1、Designation: E2232 10An American National StandardStandard Guide forSelection and Use of Mathematical Methods for CalculatingAbsorbed Dose in Radiation Processing Applications1This standard is issued under the fixed designation E2232; the number immediately following the designation indicates the ye
2、ar oforiginal adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon () indicates an editorial change since the last revision or reapproval.1. Scope1.1 This guide describes different mathematical methodstha
3、t may be used to calculate absorbed dose and criteria fortheir selection. Absorbed-dose calculations can determine theeffectiveness of the radiation process, estimate the absorbed-dose distribution in product, or supplement or complement, orboth, the measurement of absorbed dose.1.2 Radiation proces
4、sing is an evolving field and annotatedexamples are provided in Annex A6 to illustrate the applica-tions where mathematical methods have been successfullyapplied. While not limited by the applications cited in theseexamples, applications specific to neutron transport, radiationtherapy and shielding
5、design are not addressed in this docu-ment.1.3 This guide covers the calculation of radiation transportof electrons and photons with energies up to 25 MeV.1.4 The mathematical methods described include MonteCarlo, point kernel, discrete ordinate, semi-empirical andempirical methods.1.5 General purpo
6、se software packages are available for thecalculation of the transport of charged and/or unchargedparticles and photons from various types of sources of ionizingradiation. This standard is limited to the use of these softwarepackages or other mathematical methods for the determinationof spatial dose
7、 distributions for photons emitted following thedecay of137Cs or60Co, for energetic electrons from particleaccelerators, or for X-rays generated by electron accelerators.1.6 This guide assists the user in determining if mathemati-cal methods are a useful tool. This guide may assist the user inselect
8、ing an appropriate method for calculating absorbed dose.The user must determine whether any of these mathematicalmethods are appropriate for the solution to their specificapplication and what, if any, software to apply.NOTE 1The user is urged to apply these predictive techniques whilebeing aware of
9、the need for experience and also the inherent limitations ofboth the method and the available software. Information pertaining toavailability and updates to codes for modeling radiation transport, courses,workshops and meetings can be found in Annex A1. For a basicunderstanding of radiation physics
10、and a brief overview of methodselection, refer to Annex A3.1.7 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bi
11、lity of regulatory requirements prior to use.2. Referenced Documents2.1 ASTM Standards:2E170 Terminology Relating to Radiation Measurements andDosimetryE482 Guide for Application of Neutron Transport Methodsfor Reactor Vessel Surveillance, E706 (IID)2.2 ISO/ASTM Standards:251707 Guide for Estimating
12、 Uncertainties in Dosimetry forRadiation Processing2.3 International Commission on Radiation Units andMeasurements Reports:3ICRU Report 60 Fundamental Quantities and Units forIonizing RadiationICRU Report 80 Dosimetry Systems for Use in RadiationProcessing2.4 United States National Institute of Stan
13、dards andTechnology:4NIST Technical Note 1297 (1994 edition) Guidelines forEvaluating and Expressing the Uncertainty of NIST Mea-surement Results3. Terminology3.1 Definitions:3.1.1 benchmarkingcomparing model predictions to inde-pendent measurements or calculations under similar conditionsusing defi
14、ned criteria of uncertainty.1This guide is under the jurisdiction of ASTM Committee E10 on NuclearTechnology and Applications and is the direct responsibility of SubcommitteeE10.01 on Radiation Processing: Dosimetry and Applications.Current edition approved July 1, 2010. Published September 2010. Or
15、iginallyapproved in 2002. Last previous edition approved in 2002 as E2232-02. DOI:10.1520/E2232-10.2For referenced ASTM and ISO/ASTM standards, visit the ASTM website,www.astm.org, or contact ASTM Customer Service at serviceastm.org. ForAnnual Book of ASTM Standards volume information, refer to the
16、standardsDocument Summary page on the ASTM website.3Available from International Commission on Radiation Units and Measure-ments, 7910 Woodmont Ave., Suite 800, Bethesda, MD 20815 USA.4Available as a download from the NIST web site at: http:/physics.nist.gov/Pubs/guidelines/TN1297/tn1297s.pdf.1Copyr
17、ight ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.3.1.1.1 DiscussionBenchmarking is a prerequisite beforeroutine use of a mathematical model. Refer to 8.1 and AnnexA5.3.1.2 biasing (in a Monte Carlo simulation)adjustment ofthe source particl
18、e selection and/or the transported particleweight in a statistically valid manner so as to increase theparticles in a region where the detector response is mostimportant.3.1.2.1 DiscussionBiasing is a method used to reduce theestimated uncertainty or computer run times of Monte Carlosimulations. Mon
