AMF is presented, and how its amplitude influences the power loss and, implicitly, the heating temperature, observables necessary in SPMHT for the efficient destruction of tumor cells. Following our 3D study, we found for Fe<sub>3</sub>O<sub>4</sub> nanoparticles the optimal<i> </i>diameter of ~16 nm, the optimal range for the amplitude of the magnetic field of 10–25 kA/m and the optimal frequency within the biologically permissible limit in the range of 200–500 kHz. Under the optimal conditions determined for the nanoparticle diameter of 16.3 nm, the magnetic field of 15 kA/m and the frequency of 334 kHz, the magnetite nanoparticles can be quickly heated to obtain the maximum<i> </i>hyperthermic effect on the tumor cells: in only 4.1–4.3 s the temperature reaches 42–43 °C, required in magnetic hyperthermia, with major benefits in practical application in vitro and in vivo, and later in clinical trials.
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