A study on the application of Fourier series in IMRT treatment planning

In intensity-modulated radiotherapy, a set of x-ray fluence profiles is iteratively adjusted until a desired absorbed dose distribution is obtained. The purpose of this article is to present a method that allows the optimization of fluence profiles based on the Fourier series decomposition of an initial approximation to the profile. The method has the advantage that a new fluence profile can be obtained in a precise and controlled way with the tuning of only two parameters, namely the phase of the sine and cosine terms of one of the Fourier components, in contrast to the point-by-point tuning of the profile. Also, because the method uses analytical functions, the resultant profiles do not exhibit numerical artifacts. A test case consisting of a mathematical phantom with a target wrapped around a critical structure is discussed to illustrate the algorithm. It is shown that the degree of conformality of the absorbed dose distribution can be tailored by varying the number of Fourier terms made available to the optimization algorithm. For the test case discussed here, it is shown that the number of Fourier terms to be modified depends on the number of radiation beams incident on the target but it is in general in the order of 10 terms.