Optimization of proton therapy with radiosensitizing nanoparticles and antiangiogenic therapy via mathematical modeling

Kuznetsov M.B., Kolobov A.V.
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Optimization of antitumor radiotherapy represents an urgent issue, as approximately half of the patients diagnosed with cancer undergo radiotherapy during their treatment. Proton therapy is potentially more efficient than traditional X-ray radiotherapy due to fundamental differences in physics of dose deposition, leading to better targeting of tumors and less collateral damage to healthy tissue. There is increasing interest in the use of non-radioactive radiosensitizing tumor-specific nanoparticles the use of which can boost the performance of proton therapy. Such nanoparticles are small volumes of a sensitizer, such as boron-10 or various metal oxides, enclosed in a polymer layer containing tumor-specific antibodies, which allows for their targeted delivery to malignant cells. Furthermore, a combination of proton therapy with antiangiogenic therapy that normalizes tumor-associated microvasculature may yield further synergistic increase in overall treatment efficacy.

We have developed a spatially distributed mathematical model simulating the growth of a non-invasive tumor undergoing treatment by fractionated proton therapy with nanosensitizers and antiangiogenic therapy. The modeling results suggest that the most effective way to combine these treatment modalities should strongly depend on the tumor cells’ proliferation rate and their intrinsic radiosensitivity. Namely, a combination of antiangiogenic therapy with proton therapy, regardless of whether radiosensitizing nanoparticles are used, benefits treatment efficacy of rapidly growing tumors as well as radioresistant tumors with moderate growth rate. In these cases, administration of proton therapy simultaneously with antiangiogenic drugs after the initial single injection of nanosensitizers is the most effective option among those analyzed. Conversely, for slowly growing tumors, maximization of the number of nanosensitizer injections without antiangiogenic therapy proves to be a more efficient option, with enhancement in treatment efficacy growing with the increase of tumor radiosensitivity. However, the results also show that the overall efficacy of proton therapy is likely to increase only modestly with the addition of nanosensitizers and antiangiogenic drugs.

Keywords: mathematical oncology, numerical optimization
Citation in English: Kuznetsov M.B., Kolobov A.V. Optimization of proton therapy with radiosensitizing nanoparticles and antiangiogenic therapy via mathematical modeling // Computer Research and Modeling, 2025, vol. 17, no. 4, pp. 697-715
Citation in English: Kuznetsov M.B., Kolobov A.V. Optimization of proton therapy with radiosensitizing nanoparticles and antiangiogenic therapy via mathematical modeling // Computer Research and Modeling, 2025, vol. 17, no. 4, pp. 697-715
DOI: 10.20537/2076-7633-2025-17-4-697-715
URL: http://crm-en.ics.org.ru/journal/article/3637/
Creative Commons License This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License.

Copyright © 2025 Kuznetsov M.B., Kolobov A.V.

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