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Radiotherapy scheduling using prime numbers

Published online by Cambridge University Press:  22 August 2013

J. McLaughlin  and
L. Marignol
J. McLaughlin*
Affiliation:
School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland
L. Marignol
Affiliation:
Applied Radiation Therapy Trinity, Discipline of Radiation Therapy, Trinity Centre for Health Sciences, St James's Hospital, Dublin, Ireland
*
Correspondence to: Dr Jonathan McLaughlin, School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland. Tel: +353 86 1014777. E-mail: [email protected]
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Abstract

Background

The optimal delivery of radiation therapy to achieve maximum tumour cell kill while limiting damage to normal tissues underlies any radiation therapy treatment protocol. The biological effectiveness of radiation therapy is closely related to cellular reproductive activity. The scheduling of dose fraction to a time where actively dividing cells are at their most radiosensitive stage (RS) has potential to enhance therapeutic efficacy.

Materials and methods

A prime number is a natural number >1 whose only divisors are 1 and the number itself.

Purpose

We propose that the use of prime numbers in the scheduling of radiotherapy treatments could maximise biological effectiveness by facilitating the irradiation of the greatest number of cells at their most RS stage, and ultimately improve the therapeutic ratio of radiation therapy.

Conclusions

The theoretical clinical implementation of this concept into the scheduling of radiation therapy is discussed.

Keywords

prime numbersradiationscheduling
Type
Original Articles
Information
Journal of Radiotherapy in Practice , Volume 13 , Issue 3 , September 2014 , pp. 317 - 321
Copyright
Copyright © Cambridge University Press 2013 

