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Multicomponent mathematical model for tumor volume calculation with setup error using single-isocenter stereotactic radiotherapy for multiple brain metastases

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Abstract

We evaluated the tumor residual volumes considering six degrees-of-freedom (6DoF) patient setup errors in stereotactic radiotherapy (SRT) with multicomponent mathematical model using single-isocenter irradiation for brain metastases. Simulated spherical gross tumor volumes (GTVs) with 1.0 (GTV 1), 2.0 (GTV 2), and 3.0 (GTV 3)-cm diameters were used. The distance between the GTV center and isocenter (d) was set at 0–10 cm. The GTV was simultaneously translated within 0–1.0 mm (T) and rotated within 0°–1.0° (R) in the three axis directions using affine transformation. We optimized the tumor growth model parameters using measurements of non-small cell lung cancer cell lines’ (A549 and NCI-H460) growth. We calculated the GTV residual volume at the irradiation’s end using the physical dose to the GTV when the GTV size, d, and 6DoF setup error varied. The d-values that satisfy tolerance values (10%, 35%, and 50%) of the GTV residual volume rate based on the pre-irradiation GTV volume were determined. The larger the tolerance value set for both cell lines, the longer the distance to satisfy the tolerance value. In GTV residual volume evaluations based on the multicomponent mathematical model on SRT with single-isocenter irradiation, the smaller the GTV size and the larger the distance and 6DoF setup error, the shorter the distance that satisfies the tolerance value might need to be.

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Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

References

  1. Barnholtz-Sloan JS, Sloan AE, Davis FG, Vigneau FD, Lai P, Sawaya RE (2004) Incidence proportions of brain metastases in patients diagnosed (1973 to 2001) in the metropolitan detroit cancer surveillance system. J Clin Oncol 22:2865–2872

    Article  PubMed  Google Scholar 

  2. Chang EL, Wefel JS, Hess KR, Allen PK, Lang FF, Kornguth DG et al (2009) Neurocognition in patients with brain metastases treated with radiosurgery or radiosurgery plus whole-brain irradiation: a randomised controlled trial. Lancet Oncol 10:1037–1044

    Article  PubMed  Google Scholar 

  3. Kocher M, Soffietti R, Abacioglu U, Villà S, Fauchon F, Baumert BG et al (2011) Adjuvant whole-brain radiotherapy versus observation after radiosurgery or surgical resection of one to three cerebral metastases: results of the EORTC 22952–26001 study. J Clin Oncol 29:134–141

    Article  PubMed  Google Scholar 

  4. Minniti G, Esposito V, Clarke E, Scaringi C, Lanzetta G, Salvati M et al (2013) Multidose stereotactic radiosurgery (9 Gy × 3) of the postoperative resection cavity for treatment of large brain metastases. Int J Radiat Oncol Biol Phys 86(4):623–629

    Article  PubMed  Google Scholar 

  5. Nath SK, Lawson JD, Simpson DR, Vanderspek L, Wang JZ, Alksne JF et al (2010) Single-Isocenter frameless intensity-modulated stereotactic radiosurgery for simultaneous treatment of multiple brain metastases: clinical experience. Int J Radiat Oncol Biol Phys 78(1):91–97

    Article  PubMed  Google Scholar 

  6. Clark GM, Popple RA, Young PE, Fiveash JB (2010) Feasibility of single-isocenter volumetric modulated arc radiosurgery for treatment of multiple brain metastases. Int J Radiat Oncol Biol Phys 76(1):296–302

    Article  PubMed  Google Scholar 

  7. Zhang I, Antone J, Li J, Saha S, Riegel AC, Vijeh L et al (2017) Hippocampal-sparing and target volume coverage in treating 3 to 10 brain metastases: a comparison of gamma Knife, single-isocenter VMAT, cyberknife, and tomotherapy stereotactic radiosurgery. Pract Radiat Oncol 7(3):183–189

