Department of Radiation Medicine, Loma Linda University, Loma Linda, California 92350, USA.
Med Phys. 2013 Apr;40(4):041701. doi: 10.1118/1.4793408.
Monte Carlo simulations of radiation therapy require conversion from Hounsfield units (HU) in CT images to an exact tissue composition and density. The number of discrete densities (or density bins) used in this mapping affects the simulation accuracy, execution time, and memory usage in GEANT4 and other Monte Carlo code. The relationship between the number of density bins and CT noise was examined in general for all simulations that use HU conversion to density. Additionally, the effect of this on simulation accuracy was examined for proton radiation.
Relative uncertainty from CT noise was compared with uncertainty from density binning to determine an upper limit on the number of density bins required in the presence of CT noise. Error propagation analysis was also performed on continuously slowing down approximation range calculations to determine the proton range uncertainty caused by density binning. These results were verified with Monte Carlo simulations.
In the presence of even modest CT noise (5 HU or 0.5%) 450 density bins were found to only cause a 5% increase in the density uncertainty (i.e., 95% of density uncertainty from CT noise, 5% from binning). Larger numbers of density bins are not required as CT noise will prevent increased density accuracy; this applies across all types of Monte Carlo simulations. Examining uncertainty in proton range, only 127 density bins are required for a proton range error of <0.1 mm in most tissue and <0.5 mm in low density tissue (e.g., lung).
By considering CT noise and actual range uncertainty, the number of required density bins can be restricted to a very modest 127 depending on the application. Reducing the number of density bins provides large memory and execution time savings in GEANT4 and other Monte Carlo packages.
放射治疗的蒙特卡罗模拟需要将 CT 图像中的 Hounsfield 单位 (HU) 转换为精确的组织成分和密度。在这种映射中使用的离散密度（或密度-bin）的数量会影响 GEANT4 和其他蒙特卡罗代码中的模拟精度、执行时间和内存使用。检查了在使用 HU 转换为密度的所有模拟中，密度-bin 的数量与 CT 噪声之间的关系。此外，还检查了这种关系对质子辐射模拟精度的影响。
将来自 CT 噪声的相对不确定性与密度-bin 化的不确定性进行比较，以确定在存在 CT 噪声的情况下所需的密度-bin 的上限数量。还对连续慢化逼近范围计算进行了误差传播分析，以确定由于密度-bin 化引起的质子范围不确定性。这些结果通过蒙特卡罗模拟进行了验证。
即使存在适度的 CT 噪声（5 HU 或 0.5%），也发现 450 个密度-bin 仅会导致密度不确定性增加 5%（即，密度不确定性的 95%来自 CT 噪声，5%来自 binning）。不需要更多数量的密度-bin，因为 CT 噪声会阻止密度精度的提高；这适用于所有类型的蒙特卡罗模拟。在质子范围的不确定性方面，在大多数组织中，只需 127 个密度-bin 即可使质子范围误差<0.1mm，在低密度组织（例如肺）中，质子范围误差<0.5mm。
通过考虑 CT 噪声和实际范围不确定性，可以将所需的密度-bin 数量限制在非常适中的 127 个，具体取决于应用。在 GEANT4 和其他蒙特卡罗软件包中，减少密度-bin 的数量可以节省大量的内存和执行时间。
