Implications of 3-dimensional target shape and motion in aperture design

To determine the shape of a radiation beam aperture a margin is typically applied to the clinical target volume (CTV) to yield the planning target volume (PTV), and the aperture is then determined from the projection of the PTV onto the aperture plane. This margin accounts for setup variability and organ motion originating from respiration or other physiologic processes. The use of either a uniform margin, or alternatively one which takes into account only the expected magnitude and direction of target motion, fails to account for the three-dimensional nature of the target; such a method neglects the volumetric effect of target shape on the fractional target volume irradiated when the target shifts partially out of the aperture. A mathematical framework is developed to analyze and illustrate the consequences of irradiating an irregular target shape in the presence of target motion. The effect of target shape on volume coverage is demonstrated for selected cases involving conventional BEV aperture design techniques. The volumetric implications of target shape are considered from two complementary points of view. The first involves transformation into a "displacement space," which isolates the volumetric effect of the shape of the target allowing it to be studied independently of the probability distribution of target motion. The second point of view combines the effects of the 3D target shape and the probability distribution of motion in a manner independent of beam direction to yield a 3D "target distribution." The two points of view represent distinct starting points for computation of the expected value of fractional target volume coverage in the presence of target motion. In certain cases it may be beneficial to (1) employ "target distributions" for the target and normal tissues in place of the conventional static PTV and, (2) include the aperture shape, on equal footing with parameters such as beam weights and energies, into a quantitative optimization process explicitly accounting for uncertainties in the position of the target volume and critical structures.