    Article  PubMed  Google Scholar 

  8. Ziemer BP, Sanghvi P, Hattangadi-Gluth J, Moore KL (2017) Heuristic knowledge-based planning for single-Isocenter stereotactic radiosurgery to multiple brain metastases. Med Phys 44(10):5001–5009

    Article  PubMed  Google Scholar 

  9. Wu Q, Snyder KC, Liu C, Huang Y, Zhao B, Chetty IJ et al (2016) Optimization of treatment geometry to reduce normal brain dose in radiosurgery of multiple brain metastases with single-Isocenter volumetric modulated arc therapy. Sci Rep 6:34511

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  10. Gevaert T, Steenbeke F, Pellegri L, Engels B, Christian N, Hoornaert MT et al (2016) Evaluation of a dedicated brain metastases treatment planning optimization for radiosurgery: a new treatment paradigm. Radiat Oncol 11:13

    Article  PubMed  PubMed Central  Google Scholar 

  11. Nakano H, Tanabe S, Utsunomiya S, Yamada T, Sasamoto R, Nakano T et al (2020) Effect of setup error in the single-isocenter technique on stereotactic radiosurgery for multiple brain metastases. J Appl Clin Med Phys 21(12):155–165

    Article  PubMed  PubMed Central  Google Scholar 

  12. Nakano H, Tanabe S, Yamada T, Utsunomiya S, Takizawa T, Sakai M et al (2021) Maximum distance in single-isocenter technique of stereotactic radiosurgery with rotational error using margin-based analysis. Radiol Phys Technol 14(1):57–63

    Article  PubMed  Google Scholar 

  13. Rojas-López JA, Díaz Moreno RM, Venencia CD (2021) Use of genetic algorithm for PTV optimization in single isocenter multiple metastases radiosurgery treatments with Brainlab Elements™. Phys Med 86:82–90

    Article  PubMed  Google Scholar 

  14. Nakano H, Tanabe S, Sasamoto R, Takizawa T, Utsunomiya S, Sakai M et al (2021) Radiobiological evaluation considering setup error on single-isocenter irradiation in stereotactic radiosurgery. J Appl Clin Med Phys 22(7):266–275

    Article  PubMed  PubMed Central  Google Scholar 

  15. Palmiero AN, Fabian D, Randall ME, St WC, Pokhrel D (2021) Predicting the effect of indirect cell kill in the treatment of multiple brain metastases via single-isocenter/multitarget volumetric modulated arc therapy stereotactic radiosurgery. J Appl Clin Med Phys 22(10):94–103

    Article  PubMed  PubMed Central  Google Scholar 

  16. Michor F, Beal K (2015) Improving cancer treatment via mathematical modeling: surmounting the challenges is worth the effort. Cell 163(5):1059–1063

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  17. Jarrett AM, Shah A, Bloom MJ, McKenna MT, Hormuth DA, Yankeelov TE et al (2019) Experimentally-driven mathematical modeling to improve combination targeted and cytotoxic therapy for HER2+ breast cancer. Sci Rep 9(1):12830

    Article  PubMed  PubMed Central  Google Scholar 

  18. Sun X, Bao J, Shao Y (2016) Mathematical modeling of therapy-induced cancer drug resistance: connecting cancer mechanisms to population survival rates. Sci Rep 6(1):22498

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  19. Diagne ML, Rwezaura H, Tchoumi SY, Tchuenche JM (2021) A mathematical model of COVID-19 with vaccination and treatment. Comput Math Methods Med 2021:1250129

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  20. Milberg O, Gong C, Jafarnejad M, Bartelink IH, Wang B, Vicini P et al (2019) A QSP model for predicting clinical responses to monotherapy, combination and sequential therapy following CTLA-4, PD-1, and PD-L1 checkpoint blockade. Sci Rep 9(1):11286

    Article  PubMed  PubMed Central  Google Scholar 

  21. Murphy H, Jaafari H, Dobrovolny HM (2016) Differences in predictions of ODE models of tumor growth: a cautionary example. BMC Cancer 16:163

