Lax I
Phys Med Biol. 1986 Aug;31(8):879-92. doi: 10.1088/0031-9155/31/8/006.
An investigation was made of the limitations of the semi-infinite slab approximation used in pencil-beam models for electron-beam dose planning. Comparison of measured and calculated dose distributions were made for one-, two- and three-dimensional air inhomogeneities in water. The two- and three-dimensional air cavities were cylindrical with the axis parallel to the incident beam. The radii of the cavities were between 11 and 46 mm and the incident electron energies between 10 and 20 MeV. The measurements were made with a silicon diode. In the calculations the semi-infinite slab approximation was applied to a Gaussian model of the beam and to a generalised Gaussian model. The latter also takes large-angle single scattering into account. By using an absorber in front of the cavity the different fluence contributions to the central axis dose could be measured separately. The result shows that a doubling of the dose may be obtained along the central axis for narrow deep cavities. The dose contribution from the electron transport into the cavity from the cylindrical wall is shown to be underestimated by the semi-infinite slab approximation. This is shown to give large errors especially at depths where the angular distribution of the electrons is large and the electrons have a long drift space in air.
对电子束剂量规划中铅笔束模型所采用的半无限平板近似的局限性进行了研究。针对水中的一维、二维和三维空气不均匀性，对测量剂量分布与计算剂量分布进行了比较。二维和三维空气腔为圆柱形，其轴平行于入射束。腔的半径在11至46毫米之间，入射电子能量在10至20兆电子伏特之间。测量使用硅二极管进行。在计算中，半无限平板近似应用于束流的高斯模型和广义高斯模型。后者还考虑了大角度单次散射。通过在腔前使用吸收体，可以分别测量对中心轴剂量的不同注量贡献。结果表明，对于窄而深的腔，沿中心轴剂量可能会加倍。半无限平板近似低估了从圆柱形壁向腔内电子传输的剂量贡献。结果表明，这会产生很大误差，尤其是在电子角分布较大且电子在空气中有长漂移距离的深度处。
