Biologic and physical fractionation effects of random geometric errors

Abstract

Purpose: We are developing a system to model the effect of random and systematic geometric errors on radiotherapy delivery. The purpose of this study was to investigate biologic and physical fractionation effects of random geometric errors and respiration motion and compare the resulting dose distributions with Gaussian blurring of the planned dose.

Materials and methods: A hypothetical dose distribution with Gaussian penumbra was used. Random errors drawn from a normal distribution, optionally combined with simulated respiration motion (in the cranio-caudal direction), were used to displace the dose distribution for N simulated fractions. To simulate biologic effects of fractionation, the physical dose was converted to a biologically effective dose using the linear-quadratic model (including repopulation), then summed and converted back to physical dose for comparison. Differences between dose distributions were quantified in terms of the distance between selected isodose levels.

Results: A limited number of fractions led to an uncertainty in the position of isodose levels in the total dose with as standard deviation (SD) the SD of the random error divided by radical N. Due to biologic fractionation effects, the total dose distribution became slightly wider: 0.4 mm for alpha/beta = 1 Gy and a random error SD of 3 mm. The widening increased with random error and reduced with increasing alpha/beta but does not depend on the number of fractions or on repopulation. Respiration motion caused an asymmetric deviation in the shape of the total dose distribution, but no additional dose widening was seen from the biologic effect of fractionation. With a random error SD of 3 mm and respiration amplitude, A, of 1 cm or less (SD < 0.36 cm), the asymmetry was negligible. For larger respiration amplitudes (combined with the same random error), the shift of the 95% isodose level was about 0.25*A caudally, and 0.45*A cranially.

Conclusions: Gaussian blurring with a combined SD of organ motion, setup error, and respiration motion is a valid approximation for the effect of purely random errors in fractionated radiotherapy. For respiration motion in excess of 1 cm in amplitude, isodose lines shift in a distinctly asymmetric fashion and asymmetric margins need to be used.