# Modeling the Synergistic Impact of Yttrium 90 Radioembolization and Immune Checkpoint Inhibitors on Hepatocellular Carcinoma

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Mathematical Model Overview

_{0}is the activity in the target mass of interest and ${\mathrm{T}(\mathrm{Y}90-\mathrm{R}\mathrm{E})}_{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$ is the half-life of the radioactive source. The total number of disintegrations, commonly known as cumulated activity, is equal to A

_{0}× T1/2/ln (2).

#### 2.2. Virtual Patient Cohort

^{9}times the number of tumor cells per cubic cm. The number of non-targeted tumor cells was estimated to be 0.1% ($1.07\times {10}^{8})$ of the targeted tumor volume. We calculated the average baseline number of circulating lymphocytes (5.61 × ${10}^{9}$) by multiplying the average lymphocyte counts (1122 ± 469 per ${\mathrm{m}\mathrm{m}}^{3}$) with the total body volume (5 L). The distributions of initial tumor size (${T}_{0}$), circulating lymphocytes (${L}_{0}$), and tumor radiation sensitivity (αT) are illustrated in Supplementary Figure S1.

#### 2.3. Model Fitting to Yttrium 90 Radioembolization Therapy Response Data

#### 2.4. Virtual Clinical Trial and Outcome

_{durva}) was given every 2 weeks for 2 years. We investigated the effect on treatment outcome according to the timing of the Y90-RE and ICI administration interval days. The administration interval days between Y90-RE and ICIs were evaluated from 30 days to 300 days. All five treatments are depicted schematically in Figure 2.

## 3. Results

_{durva}) varies in the range of 0.08–0.16. The color column in Figure 3A represents the median PFS, and the color column in Figure 4A shows the 3-year DM rates. According to the treatment schedules for arm B and arm C, the administration of Y90-RE and ICIs was carried out with 60 interval days for each.

_{durva}and 300 Gy of Y90-RE, the median PFS from arms A, B, and C were 21.6 months (95% CI, 20.8–22.6 mo), 19.8 months (95% CI, 18.8–20.6 mo), and 18.4 months (95% CI, 17.6–19.2 mo), respectively. For 0.12 of δ

_{durva}and 400 Gy of Y90-RE, the median PFS from arms A, B, and C were 38.4 months (95% CI, 37.2–39.2 mo), 36.5 months (95% CI, 35.3–37.5 mo), and 32.6 months (95% CI, 31.4–33.8 mo), respectively. For 0.16 of δ

_{durva}and 500 Gy of Y90-RE, the median PFS from arms A, B, and C were 56.7 months (95% CI, 55–57.7 mo), 55.9 months (95% CI, 54.2–57.1 mo), and 46.5 months (95% CI, 48.2–51.1 mo), respectively.

_{durva}and 300 Gy of Y90-RE were 83.2% (95% CI, 80.7–85.3%), 3.2% (95% CI, 2.2–4.4%), and NA. The 1-, 3-, and 5-year PFS rates from 0.12 of δ

_{durva}and 400 Gy of Y90-RE were 96.4% (95% CI, 95–97.3%), 54.9% (95% CI, 51.8–58%), and NA. The 1-, 3-, and 5-year PFS rates from 0.16 of δ

_{durva}and 500 Gy of Y90-RE were 99.9% (95% CI, 99.2–99.8%), 88.5% (95% CI, 86.2–90.2%), and 33.8% (95% CI, 30.9–36.8%).

_{durva}and 300 Gy of Y90-RE were 78.2% (95% CI, 75.6–80.7%), 2.2% (95% CI, 1.4–3.2%), and NA. The 1-, 3-, and 5-year PFS rates from 0.12 of δ

_{durva}and 400 Gy of Y90-RE were 94.7% (95% CI, 93.2–96%), 49.9% (95% CI, 46.9–53.1%), and NA. The 1-, 3-, and 5-year PFS rates from 0.16 of δ

_{durva}and 500 Gy of Y90-RE were 99.8% (95% CI, 99.2–99.8%), 85.8% (95% CI, 83.4–87.8%), and 34.1% (95% CI, 31.1–37.0%).

_{durva}and 300 Gy of Y90-RE were 74.8% (95% CI, 71.9–77.3%), 1.6% (95% CI, 0.9–2.5%), and NA. The 1-, 3-, and 5-year PFS rates from 0.12 of δ

_{durva}and 400 Gy of Y90-RE were 92.6% (95% CI, 90.7–94%), 41.2% (95% CI, 38.1–44.1%), and NA. The 1-, 3-, and 5-year PFS rates from 0.16 of δ

_{durva}and 500 Gy of Y90-RE were 99.7% (95% CI, 99.2–99.9%), 76.9% (95% CI, 74.1–79.3%), and 21.1% (95% CI, 18.6–23.6%).