19、te Carlo simulations using the natural prob-abilities of physical events may require unacceptably long runtimes to accumulate statistics for rare events. The simulatedprobabilities may be altered to achieve the uncertainty goals forthe simulation in acceptable run times by biasing the samplingfrom t
20、he probability distributions. The number of particlestracked and the particle weights may be adjusted so as toensure a statistically valid sample from the probability distri-butions. Appropriate biasing requires a detailed knowledge ofthe model and the influence of rare events. As with allsimulation
21、s, results should be compared with benchmarkmeasurements or simulation results originated by a differentcode.3.1.3 build-up factorthe ratio of the total dose, particlefluence, exposure or other quantity due to primary and second-ary (scattered) radiation, at a target (or field point) location tothe
22、dose due to primary radiation at that location.3.1.3.1 DiscussionThe concept of build-up applies to thetransport of photons.3.1.4 deterministic methoda mathematical method usingtransport equations to directly calculate the radiation field overall space as a function of radiation source and boundaryc
23、onditions.3.1.4.1 DiscussionThe point kernel and discrete ordinatemethods are examples of deterministic methods.3.1.5 discrete ordinate methoda deterministic method forapproximate numerical solution of the transport equation inwhich the direction of motion is divided into a finite number ofdiscrete
24、ordinate angles.3.1.5.1 DiscussionIn the discrete ordinates approxima-tion, the transport equation becomes a set of coupled equations,one for each discrete ordinate. Particle behaviors along pathsintermediate to described paths are approximated by aweighted average (numerical quadrature) of adjacent
25、 paths(1).5The method is useful for both electron and photon sourceswhen appropriate assumptions can be made.3.1.6 empirical methoda method derived from fitting anapproximating function to experimental data or Monte Carlocalculation result3.1.6.1 DiscussionEmpirical models are generally devel-oped b
26、y fitting equations (for example, polynomial) to experi-mental data or simulation output derived from another math-ematical method.3.1.7 historya particle history is the record of all simu-lated interactions along its track as used in stochastic simula-tions (for example, Monte Carlo).3.1.7.1 Discus
27、sionA particle history begins with the start-ing position, energy and direction of a particle, follows all itsinteractions, and terminates in one of several outcomes such asabsorption, escape from the boundary of the problem, orreaching a cut-off limit (such as a cut-off energy). A particlehistory i
28、s the systematic generation of a random, simulatedparticle track that is obtained according to the known physicalinteractions of either electrons or photons with the materialbeing traversed. History and particle history are consideredsynonymous.3.1.8 mathematical methoda method of solution of anelec
29、tron and/or photon transport problem using algebraicrelations and mathematical operations to represent the systemand its dynamics.3.1.9 mathematical modela mathematical description of aphysical problem based on physical laws and/or empiricalcorrelation.3.1.10 Monte Carlo methoda simulation method us
30、ed forcalculating absorbed dose, energy spectra, charge, fluence andfluence rate in a volume of interest using a statistical summaryof the radiation interactions.3.1.10.1 DiscussionAMonte Carlo calculation consists ofrunning a large number of particle histories (simulations) untilsome acceptable sta
31、tistical uncertainty in the desired calculatedquantity (such as dose) has been reached. This calculationmethod is suitable for problems involving either electrons orphotons or both. This technique produces a probabilisticapproximation to the solution of a problem by using statisticalsampling techniq
32、ues. See also stochastic and history.3.1.11 numerical convergencethe process in which theiterative solution of an equation or set of equations changes byless than some defined value.3.1.11.1 DiscussionThe mathematical equations describ-ing a problem are often so complex that an analytical (alge-brai
33、c) solution is not possible. The solution of the equationscan be estimated by an iterative process of progressivelyrefining approximate solutions at a grid of discrete locations.Aconsistent set of solutions arrived at by this method achievesnumerical convergence. Convergence may not be obtained ifth
34、e discrete locations are too widely separated (that is, the gridis too coarse).3.1.12 point kernel methoda deterministic method forcalculating dose based on integrating the contributions frompoint sources.3.1.12.1 DiscussionThe point kernel method is typicallyused for photon transport applications.
