Ballhausen H, Li M, Hegemann N-S, Ganswindt U, Belka C
Department of Radiation Oncology, University Hospital of Ludwig-Maximilians-University Munich, Marchioninistrasse 15, D-81377 Munich, Germany.
Phys Med Biol. 2015 Jan 21;60(2):549-63. doi: 10.1088/0031-9155/60/2/549. Epub 2014 Dec 30.
A random walk model for intra-fraction motion has been proposed, where at each step the prostate moves a small amount from its current position in a random direction. Online tracking data from perineal ultrasound is used to validate or reject this model against alternatives. Intra-fraction motion of a prostate was recorded by 4D ultrasound (Elekta Clarity system) during 84 fractions of external beam radiotherapy of six patients. In total, the center of the prostate was tracked for 8 h in intervals of 4 s. Maximum likelihood model parameters were fitted to the data. The null hypothesis of a random walk was tested with the Dickey-Fuller test. The null hypothesis of stationarity was tested by the Kwiatkowski-Phillips-Schmidt-Shin test. The increase of variance in prostate position over time and the variability in motility between fractions were analyzed. Intra-fraction motion of the prostate was best described as a stochastic process with an auto-correlation coefficient of ρ = 0.92 ± 0.13. The random walk hypothesis (ρ = 1) could not be rejected (p = 0.27). The static noise hypothesis (ρ = 0) was rejected (p < 0.001). The Dickey-Fuller test rejected the null hypothesis ρ = 1 in 25% to 32% of cases. On average, the Kwiatkowski-Phillips-Schmidt-Shin test rejected the null hypothesis ρ = 0 with a probability of 93% to 96%. The variance in prostate position increased linearly over time (r(2) = 0.9 ± 0.1). Variance kept increasing and did not settle at a maximum as would be expected from a stationary process. There was substantial variability in motility between fractions and patients with maximum aberrations from isocenter ranging from 0.5 mm to over 10 mm in one patient alone. In conclusion, evidence strongly suggests that intra-fraction motion of the prostate is a random walk and neither static (like inter-fraction setup errors) nor stationary (like a cyclic motion such as breathing, for example). The prostate tends to drift away from the isocenter during a fraction, and this variance increases with time, such that shorter fractions are beneficial to the problem of intra-fraction motion. As a consequence, fixed safety margins (which would over-compensate at the beginning and under-compensate at the end of a fraction) cannot optimally account for intra-fraction motion. Instead, online tracking and position correction on-the-fly should be considered as the preferred approach to counter intra-fraction motion.
已经提出了一种用于分次内运动的随机游走模型，在该模型中，前列腺在每一步都会从其当前位置沿随机方向移动一小段距离。来自会阴超声的在线跟踪数据用于对照其他模型验证或否定该模型。在对6名患者进行的84次外照射放疗过程中，通过4D超声（医科达Clarity系统）记录前列腺的分次内运动。总共对前列腺中心进行了8小时的跟踪，时间间隔为4秒。将最大似然模型参数拟合到数据中。使用迪基 - 富勒检验对随机游走的原假设进行检验。使用Kwiatkowski - Phillips - Schmidt - Shin检验对平稳性原假设进行检验。分析了前列腺位置随时间的方差增加以及分次之间运动性的变异性。前列腺的分次内运动最好被描述为一个自相关系数为ρ = 0.92 ± 0.13的随机过程。随机游走假设（ρ = 1）不能被否定（p = 0.27）。静态噪声假设（ρ = 0）被否定（p < 0.001）。迪基 - 富勒检验在25%至32%的情况下否定了原假设ρ = 1。平均而言，Kwiatkowski - Phillips - Schmidt - Shin检验以93%至96%的概率否定了原假设ρ = 0。前列腺位置的方差随时间呈线性增加（r(2) = 0.9 ± 0.1）。方差持续增加，并未如平稳过程所预期的那样稳定在最大值。分次之间以及患者之间的运动性存在很大差异，仅一名患者距等中心的最大偏差范围就从0.5毫米到超过10毫米。总之，有力的证据表明前列腺的分次内运动是一种随机游走，既不是静态的（如分次间设置误差）也不是平稳的（如呼吸等周期性运动）。在一次分次过程中，前列腺往往会偏离等中心，并且这种方差会随时间增加，因此较短的分次对分次内运动问题有益。因此，固定的安全裕度（在分次开始时会过度补偿而在结束时会补偿不足）无法最佳地考虑分次内运动。相反，应考虑在线跟踪和实时位置校正作为应对分次内运动的首选方法。
