Abstract
Radiotherapy uses high doses of energy to eradicate cancer cells and control tumors. Various treatment schedules have been developed and tried in clinical trials, yet significant obstacles remain to improving the radiotherapy fractionation. Genetic and non-genetic cellular diversity within tumors can lead to different radiosensitivity among cancer cells that can affect radiation treatment outcome. We propose a minimal mathematical model to study the effect of tumor heterogeneity and repair in different radiation treatment schedules. We perform stochastic and deterministic simulations to estimate model parameters using available experimental data. Our results suggest that gross tumor volume reduction is insufficient to control the disease if a fraction of radioresistant cells survives therapy. If cure cannot be achieved, protocols should balance volume reduction with minimal selection for radioresistant cells. We show that the most efficient treatment schedule is dependent on biology and model parameter values and, therefore, emphasize the need for careful tumor-specific model calibration before clinically actionable conclusions can be drawn.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Al-Hajj Muhammad, Wicha Max S, Benito-Hernandez Adalberto, Morrison Sean J, Clarke Michael F (2003) Prospective identification of tumorigenic breast cancer cells. Proc Nat Acad Sci 100(7):983–3988
Bao Shideng, Qiulian Wu, McLendon Roger E, Hao Yueling, Shi Qing, Hjelmeland Anita B, Dewhirst Mark W, Bigner Darell D, Rich Jeremy N (2006) Glioma stem cells promote radioresistance by preferential activation of the DNA damage response. Nature 444:756–760
Baumann Michael, Krause Mechthild, Hill Richard (2008) Exploring the role of cancer stem cells in radioresistance. Nat Rev Cancer 8:545–554
Conforti Domenico, Guerriero Francesca, Guido Rosita (2008) Optimization models for radiotherapy patient scheduling. 4OR 6:263–278
Dhawan Andrew, Kohandel Mohammad, Hill Richard, Sivaloganathan Sivabal (2014) Tumour control probability in cancer stem cells hypothesis. PLoS ONE 9:e96093
Dionysiou Dimitra D, Stamatakos Georgios S, Uzunoglu Nikolaos K, Nikita Konstantina S, Marioli Antigoni (2004) A four-dimensional simulation model of tumour response to radiotherapy in vivo: parametric validation considering radiosensitivity, genetic profile and fractionation. J Theor Biol 230:1–20
Enderling Heiko, Park Derek, Hlatky Lynn, Hahnfeldt Philip (2009) The importance of spatial distribution of stemness and proliferation state in determining tumor radioresponse. Math Model Nat Phenom 4:117–133
Enderling Heiko, Anderson Alexander RA, Chaplain Mark AJ, Beheshti Afshin, Hlatky Lynn, Hahnfeldt Philip (2009) Paradoxical dependencies of tumor dormancy and progression on basic cell kinetics. Cancer Res 69(22):8814–8821
Fillmore Christine M, Kuperwasser Charlotte (2008) Human breast cancer cell lines contain stem-like cells that self-renew, give rise to phenotypically diverse progeny and survive chemotherapy. Breast Cancer Res 10(2):1
Fowler John F (1989) The linear-quadratic formula and progress in fractionated radiotherapy. Br Jo Radiol 62:679–694
Gao Xuefeng, McDonald John T, Hlatky Lynn, Enderling Heiko (2013) Acute and fractionated irradiation differentially modulate glioma stem cell division kinetics. Cancer Res 73(5):1481–1490
Gupta Piyush B, Fillmore Christine M, Jiang Guozhi, Shapira Sagi D, Tao Kai, Kuperwasser Charlotte, Lander Eric S (2011) Stochastic state transitions give rise to phenotypic equilibrium in populations of cancer cells. Cell 146:633–644
Hall Eric J, Giaccia Amato J (2006) Radiobiology for the radiologist. Lippincott Williams and Wilkins, Philadelphia
Haviland Joanne S, Owen J Roger, Dewar John A, Agrawal Rajiv K, Barrett Jane, Barrett-Lee Peter J, Dobbs H Jane et al (2013) The UK Standardisation of Breast Radiotherapy (START) trials of radiotherapy hypofractionation for treatment of early breast cancer: 10-year follow-up results of two randomised controlled trials. Lancet Oncol 14:1086–1094
Lagadec Chann, Vlashi Erina, Della Donna Lorenza, Meng YongHong, Dekmezian Carmen, Kim Kwanghee, Pajonk Frank (2010) Survival and self-renewing capacity of breast cancer initiating cells during fractionated radiation treatment. Breast Cancer Res 12:R13
Leder Kevin, Pitter Ken, LaPlant Quincey, Hambardzumyan Dolores, Ross Brian D, Chan Timothy A, Holland Eric C, Michor Franziska (2014) Mathematical modeling of PDGF-driven glioblastoma reveals optimized radiation dosing. Cell 156:603–616
Mathews Lesley A, Cabarcas Stephanie M, Hurt Elaine M (2013) DNA repair of cancer stem cells. Springer, Berlin
Marjanovic Nemanja D, Weinberg Robert A, Chaffer Christine L (2013) Cell plasticity and heterogeneity in cancer. Clin Chem 59:168–179
Phillips Tiffany M, McBride William H, Pajonk Frank (2006) The response of CD24-/low/CD44+ breast cancer initiating cells to radiation. J Natl Cancer Inst 98:1777–1785
Reya Tannishtha, Morrison Sean J, Clarke Michael F, Weissman Irving L (2001) Stem cells, cancer, and cancer stem cells. Nature 414:105–111
Sarcar Bhaswati et al (2011) Targeting radiation-induced G2 checkpoint activation with the Wee-1 inhibitor MK-1775 in glioblastoma cell lines. Mol Cancer Ther 10:2405–2414
Stamatakos GS, Antipas VP, Uzunoglu NK, Dale RG (2014) A four-dimensional computer simulation model of the in vivo response to radiotherapy of glioblastoma multiforme: studies on the effect of clonogenic cell density. Br J Radiol 79:389
Shackleton Mark, Quintana Elsa, Fearon Eric R, Morrison Sean J (2009) Heterogeneity in cancer: cancer stem cells versus clonal evolution. Cell 138:822–829
Trialists’ Group (2008) The START, The UK Standardisation of Breast Radiotherapy (START) Trial B of radiotherapy hypofractionation for treatment of early breast cancer: a randomised trial. Lancet 371:1098–1107
Wein Lawrence M, Cohen Jonathan E, Wu Joseph T (2000) Dynamic optimization of a linear-quadratic model with incomplete repair and volume-dependent sensitivity and repopulation. Int J Radiat Oncol Biol Phys 47:1073–1083
Withers HR (1992) Biological basis of radiation therapy for cancer. Lancet 339(8786):156–9
Acknowledgements
Financial support by the Natural Sciences and Engineering Research Council of Canada (NSERC) (MK) is gratefully acknowledged.
Author information
Authors and Affiliations
Corresponding authors
Electronic supplementary material
Below is the link to the electronic supplementary material.
Rights and permissions
About this article
Cite this article
Forouzannia, F., Enderling, H. & Kohandel, M. Mathematical Modeling of the Effects of Tumor Heterogeneity on the Efficiency of Radiation Treatment Schedule. Bull Math Biol 80, 283–293 (2018). https://doi.org/10.1007/s11538-017-0371-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11538-017-0371-5