University of Florida Proton Therapy Institute, Jacksonville, FL, USA.
Phys Med Biol. 2010 Mar 21;55(6):N141-9. doi: 10.1088/0031-9155/55/6/N01. Epub 2010 Feb 24.
The purpose of this note is to evaluate the relationship between the stochastic errors in CT numbers and the standard deviation of the computed proton beam range in radiotherapy planning. The stochastic voxel-to-voxel variation in CT numbers called 'noise,' may be due to signal registration, processing and numerical image reconstruction technique. Noise in CT images may cause a deviation in the computed proton range from the physical proton range, even assuming that the error due to CT number-stopping power calibration is removed. To obtain the probability density function (PDF) of the computed proton range, we have used the continuing slowing down approximation (CSDA) and the uncorrelated white Gaussian noise along the proton path. The model of white noise was accepted because for the slice-based fan-beam CT scanner; the power-spectrum properties apply only to the axial (x, y) domain and the noise is uncorrelated in the z domain. However, the possible influence of the noise power spectrum on the standard deviation of the range should be investigated in the future. A random number generator was utilized for noise simulation and this procedure was iteratively repeated to obtain convergence of range PDF, which approached a Gaussian distribution. We showed that the standard deviation of the range, sigma, increases linearly with the initial proton energy, computational grid size and standard deviation of the voxel values. The 95% confidence interval width of the range PDF, which is defined as 4sigma, may reach 0.6 cm for the initial proton energy of 200 MeV, computational grid 0.25 cm and 5% standard deviation of CT voxel values. Our results show that the range uncertainty due to random errors in CT numbers may be significant and comparable to the uncertainties due to calibration of CT numbers.
本注的目的是评估 CT 数中的随机误差与放射治疗计划中计算质子束射程的标准偏差之间的关系。CT 数中的随机体素间变化称为“噪声”，可能是由于信号注册、处理和数值图像重建技术所致。即使假设消除了由于 CT 数-阻止本领校准引起的误差，CT 图像中的噪声仍可能导致计算的质子射程与物理质子射程产生偏差。为了获得计算质子射程的概率密度函数 (PDF)，我们使用了连续减速近似 (CSDA) 和质子路径上的不相关白高斯噪声。之所以接受白噪声模型，是因为对于基于切片的扇形束 CT 扫描仪而言，功率谱特性仅适用于轴向 (x, y) 域，并且噪声在 z 域中是不相关的。然而，未来应研究噪声功率谱对射程标准偏差的可能影响。我们利用随机数生成器进行噪声模拟，并且该过程迭代进行以获得射程 PDF 的收敛，该收敛接近高斯分布。我们表明，射程的标准偏差 σ 与初始质子能量、计算网格大小和体素值的标准偏差呈线性关系增加。对于初始质子能量为 200 MeV、计算网格为 0.25 cm 和 CT 体素值的标准偏差为 5%，射程 PDF 的 95%置信区间宽度（定义为 4σ）可能达到 0.6 cm。我们的结果表明，由于 CT 数中的随机误差引起的射程不确定性可能是显著的，并且与 CT 数校准的不确定性相当。
