Siegel RL, Miller KD, Wagle NS, Jemal A. Cancer statistics, 2023. Ca Cancer J Clin. 2023;73(1):17–48.

PubMed  Google Scholar 

Lea D, Catcheside D. The mechanism of the induction by radiation of chromosome aberrations in Tradescantia. J Genet. 1942;44:216–45.

Google Scholar 

Fowler JF. The linear-quadratic formula and progress in fractionated radiotherapy. Br J Radiol. 1989;62(740):679–94.

CAS  PubMed  Google Scholar 

Niemierko A, Goitein M. Implementation of a model for estimating tumor control probability for an inhomogeneously irradiated tumor. Radiother Oncol. 1993;29(2):140–7.

CAS  PubMed  Google Scholar 

Goitein M, Niemierko A, Okunieff P. The probability of controlling an inhomogeneously irradiated tumor. Eval Treatm Plan Part Beam Radiother. 1987;5:1–58.

Google Scholar 

Oelkfe U, Scholz C. Dose calculation. algorithms New technologies in radiation oncology. Springer; 2006. p. 187–96.

Google Scholar 

Andreo P. Monte Carlo simulations in radiotherapy dosimetry. Radiat Oncol. 2018;13(1):121.

PubMed  PubMed Central  Google Scholar 

Wu Q, Mohan R. Algorithms and functionality of an intensity modulated radiotherapy optimization system. Med Phys. 2000;27(4):701–11.

CAS  PubMed  Google Scholar 

Mageras GS, Mohan R. Application of fast simulated annealing to optimization of conformal radiation treatments. Med Phys. 1993;20(3):639–47.

CAS  PubMed  Google Scholar 

Zhong H, Peters T, Siebers JV. FEM-based evaluation of deformable image registration for radiation therapy. Phys Med Biol. 2007;52(16):4721–38.

PubMed  Google Scholar 

Bai W, Brady M. Regularized B-spline deformable registration for respiratory motion correction in PET images. Phys Med Biol. 2009;54(9):2719–36.

PubMed  Google Scholar 

Sotiras A, Davatzikos C, Paragios N. Deformable medical image registration: a survey. IEEE Trans Med Imaging. 2013;32(7):1153–90.

PubMed  PubMed Central  Google Scholar 

Nahum AE. The radiobiology of hypofractionation. Clin Oncol (R Coll Radiol). 2015;27(5):260–9.

PubMed  Google Scholar 

Esplen N, Mendonca MS, Bazalova-Carter M. Physics and biology of ultrahigh dose-rate (FLASH) radiotherapy: a topical review. Phys Med Biol. 2020;65(23):23tr03.

CAS  PubMed  Google Scholar 

Asur R, Butterworth KT, Penagaricano JA, Prise KM, Griffin RJ. High dose bystander effects in spatially fractionated radiation therapy. Cancer Lett. 2015;356(1):52–7.

CAS  PubMed  Google Scholar 

Bekker RA, 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.

CAS  PubMed  PubMed Central  Google Scholar 

Mahlbacher GE, Reihmer KC, Frieboes HB. Mathematical modeling of tumor-immune cell interactions. J Theor Biol. 2019;469:47–60.

CAS  PubMed  PubMed Central  Google Scholar 

Yankeelov TE, An G, Saut O, Luebeck EG, Popel AS, Ribba B, et al. Multi-scale modeling in clinical oncology: opportunities and barriers to success. Ann Biomed Eng. 2016;44(9):2626–41.

PubMed  PubMed Central  Google Scholar 

Chakraborty S, Hosen MI, Ahmed M, Shekhar HU. Onco-multi-OMICS approach: a new frontier in cancer research. Biomed Res Int. 2018;2018:9836256.

PubMed  PubMed Central  Google Scholar 

Zheng D, Grandgenett PM, Zhang Q, Baine M, Shi Y, Du Q, et al. radioGWAS links radiome to genome to discover driver genes with somatic mutations for heterogeneous tumor image phenotype in pancreatic cancer. Sci Rep. 2024;14(1):12316.

CAS  PubMed  PubMed Central  Google Scholar 

Chang DS, Lasley FD, Das IJ, Mendonca MS, Dynlacht JR, Chang DS, et al. Stochastic, deterministic, and heritable effects (and some radiation protection basics). Basic Radiother Phys Biol 2021:337–48.

Jarrett D, Stride E, Vallis K, Gooding MJ. Applications and limitations of machine learning in radiation oncology. Br J Radiol. 2019;92(1100):20190001.

