Bellinzona V E, Ciocca M, Embriaco A, Fontana A, Mairani A, Mori M, Parodi K
Istituto Nazionale di Fisica Nucleare, Sezione di Pavia, Pavia, Italy; Dipartimento di Fisica, Università di Pavia, Pavia, Italy; Department of Medical Physics, Ludwig Maximilians University, Munich, Germany.
Medical Physics Unit, Centro Nazionale di Adroterapia Oncologica, Pavia, Italy.
Phys Med. 2015 Jul;31(5):484-92. doi: 10.1016/j.ejmp.2015.05.004. Epub 2015 May 29.
The accurate evaluation of the lateral dose profile is an important issue in the field of proton radiation therapy. The beam spread, due to Multiple Coulomb Scattering (MCS), is described by the Molière's theory. To take into account also the contribution of nuclear interactions, modern Treatment Planning Systems (TPSs) generally approximate the dose profiles by a sum of Gaussian functions. In this paper we have compared different parametrizations for the lateral dose profile of protons in water for therapeutical energies: the goal is to improve the performances of the actual treatment planning.
We have simulated typical dose profiles at the CNAO (Centro Nazionale di Adroterapia Oncologica) beamline with the FLUKA code and validated them with data taken at CNAO considering different energies and depths. We then performed best fits of the lateral dose profiles for different functions using ROOT and MINUIT.
The accuracy of the best fits was analyzed by evaluating the reduced χ(2), the number of free parameters of the functions and the calculation time. The best results were obtained with the triple Gaussian and double Gaussian Lorentz-Cauchy functions which have 6 parameters, but good results were also obtained with the so called Gauss-Rutherford function which has only 4 parameters.
The comparison of the studied functions with accurate and validated Monte Carlo calculations and with experimental data from CNAO lead us to propose an original parametrization, the Gauss-Rutherford function, to describe the lateral dose profiles of proton beams.
在质子放射治疗领域，准确评估侧向剂量分布是一个重要问题。由于多次库仑散射（MCS）导致的束流展宽由莫利埃理论描述。为了也考虑核相互作用的贡献，现代治疗计划系统（TPS）通常用高斯函数之和来近似剂量分布。在本文中，我们比较了治疗能量下水介质中质子侧向剂量分布的不同参数化方法：目标是提高实际治疗计划的性能。
我们使用FLUKA代码在CNAO（国家肿瘤放疗中心）束流线上模拟了典型剂量分布，并结合考虑不同能量和深度时在CNAO获取的数据对其进行了验证。然后我们使用ROOT和MINUIT对不同函数的侧向剂量分布进行了最佳拟合。
通过评估约化χ(2)、函数的自由参数数量和计算时间来分析最佳拟合的准确性。具有6个参数的三重高斯函数和双高斯洛伦兹 - 柯西函数取得了最佳结果，但具有仅4个参数的所谓高斯 - 卢瑟福函数也取得了良好结果。
将所研究的函数与精确且经过验证的蒙特卡罗计算以及来自CNAO的实验数据进行比较后，我们提出了一种原始的参数化方法——高斯 - 卢瑟福函数，用于描述质子束的侧向剂量分布。
