Coordinate transformation as a primary representation of radiotherapy beam geometry

An approach to both geometric specification of radiotherapy beams and computerized solution of geometric treatment planning problems using coordinate transformations is presented. It is demonstrated that the specification of the geometric relationship of a treatment beam to a patient can be uniquely given by a 4 x 4 coordinate transformation matrix, and that the matrix representation can be translated from (and to) the more conventional machine-based specification of geometry. This approach enables a compact representation of the patient/beam geometry which is independent of the specific labeling conventions of the treatment machine and which can be directly exploited in the solution of treatment planning problems. Beam geometry can be easily described either in terms of the natural degrees of freedom of a therapy machine or in terms of alternative, problem-specific frames of reference. The ability to use these various frames of reference interchangeably allows the designer of treatment design software to present appropriate task-specific user interfaces for arbitrarily complex tasks, and thus reduce the cognitive burden on users of the software.