## 4 Conclusions  
This study investigated changes in sarcoma-45 growth kinetics and intratumor heterogeneity evaluated using MRI, US and histology images that occur following IMH treatment.  
IMH resulted in a 34% inhibition of sarcoma-45 growth kinetics and changes in intratumor heterogeneity across tissue, cellular and molecular levels, as compared with tumor-bearing animals receiving no treatment in the control group (\(p<0.05\)). We found that tumor core, periphery and capsule ROIs displayed an average of a 42% increase in image brightness on T\({}_{2}\)-weighted MRI scans and a 37% increase in Young's modulus measured by US elastography in response to IMH. Due to the inherent differences in physical and technical principles underlying acquisition, the observed changes in [PERSON]'s index values did not follow one particular direction from the control group in all the imaging techniques. On average, the calculations of [PERSON]'s index indicated a 22% increase in image heterogeneity of all tumor ROIs on MRI in the IMH group, while there was a 31% and 14% decrease in heterogeneity of core and periphery ROIs on US elastography. This indicates a complex interplay between spatial heterogeneity patterns of tissue fluid content and biomechanical properties in response to IMH. The results of histological examination demonstrated more extensive areas of necrosis, lower expression of Ki-67 protein in the tumor periphery and more pronounced connective tissue replacement across all tumor regions after IMH than in the control group. Comparison of [PERSON]'s index values in histology and immunohistochemistry images showed a 21% and 25% decrease in image heterogeneity of all tumor regions and Ki-67 protein distribution, respectively. Whereas heterogeneity analysis revealed distinctions between all tumor ROIs on MRI, US and histology images in the untreated animals, there was no significant difference between core and periphery after treatment with IMH. In principle, we propose that the obtained results can be explained in terms of changes in electrostatic interactions of biopolymers and the surrounding media under the influence of the applied radiofrequency electromagnetic field, which translate into different patterns of intratumor heterogeneity at the molecular, cellular and tissue levels. This quantitative characterization contributes to a further understanding of IMH effects on different manifestations of intratumor heterogeneity using experimental imaging data. Future work should address the clinical application of image heterogeneity analysis to guide theranostic technology in IMH for sarcoma patients.  
Conceptualization, V.E.O. and V.B.O.; methodology, O.Y.D., O.Y.R., V.B.O. and L.M.K.; software, V.B.O., O.Y.R., K.S.M. and O.S.S.; validation, V.E.O., O.Y.G., A.G.D. and V.V.O.; formal analysis, V.B.O., K.S.M. and O.S.S.; investigation, V.B.O., O.Y.D., V.E.O. and L.M.K.; resources, V.E.O., A.G.D. and V.V.O.; data curation, V.B.O.; writing--original draft preparation, V.B.O. and V.E.O.; writing--review and editing, V.E.O. and V.B.O.; visualization, V.B.O. and L.M.K.; supervision, V.E.O. and O.Y.G.; project administration, V.E.O., A.G.D. and V.V.O.; funding acquisition, V.E.O., A.G.D. and V.V.O. All authors have read and agreed to the published version of the manuscript.  
This research was partially funded by the Ministry of Health of Ukraine to develop a method of antitumor therapy of primary malignant bone tumors based on magnetochemical technology using nanocomplexes (code BH.14.01.07.204-23, registration number 0123U100711).  
The animal study protocol was approved by the Institutional Ethics Committee of the National Cancer Institute of Ukraine (protocol code No. 211/6, approved on 21 June 2022).  
Not applicable.  
The data presented in this study are available on request from the corresponding author.  
The authors thank [PERSON] and [PERSON] for providing excellent technical assistance for this study.  
The authors declare no conflicts of interest.