TD15-Applications of Monte-Carlo Methods in Medical Physics
Chen-Shou Chui and Lu Wang
Memorial Sloan-Kettering Cancer Center, New York City, New York.
Monte Carlo method has been used to solve radiation transport problems. It simulates the physical processes by random sampling from appropriate probability distributions. Potentially, it is the most accurate method for problems involving inhomogeneities.
The method is based on two mathematical principles: the Law of Large Numbers and the Central Limit Theorem. The former states that the sample mean approaches the expected value as the sample size increases. The latter gives us a confidence interval on the sample standard deviation. For radiation transport problems, the simulation involves two major components: ‘transport’ and ‘interaction’. The ‘transport’ component selects the step size of a particle to the next interaction; and performs geometry checking and possible energy deposition along the step. The ‘interaction’ component decides the type of the interaction; and samples the energy and direction of the outgoing particles.
Monte Carlo has been applied to many problems in medical physics, including simulation of the therapy machine head; the calculation of correction factors used in chamber theory; the generation of dose kernels; and dose calculation in heterogeneous media. Prior to clinical application, Monte Carlo method needs to be validated empirically. Results from Monte Carlo have been compared to measurements in homogeneous flat and hemisphere phantoms; and in inhomogeneous phantoms imbedded with low and high density materials.
After empirical validation, Monte Carlo methods have been applied to dose calculations for head/neck and lung treatments. These two sites are expected to show the greatest effects of anatomic inhomogeneities on dose. Results from Monte Carlo were compared to that using a pencil beam model. For head/neck treatment using 6 MV photons, the difference between the two methods was in general small. For lung treatment using 6 MV photons, the PTV coverage was degraded by about a few percent while the normal organs (lungs, cord) were not much affected. For lung treatment using 15 MV photons, however, the PTV coverage was significantly degraded, by over 10%. This is due to the increased range of the secondary electrons in low density volumes (lungs) which was not properly accounted for in the pencil beam model. Similar results were observed for both conventional and IMRT treatments. Additional comparisons were also made for treatments involving metal prosthesis and for electron beams.
In conclusion, Monte Carlo can be applied to many medical physics problems to give accurate results. Moreover, it provides a powerful tool for analysis which cannot be easily done with measurement. The drawback, however, is that it requires long computation time in order to achieve good statistics.
TD15 - Monte Carlo方法在医学物理中的应用
Chen-Shou Chui and Lu Wang
Memorial Sloan-Kettering Cancer Center, New York City, New York.
Monte Carlo方法被用于解决辐射输运问题。它通过对合适的概率分布随机采样，来模拟各种物理过程。它可能是计算涉及不均匀组织的问题的最准确方法。
此方法基于两个数学原理：大数定律和中心极限定理。前者指出随着样本量增加，样本的均值接近期望值；后者给出样本标准差的置信区间。对于辐射输运问题，模拟包括两部分：输运和相互作用。输运部分选择粒子至下次相互作用的步长，沿着作用路径进行几何校验和可能的能量沉积。相互作用部分决定相互作用的类型，对出射粒子的能量和方向进行采样。
Monte Carlo已用于解决医学物理的许多问题，包括治疗机机头的模拟、计算电离室的校正因子、产生剂量核、不均匀介质中的剂量计算。在临床应用之前，Monte Carlo方法需要进行实验验证，其结果与测量结果进行了比较，模体为均匀规则和半球状模体、及嵌有低密度和高密度材料的不均匀模体。
经过实验验证，Monte Carlo方法已用于头颈部和肺部治疗的剂量计算，这两个部位组织不均匀性对剂量的影响很大。Monte Carlo计算的结果与用笔形束模型计算的结果进行了比较。头颈部治疗使用6MV光子束，两种方法的差异不大。肺部治疗使用6MV光子束，PTV的高剂量覆盖率有少许降低，而正常器官（肺、脊髓）没有太大影响；而当肺部治疗使用15MV光子束时，PTV的高剂量覆盖率显著降低，超过10%，这是由于次级电子在低密度（肺）介质中的射程增加，笔形束模型不能正确地处理这种情况。常规治疗和IMRT治疗的结果相似。对于体内有金属假体的情况和电子束治疗也进行了比较。
总之，Monte Carlo模拟可以用于解决很多医学物理问题，给出准确的结果。此外，它是个有力的分析工具，可用于某些不易测量的情况。然而，为了获得好的统计结果，Monte Carlo模拟的计算时间很长。