_{durva}and 300 Gy of Y90-RE were 53% (95% CI, 50–56.2%), 98.9% (95% CI, 98.1–99.95%), and NA. The 1-, 3-, and 5-year DM rates from 0.12 of δ

_{durva}and 400 Gy of Y90-RE were 42.3% (95% CI, 39.4–45.5%), 79.8% (95% CI, 77.3–82.3%), and NA. The 1-, 3-, and 5-year DM rates from 0.16 of δ

_{durva}and 500 Gy of Y90-RE were 41.7% (95% CI, 38.8–44.9%), 50.2% (95% CI, 47.2–53.4%), and NA.

_{durva}and 300 Gy of Y90-RE were 59.0% (95% CI, 55.9–62.0%), 99.3% (95% CI, 98.7–99.7%), and NA. The 1-, 3-, and 5-year DM rates from 0.12 of δ

_{durva}and 400 Gy of Y90-RE were 50.4% (95% CI, 47.4–53.6%), 80.9% (95% CI, 78.6–83.4%), and NA. The 1-, 3-, and 5-year DM rates from 0.16 of δ

_{durva}and 500 Gy of Y90-RE were 49.8% (95% CI, 46.8–53.0%), 51.4% (95% CI, 48.4–54.6%), and NA.

_{durva}and 300 Gy of Y90-RE were 59.4% (95% CI, 56.3–62.4%), 99.4% (95% CI, 98.7–99.7%), and NA. The 1-, 3-, and 5-year DM rates from 0.12 of δ

_{durva}and 400 Gy of Y90-RE were 49.1% (95% CI, 46.1–52.3%), 85.2% (95% CI, 83.0–87.4%), and NA. The 1-, 3-, and 5-year DM rates from 0.16 of δ

_{durva}and 500 Gy of Y90-RE were 46.2% (95% CI, 43.2–49.4%), 62.9% (95% CI, 60.0–65.9%), and NA.

_{durva}and 300 Gy of Y90-RE), intermediate (0.12 of δ

_{durva}and 400 Gy of Y90-RE), and maximum (0.16 of δ

_{durva}and 500 Gy of Y90-RE). The model predicts substantial changes in endpoint time with different interval days. Longer interval days negatively affect the efficacy of both targeted and non-targeted tumors. For the targeted tumor, the median PFS from the intensity of minimum, intermediate, and maximum decreases up to 7.4~15.2 months, 13.6~29 months, and 8.24~45 months, respectively. For the non-targeted tumor, the cumulative DM rates at 3 years from the intensity of minimum, intermediate, and maximum increased up to 0.4~0.5%, 8.3~10.4%, and 24.1~26.1% (Supplementary Figures S5 and S6).

_{durva}and 300 Gy of Y90-RE, there were no statistically significant differences between arms A and B or arms B and C when the number of administration interval days of two drugs was less than 30 days (p < 0.25). However, the median PFS from arm A was significantly longer than that of arms B and C when the number of administration interval days of the two drugs was more than 30 days, and these three groups were significantly associated with PPS from 60 days or more (p < 0.05). Of the 0.12 of δ

_{durva}and 400 Gy of Y90-RE, there were no statistically significant differences between arms A and B when the number of administration interval days for two drugs was less than 30 days (p < 0.22). All three groups had a substantial association with PFS from 60 days or longer (p < 0.05). For the 0.16 of δ

_{durva}and 500 Gy of Y90-RE, when the interval between drug administrations was less than 60 days, no statistically significant differences were observed between arms A and B (p < 0.57). There was a significant correlation with PFS between all three groups from 90 days or longer (p < 0.05), as shown in Supplementary Figure S7.

_{durva}and 300 Gy of Y90-RE, the cumulative DM rate from arm A was considerably higher than arms B and C when the administration interval days between the two drugs exceeded 30 days (p < 0.05). However, no statistically significant differences were observed between arms B and C when the number of administration interval days of the two drugs was below 60 days (p < 0.21). The three groups were significantly related to the cumulative DM rates for 90 days or longer (p < 0.05). Using 0.12 of δ

_{durva}and 400 Gy of Y90-RE, the cumulative DM rate was similar in arms A and B when the number of administration interval days for the two drugs was below 30 days (p < 0.06). The cumulative DM rate from arm A was significantly lower than that of arms B and C when the interval of days between the two drugs was 60 days or longer (p < 0.05). Concerning the 0.16 of δ

_{durva}and 500 Gy of Y90-RE, when the interval between drug administrations was less than 90 days, no statistically significant differences were observed between arms A and B (p < 0.06). There was a significant correlation with the cumulative DM rates between all three groups from 120 days or longer (p < 0.05), as demonstrated in Supplementary Figure S8.

