放射治疗摆位旋转误差数学模型的建立与可控性分析

Establishment of radiotherapy positioning rotation error mathematical model and controllability analysis

目的建立旋转误差数学模型,寻求减少旋转误差对肿瘤治疗影响的方法。方法选择2012年8月至2013年4月放疗的213例胸部肿瘤患者,其中男性121例,女性92例;年龄50~73岁,中位年龄59岁;卡氏评分(KPS)≥70;食管癌115例,肺癌83例,其他15例。运用X射线容积成像(XVI)系统获得不同配准条件下治疗摆位旋转误差;建立旋转误差模型,分析旋转误差对放射治疗靶区影响因素。结果旋转误差在X轴上为(0.65±0.52)°,因旋转误差而带来误差的变化B2F2+B3F3=[cos(90°-θy′-θy)-cos(90°-θy′)]×OA2+[cos(90°-θz′-θz)-cos(90°-θz′)]×OA3;Y轴上为(0.78±0.68)°,因旋转误差而带来误差的变化A1F1+A3F3=[sin(90°-θx′)-sin(90°-θx′-θx)]×OA1+[sin(90°-θz′)-sin(90°-θz′-θz)]×OA3;Z轴上为(0.85±0.87)°,因旋转误差而带来误差的变化B1F1+A2F2=[cos(90°-θx′-θx)-cos(90°-θx′)]×OA1+[sin(90°-θy′)-sin(90°-θy′-θy)]×OA2。结论旋转误差对放射治疗摆位误差的影响主要受到摆位中心离靶区距离影响较大,受摆位旋转角度影响较小,放射治疗摆位标记位置对减少旋转误差影响有着重要的作用。

Objective To establish mathematical model of rotation error, and seek methods to reduce rotation error on impact of cancer treatment. Methods From August 2012 to April 2013, 213 patients with chest tumors were enrolled, which included 121 males and 92 females, aged 50-73 years old with median age of 59 years old;Karnofsky(KPS) ≥ 70 scores. Among them,115 cases were esophageal cancer, 83 patients were lung cancer and 15 of others. The X-ray volume imaging(XVI) system was used to obtain rotation error of treatment position in different registration conditions, and rotation error model was established to analyze influencing factors of rotation error on radiotherapy target. Results The rotation error of X-axis was(0.65 ± 0.52)°,and error change caused by rotation error was B2 F2 + B3 F3 = [cos(90°-θy′-θy)-cos(90°-θy′)] × OA2 + cos(90°-θz′-θz)-cos(90°-θz′)] × OA3;rotation error was(0.78 ± 0.68)° on Y-axis, and error change caused by rotation error was A1 F1 +A3 F3 = [sin(90°-θx′)-sin(90°-θx′-θx)] × OA1 + [sin(90°-θz′)-sin(90°-θz′-θz)] × OA3;rotation error of Z-axis was(0.85 ± 0.87)°, and error change caused by rotation error was B1 F1 + A2 F2 = [cos(90°-θx′-θx)-cos(90°-θx′)] ×OA1 + [sin(90°-θy′)-sin(90°-θy′-θy)] × OA2. Conclusion It is demonstrated that distance between positioning center and target is the main influence factor of rotation error on radiotherapy positioning error, and it minimally influenced by rotation angle of position. So position of radiotherapy positioning displays an important role in reducing influence of rotation error.