1、Designation: E 2232 02An American National StandardStandard Guide forSelection and Use of Mathematical Methods for CalculatingAbsorbed Dose in Radiation Processing Applications1This standard is issued under the fixed designation E 2232; the number immediately following the designation indicates the
2、year 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 (e) indicates an editorial change since the last revision or reapproval.1. Scope1.1 This guide describes different mathematical methods
3、that may be used to calculate absorbed dose and criteria fortheir selection. Absorbed dose calculations determine theeffectiveness of the radiation process, estimate the absorbed-dose distribution in product, or supplement and/or complementdosimetry measurements.1.2 Radiation processing is an evolvi
4、ng field and annotatedexamples are provided in Annex A4 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 design are not ad
5、dressed in this docu-ment.1.3 This guide covers the calculation of radiation transportof electrons and photons in the energy range of 0.1 to 25 MeV.1.4 The mathematical methods described include MonteCarlo, point kernel, discrete ordinate, semi-empirical andempirical methods.1.5 General purpose soft
6、ware packages are available for thecalculation of the transport of charged and/or neutral particlesand photons from various types of sources of ionizing radia-tion. This standard is limited to the use of these softwarepackages or other mathematical methods for the determinationof spatial dose distri
7、butions for photons emitted following thedecay of137Cs or60Co, energetic electrons from particleaccelerators, or bremsstrahlung generated by electron accelera-tors.1.6 This guide assists the user in determining if mathemati-cal methods are a useful tool. This guide may assist the user inselecting an
8、 appropriate method for calculating absorbed dose.NOTE 1The user is urged to apply these predictive techniques whilebeing aware of the need for experience and also the inherent limitations ofboth the method and the available software. Information pertaining toavailability and updates to codes for mo
9、deling radiation transport, courses,workshops and meetings can be found in Annex A1. For a basicunderstanding of radiation physics 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 i
10、s theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory requirements prior to use.2. Referenced Documents2.1 ASTM Standards:E 170 Terminology Relating to Radiation Measurementsand Dosimetry2E 482 Guide for
11、Application of Neutron Transport Methodsfor Reactor Vessel Surveillance2E 666 Practice for Calculating Absorbed Dose from Gammaor X Radiation22.2 ISO/ASTM Standards:51204 Practice for Dosimetry in Gamma Irradiation Facili-ties for Food Processing251275 Practice for Use of a Radiochromic Film Dosimet
12、rySystem251400 Practice for Characterization and Performance of aHigh-Dose Radiation Dosimetry Calibration Laboratory251431 Practice for Dosimetry in Electron and Bremsstrahl-ung Irradiation Facilities for Food Processing251608 Practice for Dosimetry in an X-ray (Bremsstrahlung)Facility for Radiatio
13、n Processing251649 Practice for Dosimetry in an Electron Beam Facilityfor Radiation Processing at Energies between 300 keV and25 MeV251702 Practice for Dosimetry in a Gamma Irradiation Fa-cility for Radiation Processing251707 Guide for Estimating Uncertainties in Dosimetry forRadiation Processing251
14、818 Practice for Dosimetry in an Electron Beam Facilityfor Radiation Processing at Energies between 80 and 300keV251939 Practice for Blood Irradiation Dosimetry22.3 International Commission on Radiation Units andMeasurements Reports:3ICRU Report 14, Radiation Dosimetry: X-Rays and Gamma1This guide i
15、s under the jurisdiction of ASTM Committee E10 on NuclearTechnology and Applications and is the direct responsibility of SubcommitteeE10.01 on Dosimetry for Radiation Processing.Current edition approved Sept 10, 2002. Published November 2002.2Annual Book of ASTM Standards, Vol 12.02.3Available from
16、International Commission on Radiation Units and Measure-ments, 7910 Woodmont Ave., Suite 800, Bethesda, MD 20814 USA.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.Rays with Maximum Photon Energies Between 0.6 and 50MeVICRU Report 1
17、7, Radiation Dosimetry: X-Rays Generatedat Potentials of 5 to 150 kVICRU Report 34, The Dosimetry of Pulsed RadiationICRU Report 35, Radiation Dosimetry: Electron Beamswith Energies Between 1 and 50 MeVICRU Report 37, Stopping Powers for Electrons andPositronsICRU Report 51, Quantities and Units in
18、Radiation Protec-tion DosimetryICRU Report 60, Fundamental Quantities and Units forIonizing Radiation, 19982.4 International Organization for Standardization:4ISO 9001 Quality SystemsModel for Quality Assurancein Design/Development, Production, Installation and Ser-vicingISO 9002 Quality SystemsMode
19、l for Quality Assurancein Production and InstallationISO 11137 Sterilization of Health Care ProductsRequirements for Validation and Routine Control - Radia-tion Sterilization3. Terminology3.1 Definitions:3.1.1 benchmarkingcomparing model predictions to inde-pendent measurements or calculations under
20、 similar conditionsusing established criteria of uncertainty.3.1.2 biasingin a Monte Carlo simulation, an adjustmentof the source particle selection and/or the transported particleweight in a statistically valid manner so as to increase theparticles in a region where the detector response is mostimp
21、ortant.3.1.2.1 DiscussionBiasing is a method used to reduce theestimated uncertainty or computer run times of Monte Carlosimulations. Monte Carlo simulations using the natural prob-abilities of physical events may require unacceptably long runtimes to accumulate statistics for rare events. The simul
22、atedprobabilities may be altered to achieve the uncertainty goals forthe simulation in acceptable run times by biasing the samplingfrom the probability distributions. The number of particlestracked and the particle weights may be adjusted so as toensure a statistically valid sample from the probabil
23、ity distri-butions. Appropriate biasing requires a detailed knowledge ofthe model and the influence of rare events. As with allsimulations, results should be compared with benchmarkmeasurements or simulation results originated by a differentcode.3.1.3 build-up factorthe ratio of the total dose, part
