How should breathing motion be combined with other errors when drawing margins around clinical target volumes?

Geometric uncertainties in radiotherapy treatment may be accommodated by drawing an adequate margin around the clinical target volume (CTV). The width of the margin is commonly based upon the quadrature sum of the standard deviations of the contributory errors. This approach is satisfactory when the probability distributions of the component errors are Gaussian, but breathing-induced motion of the CTV is generally not Gaussian. This paper shows that the blurred dose distribution D(z) arising from a step function beam edge that is moving cyclically along the z-axis is given by D(z) = 2t/tau, where t(z) relates time to position and tau is the cycle duration. Applying this relation to realistic breathing models results in a dose distribution in which the sharp edge of the step function is still evident even after blurring caused by the motion. This suggests that breathing-induced motion should be accounted for separately, with the breathing margin added linearly to the quadrature sum of the other contributing errors.