PubMed  PubMed Central  Google Scholar 

O’Donoghue JA. The response of tumours with Gompertzian growth characteristics to fractionated radiotherapy. Int J Radiat Biol. 1997;72(3):325–39.

CAS  PubMed  Google Scholar 

Zhou S, Zheng D, Fan Q, Yan Y, Wang S, Lei Y, et al. Minimum dose rate estimation for pulsed FLASH radiotherapy: a dimensional analysis. Med Phys. 2020;47(7):3243–9.

CAS  PubMed  Google Scholar 

Bedford JL. Calculation of absorbed dose in radiotherapy by solution of the linear Boltzmann transport equations. Phys Med Biol. 2019;64(2):02tr1.

Google Scholar 

Kim M, Ghate A, Phillips MH. A stochastic control formalism for dynamic biologically conformal radiation therapy. Eur J Oper Res. 2012;219(3):541–56.

Google Scholar 

Sachs RK, Shuryak I, Brenner D, Fakir H, Hlatky L, Hahnfeldt P. Second cancers after fractionated radiotherapy: stochastic population dynamics effects. J Theor Biol. 2007;249(3):518–31.

PubMed  PubMed Central  Google Scholar 

Webb S. Optimum parameters in a model for tumour control probability including interpatient heterogeneity. Phys Med Biol. 1994;39(11):1895–914.

CAS  PubMed  Google Scholar 

Zaider M, Hanin L. Tumor control probability in radiation treatment. Med Phys. 2011;38(2):574–83.

PubMed  Google Scholar 

Fornalski KW, Dobrzyński L, Janiak MK. A stochastic markov model of cellular response to radiation. Dose Response. 2011;9(4):477–96.

CAS  PubMed  PubMed Central  Google Scholar 

Van Liedekerke P, Palm M, Jagiella N, Drasdo D. Simulating tissue mechanics with agent-based models: concepts, perspectives and some novel results. Comput Part Mech. 2015;2:401–44.

Google Scholar 

Frieboes HB, Jin F, Chuang YL, Wise SM, Lowengrub JS, Cristini V. Three-dimensional multispecies nonlinear tumor growth-II: Tumor invasion and angiogenesis. J Theor Biol. 2010;264(4):1254–78.

CAS  PubMed  PubMed Central  Google Scholar 

Tsoularis A, Wallace J. Analysis of logistic growth models. Math Biosci. 2002;179(1):21–55.

CAS  PubMed  Google Scholar 

Tjørve KMC, Tjørve E. The use of Gompertz models in growth analyses, and new Gompertz-model approach: an addition to the Unified-Richards family. PLoS ONE. 2017;12(6): e0178691.

PubMed  PubMed Central  Google Scholar 

Miranda LM, Souza AM. Fractality in tumor growth at the avascular stage from a generalization of the logistic-Gompertz dynamics. Physica A. 2023;618: 128664.

Google Scholar 

Szabó A, Merks RM. Cellular potts modeling of tumor growth, tumor invasion, and tumor evolution. Front Oncol. 2013;3:87.

PubMed  PubMed Central  Google Scholar 

He X, Lee B, Jiang Y. Extracellular matrix in cancer progression and therapy. Med Rev. 2022;2(2):125–39.

Google Scholar 

Zheng X, Wise SM, Cristini V. Nonlinear simulation of tumor necrosis, neo-vascularization and tissue invasion via an adaptive finite-element/level-set method. Bull Math Biol. 2005;67(2):211–59.

CAS  PubMed  Google Scholar 

Withers HR. The four R’s of radiotherapy. Advances in radiation biology, vol. 5. Elsevier; 1975. p. 241–71.

Google Scholar 

Steel GG, McMillan TJ, Peacock J. The 5Rs of radiobiology. Int J Radiat Biol. 1989;56(6):1045–8.

CAS  PubMed  Google Scholar 

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

PubMed  PubMed Central  Google Scholar 

Kirkpatrick JP, Meyer JJ, Marks LB. The linear-quadratic model is inappropriate to model high dose per fraction effects in radiosurgery. Semin Radiat Oncol. 2008;18(4):240–3.

PubMed  Google Scholar 

Brown JM, Carlson DJ, Brenner DJ. The tumor radiobiology of SRS and SBRT: are more than the 5 Rs involved? Int J Radiat Oncol Biol Phys. 2014;88(2):254–62.

PubMed  PubMed Central  Google Scholar 

Kirkpatrick JP, Brenner DJ, Orton CG. Point/Counterpoint. The linear-quadratic model is inappropriate to model high dose per fraction effects in radiosurgery. Med Phys. 2009;36(8):3381–4.

PubMed