On the use of Cimmino's simultaneous projections method for computing a solution of the inverse problem in radiation therapy treatment planning

In radiation therapy one is confronted with the task of formulating a treatment plan which delivers a specified dose to a tumour but avoids irreparable damage to surrounding uninvolved structures. Radiation therapy treatment planning (RTTP) involves an inverse and a forward problem. The inverse problem is to devise a treatment plan, i.e. a radiation beam configuration and beam weighting, which provides a specified dose distribution to the delineated region. The forward problem is to calculate the dose distribution within the patient that results from the weighted radiation beam configuration. Since no analytic closed-form mathematical formulation of the forward operator exists, the inverse problem actually calls for computerised inversion of data. This inversion is achieved by constructing a fully discretised model that leads to a system of linear inequalities. These inequalities are solved either by a row-action method or a block-Cimmino algorithm which allows the assignment of weights within each block of inequalities.