# A Computational Study on Magnetic Nanoparticles Hyperthermia of Ellipsoidal Tumors
## 4 Comparison with Experiments  
In the present section, the computational model is compared with three sets of experimental measurements by different researchers. The first comparison is with the experimental measurements by [PERSON] et al. [86]. In their work, the tumor was a squamous cell carcinoma on the cervical lymph node of female Japanese white rabbits. According to [86], the ratio of the volume of the cancerous lymph node to that of normal lymph nodes was approximately 11 (cancerous lymph node volume 1161 \(\pm\) 276.4 mm\({}^{3}\), normal lymph node volume 105.6 \(\pm\) 43.37 mm\({}^{3}\)). Twenty days after tumor transplantation, magnetite nanoparticles, of average core magnetite size \(D\) = 10 nm, were injected from the rabbit tongue. The average nanoparticle uptake from the cancerous lymph was approximately 4 mg \(\pm\) 1 mg. For the hyperthermia treatment, a transistor inverter was used with frequency 118 kHz and magnetic field strength of 384 Oe or 30.6 kA/m. From a histological section of the swollen lymph, we approximated the tumor shape with a prolate spheroid that we fitted on top of the tumor. Two tumor-shaped approximations are considered as shown in Figure 11a,b. In Case A we find AR \(\approx\) 1.8, and for case B, AR \(\approx\) 2.2. Inserting the tumor volume value in Equation (4) we calculate \(a\approx\) 5.1 mm and from Equation (2) we find \(b\approx\) 9.18 mm for Case A. In Case B we find \(a\approx\) 4.78 mm and \(b\approx\) 10.44 mm. From the values reported by [PERSON] et al. [86] and using [PERSON]'s theory (Equations (8)-(14)) we find the heat dissipated by the nanoparticles equal to 2.1 \(\times\) 10\({}^{5}\) W/m\({}^{3}\). For the blood perfusion we use 1.3 \(\times\) 10\({}^{-3}\) s\({}^{-1}\) within the range of earlier works [92; 93; 63; 94]. The treatment temperature simulation results, for Case A and Case B, are shown in Figure 11c,d, respectively. For the 4 mg dosage, the predictions are in qualitative agreement with the temperature measurements by [PERSON] et al. [86]. Some small differences are observed between the numerical result of Case A and Case B, with Case A being slightly closer to the measurements. It should be pointed it out that [PERSON] et al. [86] report that the 4 mg nanoparticle uptake from the cancerous lymph has approximately \(\pm\)1 mg uncertainty in the measurement. Interestingly, if we use a 5 mg dosage for Case A and Case B our results are in better agreement with the experimental temperature measurements by [PERSON] et al. [86]. Figure 10: Thermal damage in three tumor shapes and for a healthy tissue region close to the tumor after 22 min of treatment: (**a**) AR = 1, (**b**) prolate with AR = 2 and (**c**) oblate with AR = 2. Subsequently, the computational model predictions are compared with experimental measurements and with 3D computational results by [PERSON] et al. [92] for murine mammary adenocarcinoma tumors. The tumor volume was 329 mm\({}^{3}\) and was heated for 600 s. In their work, iron oxide nanoparticles (IONP) of 10-20 nm in diameter were. The IONNPs were exposed to magnetic field strengths between 20 and 50 kA/m (rms) at 162 kHz. [PERSON] et al. [92] report that the transient temperature was recorded at a location called \"center\" and another location separated by 3 mm, called \"tip\". They also mention that the center probe location was placed as close as possible to the approximate center of the tumor. A redrawn histologic section of the tumor in [PERSON] et al. [92] is shown in Figure 12. As in the previous experimental comparison, we approximated the tumor shape with a prolate spheroid that we fitted on top of the tumor. Two tumor shape approximations were considered, as shown in Figure 12a,b. For Case A we found AR \(\approx\) 1.29 and for case B, AR \(\approx\) 1.6. We then found \(a\approx\) 3.9 mm and \(b\approx\) 5.1 mm for Case A and for Case B we find \(a\approx\) 3.6 mm and \(b\approx\) 5.8 mm.