# A Computational Study on Magnetic Nanoparticles Hyperthermia of Ellipsoidal Tumors
## 4 Comparison with Experiments
The experimental temperature measurements close to the tumor center (probe location center) and about 3 mm from the tumor center (probe location tip), are shown in Figure 12c,f. According to [PERSON] et al. [92], the value of heat generated by the nanoparticles was \"..._adjusted somewhat until the experiment maximum transient temperature (or steady state) temperature record from the embedded probes was closely approximated by the numerical model result._\". They also report that the same approach was followed for the blood perfusion: \"_...adjusted to improve match to the measurements..._\". The numerical results given by [92] are shown in Figure 12 with broken lines. The adjusted by [PERSON] et al. [92] value for the generated heat by the nanoparticles was \(1.1\times 10^{6}\) W/m\({}^{3}\). For the adjusted perfusion, according to [PERSON] et al. [92], the initial tumor perfusion, 3 \(\times\) 10\({}^{-3}\) s\({}^{-1}\) was increased to as much as 7 \(\times\) 10\({}^{-3}\) s\({}^{-1}\), as required to match experimental results. If we follow the [PERSON] et al. [92] approach of adjusting the heat generated and the perfusion rate we find good agreement with the measurements for the probe location center, as shown in Figure 12c (Case A), using the values of 1.75 \(\times\) 10\({}^{6}\) W/m\({}^{3}\) and 2.5 \(\times\) 10\({}^{-3}\) s\({}^{-1}\). It should be pointed out that at \(t\) = 0 we have used the experimentally measured temperature (32 \({}^{\circ}\)C), while in the numerical model in [92] a higher temperature of approximately 36 \({}^{\circ}\)C was assumed by [PERSON] et al. [92], without providing an explanation for this choice. This perhaps  
Figure 11: Two cases approximating the tumor shape from a histological cross-section by [PERSON] et al. [86], with a prolate spheroid. Note that the tumor histological cross-section has been redrawn from the original: (**a**) prolate spheroid shape, case A with AR \(\approx\) 1.8, on top of the redrawn tumor and (**b**) prolate spheroid shape, case B with AR \(\approx\) 2.2, on top of the redrawn tumor. Plots (**c**,**d**) show parametric comparison of the numerically determined temperature at the tumor center with the measured temperature by [86]. Temperature data points and bars are mean values and standard deviation respectively of 5 independent experiments. explains the differences between our adjusted values with the ones by [PERSON] et al. [92]. Good agreement with the measured temperature and our model is also observed for the tip location, seen in Figure 12e, while in the prediction by [PERSON] et al. [92], the computational model gives higher temperatures than the experiment at this location. For the tumor geometry of Case B, we use the adjusted heat generated and blood perfusion values from Case A and compare our predictions with the experiments in Figure 12d (center location) and Figure 12f (tip location). Of course, due to the larger AR of the tumor than in Case A, the maximum temperatures are somewhat lower but reasonably close to the measurements. Unfortunately, due to the large range of two simultaneous parameters, namely, the nanoparticle diameter (10 to 20 nm) and the applied magnetic field (20 to 50 kA/m) reported in [PERSON] et al. [92], we could not apply [PERSON]'s theory as we did for [PERSON] et al. [86]. Subsequently, we compared the cumulative equivalent minutes at 43 \({}^{\circ}\)C (CEM43) of our model with the CEM43 measurements and model predictions reported by [PERSON] et al. [92]. According to [PERSON] et al. [92], the CEM43 in discrete interval form is written as  
\[\text{CEM43}=\sum_{i=1}^{N}R_{\text{CEM}}{}^{(43-T_{i})}\Delta t_{i} \tag{16}\]  
where \(R_{\text{CEM}}\) is the time scaling ratio, 43 \({}^{\circ}\)C is the reference temperature and \(\Delta t_{i}\) (min) is spent at temperature \(T_{i}\) (\({}^{\circ}\)C). In their work \(R_{\text{CEM}}\) = 0.45 was chosen. Using Equation (16) for our model predictions in Figure 12 we obtain CEM43 values close to the calculated by [PERSON] et al.