## 4. Discussion

_{durva}and Y90-RE increase, the point at which a statistically significant difference between arms A and B occurs in the number of interval days between two drug injections increases. Thus, to optimize the treatment outcomes, the number of interval days between the two drug injections should be reduced to a shortened duration as the two medications decrease.

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Lafaro, K.J.; Demirjian, A.N.; Pawlik, T.M. Epidemiology of Hepatocellular Carcinoma. Surg. Oncol. Clin. N. Am.
**2015**, 24, 1–17. [Google Scholar] [CrossRef] [PubMed] - European Association for the Study of the Liver. European Organisation For Research And Treatment Of Cancer. EASL-EORTC Clinical Practice Guidelines: Management of Hepatocellular Carcinoma. J. Hepatol.
**2012**, 56, 908–943. [Google Scholar] [CrossRef] [PubMed] - Yarchoan, M.; Agarwal, P.; Villanueva, A.; Rao, S.; Dawson, L.A.; Karasic, T.; Llovet, J.M.; Finn, R.S.; Groopman, J.D.; El-Serag, H.B.; et al. Recent Developments and Therapeutic Strategies against Hepatocellular Carcinoma. Cancer Res.
**2019**, 79, 4326–4330. [Google Scholar] [CrossRef] [PubMed] - Murciano-Goroff, Y.R.; Warner, A.B.; Wolchok, J.D. The Future of Cancer Immunotherapy: Microenvironment-Targeting Combinations. Cell Res.
**2020**, 30, 507–519. [Google Scholar] [CrossRef] [PubMed] - Asadian, S.; Piryaei, A.; Gheibi, N.; Aziz Kalantari, B.; Reza Davarpanah, M.; Azad, M.; Kapustina, V.; Alikhani, M.; Moghbeli Nejad, S.; Keshavarz Alikhani, H.; et al. Rhenium Perrhenate (188ReO4) Induced Apoptosis and Reduced Cancerous Phenotype in Liver Cancer Cells. Cells
**2022**, 11, 305. [Google Scholar] [CrossRef] [PubMed] - Yu, J.I.; Park, H.C. Radiotherapy as Valid Modality for Hepatocellular Carcinoma with Portal Vein Tumor Thrombosis. World J. Gastroenterol.
**2016**, 22, 6851. [Google Scholar] [CrossRef] - Nault, J.-C.; Cheng, A.-L.; Sangro, B.; Llovet, J.M. Milestones in the Pathogenesis and Management of Primary Liver Cancer. J. Hepatol.
**2020**, 72, 209–214. [Google Scholar] [CrossRef] - Ferlay, J.; Colombet, M.; Soerjomataram, I.; Parkin, D.M.; Piñeros, M.; Znaor, A.; Bray, F. Cancer Statistics for the Year 2020: An Overview. Int. J. Cancer
**2021**, 149, 778–789. [Google Scholar] [CrossRef] - Bruix, J.; Sherman, M. Management of Hepatocellular Carcinoma. Hepatology
**2005**, 42, 1208–1236. [Google Scholar] [CrossRef] - Kalbasi, A.; June, C.H.; Haas, N.; Vapiwala, N. Radiation and Immunotherapy: A Synergistic Combination. J. Clin. Investig.
**2013**, 123, 2756–2763. [Google Scholar] [CrossRef] - Okusaka, T.; Ikeda, M. Immunotherapy for hepatocellular carcinoma: Current status and future perspectives. ESMO Open
**2018**, 3 (Suppl. 1), e000455. [Google Scholar] [CrossRef] [PubMed] - Finn, R.S.; Qin, S.; Ikeda, M.; Galle, P.R.; Ducreux, M.; Kim, T.-Y.; Kudo, M.; Breder, V.; Merle, P.; Kaseb, A.O.; et al. Atezolizumab plus Bevacizumab in Unresectable Hepatocellular Carcinoma. N. Engl. J. Med.
**2020**, 382, 1894–1905. [Google Scholar] [CrossRef] [PubMed] - Cheng, A.-L.; Qin, S.; Ikeda, M.; Galle, P.R.; Ducreux, M.; Kim, T.-Y.; Lim, H.Y.; Kudo, M.; Breder, V.; Merle, P.; et al. Updated Efficacy and Safety Data from IMbrave150: Atezolizumab plus Bevacizumab vs. Sorafenib for Unresectable Hepatocellular Carcinoma. J. Hepatol.
**2021**, 76, 862–873. [Google Scholar] [CrossRef] [PubMed] - Abou-Alfa, G.K.; Lau, G.; Kudo, M.; Chan, S.L.; Kelley, R.K.; Furuse, J.; Sukeepaisarnjaroen, W.; Kang, Y.-K.; Van Dao, T.; De Toni, E.N.; et al. Tremelimumab plus Durvalumab in Unresectable Hepatocellular Carcinoma. NEJM Evid.
