Siddon R L
Med Phys. 1981 Nov-Dec;8(6):766-74. doi: 10.1118/1.594853.
The majority of radiation treatment planning problems are relatively straightforward, involving only specified gantry angles in a treatment plane which is perpendicular to the patient longitudinal axis. In addition, there are a number of more complex three-dimensional problems which require combined rotation of the gantry, collimator, and turntable for their solutions. These include, for example, the use of non-coplanar fields and oblique treatment planes, the matching of field edges in three dimensions, the treatment of the breast with opposing tangential fields, and the treatment of inclined elongated lesions. Unfortunately, there is no general systematic approach to the solution of these more complex problems. One may attempt an analytic solution, but this approach is often too cumbersome and tedious. On the other hand, one may resort to a "trial and error" session with the simulator. This paper, therefore, presents a mathematical method which is easily applied and applicable to a wide variety of complex three-dimensional treatment planning problems. The method considers the gantry, collimator, and turntable as coordinate systems. These coordinate systems are derivable from each other by specified coordinate transformations, which contain the rotation angles of the gantry, collimator, and turntable. Within this mathematical framework, the treatment planning problems are found to reduce to two general types, of which various clinical examples are then given.
大多数放射治疗计划问题相对简单，仅涉及与患者纵轴垂直的治疗平面中的特定机架角度。此外，还有一些更复杂的三维问题，需要联合旋转机架、准直器和转台来解决。例如，这些问题包括使用非共面射野和倾斜治疗平面、三维射野边缘匹配、用对置切线野治疗乳腺以及治疗倾斜的细长病变。不幸的是，对于解决这些更复杂的问题，没有通用的系统方法。人们可能会尝试解析解，但这种方法往往过于繁琐和冗长。另一方面，人们可能会在模拟机上进行“试错”操作。因此，本文提出了一种易于应用且适用于各种复杂三维治疗计划问题的数学方法。该方法将机架、准直器和转台视为坐标系。这些坐标系可通过特定的坐标变换相互推导，这些坐标变换包含机架、准直器和转台的旋转角度。在这个数学框架内，发现治疗计划问题可归结为两种一般类型，随后给出了各种临床实例。