    Article  PubMed  PubMed Central  Google Scholar 

  22. Yin A, Dirk Jan AR, van Hasselt JGC, Swen JJ, Guchelaar HJ (2019) A review of mathematical models for tumor dynamics and treatment resistance evolution of solid tumors. CPT Pharmacometr Syst Pharmacol 8(10):720–737

    Article  CAS  Google Scholar 

  23. Watanabe Y, Dahlman EL, Leder KZ, Hui SK (2016) A mathematical model of tumor growth and its response to single irradiation. Theor Biol Med Model 13:6

    Article  PubMed  PubMed Central  Google Scholar 

  24. Kosinsky Y, Dovedi SJ, Peskov K, Voronova V, Chu L, Tomkinson H et al (2018) Radiation and PD-(L)1 treatment combinations: immune response and dose optimization via a predictive systems model. J Immunother Cancer 6(1):17

    Article  PubMed  PubMed Central  Google Scholar 

  25. Hong WS, Wang SG, Zhang GQ (2021) Lung cancer radiotherapy: simulation and analysis based on a multicomponent mathematical model. Comput Math Methods Med 2021:6640051

    Article  PubMed  PubMed Central  Google Scholar 

  26. Hong WS, Zhang GQ (2019) Simulation analysis for tumor radiotherapy based on three-component mathematical models. J Appl Clin Med Phys 20(3):22–26

    Article  PubMed  PubMed Central  Google Scholar 

  27. Slagowski JM, Wen Z (2020) Selection of single-Isocenter for multiple-target stereotactic brain radiosurgery to minimize total margin volume. Phys Med Biol 1361:ab9703

    Google Scholar 

  28. Oh SA, Yea JW, Kang MK, Park JW, Kim SK (2016) Analysis of the setup uncertainty and margin of the daily exactrac 6D image guide system for patients with brain tumors. PLoS ONE 11:e0151709

    Article  PubMed  PubMed Central  Google Scholar 

  29. Oh Y-K, Baek J, Kim O-B, Kim J-H (2014) Assessment of setup uncertainties for various tumor sites when using daily CBCT for more than 2200 VMAT treatments. J Appl Clin Med Phys 15(2):4418

    Article  PubMed  Google Scholar 

  30. Mangesius J, Seppi T, Weigel R et al (2019) Intrafractional 6D head movement ncreases with time of mask fixation during stereotactic intracranial RT-sessions. Radiat Oncol 14(1):231

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  31. Vergalasova I, Liu H, Alonso-Basanta M, Dong L, Li J, Nie K et al (2019) Multi-institutional dosimetric evaluation of modern day stereotactic radiosurgery (SRS) treatment options for multiple brain metastases. Front Oncol 9:483

    Article  PubMed  PubMed Central  Google Scholar 

  32. Chougule MB, Patel A, Sachdeva P, Jackson T, Singh M (2011) Enhanced anticancer activity of gemcitabine in combination with noscapine via antiangiogenic and apoptotic pathway against non-small cell lung cancer. PLoS ONE 6(11):e27394

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  33. Rhyu JJ, Yun JW, Kwon E, Che JH, Kang BC (2015) Dual effects of human adipose tissue-derived mesenchymal stem cells in human lung adenocarcinoma A549 xenografts and colorectal adenocarcinoma HT-29 xenografts in mice. Oncol Rep 34(4):1733–1744

    Article  CAS  PubMed  Google Scholar 

  34. King RB, Hyland WB, Cole AJ, Butterworth KT, McMahon SJ, Redmonda KM et al (2013) An in vitro study of the radiobiological effects of flattening filter free radiotherapy treatments. Phys Med Biol 58(5):N83-94

