Abstract
A method of tumour control probability (TCP) evaluation that intrinsically accounts for the dose uncertainties is demonstrated in this paper. The dose uncertainty is taken into account through the concept of an equivalent stochastic dose (ESD) defined as the dose to a voxel that results in the mean expected survival fraction from a process randomly depositing a dose D. ApplyingESD to a non-uniform dose distribution yields the concept of equivalent uniform stochastic dose (EUSD). TCP is modeled to include dose uncertainty and dose inhomogeneity as TCP(EUSD). It is shown that Webb-Nahum and Niemierko-Goitein TCP models both converge to TCP(EUSD) when dose uncertainty is accounted for. TCPs were calculated for a tumour irradiated with a dose of 60 and 70 Gy at 2 Gy per fraction, where the dose uncertainty in tumour sub-volumes was variable. Effect of the dose fractionation on TCP in the presence of the dose uncertainty was also investigated using TCP(EUSD) model.Tolerance uncertainty on the dose resulting intolerance TCP loss (assumed as 5%) was calculated for a range of radiobiological parameters. TCP degradation due to the treatment dose uncertainty was evaluated. It is shown that degradation of the TCP is controlled by the voxels where the dose has high uncertainty. For a modeled tumour (α0.3, α/β=10, N0=108) irradiated with 60 Gy, 12 % dose uncertainty at 1% fractional tumour sub-volume reduced the TCP from 95% to 50%. Presented TCP(EUSD) model also demonstrated capability to robustly evaluate the loss of TCP due to the dose uncertainties at different fractionation regimens. It is shown that thetolerance uncertainty reduces with decreased number of fractions indicating that hypo-fractionated treatments may require more accurate dose delivery.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Lujan, A.E., Haken, R.K.T., Larsen, E.W. and Balter, J.M.,Quantization of setup uncertainties in 3-D dose calculations, Med. Phys.. 26: 2397–2402, 1999.
Keall, P.J., Siebers, J.V., Jeraj, R. and Mohan, R.,The effect of dose calculation uncertainty on the evaluation of radiotherapy plans, Med Phys, 27: 478–484, 2000.
Boyer, A.L. and Schultheiss, T.,Effects of dosimetric and clinical uncertainty on complication-free local tumor control, Radiother Oncol, 11: 65–71, 1988.
Brahme, A.,Dosimetric precision requirements in radiation therapy., Acta Radiol Oncol, 23: 379–391, 1984.
Booth, J.T. and Zavgorodni, S.F.,The effects of radiotherapy treatment uncertainties on the delivered dose distribution and tumour control probability, Australas Phys Eng Sci Med, 24: 71–78, 2001.
Ebert, M.A.,Viability of the EUD and TCP concepts as reliable dose indicators, Phys Med Biol, 45: 441–457, 2000.
Song, W.Y., Schaly, B., Bauman, G., Battista, J.J. and Van Dyk, J.,Evaluation of image-guided radiation therapy (IGRT) technologies and their impact on the outcomes of hypofractionated prostate cancer treatments: A radiobiologic analysis, Int J Radiat Oncol Biol Phys, 64: 289–300, 2006.
Craig, T., Moiseenko, V., Battista, J. and Van Dyk, J.,The impact of geometric uncertainty on hypofractionated external beam radiation therapy of prostate cancer, Int J Radiat Oncol Biol Phys, 57: 833–842, 2003.
Fowler, J.F.,The linear-quadratic formula and progress in fractionated radiotherapy, Br J Radiol, 62: 679–694, 1989.
Zavgorodni, S.,The impact of inter-fraction dose variations on biological equivalent dose (BED): the concept of equivalent constant dose, Phys. Med. Biol., 5333–5345, 2004.
Cranmer-Sargison, G. and Zavgorodni, S.,EUD-based radiotherapy treatment plan evaluation: incorporating physical and Monte Carlo statistical dose uncertainties, Physics in Medicine and Biology, 4097–4109, 2005.
Niemierko, A.,Reporting and analyzing dose distributions: A concept of equivalent uniform dose, Med Phys, 24: 103–110, 1997.
Song, W., Battista, J. and Van Dyk, J.,Limitations of a convolution method for modeling geometric uncertainties in radiation therapy: the radiobiological dose-per-fraction effect, Med Phys, 31: 3034–3045, 2004.
Niemierko, A. and Goitein, M.,Implementation of a model for estimating tumor control probability for an inhomogeneously irradiated tumor, Radiother Oncol, 29: 140–147, 1993.
Webb, S. and Nahum, A.E., A model for calculating tumour control probability in radiotherapy including the effects of inhomogeneous distributions of dose and clonogenic cell density, Phys Med Biol, 38: 653–666, 1993.
Webb, S., Evans, P.M., Swindell, W. and Deasy, J.O.,A proof that uniform dose gives the greatest TCP for fixed integral dose in the planning target volume, Phys. Med. Biol., 39: 2091, 1994.
Tome, W.A. and Fowler, J.F.,On cold spots in tumor subvolumes., Med Phys., 29: 1590–1598, 2002.
Wigg, D.Applied radiobiology and bioeffect planning Medical Physics Publishing, Madison, Wisconsin, 486, 2001.
Ebert, M.A. and Hoban, P.W.,Some characteristics of tumour control probability for heterogeneous tumours, Physics in Medicine and Biology, 41: 2125–2133, 1996.
Niemierko, A.,Response to “Comment on ‘Reporting and analyzing dose distributions: A concept of equivalent uniform dose’ ”[Med Phys. [bold 24], 1323-1324 (1997)], Medical Physics, 24: 1325–1327, 1997.
Brahme, A. and Agren, A.K.,Optimal dose distribution for eradication of heterogeneous tumours, Acta Oncol, 26: 377–385, 1987.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zavgorodni, S. Application of the equivalent uniform stochastic dose (EUSD) to TCP calculations incorporating dose uncertainty and fractionation effects. Australas. Phys. Eng. Sci. Med. 31, 1–9 (2008). https://doi.org/10.1007/BF03178447
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF03178447