Forward and adjoint methods for radiotherapy planning

The sensitivity theory developed for nuclear engineering applications is applied to radiotherapy planning. After emphasizing the mathematical equivalence of solving the Boltzmann equation in forward and adjoint spaces both mathematical approaches are implemented to calculate the sensitivities of the dose distributions in a mathematical phantom to changes in the source of radiation. The tagging of the functionals of the radiation field with the origin of the source (forward or adjoint) makes possible the calculation of the sensitivity of the dose to the position, angular distribution, intensity, and spectra of the source, in a very efficient way by using present day available codes and hardware. There is then a potential for a new, accurate and potentially faster method that does not rely on a trial and error methodology.