    Article  CAS  PubMed  Google Scholar 

  35. Butterworth KT, McMahon SJ, McKee JC, Patel G, Ghita M, Cole AJ et al (2015) Time and cell type dependency of survival responses in co-cultured tumor and fibroblast cells after exposure to modulated radiation fields. Radiat Res 183(6):656–664

    Article  CAS  PubMed  Google Scholar 

  36. Bogaerts J, Ford R, Sargent D, Schwartz LH, Rubinstein L, Lacombe D et al (2009) Individual patient data analysis to assess modifications to the RECIST criteria. Eur J Cancer 45(2):248–260

    Article  PubMed  Google Scholar 

  37. Lin NU, Lee EQ, Aoyama H, Barani IJ, Barboriak DP, Baumert BG et al (2015) Response assessment criteria for brain metastases: proposal from the RANO group. Lancet Oncol 16(6):e270-278

    Article  PubMed  Google Scholar 

  38. Agarwal A, Chang GJ, Hu CY, Taggart M, Rashid A, Park IJ (2013) Quantified pathologic response assessed as residual tumor burden is a predictor of recurrence-free survival in patients with rectal cancer who undergo resection after neoadjuvant chemoradiotherapy. Cancer 119(24):4231–4241

    Article  PubMed  Google Scholar 

  39. Moding EJ, Kastan MB, Kirsch DG (2013) Strategies for optimizing the response of cancer and normal tissues to radiation. Nat Rev Drug Discov 12(7):526–542

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  40. Park SY, Choi N, Jang NY (2021) Frameless immobilization system with roll correction for stereotactic radiosurgery of intracranial brain metastases. J Radiat Res 62(6):1015–1021

    Google Scholar 

  41. Yoon JW, Park S, Cheong KH, Kang SK, Han TJ (2021) Combined effect of dose gradient and rotational error on prescribed dose coverage for single isocenter multiple brain metastases in frameless stereotactic radiotherapy. Radiat Oncol 16(1):169

    Article  PubMed  PubMed Central  Google Scholar 

  42. Kraft J, van Timmeren JE, Mayinger M, Frei S, Borsky K, Stark LS et al (2021) Distance to isocenter is not associated with an increased risk for local failure in LINAC-based single-isocenter SRS or SRT for multiple brain metastases. Radiother Oncol 159:168–175

    Article  PubMed  Google Scholar 

  43. Enderling H, Chaplain MAJ (2014) Mathematical modeling of tumor growth and treatment. Curr Pharm Des 20(30):4934–4940

    Article  CAS  PubMed  Google Scholar 

  44. Prokopiou S, Moros EG, Poleszczuk J, Caudell J, Torres-Roca JF, Latifi K et al (2015) A proliferation saturation index to predict radiation response and personalize radiotherapy fractionation. Radiat Oncol 10:159

    Article  PubMed  PubMed Central  Google Scholar 

  45. Vaghi C, Rodallec A, Fanciullino R, Ciccolini J, Mochel JP, Mastri M et al (2020) Population modeling of tumor growth curves and the reduced Gompertz model improve prediction of the age of experimental tumors. PLoS Comput Biol 16(2):e1007178

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  46. van Leeuwen CM, Oei AL, Crezee J, Bel A, Franken NAP, Stalpers LJA et al (2018) The alfa and beta of tumours: a review of parameters of the linear-quadratic model, derived from clinical radiotherapy studies. Radiat Oncol 13(1):96

    Article  PubMed  PubMed Central  Google Scholar 

  47. Liu Z, Yanga C (2014) A mathematical model of cancer treatment by radiotherapy. Comput Math Methods Med 2014:172923

    Article  PubMed  PubMed Central  Google Scholar 

  48. Yu VY, Nguyen D, O’Connor D, Ruan D, Kaprealian T, Chin R et al (2021) Treating Glioblastoma Multiforme (GBM) with super hyperfractionated radiation therapy: implication of temporal dose fractionation optimization including cancer stem cell dynamics. PLoS ONE 16(2):e0245676

