Optimization of Radiation Therapy Fractionation Schedules in the Presence of Tumor Repopulation

References

• Almquist KJ, Banks HT (1976) A theoretical and computational method for determining optimal treatment schedules in fractionated radiation therapy. Math. Biosciences 29:159–179.Crossref, Google Scholar
• Ang KK, Peters LJ (1992) Concomitant boost radiotherapy in the treatment of head and neck cancers. Seminars Radiation Oncology 2:31–33.Crossref, Google Scholar
• Armpilia CI, Dale RG, Jones B (2004) Determination of the optimum dose per fraction in fractionated radiotherapy when there is delayed onset of tumour repopulation during treatment. British J. Radiology 77:765–767.Crossref, Google Scholar
• Bading JR, Shields AF (2008) Imaging of cell proliferation: Status and prospects. J. Nucl. Med. 49:64S–80S.Crossref, Google Scholar
• Barendsen GW (1982) Dose fractionation, dose rate and iso-effect relationships for normal tissue responses. Internat. J. Radiation Oncology Biol. Phys. 8:1981–1997.Crossref, Google Scholar
• Bertuzzi A, Bruni C, Papa F, Sinisgalli C (2013) Optimal solution for a cancer radiotherapy problem. J. Math. Biol. 66:311–349.Crossref, Google Scholar
• Brahme A, Agren AK (1987) Optimal dose distribution for eradication of heterogeneous tumors. Acta Oncology 26:1–9.Crossref, Google Scholar
• Brenner DJ (1993) Accelerated repopulation during radiotherapy: Quantitative evidence for delayed onset. Radiation Oncology Investigations 1:167–172.Crossref, Google Scholar
• Chen M, Lu W, Chen Q, Ruchala K, Olivera G (2008) Adaptive fractionation therapy: II. Biological effective dose. Phys. Med. Biol. 53:5513–5525.Crossref, Google Scholar
• de la Zerda A, Armbruster B, Xing L (2007) Formulating adaptive radiation therapy (ART) treatment planning into a closed-loop control framework. Phys. Med. Biol. 52:4137–4153.Crossref, Google Scholar
• Deng G, Ferris MC (2008) Neuro-dynamic programming for fractionated radiotherapy planning. Springer Optim. Its Appl. 12:47–70.Crossref, Google Scholar
• Ferris MC, Voelker MM (2004) Fractionation in radiation treatment planning. Math. Programming 101:387–413.Crossref, Google Scholar
• Fowler JF (1989) The linear-quadratic formula and progress in fractionated radiotherapy. British J. Radiology 62:679–694.Crossref, Google Scholar
• Ghate A (2011) Dynamic optimization in radiotherapy. Geunes J, ed. TutORials in Operations Research: Transforming Research into Action (INFORMS, Catonsville, MD), 60–74.Google Scholar
• Guerrero M, Li XA (2003) Analysis of a large number of clinical studies for breast cancer radiotherapy: Estimation of radiobiological parameters for treatment planning. Phys. Med. Biol. 48:3307–3326.Crossref, Google Scholar
• Hall EJ, Giaccia AJ (2006) Radiobiology for the Radiologist (Lippincott Williams & Wilkins, Philadelphia).Google Scholar
• Harari PM (1992) Adding dose escalation to accelerated hyperfractionation for head and neck cancer: 76 Gy in 5 weeks. Seminars Radiation Oncology 2:58–61.Crossref, Google Scholar
• Hethcote HW, Waltman P (1973) Theoretical determination of optimal treatment schedules for radiation therapy. Radiation Res. 56:150–161.Crossref, Google Scholar
• Huang Z, Mayr NA, Gao M, Lo SS, Wang JZ, Jia G, Yuh WTC (2012) Onset time of tumor repopulation for cervical cancer: First evidence from clinical data. Internat. J. Radiation Oncology Biol. Phys. 84:478–484.Crossref, Google Scholar
• Jones B, Tan LT, Dale RG (1995) Derivation of the optimum dose per fraction from the linear quadratic model. British J. Radiology 68:894–902.Crossref, Google Scholar
• Keller H, Hope A, Meier G, Davison M (2013) A novel dose-volume metric for optimizing therapeutic ratio through fractionation: Retrospective analysis of lung cancer treatments. Med. Phys. 40:084101-1–084101-10.Crossref, Google Scholar
