Optimization of aperture shape to explicitly account for organ motion and setup error

Purpose: To explicitly account for organ motion and setup error in the design of apertures for non intensity modulated beams in external beam radiotherapy. For sites in which the target dose is severely limited by irradiation of adjacent critical structures, a promising alternative to the ICRU-50 methodology involves abandoning the concept of a Planning Target Volume(PTV) in favor of quantitatively accounting for target motion by directly optimizing the shape of the beam apertures based on the choice of beam configuration, the 3D shape of the Clinical Target Volume(CTV) and Organs at Risk(OARs), and the corresponding probability distributions of motion. However, an optimization with dosimetric or biological score functions requires re-computation of the dose distribution for each iterative modification of the aperture shape. Searching the entire space of possible aperture shapes in a multi-beam plan is computationally intensive, and also can result in wasted computation for shapes that would clearly be classified as unreasonable apertures. We present an algorithm that efficiently produces for each beam portal a small family of aperture shapes of increasing sizes, comprising a particular subset of all possible shapes. For a given configuration of beams, this subset maximizes a linear score function S of the expected values of the volume of CTV and OARs irradiated, explicitly accounting for the 3D shape of the CTV and OARs, their joint probability distribution of motion, and the choice of beam configuration. This permits a dosimetric optimization to be carried out computing dose only for apertures in a small sub-space of the larger parameter space of all possible aperture shapes. Materials and Methods: A method has been developed to estimate the 3D probability distribution of motion of each Volume of Interest(VOI) using data from serial imaging studies. This probability distribution is folded with the 3D shape of the VOI to generate a function that will be referred to as the 'target distribution' of the VOI. The value of the target distribution at a fixed point in space, (x', y', z'), is equal to the probability that during the delivery of any given fraction (x', y', z') will be enclosed by the corresponding VOI. Projections are computed of the target distribution of each VOI onto the aperture plane of each beam. These projections are used to calculate the unique aperture shape that maximizes the score function S =< Vt - Σ wi · VOARi >. The score S is a linear combination of the expected value of the volume of CTV irradiated, Vt, and a weighed sum of expected values of normal tissue irradiated, VOARi. We show that given a set of weightswi , the maximum of S can be found by single iteration over the pixels on the aperture plane. Results: A family of apertures for AP and lateral prostate fields is presented. In this particular site, two weightswi are involved, corresponding to the bladder and rectum. Conclusion: It is conceptually useful to define an N dimensional 'weight space', with N is equal to number of OARs(typically one or two) and the position along the ith axis in this space, wi, corresponding to the arbitrary weight assigned to the ith OAR in the score function S. The choice of weights is analogous to a choice of aperture size, with larger weights corresponding to smaller apertures. Each beam is conceptually parametrized by a single point in weight space, defining the shape of the portal, and by a uniform beam intensity. Aperture shape can thereby be incorporated into a dosimetric treatment plan optimization process on equal footing with beam weights and energies