**2022**, 1, EVIDoa2100070. [Google Scholar] [CrossRef] - Yau, T.; Park, J.-W.; Finn, R.S.; Cheng, A.-L.; Mathurin, P.; Edeline, J.; Kudo, M.; Harding, J.J.; Merle, P.; Rosmorduc, O.; et al. Nivolumab Versus Sorafenib Treatment in Advanced Hepatocellular Carcinoma (CheckMate 459): A Randomised, Multicentre, Open-Label, Phase 3 Trial. Lancet Oncol.
**2022**, 23, 77–90. [Google Scholar] [CrossRef] [PubMed] - Rimassa, L.; Finn, R.S.; Sangro, B. Combination Immunotherapy for Hepatocellular Carcinoma. J. Hepatol.
**2023**, 79, 506–515. [Google Scholar] [CrossRef] - Di Federico, A.; Rizzo, A.; Carloni, R.; De Giglio, A.; Bruno, R.; Ricci, D.; Brandi, G. Atezolizumab-Bevacizumab plus Y-90 TARE for the Treatment of Hepatocellular Carcinoma: Preclinical Rationale and Ongoing Clinical Trials. Expert Opin. Investig. Drugs
**2021**, 31, 361–369. [Google Scholar] [CrossRef] - Zhang, Z.; Liu, X.; Chen, D.; Yu, J. Radiotherapy Combined with Immunotherapy: The Dawn of Cancer Treatment. Signal Transduct. Target. Ther.
**2022**, 7, 258. [Google Scholar] [CrossRef] - Bernstein, M.B.; Krishnan, S.; Hodge, J.W.; Chang, J.Y. Immunotherapy and Stereotactic Ablative Radiotherapy (ISABR): A Curative Approach? Nat. Rev. Clin. Oncol.
**2016**, 13, 516–524. [Google Scholar] [CrossRef] - Menon, H.; Ramapriyan, R.; Cushman, T.R.; Verma, V.; Kim, H.H.; Schoenhals, J.E.; Atalar, C.; Selek, U.; Chun, S.G.; Chang, J.Y.; et al. Role of Radiation Therapy in Modulation of the Tumor Stroma and Microenvironment. Front. Immunol.
**2019**, 10, 193. [Google Scholar] [CrossRef] - Tai, D.; Loke, K.; Gogna, A.; Kaya, N.A.; Tan, S.H.; Hennedige, T.; Ng, D.; Irani, F.; Lee, J.; Lim, J.Q.; et al. Radioembolisation with Y90-Resin Microspheres Followed by Nivolumab for Advanced Hepatocellular Carcinoma (CA 209-678): A Single Arm, Single Centre, Phase 2 Trial. Lancet Gastroenterol. Hepatol.
**2021**, 6, 1025–1035. [Google Scholar] [CrossRef] [PubMed] - de la Torre-Aláez, M.; Matilla, A.; Varela, M.; Iñarrairaegui, M.; Reig, M.; Lledó, J.L.; Arenas, J.I.; Lorente, S.; Testillano, M.; Márquez, L.; et al. Nivolumab after Selective Internal Radiation Therapy for the Treatment of Hepatocellular Carcinoma: A Phase 2, Single-Arm Study. J. ImmunoTherapy Cancer
**2022**, 10, e005457. [Google Scholar] [CrossRef] [PubMed] - Kim, K.J.; Kim, J.H.; Lee, S.J.; Lee, E.J.; Shin, E.C.; Seong, J. Radiation Improves Antitumor Effect of Immune Checkpoint Inhibitor in Murine Hepatocellular Carcinoma Model. Oncotarget
**2017**, 8, 41242. [Google Scholar] [CrossRef] [PubMed] - Wehrenberg-Klee, E.; Goyal, L.; Dugan, M.C.; Zhu, A.X.; Ganguli, S. Y-90 Radioembolization Combined with a PD-1 Inhibitor for Advanced Hepatocellular Carcinoma. Cardiovasc. Interv. Radiol.
**2018**, 41, 1799–1802. [Google Scholar] [CrossRef] - Valery, M.; Cervantes, B.; Samaha, R.; Gelli, M.; Smolenschi, C.; Fuerea, A.; Tselikas, L.; Klotz-Prieux, C.; Hollebecque, A.; Boige, V.; et al. Immunotherapy and Hepatocellular Cancer: Where Are We Now? Cancers
**2022**, 14, 4523. [Google Scholar] [CrossRef] - Chew, V.; Lee, Y.H.; Pan, L.; Nasir, N.J.; Lim, C.J.; Chua, C.; Lai, L.; Hazirah, S.N.; Lim, T.K.; Goh, B.K.; et al. Immune Activation Underlies a Sustained Clinical Response to Yttrium-90 Radioembolisation in Hepatocellular Carcinoma. Gut
**2018**, 68, 335–346. [Google Scholar] [CrossRef] - Zheng, J.; Irani, Z.; Lawrence, D.P.; Flaherty, K.T.; Arellano, R.S. Combined Effects of Yttrium-90 Transarterial Radioembolization around Immunotherapy for Hepatic Metastases from Uveal Melanoma: A Preliminary Retrospective Case Series. J. Vasc. Interv. Radiol.
