Analysis of stochastic noise in intensity-modulated beams

Inverse planning techniques are known to produce intensity-modulated beams (IMBs) that are highly modulated. They are characterized by the fact that they contain high-frequency modulations that are absent in the profiles that are easier to deliver. For the purpose of this study these clinically unwanted fluctuations are being defined as 'noise'. Although these highly modulated solutions are also optimal solutions, as soon as the profiles are being delivered, they become unfavourable with respect to delivery efficiency and the analysis and verification of treatment. The aim of this work was therefore to understand the origins of the structure and complexity of IMBs. Ultimately, if one can characterize the essential features in optimum beam profiles, it might be possible to control the frequency distribution of IMBs and simplify the IMRT planning and delivery process. The study was based on two common optimization techniques: simulated annealing (SA) and gradient-descent (GD). The assumptions made at the start of this work were that the stochastic noise caused by the SA optimization technique is dominant over other sources of noise and that it could be separated out from the essential modulation after convergence of the cost function by averaging minimum-cost fluence profiles. The results indicate that there are three possible sources of stochastic noise in IMBs, i.e. the optimization technique, the cost function and the definition of convergence of that cost function. In terms of the optimization technique itself, it was confirmed that the gradient-descent technique does not introduce stochastic noise in the IMBs. The SA technique does introduce stochastic noise but averaging of minimum-cost fluence profiles does not result in smoother beam profiles. This originates from the fact that this type of noise is not the dominant factor in the optimization, but rather the curvature of the cost function close to the global minimum. It is shown that the choice of initial temperature in the SA optimization technique is crucial for the convergence of the cost function and the frequency distribution of the fluence profiles. If the initial temperature is too small the stochastic noise will get frozen into the fluence profiles and become the dominant component of noise, resulting in very random-looking and difficult to deliver patterns.