Coolens Catherine, Evans Phil M, Seco Joao, Webb Steve
Joint Department of Physics, Institute of Cancer Research and Royal Marsden NHS Trust, Sutton, Surrey SM2 5PT, UK.
Phys Med Biol. 2004 Sep 7;49(17):3857-75. doi: 10.1088/0031-9155/49/17/003.
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.
已知逆向计划技术会产生高度调制的调强射束（IMB）。其特点是包含高频调制，而在更易于传输的射野分布图中则不存在这种调制。在本研究中，这些临床上不需要的波动被定义为“噪声”。尽管这些高度调制的解决方案也是最优解，但一旦开始传输射野分布图，它们在传输效率以及治疗分析和验证方面就会变得不利。因此，这项工作的目的是了解IMB的结构和复杂性的根源。最终，如果能够表征最优射野分布图中的基本特征，就有可能控制IMB的频率分布，并简化调强放射治疗（IMRT）的计划和传输过程。该研究基于两种常见的优化技术：模拟退火（SA）和梯度下降（GD）。在这项工作开始时所做的假设是，由SA优化技术引起的随机噪声比其他噪声源更占主导地位，并且在成本函数收敛后，可以通过对最小成本注量分布图进行平均，将其与基本调制区分开来。结果表明，IMB中存在三种可能的随机噪声源，即优化技术、成本函数以及该成本函数收敛的定义。就优化技术本身而言，已证实梯度下降技术不会在IMB中引入随机噪声。SA技术确实会引入随机噪声，但对最小成本注量分布图进行平均并不会使射野分布图更平滑。这源于这样一个事实，即这种类型的噪声在优化中并非主导因素，而是接近全局最小值时成本函数的曲率。结果表明，SA优化技术中初始温度的选择对于成本函数的收敛以及注量分布图的频率分布至关重要。如果初始温度太小，随机噪声将冻结在注量分布图中，并成为噪声的主导成分，并导致非常随机且难以传输的模式。
