Linear algebraic methods applied to intensity modulated radiation therapy

Methods of linear algebra are applied to the choice of beam weights for int ensity modulated radiation therapy (IMRT). It is shown that the physical in terpretation of the beam weights, target homogeneity and ratios of deposite d energy can be given in terms of matrix equations and quadratic forms. The methodology of fitting using linear algebra as applied to IMRT is examined . Results are compared with IMRT plans that had been prepared using a comme rcially available IMRT treatment planning system and previously delivered t o cancer patients.