24、iclefluence, exposure or other quantity due to primary and second-ary (scattered) radiation, at a target (or field point) location tothe dose due to primary radiation at that location. The conceptof build-up applies to the transport of photons.3.1.4 deterministic methoda method using mathematicalequ
25、ations (transport equations) to directly calculate the radia-tion field over all space as a function of radiation source andboundary conditions.3.1.4.1 DiscussionThe point kernel and discrete ordinatemethods are examples of deterministic methods.3.1.5 discrete ordinatesa deterministic method for ap-
26、proximate numerical solution of the transport equation inwhich the direction of motion is divided into a finite number ofdiscrete 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. Part
27、icle behaviors along pathsintermediate to described paths are approximated by aweighted average (numerical quadrature) of adjacent paths(1).5The method is useful for both electron and photon beamsources when appropriate assumptions can be made.3.1.6 empirical modela method derived from fitting anapp
28、roximating function to experimental data or Monte Carlocalculation result.3.1.6.1 DiscussionEmpirical models are generally devel-oped by fitting equations (for example, polynomial) to experi-mental data or simulation output derived from another math-ematical method.3.1.7 historiesa particle history
29、is the record of all simu-lated interactions along its track as used in stochastic or MonteCarlo simulations.3.1.7.1 DiscussionA history begins with the starting po-sition, energy and direction of a particle, follows all itsinteractions, and terminates in one of several outcomes such asabsorption, e
30、scape from the boundary of the problem, orreaching a cut-off limit (such as a cut-off energy). A particlehistory is the systematic generation of a random, simulatedparticle track that is obtained according to the known physicalinteractions of either electrons or photons with the materialbeing traver
31、sed.3.1.8 mathematical methoda method of solution of anelectron 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 empirical
32、correlation.3.1.10 Monte Carlo methoda simulation method used forcalculating absorbed dose, energy spectra, charge, fluence andfluence rate in a volume of interest using a statistical summaryof the radiation interactions. A Monte Carlo calculation con-sists of running a large number of particle hist
33、ories (simula-tions) until some acceptable statistical uncertainty in thedesired calculated quantity (such as dose) has been reached.3.1.10.1 DiscussionThis calculation method is suitablefor problems involving either electrons or photons or both.This technique produces a probabilistic approximation
34、to thesolution of a problem by using statistical sampling techniques.See also stochastic and history.4Available from American National Standards Institute (ANSI), 25 W. 43rd St.,4th Floor, New York, NY 10036 USA.5The boldface numbers in parentheses refer to the list of references at the end ofthis s
35、tandard.E22320223.1.11 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-braic) solution is not po
36、ssible. 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 ifthe discrete locations
37、 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. The radiation source
38、 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 from scattered (indi
39、rect)radiation from regions not in the direct path between the sourcepoint and field point.3.1.13 radiation fielda function describing the particledensity and the distributions of energy, direction and particletype at any point.3.1.14 radiation transport theoryan analytical descriptionof the propaga
40、tion of a radiation field according to the physicallaws governing the interactions of the radiation.3.1.14.1 DiscussionIn its most general form, transporttheory is a special branch of statistical mechanics, which dealswith the interaction of the radiation field with matter.3.1.15 semi-empirical mode
41、lan 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 such physicalrules may enable the model to be applicable over a wide rangeof energies and materials. A good example of a semi-empiri
42、calmodel 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 performing a transport calculationinto a grid of discrete spatial elements.3.1.17 stochastic methodsmethods using mathematicalequations cont
43、aining 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 astatistical distribution of random values. The Monte Carlomethod is the only stochastic method discussed in this guide.See also Monte Car
44、lo and history.3.1.18 transport equationan integrodifferential equationdescribing the motion of particles or radiation through amedium. This equation contains various terms correspondingto sources of particles, particle streaming and particle scatter-ing in and out of an infinitesimal volume of phas
45、e space.3.1.19 uncertaintya parameter associated with the resultof a measurement, that characterises the spread of values thatcould reasonably be attributed to the measurand or derivedquantity.3.1.20 validationaccumulation of documented experi-mental evidence, used to demonstrate that the mathematic
46、almethod is a reliable prediction technique.3.1.20.1 DiscussionValidation compares a code or theorywith results of an appropriate experiment.3.1.21 verificationconfirmation by examination of evi-dence that the mathematical method has been properly andsuccessfully applied to the problem.3.1.21.1 Disc
47、ussionIt 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 cutoff energy (forMonte Carlo) or mesh size (for discrete ordinate methods).Verification demon
48、strates that theory was implemented in theway intended, and that the simulation was performed inaccordance with its requirements and specifications.3.1.22 zoningThe geometric description used to break upa larger region into smaller segments in which to calculate thedose. Partitioning a zone into sma
49、ller segments is referred to assubzoning.3.2 Definitions of other terms used in this standard thatpertain to radiation measurement and dosimetry may be foundin Terminology E 170. Definitions in Terminology E 170 arecompatible with ICRU 51 and 60; those documents, therefore,may be used as alternative references.4. Significance and Use4.1 Use as an Analytical ToolMathematical methods pro-vide an analytical tool to be employed for many applicationsrelated to absorbed dose determinations in radiation process-ing. Mathematical calculations may not be use
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