35、The radiation source ismodeled as a large set of point sources. The absorbed dose,dose equivalent or exposure is estimated at a dose point byintegrating the contribution from each of the point sources. Amultiplicative value (the semi-empirical build-up factor) isused to account for the contribution
36、from scattered (indirect)radiation from regions not in the direct path between the sourcepoint and field point.5The boldface numbers in parentheses refer to the list of references at the end ofthis standard.E2232 1023.1.13 radiation fielda function describing the particledensity and the distribution
37、s of energy, direction and particletype at any point.3.1.14 radiation transport theoryan analytical descriptionof the propagation of a radiation field according to the physicallaws governing the interaction of radiation with matter.3.1.14.1 DiscussionIn its most general form, transporttheory is a sp
38、ecial branch of statistical mechanics, which dealswith the interaction of the radiation field with matter.3.1.15 semi-empirical modelan empirical model in whichthe fitting parameters are constrained so that the model satisfiesone or more physical laws or rules.3.1.15.1 DiscussionThe satisfaction of
39、such physicalrules may enable the model to be applicable over a wide rangeof energies and materials. A good example of a semi-empiricalmodel for electron beam energy deposition is found in refer-ence (2).3.1.16 spatial meshthe subdivision of the radiation inter-action volume of interest for performi
40、ng a transport calculationinto a grid of discrete spatial elements.3.1.17 stochastic methodsmethods using mathematicalequations containing random variables to describe or summa-rize the physical processes in the system being studied. Arandom variable is a variable whose value is a function of astati
41、stical distribution of random values.3.1.17.1 DiscussionThe Monte Carlo method is the onlystochastic method discussed in this guide. See also MonteCarlo and history.3.1.18 transport equationan integro-differential equationdescribing the motion of particles or radiation through amedium.3.1.18.1 Discu
42、ssionThe transport equation contains vari-ous terms corresponding to sources of particles, particlestreaming and particle scattering in and out of an infinitesimalvolume of phase space.3.1.19 Type A evaluation (of standard uncertainty)method of evaluation of a standard uncertainty by the statistical
43、analysis of a series of observations.3.1.19.1 DiscussionThe inherent sampling uncertainty ofthe Monte Carlo method can be estimated as a Type Auncertainty by applying statistical sampling techniques to thenumber of simulated histories. For calculations without bias-ing, the statistical uncertainty s
44、cales as the reciprocal of thesquare root of the number of histories.3.1.20 Type B evaluation (of standard uncertainty)method of evaluation of a standard uncertainty by means otherthan the statistical analysis of a series of observations.3.1.20.1 DiscussionThere are Type B uncertainties asso-ciated
45、with the necessary simplifying assumptions needed toapproximate the physical paths of electrons in the model anduncertainties in the cross-sections for the different interactions.These Type B uncertainties can be estimated by analyticaltechniques. A Type B uncertainty could result from thedifference
46、 in geometry and material composition of the mod-elled irradiator versus the actual irradiator. Other sources ofType B uncertainty are the inadequate description of theproblem and approximations to actual physics.3.1.21 uncertaintya parameter associated with the resultof a calculation that character
47、izes the spread of values thatcould reasonably be attributed to the derived quantity.3.1.21.1 DiscussionLike absorbed-dose measurement, theabsorbed-dose calculation should also be accompanied by anestimate of uncertainty.3.1.22 validationaccumulation of documented experi-mental evidence, used to dem
48、onstrate that the mathematicalmethod is a reliable prediction technique.3.1.22.1 DiscussionValidation compares a code or theorywith results of an appropriate experiment.3.1.23 verificationconfirmation by examination of evi-dence that the mathematical method has been properly andsuccessfully applied
49、to the problem.3.1.23.1 DiscussionIt is important to know the type ofradiation sources, geometries, energies, etc. for which a codehas been validated. The calculated results will also depend onquantities at the users disposal such as cut-off energy (forMonte Carlo) or mesh size (for discrete ordinate methods).Verification demonstrates that theory was implemented in theway intended, and that the simulation was performed inaccordance with its requirements and specifications.3.1.24 zoningThe geometric description used to break upa larger regi
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