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References

1.McKay, M, Peters, L. Genetic determinants of radiation response. Report on a symposium held at Peter MacCallum Cancer Institute, Melbourne, Australia, 8 August 1996. Int J Radiat Biol 1997; 71: 225–229.Google Scholar
2.Marcu, L G. Altered fractionation in radiotherapy: from radiobiological rationale to therapeutic gain. Cancer Treat Rev 2010; 36: 606–614.Google Scholar
3.Gregoire, V, Jeraj, R, Lee, J A, O'Sullivan, B. Radiotherapy for head and neck tumours in 2012 and beyond: conformal, tailored, and adaptive? Lancet Oncol 2012; 13: e292–e300.CrossRefGoogle ScholarPubMed
4.Bauman, G, Rumble, R B, Chen, J, Loblaw, A, Warde, P, Members of the IIEP. Intensity-modulated radiotherapy in the treatment of prostate cancer. Clin Oncol (R Coll Radiol) 2012; 24: 461–473.CrossRefGoogle ScholarPubMed
5.Seel, M, Foroudi, F. Waiting for radiation therapy: does it matter? Australas Radiol 2002; 46: 275–279.CrossRefGoogle ScholarPubMed
6.Lawrence, Y R, Blumenthal, D T, Matceyevsky, D, Kanner, A A, Bokstein F Corn, B W. Delayed initiation of radiotherapy for glioblastoma: how important is it to push to the front (or the back) of the line? J Neurooncol 2011; 105: 1–7.CrossRefGoogle Scholar
7.Scoccianti, S, Agresti, B, Simontacchi, Get al. From a waiting list to a priority list: a computerized model for an easy-to-manage and automatically updated priority list in the booking of patients waiting for radiotherapy. Tumori 2012; 98: 728–735.Google Scholar
8.Martin, J M, Ryan, G, Duchesne, G. Clinical prioritisation for curative radiotherapy: a local waiting list initiative. Clin Oncol (R Coll Radiol) 2004; 16: 299–306.Google Scholar
9.Brown, A M, Atyeo, J, Field, N, Cox, J, Bull, C, Gebski, V J. Evaluation of patient preferences towards treatment during extended hours for patients receiving radiation therapy for the treatment of cancer: a time trade-off study. Radiother Oncol 2009; 90: 247–252.CrossRefGoogle Scholar
10.Calman, F, White, L, Beckingham, E, Deehan, C. When would you like to be treated?--A short survey of radiotherapy outpatients. Clin Oncol (R Coll Radiol) 2008; 20: 184–190.CrossRefGoogle ScholarPubMed
11.Gupta, T, Dutta, D, Trivedi, S, Upasani, M, Jalali, R, Sarin, R. Assessment of compliance to treatment and efficacy of a resource-sparing hypofractionated radiotherapy regimen in patients with poor-prognosis high-grade gliomas. J Cancer Res Ther 2010; 6: 272–277.CrossRefGoogle ScholarPubMed
12.Tang, J I, Shakespeare, T P, Lu, J Jet al. Patients’ preference for radiotherapy fractionation schedule in the palliation of symptomatic unresectable lung cancer. J Med Imaging Radiat Oncol 2008; 52: 497–502.Google Scholar
13.Dwyer, P, Hickey, B, Burmeister, E, Burmeister, B. Hypofractionated whole-breast radiotherapy: impact on departmental waiting times and cost. J Med Imaging Radiat Oncol 2010; 54: 229–234.Google Scholar
14.Bergonie, J, Tribondeau, L. Interpretation of some results from radiotherapy and an attempt to determine a rational treatment technique. 1906. Yale J Biol Med 2003; 76: 181–182.Google Scholar
15.Krause, M, Yaromina, A, Eicheler, W, Koch, U, Baumann, M. Cancer stem cells: targets and potential biomarkers for radiotherapy. Clin Cancer Res 2011; 17: 7224–7229.Google Scholar
16.Marples, B, Wouters, B G, Collis, S J, Chalmers, A J, Joiner, M C. Low-dose hyper-radiosensitivity: a consequence of ineffective cell cycle arrest of radiation-damaged G2-phase cells. Radiat Res 2004; 161: 247–255.Google Scholar
17.Sinclair, W K. Cyclic X-ray responses in mammalian cells in vitro. Radiat Res 1968; 33: 620–643.CrossRefGoogle ScholarPubMed
18.Endlich, B, Radford, I R, Forrester, H B, Dewey, W C. Computerized video time-lapse microscopy studies of ionizing radiation-induced rapid-interphase and mitosis-related apoptosis in lymphoid cells. Radiat Res 2000; 153: 36–48.Google Scholar
19.Quiet, C A, Weichselbaum, R R, Grdina, D J. Variation in radiation sensitivity during the cell cycle of two human squamous cell carcinomas. Int J Radiat Oncol Biol Phys 1991; 20: 733–738.CrossRefGoogle ScholarPubMed
20.Saito, S, Hasegawa, S, Sekita, Aet al. Manganese-enhanced MRI reveals early-phase radiation-induced cell alterations in vivo. Cancer Res 2013; 73: 3216–3224.Google Scholar
21.McKinley, E T, Ayers, G D, Smith, R Aet al. Limits of [18F]-FLT PET as a biomarker of proliferation in oncology. PLoS One 2013; 8: e58938.CrossRefGoogle ScholarPubMed
22.McIntosh, A, Hagspiel, K D, Al-Osaimi, A Met al. Accelerated treatment using intensity-modulated radiation therapy plus concurrent capecitabine for unresectable hepatocellular carcinoma. Cancer 2009; 115: 5117–5125.CrossRefGoogle ScholarPubMed
23.Rich, T A, Shelton, C H 3rd, Kirichenko, A, Straume, M. Chronomodulated chemotherapy and irradiation: an idea whose time has come? Chronobiol Int 2002; 19: 191–205.CrossRefGoogle ScholarPubMed
24.Liao, C, Li, J, Bin, Q, Cao, Y, Gao, F. Chronomodulated chemotherapy versus conventional chemotherapy for advanced colorectal cancer: a meta-analysis of five randomized controlled trials. Int J Colorectal Dis 2010; 25: 343–350.Google Scholar
25.Brizel, D M. Pharmacologic approaches to radiation protection. J Clin Oncol 2007; 25: 4084–4089.Google Scholar
26.Begg, A C, Stewart, F A, Vens, C. Strategies to improve radiotherapy with targeted drugs. Nat Rev Cancer 2011; 11: 239–253.Google Scholar
27.Baker, F L, Sanger, L J, Rodgers, R W, Jabboury, K, Mangini, O R. Cell proliferation kinetics of normal and tumour tissue in vitro: quiescent reproductive cells and the cycling reproductive fraction. Cell Prolif 1995; 28: 1–15.Google Scholar
28.Bernard, S, Cajavec Bernard, B, Levi, F, Herzel, H. Tumor growth rate determines the timing of optimal chronomodulated treatment schedules. PLoS Comput Biol 2010; 6: e1000712.CrossRefGoogle ScholarPubMed