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The first purpose of this paper is to shed some new light on the old questionof selecting the number of beams in intensity-modulated radiation therapy(IMRT). The second purpose is to illuminate the related issue of discretestatic beam angles vs. rotational techniques, which has recently re-surfaceddue to the advancement of volumetric arc therapy (VMAT). A specific objectiveis to find analytical expressions that allow one to address the points raisedabove. To make the problem mathematically tractable, it is assumed that thedepth dose is flat and that the lateral dose profile can be approximated bypolynomials, specifically Chebyshev polynomials of the first kind, of finitedegree. The application of methods known from image reconstruction then allowsone to answer the first question above as follows: The required number of beamsis determined by the maximum degree of the polynomials used in theapproximation of the beam profiles, which is a measure of the dose variability.There is nothing to be gained by using more beams. In realistic cases, in whichthe variability of the lateral dose profile is restricted in several ways, therequired number of beams is of the order of 10 to 20. The consequence ofdelivering the beams with a `leaf sweep' technique during continuous rotationof the gantry, as in VMAT, is also derived in analytical form. The main effectis that the beams fan out, but the effect near the axis of rotation is small.This result can serve as a theoretical justification of VMAT. Overall theanalytical derivations in this paper, albeit based on strong simplifications,provide new insights into, and a deeper understanding of, the beam angleproblem in IMRT.

The number of beams in IMRT - theoretical investigations and implications for single-arc IMRT