Hyperthermic cancer treatments have been used for many years, particularly in anticancer therapy 1. However, efficiency of the treatment did not satisfy in the clinical scene, because of its difficulty of raising the objective tissue temperature properly 2. There Magnetic Fluid Hyperthermia (MFH), by using the magnetite (Fe₃O₄) as a preferable heating source, due to its strong magnetic property and low toxicity, is a promising approach for treating cancer 3. MFH can raise the temperature in the tumor locally up to 41–46°C if magnetic fluid was selectively introduced and therefore kill tumor cells directory without damages of ambient healthy cells. In this technique, magnetite particles that have ferromagnetic or superparamagnetic property are dispersed into the aqueous phase and introduced into tumor cells. In our previous study, magnetite nanopaticles covered with the cationic liposome (magnetite cationic liposomes, MCLs) to show higher adhesion properties to the cell surfaces that is charged negatively 456. In previous animal studies, we have demonstrated the efficacy of hyperthermia induce using MCLs in several types of tumor model; for instance, B16 melanoma in mice 78, T9 glioma in rats 69, osteosarcoma in hamsters 10, prostate cancer in mice 11 and MM46 mouse mammary carcinoma 12. magnetite cationic liposomes (MCLs) Introduced magnetite particles transform the energy of the AC magnetic field into heat by several physical mechanisms, and its efficacy strongly depends on the frequency of the outer field as well as the particle's magnetic properties correlated to its diameter 313.

In our present study, we drew attention to the specific-surface area (SSA) as an represented mediator for expressing particle size and microscopic structure. The SARs of those magnetic particles were studied under several conditions of AC magnetic field or strength of the power and the frequency were changed. Here, SAR is defined as the energy amount converted into heat per unit time and unit mass.

In the present study, 13 magnetic nanoparticles that are various diameters of the same materials Fe₃O₄ were precisely prepared by the same way and SAR was measured under various AC frequency and AC power. Such summarized data have been firstly reported by us in the present paper. To the best of our knowledge, it was firstly found that SSA is better index for SAR.

From polydespersity index of DLS listed in Table 1 and TEM photographs, it was found that there was not any particle with extremely wide size distribution. Therefore, it is considerable that there are different degree of aggregates and different packing density of aggregate, because large SSA was obtained even in samples with similar DLS diameter. It is considerable that samples with high packing density behave as a multidomain particle and higher saturated magnetization was obtained.

In Fig. 4, we showed the SARs of the magnetite particles which were measured under variable AMF conditions. There were two local maximum values of the SAR observed when the SARs were plotted against to the SSAs, which were approximately 90 m²/g (a) and 120 m²/g (b) separately in all the experimental intensities of AC magnetic fields.

It has been reported that the SAR of magnetite particles in an external AC magnetic field can be attributed to two kinds of power loss mechanisms; one is hysteresis loss and others is relaxation loss 161718. The grade of these two power losses depends on the particle sizes. The heating due to hysteresis losses are caused by magnetic domain wall displacements under an AC magnetic field. Therefore, it has been reported that the hysteresis loss induced heating needs larger size of magnetic multidomain particles. On the other hand, heating induced by relaxation loss under an AC magnetic field occur to smaller particles that has not domain wall and consists of the single domain structure 18.

The SAR values for the particles below the dividing line which exist around 110 m²/g of SSA seemed more susceptible against to the power of AC magnetic field in all frequencies as well. As shown in Fig. 5, it was found that heat generation by two processes was found against SSA. It is strongly suggested that these are happened by clearly different mechanism for heat generation. It is likely that those are relaxation loss and hysteresis loss, respectively, although we could not mention the reason why local maximum is 120 m²/g and that was not the smallest SSA in the particles. More profound discussion might be revealed by further experiment. From Table 1, it was found that saturated magnetization was strongly correlated with SSA. In the hysteresis loss, SAR is defined by the area of hysteresis curve. This might be one of the reasons why SSA is better index for SAR, although the reason why saturated magnetization is correlated with SSA still remains to be elucidated.

Since the heating mechanism of the magnetite nanoparticles of different SSA have different attributions from the intensity of AMF, it is considerably needed to optimize the particle SSA for the treatment of MFH. As shown in Fig. 5, the diagram of SAR of the sample K, which has larger SSA, was maintained virtually constant against to the power of AMF in all range of its frequency (Slopes are closed to 0). Therefore for the MFH treatment, when the magnetite particles those have more than 110 m²/g of SSA and less than 10 nm of particle diameter are used as the heating mediator, we expect the stable supply of heat could be performed imperviously to the power of AMF.

Comparably, smaller SSA particles generates heat linearly against the strength of the AMF (Slopes in Table 3 are large). That is to say, smaller SSA particles seem to be suited for treating various region of the body part for the MFH treatment because the SAR curve for the smaller SSA particles are adjustable and easily increased linearly by manipulating the power of AMF. In addition the dose of the smaller SSA particles possibly could be hold down when the high-power of AMF are applicable for treatment. It would be also able to heat deep portion of the body part sufficiently by controlling higher dose of the magnetic particles or intensity of the AMF power.

As for the AMF frequency, it should be noted that lower ones within the range of 50 kHz to 100 kHz of AMF are recommended for human therapy depending on the body cross-section and tissue conductivity 714. When we use smaller SSA particles, we could overcome the disadvantage of smaller frequency of the AMF by controlling the intensity of power of the AMF.

Our group is now planning to the application to actual cancer patients. SSA and AC frequency was one of the important criteria for magnetite particle preparation. Actual apparatus for cancer patient was already designed and fabricated, that is AC frequency of 110 kHz. Sample C or D was applicable to actual cancer treatment.

In the present study, we observed collateral evidence that the SAR of the magnetite nanoparticles in an external AMF are induced by two heating mechanisms that depends on the SSA of the particles. The critical change of the SAR value was observed at approximately 110 m²/g of the SSA which exists among the 10 nm diameter particles. This is likely due to the structure change of magnetic domain. Additionally, we suggested that heating property of these two mechanisms is defined under the different influences of the frequency and the power of the AC magnetic field.

In conclusion, we provided the basic data for selection of the magnetite particles for the MFH treatment along with the treating part of the body or purpose of the treatment, and we suggested that for the selection of the particles, SSA could be one of the good criteria.

The authors declare that they have no competing interests.

All authors contributed equally to the manuscript. All authors have made a significant contribution to this manuscript, and all authors read and approved the final manuscript.