On probabilistically defined margins in radiation therapy

Margins about a target volume subject to external beam radiation therapy are designed to assure that the target volume of tissue to be sterilized by treatment is adequately covered by a lethal dose. Thus, margins are meant to guarantee that all potential variation in tumour position relative to beams allows the tumour to stay within the margin. Variation in tumour position can be broken into two types of dislocations, reducible and irreducible. Reducible variations in tumour position are those that can be accommodated with the use of modern image-guided techniques that derive parameters for compensating motions of patient bodies and/or motions of beams relative to patient bodies. Irreducible variations in tumour position are those random dislocations of a target that are related to errors intrinsic in the design and performance limitations of the software and hardware, as well as limitations of human perception and decision making. Thus, margins in the era of image-guided treatments will need to accommodate only random errors residual in patient setup accuracy (after image-guided setup corrections) and in the accuracy of systems designed to track moving and deforming tissues of the targeted regions of the patient's body. Therefore, construction of these margins will have to be based on purely statistical data. The characteristics of these data have to be determined through the central limit theorem and Gaussian properties of limiting error distributions. In this paper, we show how statistically determined margins are to be designed in the general case of correlated distributions of position errors in three-dimensional space. In particular, we show how the minimal margins for a given level of statistical confidence are found. Then, how they are to be used to determine geometrically minimal PTV that provides coverage of GTV at the assumed level of statistical confidence. Our results generalize earlier recommendations for statistical, central limit theorem-based recommendations for margin construction that were derived for uncorrelated distributions of errors (van Herk, Remeijer, Rasch and Lebesque 2000 Int. J. Radiat. Oncol. Biol. Phys. 47 1121-35; Stroom, De Boer, Huizenga and Visser 1999 Int. J. Radiat. Oncol. Biol. Phys. 43 905-19).