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Mathematical Biosciences and Engineering (MBE)
 

The consequence of day-to-day stochastic dose deviation from the planned dose in fractionated radiation therapy
Pages: 159 - 170, Issue 1, February 2016

doi:10.3934/mbe.2016.13.159      Abstract        References        Full text (664.3K)           Related Articles

Subhadip Paul - National Brain Research Centre, Manesar, Gurgaon, Haryana-122051, India (email)
Prasun Kumar Roy - National Brain Research Centre, Manesar, Gurgaon, Haryana-122051, India (email)

1 E. Budiarto, M. Keijzer, P. R. M. Storchi, A. W. Heemink, S. Breedveld and B. J. M. Heijmen, Computation of mean and variance of the radiotherapy dose for PCA-modeled random shape and position variations of the target, Phys. Med. Biol., 59 (2014), 289-310.
2 J. F. Fowler, The linear-quadratic formula and progress in fractionated radiotherapy, Br. J. Radiol., 62 (1989), 679-694.
3 L. Gammaitoni, P. Hänggi, P. Jung and F. Marchesoni, Stochastic Resonance: A remarkable idea that changed our perception of noise, Eur. Phys. J. B, 69 (2009), 1-3.
4 A. Godley, E. Ahunbay, C. Peng and X. A. Li, Accumulating daily-varied dose distributions of prostate radiation therapy with soft-tissue-based kV CT guidance, J. Appl. Clin. Med. Phys., 13 (2012), 1-3.
5 M. Guerrero and M. Carlone, Mechanistic formulation of a lineal-quadratic-linear (LQL) model: Split-dose experiments and exponentially decaying sources, Med. Phys., 37 (2010), 4173-4181.
6 W. Horsthemke and R. Lefever, Noise-Induced Transitions in Physics, Chemistry, and Biology, $2^{nd}$ edition, Springer, Berlin, 2006.
7 B. Huang, W. Wang, M. Bates and X. Zhuang, Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy, Science, 319 (2008), 810-813.
8 J. L. W. V. Jensen, Sur les fonctions convexes et les inégalités entre les valeurs moyennes, Acta Math., 30 (1906), 175-193.       
9 M. C. Joiner and A. Kogel, Basic Clinical Radiobiology, $4^{th}$ edition, CRC Press, Boca Raton, 2009.
10 P. E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations, $1^{st}$ edition, Springer, London, 1992.       
11 D. E. Lea, Actions of Radiations on Living Cells, $2^{nd}$ edition, Cambridge University Press, New York, 1962.
12 G. Murphy, W. Lawrence and R. Lenard, ACS Textbook of Clinical Oncology, $2^{nd}$ edition, The American Cancer Society, Inc., Atlanta, 1995.
13 T. Needham, A visual explanation of Jensen's inequality, Amer. Math. Monthly, 100 (1993), 768-771.       
14 J. J. Ruel and M. P. Ayres, Jensen's inequality predicts effects of environmental variation, Trends Ecol. Evol., 14 (1999), 361-366.
15 F. C. Su, C. Shi, P. Mavroidis, P. R. Szegedi and N. Papanikolaou, Evaluation on lung cancer patients' adaptive planning of TomoTherapy utilising radiobiological measures and planned adaptive module, J. Radiother. Pract., 8 (2009), 185-194.
16 E. Ullner, J. Buceta, A. Díez-Noguera and J. García-Ojalvo, Noise-induced coherence in multicellular circadian clocks, Biophys. J., 96 (2009), 3573-3581.
17 D. Yan, F. Vicini, J. Wong and A. Martinez, Adaptive radiation therapy, Phys. Med. Biol., 42 (1997), 123-132.
18 E. C. Zimmermann and J. Ross, Light induced bistability in $S_2 0_6 F_2$ ⇌ $2S0_3 F$: Theory and experiment, J. Chem. Phys., 80 (1984), 720-729.

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