Clinical applications of geometrical field matching in radiotherapy based on a new analytical solution

A new analytical formalism has been published recently that provides all the parameters necessary for geometrical field matching in radiotherapy. The present work applies the general expressions for craniospinal irradiation, breast irradiation with a supraclavicular half-field, and breast irradiation with a supraclavicular full-field. We also explore the formalism as a tool to analyze and compare different techniques. Field matching is achieved by imposing both parallelism and coincidence between the side planes of adjacent fields. The rotation angles and either the field aperture for a certain isocenter position or the isocenter coordinates for a given field aperture are supplied. All of the already known exact solutions are reproduced. New expressions for the field aperture and for the isocenter coordinates, which were not previously available, are also computed. If tangential fields at a fixed source-to-skin distance are used together with a supraclavicular full-field, different apertures for each tangential field are required to achieve a correct match. If an isocentric technique for the tangential fields or a supraclavicular half-field is used, this complication is avoided. The breast technique with the supraclavicular half-field is recommended, because it presents several advantages with respect to the supraclavicular full-field. This formalism provides a useful tool in cases where matching of adjacent fields is necessary.