In two dimensions, 2-Step Intensity Modulated Arc Therapy (2-Step IMAT) and 2-Step Intensity Modulated Radiation Therapy (IMRT) were shown to be powerful methods for the optimization of plans with organs at risk (OAR) (partially) surrounded by a target volume (PTV). In three dimensions, some additional boundary conditions have to be considered to establish 2-Step IMAT as an optimization method. A further aim was to create rules for ad hoc adaptations of an IMRT plan to a daily changing PTV-OAR constellation. As a test model, a cylindrically symmetric PTV-OAR combination was used. The centrally placed OAR can adapt arbitrary diameters with different gap widths toward the PTV. Along the rotation axis the OAR diameter can vary, the OAR can even vanish at some axis positions, leaving a circular PTV. The width and weight of the second segment were the free parameters to optimize. The objective function f to minimize was the root of the integral of the squared difference of the dose in the target volume and a reference dose. For the problem, two local minima exist. Therefore, as a secondary criteria, the magnitude of hot and cold spots were taken into account. As a result, the solution with a larger segment width was recommended. From plane to plane for varying radii of PTV and OAR and for different gaps between them, different sets of weights and widths were optimal. Because only one weight for one segment shall be used for all planes (respectively leaf pairs), a strategy for complex three-dimensional (3-D) cases was established to choose a global weight. In a second step, a suitable segment width was chosen, minimizing f for this global weight. The concept was demonstrated in a planning study for a cylindrically symmetric example with a large range of different radii of an OAR along the patient axis. The method is discussed for some classes of tumor/organ at risk combinations. Noncylindrically symmetric cases were treated exemplarily. The product of width and weight of the additional segment as well as the integral across the segment profile was demonstrated to be an important value. This product was up to a factor of 3 larger than in the 2-D case. Even in three dimensions, the optimized 2-Step IMAT increased the homogeneity of the dose distribution in the PTV profoundly. Rules for adaptation to varying target-OAR combinations were deduced. It can be concluded that 2-Step IMAT and 2-Step IMRT are also applicable in three dimensions. In the majority of cases, weights between 0.5 and 2 will occur for the additional segment. The width-weight product of the second segment is always smaller than the normalized radius of the OAR. The width-weight product of the additional segment is strictly connected to the relevant diameter of the organ at risk and the target volume. The derived formulas can be helpful to adapt an IMRT plan to altering target shapes.
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