**2018**, 29, 1369–1375. [Google Scholar] [CrossRef] - Salem, R.; Greten, T.F. Interventional Radiology Meets Immuno-Oncology for Hepatocellular Carcinoma. J. Hepatol.
**2022**, S0168-8278(22)03003-3. [Google Scholar] [CrossRef] - Zhan, C.; Ruohoniemi, D.M.; Shanbhogue, K.; Lee, J.; Welling, T.H.; Gu, P.; Park, J.S.; Dagher, N.N.; Taslakian, B.; Hickey, R. Safety of Combined Yttrium-90 Radioembolization and Immune Checkpoint Inhibitor Immunotherapy for Hepatocellular Carcinoma. J. Vasc. Interv. Radiol.
**2020**, 31, 25–34. [Google Scholar] [CrossRef] - Ruohoniemi, D.M.; Zhan, C.; Wei, J.; Kulkarni, K.; Aaltonen, E.T.; Horn, J.C.; Hickey, R.M.; Taslakian, B. Safety and Effectiveness of Yttrium-90 Radioembolization around the Time of Immune Checkpoint Inhibitors for Unresectable Hepatic Metastases. J. Vasc. Interv. Radiol. JVIR
**2020**, 31, 1233–1241. [Google Scholar] [CrossRef] - Sung, W.; Hong, T.S.; Poznansky, M.C.; Paganetti, H.; Grassberger, C. Mathematical Modeling to Simulate the Effect of Adding Radiation Therapy to Immunotherapy and Application to Hepatocellular Carcinoma. Int. J. Radiat. Oncol. Biol. Phys.
**2022**, 112, 1055–1062. [Google Scholar] [CrossRef] [PubMed] - Rodríguez-Pérez, D.; Sotolongo-Grau, O.; Espinosa Riquelme, R.; Sotolongo-Costa, O.; Santos Miranda, J.A.; Antoranz, J.C. Assessment of Cancer Immunotherapy Outcome in Terms of the Immune Response Time Features. Math. Med. Biol. A J. IMA
**2007**, 24, 287–300. [Google Scholar] [CrossRef] [PubMed] - Sotolongo-Costa, O.; Morales Molina, L.; Rodríguez Perez, D.; Antoranz, J.C.; Chacón Reyes, M. Behavior of Tumors under Nonstationary Therapy. Phys. D Nonlinear Phenom.
**2003**, 178, 242–253. [Google Scholar] [CrossRef] - Sotolongo-Grau, O.; Rodríguez-Pérez, D.; Santos-Miranda, J.A.; Sotolongo-Costa, O.; Antoranz, J.C. Immune System-Tumour Efficiency Ratio as a New Oncological Index for Radiotherapy Treatment Optimization. Math. Med. Biol. A J. IMA
**2009**, 26, 297–307. [Google Scholar] [CrossRef] - Loevinger, R. MIRD Primer for Absorbed Dose Calculations. Clin. Nucl. Med.
**1989**, 14, 723–724. [Google Scholar] - Dezarn, W.A.; Cessna, J.T.; DeWerd, L.A.; Feng, W.; Gates, V.L.; Halama, J.; Kennedy, A.S.; Nag, S.; Sarfaraz, M.; Sehgal, V.; et al. Recommendations of the American Association of Physicists in Medicine on Dosimetry, Imaging, and Quality Assurance Procedures for 90Y Microsphere Brachytherapy in the Treatment of Hepatic Malignancies. Med. Phys.
**2011**, 38, 4824–4845. [Google Scholar] [CrossRef] - Park, Y.; Choi, D.; Lim, H.K.; Rhim, H.; Kim, Y.-S.; Kim, S.H.; Lee, W.J. Growth Rate of New Hepatocellular Carcinoma after Percutaneous Radiofrequency Ablation: Evaluation with Multiphase CT. AJR Am. J. Roentgenol.
**2008**, 191, 215–220. [Google Scholar] [CrossRef] - Kuznetsov, V.A.; Makalkin, I.A.; Taylor, M.A.; Perelson, A.S. Nonlinear Dynamics of Immunogenic Tumors: Parameter Estimation and Global Bifurcation Analysis. Bull. Math. Biol.
**1994**, 56, 295–321. [Google Scholar] [CrossRef] - Tai, A.; Erickson, B.; Khater, K.A.; Li, X.A. Estimate of Radiobiologic Parameters from Clinical Data for Biologically Based Treatment Planning for Liver Irradiation. Int. J. Radiat. Oncol. Biol. Phys.
**2008**, 70, 900–907. [Google Scholar] [CrossRef] - Serre, R.; Barlési, F.; Muracciole, X.; Barbolosi, D. Immunologically Effective Dose: A Practical Model for Immuno-Radiotherapy. Oncotarget
**2018**, 9, 31812–31819. [Google Scholar] [CrossRef] - Byun, H.K.; Kim, N.; Park, S.; Seong, J. Acute Severe Lymphopenia by Radiotherapy Is Associated with Reduced Overall Survival in Hepatocellular Carcinoma. Strahlenther. Onkol.
