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An alternative VMAT with prior knowledge about the type of leaf motion utilizing projection method for concave targets.

The authors present an alternative approach to inverse planning optimization and apply it to volumetric modulated are therapy (VMAT) in one rotation with a prior knowledge about the type of leaf motions. The optimization is based on the projection theorem in inner product spaces. MLC motion is directly considered in the optimization, thus avoiding leaf segmentation characteristic of IMRT optimization. In this work they realize the method for concave irregular targets encompassing an organ at risk leading to a repetitive MLC motion pattern. Applying the projection theorem leads to a noniterative optimization method and reduces to solving few systems of linear equations with small numbers of dimensions. The solution of the inverse problem is unique, and false minima are naturally excluded. They divided the full rotation into about 50 short arc segments and for each segment decomposed dose into separate contributions related to stages of MLC motion. This results generally in an inverse problem with just four free parameters per arc segment. Practically three degrees of freedom will be used for the purpose of a constant angular speed of the gantry. Therefore the total number of degrees of freedom for a 3D problem is about 3 x 50 x number of collimator leaf pairs for irradiating the whole target volume in one rotation. Two 2D and one 3D concave target volumes are applied for a slice by slice optimization. A 6 MV photon beam model is used, including realistic scattering and attenuation, and a maximal leaf velocity of 3 cm/s is regarded. The resulting dose distributions cover the PTVs very well and have maxima at about 108% of dose in the PTVs. The OAR is spared very strong in all cases. As a result of optimization, the MLC apertures are repetitively opening and closing and can be interpreted in an intuitive way. Applying the projection method for this knowledge-based VMAT delivery scheme for concave target volumes is an alternative technique for dose optimization. There are several properties, such as uniqueness of MLC motions and their continuous dependence on geometry and prescribed dose, that make this approach interesting to inverse planning. This method is still in an investigational stage, but promising results are presented. In future work it will be extended directly (without conceptual changes) in several directions to be more clinically applicable.