## 3 Results and Discussion
### Histological Image Evaluation of Intratumor Sarcoma-45 Heterogeneity
During mitosis, Ki-67 is enriched on the surface of chromosomes, where it serves as a positively charged electrostatic coating against aggregation of chromosome arms and ensures symmetric distribution of nucleolar components in daughter cells. After mitosis, the protein moves to the nucleolar periphery to assist heterochromatin compaction [79]. The transition from symmetrical to asymmetrical charge distributions on the macroion surface in complex colloidal systems can considerably modify the electrostatic interactions from repulsion to attraction [80]. It is not without interest to note that the amplitude of an electrostatic field around protein filaments was calculated to exert forces on the order of pN [81] and, even more, protein-protein (1-10 pN) and antigen-antibody (10-100 pN) interactions typically require mechanical forces of the same order of magnitude [82]. Both of these interactions are related to the structural complementarity of one protein molecule with another as a result of numerous conformational state transitions occurring through the direct transformation of chemical energy into mechanical work in such mechanochemical systems [83]. The electrostatic interactions thus play an important role in mechanochemical effects underlying the formation and heterogeneity of collagen fibrils and Ki-67 domains [84; 85]. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Feature** & \multicolumn{3}{c}{**Control Group**} & \multicolumn{3}{c}{**IMH Group**} \\ \hline  & **Core** & **Periphery** & **Capsule** & **Core** & **Periphery** & **Capsule** \\ \hline necrosis & 1 & 1 & 1 & 1 & 2 & 1 \\ apoptosis & 2 & 2 & 0 & 1 & 1 & 0 \\ connective tissue replacement & 1 & 0 & 0 & 3 & 3 & 2 \\ \hline Total & 4 & 3 & 1 & 5 & 6 & 3 \\ \hline \hline Scores: 0—not observed; 1—mid; 2—moderate; 3—severe. & & & & & \\ \end{tabular}
\end{table} 
Table 6: Histological analysis of sarcoma-45. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Region of Interest** & **Control Group** & **IMH Group** \\ \hline  & Cellular level & \\ \hline Tumor core & 0.49 \(\pm\) 0.01 & 0.73 \(\pm\) 0.01 1  \\ Tumor periphery & 0.61 \(\pm\) 0.01 2  \\ Tumor capsule & 0.51 \(\pm\) 0.01 3  \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Sarcoma-45 heterogeneity (Moran’s I, a.u.) in histological images, M \(\pm\) m.  
When exposed to radiofrequency electromagnetic fields in the MHz range (i.e., the polarization contribution to dielectric constant is higher than dielectric loss), the rotation of polar and charged side groups in a protein, as well as the orientation of the surrounding water molecules and ions along the applied field direction, can initiate changes in electrostatic interactions and the cross-linking of proteins [86]. For instance, applying a 300 MHz electromagnetic field initiated stronger electrostatic interactions in proteins by nearly 9% and, at the same time, limited their interactions with the surrounding water by 31% on average, leading to a more compact conformational state [87]. Therefore, we propose that the observed effects of IMH on sarcoma-45 can be interpreted in terms of changes in the symmetry of charge distribution and electrostatic interactions in biopolymers and the surrounding media under the influence of the applied field, which translate into patterns of intratumor heterogeneity at the molecular, cellular and tissue levels. Such quantitative characterization of intratumor heterogeneity is valuable for guiding theranostic technology in regional hyperthermia for sarcoma patients [88]. Further research should assess the role of intratumor heterogeneity in image-guided IMH for sarcoma patients in a clinical setting.