Beam configurations for 3D tomographic intensity modulated radiation therapy.

We extend the theory of three-dimensional (3D) tomographic intensity modulated radiation therapy (IMRT). The geometry consists of two-dimensional modulated beams on a sphere centred in the tumour. The theory provides an efficient algorithm for computing beam modulation patterns that approximately 'reconstruct' the prescribed dose function. In this paper optimum beam numbers are estimated from dose function spherical harmonics using the 3D projection-slice theorem. An extension to three dimensions of the 'Bow Tie' criterion for beam numbers is derived. The effects of insufficient beam front sampling and beam numbers are characterized with a configuration-dependent matrix. Factors that independently increase beam numbers, such as tumour size and shape, are related to the spherical harmonic content in the dose function. Examples of tomographic IMRT reconstruction with a 3D concave tumour are given.