## 3 Results and Discussion
### The Specific Loss Power in the Linear Approximation
#### 3.3.1 Maximum Specific Loss Power
The identified values are shown in Figure 3:3  
The dependence of the maximum specific loss power (P\({}_{\rm{SM}}\))\({}_{\rm{h}}\) in the admissible biological limit (Equation (13)) as a function of the amplitude of magnetic field (H) is shown in Figure 3:4 The mean values of the function (P\({}_{\rm{SM}}\))\({}_{\rm{i}}\) are shown in figure by the red fit curve, and the predict limits interval is shown by the light blue color. While analyzing this dependence, it was observed that, in the case of CoFe\({}_{2}\)O\({}_{4}\) nanoparticles, the maximum specific loss power (P\({}_{\rm{SM}}\))\({}_{\rm{i}}\) increases proportionally with the increase of the magnetic field up to 90-100 kA/m. Above these values, the maximum specific loss power tends towards saturation. Therefore, exploring different values for the magnetic field higher than 100 kA/m is not recommended for practical use, at least for two reasons: (i) the power gain is reduced more and more as the field increases, decreasing its efficiency, and (ii) obtaining large magnetic fields at frequencies in the order of hundreds of kHz is difficult to achieve in  
Figure 3:5 The variation of maximum specific loss power within the admissible biological limits (P\({}_{\rm{SM}}\))\({}_{\rm{h}}\) as a function of the magnetic field H in the case of CoFe\({}_{2}\)O\({}_{4}\) nanoparticles. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**No.** & **H (kA/m)** & **f\({}_{\rm{I}}\) (kHz)** & **D\({}_{\rm{o}}\) (nm)** & **(P\({}_{\rm{SM}}\)) (W/g)** \\ \hline
1 & 5 & 1000 & 5.88 & 2.69 (+0.48) \\
2 & 15 & 334 & 6.25 & 9.73 (+0.43) \\
3 & 30 & 167 & 6.46 & 21.26 (+0.15) \\
4 & 45 & 111 & 6.58 & 32.70 (+0.02) \\
5 & 60 & 83 & 6.67 & 43.36 (+0.07) \\
6 & 75 & 67 & 6.72 & 53.43 (\(-0.30\)) \\
7 & 90 & 56 & 6.77 & 62.04 (\(-0.40\)) \\
8 & 100 & 50 & 6.80 & 66.46 (+0.14) \\
9 & 120 & 42 & 6.84 & 75.19 (\(-0.31\)) \\
10 & 135 & 37 & 6.88 & 79.50 (+0.27) \\
11 & 150 & 33 & 6.91 & 82.87 (+0.80) \\
12 & 165 & 30 & 6.93 & 86.27 (+0.47) \\
13 & 180 & 28 & 6.95 & 89.99 (\(-0.89\)) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The values of maximum specific loss power (P\({}_{\rm{SM}}\))\({}_{\rm{h}}\) for the optimal diameter (D\({}_{\rm{o}}\)) of CoFe\({}_{2}\)O\({}_{4}\) nanoparticles at the admissible biological limit for the parameters of magnetic field H and f\({}_{\rm{I}}\) (the limit frequency) resulting from the condition given by Equation (13). practice. In addition, considering the results from Section 3.3.2 and even Section 3.3.1, we recommend the use of a magnetic field up to the maximum limit of 60 kA/m, respectively in the range 5-60 kA/m. This is the optimal range, shown by the green color in Table 3, which can be used with maximum efficiency in the case of superparamagnetic hyperthermia with CoFe\({}_{2}\)O\({}_{4}\) ferrimagnetic nanoparticles. The optimal values corresponding to the diameter of the magnetic nanoparticles D\({}_{\text{op}}\) and the limit frequency of the magnetic field f\({}_{\text{l}}\) are given in Table 3.  
Comparing these results with those obtained in the case of magnetite nanoparticles [53], having 10-25 kA/m for the amplitude of the magnetic field and 200-500 kHz for the frequency, we find that in the case of CoFe\({}_{2}\)O\({}_{4}\) nanoparticles we've achieved a much wider range for both the magnetic field and frequency, respectively 5-60 kA/m and 83-1000 kHz. This is of great practical advantage, as having a very wide range of values for the magnetic field and frequency in which superparamagnetic hyperthermia can be efficiently obtained for nanoparticles with sizes in the range 5.88-6.67 nm. Such a major advantage of the CoFe\({}_{2}\)O\({}_{4}\) nanoparticles together with obtaining intracellular hyperthermia due to the very small sizes of these nanoparticles can make the superparamagnetic hyperthermia with CoFe\({}_{2}\)O\({}_{4}\) ferrite nanoparticles more versatile than the one with Fe\({}_{3}\)O\({}_{4}\) nanoparticles, although the latter has been mostly used so far in cancer therapy.