## 3 Results and Discussion
### Ultrasound Imaging Evaluation of Intratumor Sarcoma-45 Heterogeneity
As shown in Table 4, core ROIs had the lowest values of [PERSON]'s modulus, which occurs due to necrosis formation in the later stages of tumor growth [57]. On the other hand, tumor capsule ROIs displayed the highest values of Young's modulus. The stiffness of core, periphery and capsule ROIs was 1.8-fold, 1.3-fold and 1.9-fold higher in the IMH group than in the control group, respectively. Also, IMH led to a 31% and 14% reduction in heterogeneity within tumor core and periphery ROIs as determined by higher Moran's index (\(p<0.05\)). Greater heterogeneity was noted in the capsule ROIs on both US and MRI scans. These results mirror previous findings, wherein high T\({}_{2}\) values on MRI positively correlated with tissue stiffness on US shear wave elastography [58]. Nevertheless, the relationship between imaging features extracted from US and MRI scans cannot be unambiguously summarized owing to the different underlying physical and technical principles of image acquisition. In agreement with previous observations [59], the mean blood flow velocity measured using Doppler US in the most proximal vessel adjacent to the tumor capsule (9.87 \(\pm\) 0.18 cm/s) was nearly three times as much as that of the skeletal muscle vasculature in the intact hindlimb of a healthy rat (3.13 \(\pm\) 0.03 cm/s). We found a 21% decrease in the flow velocity in response to IMH, given that the last treatment session was delivered 14 days earlier. Vessels surrounding the tumor in the IMH group possessed a 35% higher resistive index than those in the control group (\(p<0.05\), Table 5). This is likely to be explained by vascular damage, compression and increased resistance under the conditions of higher tumor stiffness (Table 4) [60]. In addition, a continuous wavelet transform analysis was applied to characterize changes in blood flow waveforms between the groups. Comparing Figure 5a,b note two higher energy bands around scales 70 and 200-225 as well as a lower energy band around scales 250-300 in the IMH group, which reflect changes in cardiac effects within the 2-6 Hz frequency range on vessel blood flow [61; 62]. Wavelet energy distribution in the IMH group tended to have lower average energy (2.4 \(\pm\) 1.3), skewness (0.3) and kurtosis (2.9) values than the control group (energy--2.7 \(\pm\) 1.9, skewness--1.0; kurtosis--4.1). We cannot exclude the possibility that these results are related to the influence of radiofrequency electromagnetic fields on the cardiovascular system [63; 64]. Similar to tumor capsule ROIs in US elastography images, [PERSON]'s index of obtained wavelet transform scalograms decreased in animals exposed to IMH (0.87 \(\pm\) 0.005 a.u.) in comparison to those undergoing no treatment (0.91 \(\pm\) 0.003 a.u., \(p<0.05\)), presumably indicating the relationship between spatial heterogeneity of tumor stiffness and vasculature. Sarcomas are stiffer than normal muscle or adipose tissues, the biomechanical properties of which are routinely visualized using US elastography [65]. Activation of cancer-associated fibroblasts and tumor-associated macrophages in the local microenvironment during tumor progression stimulates collagen accumulation, overexpression and cross-linking, resulting in increased stiffness and heterogeneous patterns of the extracellular matrix organization [66; 67; 68]. As tumors grow, the cells are eventually exposed to a greater \begin{table}
\begin{tabular}{c c c} \hline
**Region of Interest** & **Control Group** & **IMH Group** \\ \hline  & [PERSON]’s modulus, kPa & \\ \hline Tumor core & 35.1 \(\pm\) 2.3 & 61.5 \(\pm\) 2.5 a  \\ Tumor periphery & 0.42 \(\pm\) 0.01 * & 0.49 \(\pm\) 0.01 b  \\ Tumor capsule & 0.38 \(\pm\) 0.01 ** & 0.29 \(\pm\) 0.01 ** \\ \hline \end{tabular}
\end{table} 
Table 4: Sarcoma-45 stiffness and heterogeneity in US scans, M \(\pm\) m.  
degree of mechanical compression, also referred to as solid stress. Importantly, the nonuniformity of solid stress distribution plays a role in mechanochemical transduction signals that regulate cell division and death.