The width of margins in radiotherapy treatment plans

Publication of ICRU Reports 50 and 62 has highlighted the need to devise protocols for the process of drawing the planning target volume (PTV) around the clinical target volume (CTV). The margin surrounding the CTV should be wide enough to account for all geometric errors so that no part of the CTV accumulates a dose less than, for instance, 95% of that prescribed. One approach to the problem has been to draw a margin around the CTV delineated at the treatment preparation stage which is sufficiently wide that the mean position of the CTV will be encompassed in a specific percentage of cases, for example 90%. This accounts for the systematic errors. A further margin is then drawn to account for random set-up and organ-motion uncertainties during treatment. The width of this second margin has previously been shown to be 1.64(sigma - sigma (p)). Here sigma, a vector quantity, is the standard deviation which results from convolving the penumbra spread function of standard deviation sigma (p) with the Gaussian distributions of the daily positional uncertainties of organ motion and set-up error. However, it is shown in this paper that the calculation should take into account the beam configuration of the treatment plan. In a typical coplanar multibeam plan, usually in the transverse plane, any given edge of the target volume is normally defined by a single beam or two parallel and opposed beams. However, because of the presence of the other beams, the effect of the blurring of the edge-defining beam(s) is reduced, which changes the value of the required margin to beta(sigma - sigma (p)) where, for example, beta can be as low as 1.04 in the transverse plane of a three-beam plan. The width of the required margins is calculated for up to six beams and presented in a table. It is shown that, while the table was derived using an idealized plan of equally weighted plane beams irradiating a spherical target, it is also valid for non-uniform beam weightings, wedged-beam plans, target volumes of general shape and intensity-modulated radiotherapy (IMRT).