**2019**, 195, 1007–1017. [Google Scholar] [CrossRef] [PubMed] - Nakamura, N.; Kusunoki, Y.; Akiyama, M. Radiosensitivity of CD4 or CD8 Positive Human T-Lymphocytes by an In Vitro Colony Formation Assay. Radiat. Res.
**1990**, 123, 224–227. [Google Scholar] [CrossRef] [PubMed] - Walker, R.; Poleszczuk, J.; Pilon-Thomas, S.; Kim, S.; Anderson, A.A.R.A.; Czerniecki, B.J.; Harrison, L.B.; Moros, E.G.; Enderling, H. Immune Interconnectivity of Anatomically Distant Tumors as a Potential Mediator of Systemic Responses to Local Therapy. Sci. Rep.
**2018**, 8, 9474. [Google Scholar] [CrossRef] [PubMed] - Basler, L.; Andratschke, N.; Ehrbar, S.; Guckenberger, M.; Tanadini-Lang, S. Modelling the Immunosuppressive Effect of Liver SBRT by Simulating the Dose to Circulating Lymphocytes: An In-Silico Planning Study. Radiat. Oncol.
**2018**, 13, 10. [Google Scholar] [CrossRef] [PubMed] - Yang, H.; Shen, K.; Zhu, C.; Li, Q.; Zhao, Y.; Ma, X. Safety and Efficacy of Durvalumab (MEDI4736) in Various Solid Tumors. Drug Des. Dev. Ther.
**2018**, 12, 2085–2096. [Google Scholar] [CrossRef] - Sung, W.; Grassberger, C.; McNamara, A.L.; Basler, L.; Ehrbar, S.; Tanadini-Lang, S.; Hong, T.S.; Paganetti, H. A Tumor-Immune Interaction Model for Hepatocellular Carcinoma Based on Measured Lymphocyte Counts in Patients Undergoing Radiotherapy. Radiother. Oncol.
**2020**, 151, 73–81. [Google Scholar] [CrossRef] - De la Garza-Ramos, C.; Montazeri, S.A.; Croome, K.P.; LeGout, J.D.; Sella, D.M.; Cleary, S.; Burns, J.; Mathur, A.K.; Overfield, C.J.; Frey, G.T.; et al. Radiation Segmentectomy for the Treatment of Solitary Hepatocellular Carcinoma: Outcomes Compared with Those of Surgical Resection. J. Vasc. Interv. Radiol.
**2022**, 33, 775–785.e2. [Google Scholar] [CrossRef] - Toskich, B.; Vidal, L.L.; Olson, M.T.; Lewis, J.T.; LeGout, J.D.; Sella, D.M.; Montazeri, S.A.; Devcic, Z.; Lewis, A.R.; Frey, G.T.; et al. Pathologic Response of Hepatocellular Carcinoma Treated with Yttrium-90 Glass Microsphere Radiation Segmentectomy prior to Liver Transplantation: A Validation Study. J. Vasc. Interv. Radiol.
**2021**, 32, 518–526.e1. [Google Scholar] [CrossRef] - McBride, S.; Sherman, E.; Tsai, C.J.; Baxi, S.; Aghalar, J.; Eng, J.; Zhi, W.I.; McFarland, D.; Michel, L.S.; Young, R.; et al. Randomized Phase II Trial of Nivolumab with Stereotactic Body Radiotherapy versus Nivolumab Alone in Metastatic Head and Neck Squamous Cell Carcinoma. J. Clin. Oncol.
**2021**, 39, 30–37. [Google Scholar] [CrossRef] - Brooks, E.D.; Chang, J.Y. Time to Abandon Single-Site Irradiation for Inducing Abscopal Effects. Nat. Rev. Clin. Oncol.
**2019**, 16, 123–135. [Google Scholar] [CrossRef] - Bertaglia, V.; Petrelli, F.; Porcu, M.; Saba, L.; Pearce, J.; Luciani, A.; Solinas, C.; Scartozzi, M. Assessment of Clinical Studies Evaluating Combinations of Immune Checkpoint Inhibitors with Locoregional Treatments in Solid Tumors. Cytokine Growth Factor Rev.
**2022**, 67, 1–10. [Google Scholar] [CrossRef] [PubMed] - Walker, R.; Schoenfeld, J.D.; Pilon-Thomas, S.; Poleszczuk, J.; Enderling, H. Evaluating the Potential for Maximized T Cell Redistribution Entropy to Improve Abscopal Responses to Radiotherapy. Converg. Sci. Phys. Oncol.
**2017**, 3, 034001. [Google Scholar] [CrossRef] [PubMed] - Bekker, R.A.; Kim, S.; Pilon-Thomas, S.; Enderling, H. Mathematical Modeling of Radiotherapy and Its Impact on Tumor Interactions with the Immune System. Neoplasia
**2022**, 28, 100796. [Google Scholar] [CrossRef] [PubMed]

