title: Application of the equivalent uniform stochastic dose (EUSD) to TCP calculations incorporating dose uncertainty and fractionation effects.
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. Applying ESD 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 in tolerance 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 (alpha=0.3, alpha/beta=10, N0=10(8)) 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 the tolerance uncertainty reduces with decreased number of fractions indicating that hypo-fractionated treatments may require more accurate dose delivery.
authors.affiliation: Department of Medical Physics, British Columbia Cancer Agency, Vancouver Island Centre, Victoria, BC, Canada. szavgorodni@bccancer.bc.ca
authors.forename: Sergei
authors.initials: S
authors.lastname: Zavgorodni
mesh_terms: D001822:Body Burden; D003198:Computer Simulation; D019583:Dose Fractionation, Radiation; D006801:Humans; D008954:Models, Biological; D009369:Neoplasms / Q000532:radiotherapy*; D011874:Radiometry / Q000379:methods*; D011880:Radiotherapy Planning, Computer-Assisted / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D013269:Stochastic Processes