Real-time definition of single seed placement sensitivity in low-dose-rate prostate brachytherapy [code and patient data]

PURPOSE: In low-dose-rate brachytherapy iodine seeds are implanted based on a treatment plan, generated with respect to different dose constraints. The quality of the dose distribution depends on a precise seed placement, however, it is not clear which seed misplacements have a large impact. MATERIALS AND METHODS: We developed a method using automatic differentiation to calculate gradients of dose parameters with regard to the seeds' positions. Thus, we understand their sensitivity with respect to the seed placement. A statistical analysis is performed on a data set with 35 prostate brachytherapy patients. RESULTS: The most sensitive seeds regarding the dosimetric parameters of both rectum and urethra are close to the corresponding organ. Their gradient directions are mainly orthogonal to their surfaces. However, not all seeds close to the surface are equally sensitive with regard to the dose parameter. The most sensitive seeds regarding the prostate's dose parameters are distributed throughout the prostate and the direction of the gradients are mainly parallel to its surface. A linear regression with respect to different patient parameters shows that dose constraints which are barely fulfilled have large gradients and thus are additionally sensitive to misplacement. CONCLUSION: Automatic differentiation can be used to analyze dose parameter sensitivity with respect to seed placement. Integrating this into treatment planning systems is valuable as it speeds up the planning procedure, making it more robust and less dependent on user experience while showing the operating physician which needle placements require greater accuracy than others.

研究目的：在低剂量率近距离放射治疗中，碘粒子需依据针对不同剂量约束制定的治疗计划进行植入。剂量分布的质量高度依赖粒子植入的精准度，但目前尚不明确哪些粒子位置偏差会对剂量分布产生显著影响。
材料与方法：本研究开发了一种基于自动微分（automatic differentiation）的方法，用于计算剂量参数相对于粒子位置的梯度，以此明确粒子植入位置的剂量敏感性。我们对包含35例前列腺近距离放射治疗患者的数据集开展了统计分析。
结果：针对直肠与尿道的剂量学参数（dosimetric parameters）而言，敏感性最高的粒子均紧邻对应靶器官，其梯度方向主要与器官表面正交。但并非所有贴近器官表面的粒子都会对剂量参数产生同等程度的影响。针对前列腺的剂量学参数而言，敏感性最高的粒子分布于前列腺整体范围内，其梯度方向主要与前列腺表面平行。针对不同患者参数开展的线性回归（linear regression）分析显示，勉强达到约束要求的剂量参数往往具有较大的梯度值，因此对粒子位置偏差更为敏感。
结论：自动微分可用于分析粒子植入位置对剂量参数的敏感性。将该方法整合至治疗计划系统（treatment planning systems）中具有重要应用价值：可加快治疗计划制定流程，提升计划的鲁棒性，降低对操作人员临床经验的依赖，并可提示术者哪些穿刺针植入位置需要更高的操作精度。