Effects of averaging over motion and the resulting systematic errors in radiation therapy

The potential for systematic errors in radiotherapy of a breathing patient is considered using the statistical model of Bortfeld et al (2002 Phys. Med. Biol. 47 2203-20). It is shown that although averaging over 30 fractions does result in a narrow Gaussian distribution of errors, as predicted by the central limit theorem, the fact that one or a few samples of the breathing patient's motion distribution are used for treatment planning (in contrast to the many treatment fractions that are likely to be delivered) may result in a much larger error with a systematic component. The error distribution may be particularly large if a scan at breath-hold is used for planning.