Optimum beam configurations in tomographic intensity modulated radiation therapy

We review and extend the theory of tomographic dose reconstruction for intensity modulated radiotherapy (IMRT). We derive the basis for a saturation with beam number of dose conformation, and provide an analysis which ranks particular beam orientations in terms of the contribution to the delivered dose. Preferred beam directions are found which effectively reduce the number of beams necessary to achieve a given level of dose conformation. The analysis is a new application of the tomographic projection-slice theorem to the problem of beam orientation determination. The effects of the beam front filter and the positivity constraint arising from the tomographic approach are analysed, and modifications of the beam front filter for small beam numbers are suggested. The theory is applied to simple geometric shapes in two dimensions. A Gaussian ellipse, where analytical results are obtained, and simple hard-edged convex prescribed dose shapes are examined to illustrate beam selection based on the beam overlap metric. More complex concave prescribed dose shapes which contain a sensitive organ are also analysed and for low beam numbers are found to have preferred beam directions.