Jette D
Institute of Applied Physiology and Medicine, Seattle, Washington 98122.
Med Phys. 1991 Mar-Apr;18(2):123-32. doi: 10.1118/1.596698.
In this fourth article in a series on the calculation of electron dose using multiple-scattering theory, we deal with localized inhomogeneities by solving the Fermi equation for scattering power which is an arbitrary function of position. In fact, we go further, by solving the second-order multiple-scattering equation which supersedes the (first-order) Fermi equation, again for scattering power which is an arbitrary function of position. Thus, we are no longer restricted to a horizontally layered medium, as is the case with the Fermi-Eyges theory. Our general solution is in the form of a perturbation series which evidently converges rapidly enough that only its first two or three terms need be taken for accurate dose calculation. Regarding the energy directly deposited by the primary electrons, the formulas developed in this article give very good agreement with Monte Carlo calculations for the thick half-slab configuration, as will be seen in the next article in this series. Moreover, our first-rank, second-order formulas, when expressed in Fourier-transformed space, are simple enough to be implemented in a treatment planning system providing full three-dimensional electron dose calculation for arbitrary configurations of inhomogeneities.
在关于使用多重散射理论计算电子剂量的系列文章的第四篇中，我们通过求解散射功率的费米方程来处理局部不均匀性，散射功率是位置的任意函数。实际上，我们更进一步，通过求解二阶多重散射方程（它取代了（一阶）费米方程），同样针对作为位置任意函数的散射功率。因此，我们不再局限于费米 - 艾格斯理论所适用的水平分层介质。我们的一般解采用微扰级数的形式，显然其收敛速度足够快，以至于在进行精确剂量计算时仅需取其前两三项即可。关于初级电子直接沉积的能量，本文所推导的公式与厚半平板构型的蒙特卡罗计算结果吻合得非常好，正如在本系列的下一篇文章中将会看到的那样。此外，我们的一阶二阶公式在傅里叶变换空间中表达时足够简单，能够在一个治疗计划系统中实现，该系统可为任意不均匀性构型提供完整的三维电子剂量计算。
