1.1 本指南描述了可用于计算剂量测定量的不同数学方法及其选择标准。剂量测量量计算可以确定辐射过程的有效性，估计产品中的剂量分布，或补充剂或补充剂，或两者，吸收剂量的测量。 1.2 辐射处理是一个不断发展的领域，中提供了带注释的示例 Annex A6 说明数学方法已经成功应用的应用。虽然不受这些实施例中引用的应用的限制，但在本文件中不涉及特定于中子传输、辐射治疗和屏蔽设计的应用。 1.3 本指南涵盖了能量高达25兆电子伏的电子和光子的辐射传输的计算。1.4 描述的数学方法包括蒙特卡罗、点核、离散纵坐标、半经验和经验方法。 1.5 本指南仅限于使用通用软件包来计算来自各种类型电离辐射源的带电或不带电粒子和光子或两者的传输。本标准仅限于使用这些软件包或其他数学方法来确定衰变后发射的光子的空间剂量分布 137 Cs或 60 Co，用于来自粒子加速器的高能电子，或用于电子加速器产生的X射线。 1.6 本指南帮助用户确定数学方法是否是一个有用的工具。该指南可以帮助用户选择用于计算吸收剂量的适当方法。用户必须确定这些数学方法中的任何一种是否适合其特定应用的解决方案，以及应用什么软件（如果有）。 附注1: 敦促用户应用这些预测技术，同时意识到对经验的需求以及方法和可用软件的固有局限性。有关辐射传输建模代码的可用性和更新的信息可在 附件A1 有关辐射物理学的基本了解和方法选择的简要概述，请参阅 Annex A3 . 1.7 本标准并不旨在解决与其使用相关的所有安全性问题（如果有）。本标准的使用者有责任在使用前建立适当的安全、健康和环境实践并确定法规限制的适用性。1.8 本国际标准是根据世界贸易组织技术性贸易壁垒（TBT）委员会发布的《关于制定国际标准、指南和建议的原则的决定》中确立的国际公认的标准化原则制定的。 ======意义和用途====== 4.1 用作分析工具- 数学方法提供了一种分析工具，可用于与辐射处理中的吸收剂量测定相关的许多应用。在某些应用（例如，医疗器械灭菌、食品辐照）中，数学计算可能不被用作常规剂量测定的替代品。 4.2 剂量计算- 剂量测定量的范围可以通过数学方法计算。我们定义感兴趣区域的剂量学量。当该区域仅由空气组成时，该区域内释放的所有电子电荷的总和除以空气的质量，得出暴露量。暴露只与空气中沉积的能量有关，因此需要额外的概念来应用于其他种类的辐射和其他种类的材料。 4.2.1 剂量测定中使用的主要物理量是吸收剂量。它被定义为任何材料中每单位质量从任何种类的电离辐射中吸收的能量。在辐射处理中，通常根据对水的吸收剂量来进行剂量测定系统的校准，但是可以使用对其他材料的吸收剂量，例如在半导体辐射的情况下对硅的吸收剂量。数学方法中吸收剂量的计算考虑了在感兴趣区域内沉积能量的相互作用以及可能从该区域移除能量的二次相互作用。 4.2.2 当假设在该区域中发生的所有相互作用将它们的能量完全沉积在感兴趣的区域内时，计算量比释动能。Kerma包括在感兴趣区域内产生的俄歇电子和轫致辐射的能量，认为它们在相互作用位点被局部吸收。当在感兴趣区域内建立带电粒子平衡时，Kerma用于计算剂量学量的数学方法。 4.2.2.1 计算比释能在减少计算负荷的愿望和精确的需要之间取得平衡，因为它避免了对二次相互作用的大量跟踪，特别是在材料边界。为了使比释动能等于区域中的吸收剂量，需要带电粒子平衡，而这在表面和材料边界处或附近不存在。 4.2.3 可以针对各种光子/电子环境和辐照器几何形状执行剂量计算。 4.3 评估过程有效性- 数学模型可用于评估产品组成、装载配置和辐照器设计的变化对剂量分布的影响。 4.4 剂量测定的补充或补充- 剂量计算可用于建立对剂量分布的详细理解，提供无法通过测量获得的空间分辨率。计算可用于减少表征程序或过程(例如，剂量映射)所需的剂量计的数量。4.5 剂量测定的替代方案- 当剂量测定法不切实际时（例如，颗粒材料、具有复杂几何形状的材料、剂量测定法不切实际或不可能的包装中包含的材料），可以使用剂量计算。 4.6 设施设计- 剂量计算通常用于新辐照器的设计，并可用于帮助优化现有设施或辐射过程中的剂量分布。辐照器设计中建模的使用可在参考文献中找到 ( 2- 7 ) . 4.7 验证- 模型的验证应通过与可靠和可追溯的剂量测量进行比较来完成。验证的目的是证明数学方法可以可靠地预测剂量和其他转运量。验证将预测或理论与适当实验的结果进行比较。验证程度与应用相称。中引用的文档中给出了指导 Annex A2 . 4.8 验证- 验证是对数学方法的计算机实现的数学正确性的确认。例如，这可以通过将数值结果与已知的解析解或与先前已验证的其他计算机代码进行比较来完成。应进行验证，以确保模拟适合预期应用。请参阅 3.1.24 . 附注2: 数学模型的某些应用涉及辐射加工中的操作鉴定（OQ）、性能鉴定（PQ）和过程控制，例如医疗保健产品的灭菌。数学模型在这些应用中的应用和使用可能必须满足监管要求。参考章节 6 应用数学方法和部分的先决条件 8 用于常规使用数学方法之前的要求。 4.9 不确定性- 与吸收剂量测量一样，吸收剂量预测应伴随总不确定度的估计（参见ASTM 51707 和JCGM 100:2008和JCGM 200:2012)。在许多情况下，吸收剂量测量有助于确定剂量计算的不确定性。 4.10 本指南不应作为数学模型选择和使用的唯一参考。鼓励用户联系在数学建模方面有经验的个人，并阅读相关出版物，以便为其应用选择最佳工具。辐射处理是一个不断发展的领域，在注释示例中引用的参考文献 Annex A6 是各种公开应用的代表。当一种方法通过剂量测定法进行验证时，它就成为该特定应用的基准。

1.1 This guide describes different mathematical methods that may be used to calculate dosimetric quantities and criteria for their selection. Dosimetric quantities calculations can determine the effectiveness of the radiation process, estimate the dose distribution in product, or supplement or complement, or both, the measurement of absorbed dose. 1.2 Radiation processing is an evolving field and annotated examples are provided in Annex A6 to illustrate the applications where mathematical methods have been successfully applied. While not limited by the applications cited in these examples, applications specific to neutron transport, radiation therapy and shielding design are not addressed in this document. 1.3 This guide covers the calculation of radiation transport of electrons and photons with energies up to 25 MeV. 1.4 The mathematical methods described include Monte Carlo, point kernel, discrete ordinate, semi-empirical and empirical methods. 