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  49. Nakano H, Kawahara D, Ono K, Akagi Y, Hirokawa Y (2018) Effect of dose-delivery time for flattened and flattening filter-free photon beams based on microdosimetric kinetic model. PLoS ONE 13(11):e0206673

    Article  PubMed  PubMed Central  Google Scholar 

  50. Dale RG (1989) Time-dependent tumour repopulation factors in linear-quadratic equations–implications for treatment strategies. Radiother Oncol 15(4):371–381

    Article  CAS  PubMed  Google Scholar 

  51. Boscolo D, Scifoni E, Durante M, Krämer M, Fuss MC (2021) May oxygen depletion explain the FLASH effect? A chemical track structure analysis. Radiother Oncol 162:68–75

    Article  CAS  PubMed  Google Scholar 

  52. Bopp C, Hirayama R, Inaniwa T, Kitagawa A, Matsufuji N, Noda K (2016) Adaptation of the microdosimetric kinetic model to hypoxia. Phys Med Biol 61(21):7586–7599

    Article  CAS  PubMed  Google Scholar 

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Acknowledgements

This research was supported by Grants from the Japan Society for the Promotion of Science (JSPS) KAKENHI, nos. 19K17227, 20K16819, and 21K07722.

Funding

This work was supported by by Grants from the Japan Society for the Promotion of Science (JSPS) KAKENHI, nos. 19K17227, 20K16819, and 21K07722.

Author information

Authors and Affiliations

  1. Department of Radiation Oncology, Niigata University Medical and Dental Hospital, 1-757 Asahimachi-Dori, Chuo-Ku, Niigata-Shi, Niigata, Japan

    Hisashi Nakano, Satoshi Tanabe, Madoka Sakai, Shunpei Tanabe & Atsushi Ohta

  2. Department of Medical Physics and Engineering, Osaka University Graduate School of Medicine, 1-7 Yamadaoka, Suita-Shi, Osaka, Japan

    Hisashi Nakano & Teiji Nishio

  3. Department of Radiation Oncology, Yamaguchi University, Minamikogushi 1-1-1 Ube, Yamaguchi, Japan

    Takehiro Shiinoki

  4. Department of Radiology and Radiation Oncology, Niigata University Graduate School of Medical and Dental Sciences, 1-757 Asahimachi-Dori, Chuo-Ku, Niigata-Shi, Niigata, Japan

    Toshimichi Nakano, Takeshi Takizawa, Motoki Kaidu & Hiroyuki Ishikawa

  5. Department of Radiation Oncology, Niigata Neurosurgical Hospital, 3057 Yamada, Nishi-Ku, Niigata-Shi, Niigata, Japan

    Takeshi Takizawa

  6. Department of Radiological Technology, Niigata University Graduate School of Health Sciences, 2-746 Asahimachi-Dori, Chuo-Ku, Niigata-Shi, Niigata, Japan

    Satoru Utsunomiya

Authors
  1. Hisashi Nakano
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  2. Takehiro Shiinoki
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  3. Satoshi Tanabe
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  4. Toshimichi Nakano
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  5. Takeshi Takizawa
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  6. Satoru Utsunomiya
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  7. Madoka Sakai
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  8. Shunpei Tanabe
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  9. Atsushi Ohta
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  10. Motoki Kaidu
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  11. Teiji Nishio
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  12. Hiroyuki Ishikawa
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Contributions

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by HN, TS, ST, TN, TT, and SU. The first draft of the manuscript was written by HN, TS and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Corresponding author

Correspondence to Hisashi Nakano.

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Ethical approval

This study did not require ethical approval because of the simulation study.

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Nakano, H., Shiinoki, T., Tanabe, S. et al. Multicomponent mathematical model for tumor volume calculation with setup error using single-isocenter stereotactic radiotherapy for multiple brain metastases. Phys Eng Sci Med 46, 945–953 (2023). https://doi.org/10.1007/s13246-023-01241-8

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