## 3 Results and Discussion
### The Specific Loss Power in the Linear Approximation
#### 3.3.1 Maximum Specific Loss Power
However, under these conditions, there's still another matter that should be verified in order to be able to support without a doubt the versatility of the superparamagnetic hyperthermia with CoFe\({}_{2}\)O\({}_{4}\) nanoparticles, namely, if the power is significantly lower in the case of CoFe\({}_{2}\)O\({}_{4}\) nanoparticles compared to that obtained for Fe\({}_{3}\)O\({}_{4}\) nanoparticles would be sufficient to heat CoFe\({}_{2}\)O\({}_{4}\) nanoparticles to the optimum temperature of 43 \({}^{\circ}\)C used in hyperthermia for the effective destruction of tumor cells. This issue is presented and discussed in the next section. Heating Characteristics and Optimum Heating Time in the Case of Superparamagnetic Hyperthermia with CoFe\({}_{2}\)O\({}_{4}\) Nanoparticles  
Using Equation (8) where the specific loss power P\({}_{\text{s}}\) is given by Equation (2) or (7) depending on the magnetic field used (as we have shown above), with the quantities \(\xi_{\text{v}}\), \(\chi_{\text{i}}\) and \(\tau\) given by Equations (3), (5) and (6), we calculated the variation of the heating temperature (\(\Delta\)T\({}_{\text{h}}\)) of the CoFe\({}_{2}\)O\({}_{4}\) nanoparticles and the heating time (\(\Delta\)t\({}_{\text{o}}\)) to reach the optimal heating temperature (T\({}_{\text{o}}\)) of -43 \({}^{\circ}\)C required in magnetic hyperthermia of cancer. In the calculations we took into account the room temperature (T\({}_{\text{r}}\)) of 25 \({}^{\circ}\)C as the initial temperature at which the nanoparticles are found. In order to reach the optimum temperature (T\({}_{\text{o}}\)) of 43 \({}^{\circ}\)C it would be necessary to increase the heating temperature (\(\Delta\)T\({}_{\text{ho}}\)) by 18 \({}^{\circ}\)C compared to the room temperature (T\({}_{\text{o}}\) = T\({}_{\text{r}}\) + \(\Delta\)T\({}_{\text{ho}}\)). At the same time, we took into account in the calculations the dependence of the parameters in Equations (3), (5) and (6) on the temperature increase above the room temperature. Thus, we calculated the variation (increase) of the heating temperature \(\Delta\)T\({}_{\text{h}}\) starting from the room temperature T\({}_{\text{r}}\) (25 \({}^{\circ}\)C). This increase must be at least 18 \({}^{\circ}\)C in order to reach the optimum temperature T\({}_{\text{o}}\) of 43 \({}^{\circ}\)C.  
The results obtained for the magnetic field of 5 kA/m and 60 kA/m (the limits of the optimal range) in optimal conditions, and within the admissible biological limit (according to the values in Table 3) are shown in Figure 9. The results show that in both cases a \(\Delta\)T\({}_{\text{h}}\) increase of the temperature is obtained by more than 18 \({}^{\circ}\)C above the room temperature (25 \({}^{\circ}\)C), thus reaching the optimal temperature of 43 \({}^{\circ}\)C for both values of the magnetic field. For example, in the case of the magnetic field of 5 kA/m (Figure 9a) the temperature \(\Delta\)T\({}_{\text{ho}}\) increased by 18 \({}^{\circ}\)C more than the room temperature and takes place in the \(\Delta\)t\({}_{\text{o}}\) time interval of 5.01 s. The maximum heating temperature variation (\(\Delta\)T\({}_{\text{hm}}\)) of 42.43 \({}^{\circ}\)C is reached after time interval \(\Delta\)t\({}_{\text{m}}\) of 23.63 s. However, if the magnetic field has a high value of 60 kA/m (Figure 9b) the temperature variation of 18 \({}^{\circ}\)C is obtained faster, in a shorter period of time (\(\Delta\)t\({}_{\text{o}}\)) of only 0.35 s, and the maximum heating temperature (\(\Delta\)T\({}_{\text{hm}}\)) in this case is lower, being 26.74 \({}^{\circ}\)C compared to 42.43 \({}^{\circ}\)C as in the previous case, a value that is reached in a period of time (\(\Delta\)t\({}_{\text{m}}\)) of only 0.92 s.  
Thus, when the magnetic field increases to 60 kA/m a significant reduction in the heating time of the nanoparticles is obtained, approx. 14 times lower, which is greatly advantageous in terms of the hyperthermic effect (heating must be done in the shortest possible time so as not to affect healthy cells).