1.5 This guide is limited to the use of general purpose software packages for the calculation of the transport of charged or uncharged particles and photons, or both, from various types of sources of ionizing radiation. This standard is limited to the use of these software packages or other mathematical methods for the determination of spatial dose distributions for photons emitted following the decay of 137 Cs or 60 Co, for energetic electrons from particle accelerators, or for X-rays generated by electron accelerators. 1.6 This guide assists the user in determining if mathematical methods are a useful tool. This guide may assist the user in selecting an appropriate method for calculating absorbed dose. The user must determine whether any of these mathematical methods are appropriate for the solution to their specific application and what, if any, software to apply. Note 1: The user is urged to apply these predictive techniques while being aware of the need for experience and also the inherent limitations of both the method and the available software. Information pertaining to availability and updates to codes for modeling radiation transport can be found in Annex A1 . For a basic understanding of radiation physics and a brief overview of method selection, refer to Annex A3 . 1.7 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use. 1.8 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee. ====== Significance And Use ====== 4.1 Use as an Analytical Tool— Mathematical methods provide an analytical tool to be employed for many applications related to absorbed dose determinations in radiation processing. Mathematical calculations may not be used as a substitute for routine dosimetry in some applications (for example, medical device sterilization, food irradiation). 4.2 Dose Calculation— A range of dosimetric quantities may be calculated through mathematical methods. We define dosimetric quantities for a region of interest. When the region is composed only of air, the sum of all the charges of electrons liberated within the region, divided by the mass of the air, gives the quantity exposure. Exposure is only related to the energy deposited within air, so additional concepts are needed to apply to other kinds of radiation and other kinds of materials. 4.2.1 The primary physical quantity used in dosimetry is the absorbed dose. It is defined as the energy absorbed per unit mass from any kind of ionizing radiation in any material. In radiation processing, calibrations of dosimetry systems are commonly made in terms of absorbed dose to water, but absorbed dose to other materials might be used, for example, absorbed dose to silicon in the case of semiconductor irradiations. The calculation of absorbed dose in mathematical methods considers the interactions depositing energy within the region of interest as well as the secondary interactions that may remove energy from the region. 4.2.2 When all interactions occurring in the region are assumed to deposit their energy entirely within the region of interest, the quantity Kerma is calculated. Kerma includes the energy of the auger electrons and bremsstrahlung created within the region of interest, considering them as being absorbed locally at the interaction site. Kerma is used in mathematical methods calculating dosimetric quantities when charge particle equilibrium has been established within the region of interest. 4.2.2.1 Calculating Kerma is balanced between the desire to reduce computational load as it avoids the numerous tracking of secondary interactions and the need to be accurate, especially at material boundaries. For the Kerma to equal the absorbed dose in a region requires charged-particle equilibrium, and this is not present at or near surfaces and material boundaries. 