**Figure 1.**A schematic representation of the model. The model has four compartments: targeted tumor cells (${T}_{I}$), inactivated tumor cells (I), non-targeted tumor cells (${T}_{NI}$), and circulating lymphocytes (L). The targeted tumor cell and circulating lymphocytes are exposed to radiation emitted from the decay of yttrium 90, but not non-targeted tumor cells. Both targeted and non-targeted tumor cells are cytotoxic according to immune response. The immune response can be upregulated by the administration of Programmed Death-Ligand 1 (PD-L1) immune checkpoint inhibitors (durvalumab).

**Figure 2.**A schematic virtual trial schedule of the model with five different treatment groups. The blue arrows indicate the administrating timing of Y90-RE, and the yellow arrows indicate the administrating period of ICIs. Arms A, B, and C are shown according to the order in which Y90-RE and ICIs were administered, respectively. The administration interval days between the two drugs were investigated from 30 days to 300 days.

**Figure 3.**(

**A**) The heatmap of median progression-free survival (PFS) for different dosages of Y90-RE and ICIs in the three arms (A, B, and C). The radiation intensity varies in the range of 300–500 Gy, and the PD-L1 (δ

_{durva}) varies in the range of 0.08–0.16. The color columns represent the median PFS. The black frames represent the minimum, median, and maximum points of the drugs, respectively, and are shown in graph (

**B**). (

**B**) Kaplan–Meier graph represents PFS for arm A (green), arm B (blue), and arm C (orange). Abbreviation: Y90-RE = yttrium 90 radioembolization; ICIs = immune checkpoint inhibitors.

**Figure 4.**(

**A**) The heatmap of the cumulative distant metastasis (DM) at 3 years for different dosages of Y90-RE and ICIs for three arms (A, B, and C) for non-targeted tumors. Radiation intensity varies in the range of 300–500 Gy, and the PD-L1 (δ

_{durva}) varies in the range of 0.08–0.16. The color columns represent the DM rates at 3 years. The black frames represent the minimum, median, and maximum points of the drugs, respectively, and are shown in graph (

**B**). (

**B**) The cumulative DM curve for arm A (green), arm B (blue), and arm C (orange). Abbreviation: Y90-RE = yttrium 90 radioembolization; ICIs = immune checkpoint inhibitors.