• Kim JJ, Tannock IF (2005) Repopulation of cancer cells during therapy: An important cause of treatment failure. Nature 5:516–525.Google Scholar
• Kim M (2010) A mathematical framework for spatiotemporal optimality in radiation therapy. Unpublished doctoral dissertation, University of Washington, Seattle.Google Scholar
• Kim M, Ghate A, Phillips MH (2009) A Markov decision process approach to temporal modulation of dose fractions in radiation therapy planning. Phys. Med. Biol. 54:4455–4476.Crossref, Google Scholar
• Kim M, Ghate A, Phillips MH (2012) A stochastic control formalism for dynamic biologically conformal radiation therapy. Eur. J. Oper. Res. 219:541–556.Crossref, Google Scholar
• Kutcher GJ, Burman C (1989) Calculation of complication probability factors for nonuniform normal tissue irradiation: The effective volume method. Internat. J. Radiation Oncology Biol. Phys. 16:1623–1630.Crossref, Google Scholar
• Kutcher GJ, Burman C, Brewster L, Goitein M, Mohan R (1991) Histogram reduction method for calculating complication probabilities for three-dimensional treatment planning evaluations. Internat. J. Radiation Oncology Biol. Phys. 21:137–146.Crossref, Google Scholar
• Laird AK (1964) Dynamics of tumor growth. British J. Cancer 18:490–502.Crossref, Google Scholar
• Ledzewicz U, Schättler H (2004) Application of control theory in modelling cancer chemotherapy. Internat. Conf. Control, Automation, Systems, Bangkok, Thailand.Google Scholar
• Lu W, Chen M, Chen Q, Ruchala K, Olivera G (2008) Adaptive fractionation therapy: I. Basic concept and strategy. Phys. Med. Biol. 53:5495–5511.Crossref, Google Scholar
• Lyman JT (1985) Complication probability as assessed from dose-volume histograms. Radiation Res. Suppl. 8:S13–S19.Crossref, Google Scholar
• Marks LB, Dewhirst M (1991) Accelerated repopulation: Friend or foe? Exploiting changes in tumor growth characteristics to improve the “efficiency” of radiotherapy. Internat. J. Radiation Oncology Biol. Phys. 21:1377–1383.Crossref, Google Scholar
• McAneney H, O’Rourke SFC (2007) Investigation of various growth mechanisms of solid tumour growth within the linear-quadratic model for radiotherapy. Phys. Med. Biol. 52:1039–1054.Crossref, Google Scholar
• Miralbell R, Roberts SA, Zubizarreta E, Hendry JH (2012) Dose-fractionation sensitivity of prostate cancer deduced from radiotherapy outcomes of 5,969 patients in seven international institutional data sets: α/β = 1.4 (0.9–2.2) Gy. Internat. J. Radiation Oncology Biol. Phys. 82:e17–e24.Crossref, Google Scholar
• Mizuta M, Takao S, Date H, Kishimoto N, Sutherland KL, Onimaru R, Shirato H (2012) A mathematical study to select fractionation regimen based on physical dose distribution and the linear-quadratic model. Internat. J. Radiation Oncology Biol. Phys. 84:829–833.Crossref, Google Scholar
• Munro TR, Gilbert CW (1961) The relation between tumour lethal doses and the radiosensitivity of tumour cells. British J. Radiology 34:246–251.Crossref, Google Scholar
• Norton L (1988) A Gompertzian model of human breast cancer growth. Cancer Res. 48:7067–7071.Google Scholar
• Norton L, Simon R (1977) Tumor size, sensitivity to therapy, and design of treatment schedules. Cancer Treatment Rep. 61:1307–1317.Google Scholar
• Norton L, Simon R (1986) The Norton-Simon hypothesis revisited. Cancer Treatment Rep. 70:163–169.Google Scholar
• Norton L, Simon R, Brereton HD, Bogden AE (1976) Predicting the course of Gompertzian growth. Nature 264:542–545.Crossref, Google Scholar
• O’Rourke S, McAneney H, Hillen T (2009) Linear quadratic and tumour control probability modelling in external beam radiotherapy. J. Math. Biol. 58:799–817.Crossref, Google Scholar
• Pedreira CE, Vila VB (1991) Optimal schedule for cancer chemotherapy. Math. Programming 52:11–17.Crossref, Google Scholar