4.2.3 Dose calculations may be performed for a variety of photon/electron environments and irradiator geometries. 4.3 Evaluate Process Effectiveness— Mathematical models may be used to evaluate the impact of changes in product composition, loading configuration, and irradiator design on dose distribution. 4.4 Complement or Supplement to Dosimetry— Dose calculations may be used to establish a detailed understanding of dose distribution, providing a spatial resolution not obtainable through measurement. Calculations may be used to reduce the number of dosimeters required to characterize a procedure or process (for example, dose mapping). 4.5 Alternative to Dosimetry— Dose calculations may be used when dosimetry is impractical (for example, granular materials, materials with complex geometries, material contained in a package where dosimetry is not practical or possible). 4.6 Facility Design— Dose calculations are often used in the design of a new irradiator and can be used to help optimize dose distribution in an existing facility or radiation process. The use of modeling in irradiator design can be found in Refs ( 2- 7 ) . 4.7 Validation— The validation of the model should be done through comparison with reliable and traceable dosimetric measurements. The purpose of validation is to demonstrate that the mathematical method makes reliable predictions of dose and other transport quantities. Validation compares predictions or theory to the results of an appropriate experiment. The degree of validation is commensurate with the application. Guidance is given in the documents referenced in Annex A2 . 4.8 Verification— Verification is the confirmation of the mathematical correctness of a computer implementation of a mathematical method. This can be done, for example, by comparing numerical results with known analytic solutions or with other computer codes that have been previously verified. Verification should be done to ensure that the simulation is appropriate for the intended application. Refer to 3.1.24 . Note 2: Certain applications of the mathematical model deal with Operational Qualification (OQ), Performance Qualification (PQ) and process control in radiation processing such as the sterilization of healthcare products. The application and use of the mathematical model in these applications may have to meet regulatory requirements. Refer to Section 6 for prerequisites for application of a mathematical method and Section 8 for requirements before routine use of the mathematical method. 4.9 Uncertainty— An absorbed dose prediction should be accompanied by an estimate of overall uncertainty, as it is with absorbed-dose measurement (refer to ASTM 51707 and JCGM 100:2008 and JCGM 200:2012). In many cases, absorbed-dose measurement helps to establish the uncertainty in the dose calculation. 4.10 This guide should not be used as the only reference in the selection and use of mathematical models. The user is encouraged to contact individuals who are experienced in mathematical modelling and to read the relevant publications in order to select the best tool for their application. Radiation processing is an evolving field and the references cited in the annotated examples of Annex A6 are representative of the various published applications. Where a method is validated with dosimetry, it becomes a benchmark for that particular application.