Shiu A S, Hogstrom K R
Department of Radiation Physics, University of Texas M.D. Anderson Cancer Center, Houston 77030.
Med Phys. 1991 Jan-Feb;18(1):7-18. doi: 10.1118/1.596697.
A pencil-beam redefinition algorithm has been developed for the calculation of electron-beam dose distributions on a three-dimensional grid utilizing 3-D inhomogeneity correction. The concept of redefinition was first used for both fixed and arced electron beams by Hogstrom et al. but was limited to a single redefinition. The success of those works stimulated the development of the pencil-beam redefinition algorithm, the aim of which is to solve the dosimetry problems presented by deep inhomogeneities through development of a model that redefines the pencil beams continuously with depth. This type of algorithm was developed independently by Storchi and Huizenga who termed it the "moments method." Such a pencil beam within the patient is characterized by a complex angular distribution, which is approximated by a Gaussian distribution having the same first three moments as the actual distribution. Three physical quantities required for dose calculation and subsequent radiation transport--namely planar fluence, mean direction, and root-mean-square spread about the mean direction--are obtained from these moments. The primary difference between the moments method and the redefinition algorithm is that the latter subdivides the pencil beams into multiple energy bins. The algorithm then becomes a macroscopic method for transporting the complete phase space of the beam and allows the calculation of physical quantities such as fluence, dose, and energy distribution. Comparison of calculated dose distributions with measured dose distributions for a homogeneous water phantom, and for phantoms with inhomogeneities deep relative to the surface, show agreement superior to that achieved with the pencil-beam algorithm of Hogstrom et al. in the penumbral region and beneath the edges of air and bone inhomogeneities. The accuracy of the redefinition algorithm is within 4% and appears sufficient for clinical use, and the algorithm is structured for further expansion of the physical model if required for site-specific treatment planning problems.
已开发出一种铅笔束重新定义算法，用于在三维网格上计算电子束剂量分布，并利用三维不均匀性校正。重新定义的概念最早由霍格斯特伦等人用于固定和弧形电子束，但仅限于单次重新定义。这些工作的成功推动了铅笔束重新定义算法的发展，其目的是通过开发一种随深度连续重新定义铅笔束的模型来解决深部不均匀性带来的剂量测定问题。这种类型的算法由斯托尔奇和惠曾加独立开发，他们将其称为“矩量法”。患者体内的这种铅笔束具有复杂的角分布，可通过具有与实际分布相同的前三个矩的高斯分布来近似。从这些矩中获得剂量计算和后续辐射传输所需的三个物理量，即平面注量、平均方向以及围绕平均方向的均方根展宽。矩量法和重新定义算法之间的主要区别在于，后者将铅笔束细分为多个能量 bin。然后，该算法成为一种用于传输束的完整相空间的宏观方法，并允许计算诸如注量、剂量和能量分布等物理量。对于均匀水体模以及相对于表面具有深部不均匀性的体模，将计算得到的剂量分布与测量得到的剂量分布进行比较，结果表明，在半影区以及空气和骨不均匀性边缘下方，该算法的一致性优于霍格斯特伦等人的铅笔束算法。重新定义算法的精度在 4%以内，似乎足以用于临床，并且如果特定部位的治疗计划问题需要，该算法的结构便于进一步扩展物理模型。