• Porter EH (1980a) The statistics of dose/cure relationships for irradiated tumours. Part I. British J. Radiology 53:210–227.Crossref, Google Scholar
• Porter EH (1980b) The statistics of dose/cure relationships for irradiated tumours. Part II. British J. Radiology 53:336–345.Crossref, Google Scholar
• Ramakrishnan J, Craft D, Bortfeld T, Tsitsiklis JN (2012) A dynamic programming approach to adaptive fractionation. Phys. Med. Biol. 57:1203–1216.Crossref, Google Scholar
• Saberian F, Ghate A, Kim M (2014) Optimal fractionation in radiotherapy with multiple normal tissues. Accessed November 2014, http://ssrn.com/abstract=2478481.Google Scholar
• Saberian F, Ghate A, Kim M (2015) A two-variable linear program solves the standard linear-quadratic formulation of the fractionation problem in cancer radiotherapy. Oper. Res. Lett. 43:254–258.Crossref, Google Scholar
• Salari E, Unkelbach J, Bortfeld T (2014) A mathematical programming approach to the fractionation problem in chemoradiotherapy. Accessed November 2014, http://arxiv.org/abs/1312.5657.Google Scholar
• Sir MY, Epelman MA, Pollock SM (2012) Stochastic programming for off-line adaptive radiotherapy. Ann. Oper. Res. 496:767–797.Crossref, Google Scholar
• Swan GW (1981) Optimization of Human Cancer Radiotherapy (Springer, New York).Crossref, Google Scholar
• Swan GW (1984) Applications of Optimal Control Theory in Biomedicine (CRC Press, Boca Raton, FL).Google Scholar
• Tucker SL, Thames HD, Taylor JMG (1990) How well is the probability of tumor cure after fractionated irradiation described by Poisson statistics? Radiation Res. 124:273–282.Crossref, Google Scholar
• Unkelbach J, Craft D, Salari E, Ramakrishnan J, Bortfeld T (2013) The dependence of optimal fractionation schemes on the spatial distribution. Phys. Med. Biol. 58:159–167.Crossref, Google Scholar
• Usher JR (1980) Mathematical derivation of optimal uniform treatment schedules for the fractionated irradiation of human tumors. Math. Biosciences 49:157–184.Crossref, Google Scholar
• Wang JZ, Li XA (2005) Impact of tumor repopulation on radiotherapy planning. Internat. J. Radiation Oncology Biol. Phys. 61:220–227.Crossref, Google Scholar
• Wein LM, Cohen JE, Wu JT (2000) Dynamic optimization of a linear-quadratic model with incomplete repair and volume-dependent sensitivity and repopulation. Internat. J. Radiation Oncology Biol. Phys. 47:1073–1083.Crossref, Google Scholar
• Wheldon TE (1988) Mathematical Models in Cancer Research (IOP Publishing Ltd., Bristol, UK).Google Scholar
• Wheldon TE, Kirk J, Orr JS (1977) Optimal radiotherapy of tumour cells following exponential-quadratic survival curves and exponential repopulation kinetics. British J. Radiology 50:681–682.Crossref, Google Scholar
• Withers HR (1993) Treatment-induced accelerated human tumor growth. Seminars Radiation Oncology 3:135–143.Crossref, Google Scholar
• Withers HR, Taylor JMG, Maciejewski B (1988) The hazard of accelerated tumor clonogen repopulation during radiotherapy. Acta Oncologica 27:131–146.Crossref, Google Scholar
• Yakovlev AY, Pavlova L, Hanin LG (1994) Biomathematical Problems in Optimization of Cancer Radiotherapy (CRC Press, Boca Raton, FL).Google Scholar
• Yang Y, Xing L (2005) Optimization of radiotherapy dose-time fractionation with consideration of tumor specific biology. Med. Phys. 32:3666–3677.Crossref, Google Scholar
• Yorke ED, Fuks Z, Norton L, Whitmore W, Ling CC (1993) Modeling the development of metastasis from primary and locally recurrent tumors: Comparison with clinical data base for prostate cancer. Cancer Res. 53:2987–2993.Google Scholar
• Zietz S, Nicolini C (2007) Mathematical approaches to optimization of cancer chemotherapy. Phys. Med. Biol. 52:4137–4153.Crossref, Google Scholar