## 2 Materials and Methods
### Inductive Moderate Hyperthermia  
IMH was delivered with an experimental prototype of the MagTherm medical device (Radmir, Kharkiv, Ukraine) at 42 MHz frequency and 20 W power. IMH was localized to the tumor region of sarcoma-bearing animals using an applicator composed of a loop and ferromagnetic dipoles (NCI, Kyiv, Ukraine) with adjustable size, allowing us to fit and irradiate the entire tumor in a more personalized manner [25]. Preliminary work showed that the intensity of the magnetic and electric components depended on the number and size of magnetic dipoles in the applicator and the distance between them. The choice of this set can be beneficial in acting on viable and proliferating cells predominantly located on the tumor periphery [26], as more pronounced heating is observed adjacent to the applicator rather than in the center of its loop [27]. Treatment consisted of 5 IMH sessions of 15 min each delivered every other day starting on day 2 post tumor cell implantation. Tumor-bearing animals were anesthetized with 1-2% isoflurane and immobilized in the prone position for all treatment procedures. The maximum temperatures in the tumor were \(\leq\)36.1 \({}^{\circ}\)C in the control group and \(\sim\)39 \({}^{\circ}\)C during IMH sessions, as measured by TM-4 fiber optical thermometers (Radmir, Ukraine).  
In order to find the optimal treatment plan, IMH was modeled in COMSOL Multiphysics v. 5.6 (COMSOL AB, Stockholm, Sweden) by coupling the AC/DC and heat transfer modules. Circular regions of interest (ROIs) encompassing the tumor core, periphery and capsule were generated based on the average size of intratumoral and peritumoral ROIs typically selected in radiation treatment planning [28; 29]. The model integrated tissue properties (density, heat capacity, thermal and electrical conductivity and relative permittivity) taken from [30; 31; 32; 33] using the finite element method. Figure 1 and Table 1 display the distribution of the specific absorption rate (SAR) and temperature as well as the maximum values for different tumor ROIs in response to IMH. While the maximum value of SAR is computed for the tumor core ROI, the capsule ROI has the highest temperature due to its proximity to the applicator [34]. Optimal SAR values are designed to balance effective tumor treatment while minimizing thermal damage to surrounding healthy tissues. The human basal metabolic rate is above 1 W/kg [35]. In general, temperatures \(\sim\)42 \({}^{\circ}\)C in the tumor and surrounding tissues are close to the pain threshold induced by heat in human tissues [36]; therefore, a slightly lower temperature, around 39 \({}^{\circ}\)C, may produce better outcomes minimizing pain caused by heating.  
The obtained simulations illustrate that SAR distribution was not uniform within the tumor. Several reasons may explain this: (1) the loop applicator itself forms a nonuniform field geometry with a strong electric component in the near field region; (2) the intratumor  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Tumor Core** & **Tumor Periphery** & **Tumor Capsule** \\ \hline Specific absorption rate, W/kg & 4.5 & 4.1 & 2.9 \\ Temperature, \({}^{\circ}\)C & 38.9 & 39.0 & 39.1 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Maximum values of IMH parameters in sarcoma-45.  
heterogeneity of tissue architecture; (3) the intertumor heterogeneity between individual animals [37]. Morphological changes, such as tumor necrosis, also influence SAR owing to increased tissue electrical conductivity [38]. For the same reasons, we did not find a direct relationship between the nonuniformity of SAR distribution and heterogeneity of tumor ROIs in MRI scans.