Parameter | Function | Value | Ref. |
---|---|---|---|

$a$ | Tumor growth | $0.01{\mathrm{d}}^{-1}$ | [37] |

$f$ | Lymphocyte decay rate | $0.033{\mathrm{d}}^{-1}$ | [38] |

${\alpha}_{T}/{\beta}_{T}$ | Tumor—LQ cell death | $10\mathrm{G}\mathrm{y}$ | [39] |

$r$ | Inactivated tumor cell decay rate | $0.14{\mathrm{d}}^{-1}$ | [40] |

${\omega}_{1}$ | Tumor-directed lymphocyte efficiency | $0.119{\mathrm{d}}^{-1}$ | [33,34] |

${\omega}_{2}$ | Tumor/inactivated tumor | $0.003{\mathrm{d}}^{-1}$ | |

${\omega}_{3}$ | Tumor–lymphocyte recruitment constant | $0.009{\mathrm{d}}^{-1}$ | [33,34] |

$g$ | Geometric saturation constant | $7.330\times {10}^{10}$ | [33,34] |

$s$ | Lymphocyte regeneration | $1.470\times {10}^{8}{\mathrm{d}}^{-1}$ | [41] |

${\alpha}_{T}$ | Tumor—LQ cell death | Normally distributed $(\mathsf{\mu}=0.148\mathsf{\sigma}=0.024)$ | [39] |

${\alpha}_{L}$ | Lymphocytes—LQ cell death | $0.737{\mathrm{G}\mathrm{y}}^{-1}$ | [42,43] |

C_{max} | Maximum concentration | 10 mg/kg | [44] |

${\mathrm{T}\left(\mathsf{\omega}\right)}_{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$ | Half-life of immune checkpoint inhibitor (durvalumab) in the body | 21 days | [44] |

δ_{durva} | Effectiveness of immune checkpoint Inhibitor (durvalumab) | Normally distributed (μ = 0.12 σ = 0.04) | [45] |

${\mathrm{T}\left(\mathrm{Y}90\mathrm{R}\mathrm{E}\right)}_{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$ | Half-life of yttrium 90 in the body | 2.6 days | [36], added in this study |

q | Effectiveness of yttrium 90 | Normally distributed (μ = 0.12 σ = 0.04) | This study, added in this study |

k | Constant to produce the dose rate in desired units | (0.9267 $\raisebox{1ex}{$\mathrm{M}\mathrm{e}\mathrm{v}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{d}\mathrm{i}\mathrm{s}$}\right.)\xb7(1.6022\times {10}^{-13}\raisebox{1ex}{$\mathrm{J}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{M}\mathrm{e}\mathrm{v}$}\right.$) | [36], added in this study |

<E> | Average energy emitted per nuclear transition | $\left(\raisebox{1ex}{$\mathrm{G}\mathrm{y}\mathrm{k}\mathrm{g}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{J}$}\right.\right)\xb7\left(\raisebox{1ex}{${10}^{9}\mathrm{d}\mathrm{i}\mathrm{s}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{s}\mathrm{G}\mathrm{B}\mathrm{q}$}\right.\right)\xb7\left(\raisebox{1ex}{$86400\mathrm{s}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{d}\mathrm{a}\mathrm{y}$}\right.\right)$ | [36], added in this study |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Kang, M.; Shin, Y.; Kim, Y.; Ha, S.; Sung, W.
Modeling the Synergistic Impact of Yttrium 90 Radioembolization and Immune Checkpoint Inhibitors on Hepatocellular Carcinoma. *Bioengineering* **2024**, *11*, 106.
https://doi.org/10.3390/bioengineering11020106

**AMA Style**

Kang M, Shin Y, Kim Y, Ha S, Sung W.
Modeling the Synergistic Impact of Yttrium 90 Radioembolization and Immune Checkpoint Inhibitors on Hepatocellular Carcinoma. *Bioengineering*. 2024; 11(2):106.
https://doi.org/10.3390/bioengineering11020106

**Chicago/Turabian Style**

Kang, Minah, Yerim Shin, Yeseul Kim, Sangseok Ha, and Wonmo Sung.
2024. "Modeling the Synergistic Impact of Yttrium 90 Radioembolization and Immune Checkpoint Inhibitors on Hepatocellular Carcinoma" *Bioengineering* 11, no. 2: 106.
https://doi.org/10.3390/bioengineering11020106