ASTM E2232-02
(Guide)Standard Guide for Selection and Use of Mathematical Methods for Calculating Absorbed Dose in Radiation Processing Applications
Standard Guide for Selection and Use of Mathematical Methods for Calculating Absorbed Dose in Radiation Processing Applications
SCOPE
1.1 This guide describes different mathematical methods that may be used to calculate absorbed dose and criteria for their selection. Absorbed dose calculations determine the effectiveness of the radiation process, estimate the absorbed-dose distribution in product, or supplement and/or complement dosimetry measurements.
1.2 Radiation processing is an evolving field and annotated examples are provided in 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 in the energy range of 0.1 to 25 MeV.
1.4 The mathematical methods described include Monte Carlo, point kernel, discrete ordinate, semi-empirical and empirical methods.
1.5 General purpose software packages are available for the calculation of the transport of charged and/or neutral particles and photons 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 137Cs or 60Co, energetic electrons from particle accelerators, or bremsstrahlung 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.
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, courses, workshops and meetings can be found in . For a basic understanding of radiation physics and a brief overview of method selection, refer to .
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 and health practices and determine the applicability of regulatory requirements prior to use.
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An American National Standard
Designation:E2232–02
Standard Guide for
Selection and Use of Mathematical Methods for Calculating
Absorbed Dose in Radiation Processing Applications
This standard is issued under the fixed designation E2232; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope 1.7 This standard does not purport to address all of the
safety concerns, if any, associated with its use. It is the
1.1 This guide describes different mathematical methods
responsibility of the user of this standard to establish appro-
that may be used to calculate absorbed dose and criteria for
priate safety and health practices and determine the applica-
their selection. Absorbed dose calculations determine the
bility of regulatory requirements prior to use.
effectiveness of the radiation process, estimate the absorbed-
dose distribution in product, or supplement and/or complement
2. Referenced Documents
dosimetry measurements.
2.1 ASTM Standards:
1.2 Radiation processing is an evolving field and annotated
E170 TerminologyRelatingtoRadiationMeasurementsand
examples are provided in Annex A4 to illustrate the applica-
Dosimetry
tions where mathematical methods have been successfully
E482 Guide for Application of Neutron Transport Methods
applied. While not limited by the applications cited in these
for Reactor Vessel Surveillance, E706 (IID)
examples, applications specific to neutron transport, radiation
E666 PracticeforCalculatingAbsorbedDoseFromGamma
therapy and shielding design are not addressed in this docu-
or X Radiation
ment.
2.2 ISO/ASTM Standards:
1.3 This guide covers the calculation of radiation transport
51204 Practice for Dosimetry in Gamma Irradiation Facili-
of electrons and photons in the energy range of 0.1 to 25 MeV.
ties for Food Processing
1.4 The mathematical methods described include Monte
51275 Practice for Use of a Radiochromic Film Dosimetry
Carlo, point kernel, discrete ordinate, semi-empirical and
System
empirical methods.
51400 Practice for Characterization and Performance of a
1.5 General purpose software packages are available for the
High-Dose Radiation Dosimetry Calibration Laboratory
calculation of the transport of charged and/or neutral particles
51431 Practice for Dosimetry in Electron and Bremsstrahl-
and photons from various types of sources of ionizing radia-
ung Irradiation Facilities for Food Processing
tion. This standard is limited to the use of these software
51608 Practice for Dosimetry in an X-ray (Bremsstrahlung)
packages or other mathematical methods for the determination
Facility for Radiation Processing
of spatial dose distributions for photons emitted following the
137 60 51649 Practice for Dosimetry in an Electron Beam Facility
decay of Cs or Co, energetic electrons from particle
forRadiationProcessingatEnergiesbetween300keVand
accelerators, or bremsstrahlung generated by electron accelera-
25 MeV
tors.
51702 Practice for Dosimetry in a Gamma Irradiation Fa-
1.6 This guide assists the user in determining if mathemati-
cility for Radiation Processing
cal methods are a useful tool. This guide may assist the user in
51707 Guide for Estimating Uncertainties in Dosimetry for
selecting an appropriate method for calculating absorbed dose.
Radiation Processing
NOTE 1—The user is urged to apply these predictive techniques while
51818 Practice for Dosimetry in an Electron Beam Facility
being aware of the need for experience and also the inherent limitations of
for Radiation Processing at Energies between 80 and 300
both the method and the available software. Information pertaining to
keV
availabilityandupdatestocodesformodelingradiationtransport,courses,
51939 Practice for Blood Irradiation Dosimetry
workshops and meetings can be found in Annex A1. For a basic
2.3 International Commission on Radiation Units and
understanding of radiation physics and a brief overview of method
selection, refer to Annex A3. Measurements Reports:
ICRUReport14, RadiationDosimetry:X-RaysandGamma
This guide is under the jurisdiction of ASTM Committee E10 on Nuclear
Technology and Applications and is the direct responsibility of Subcommittee
E10.01 on Radiation Processing: Dosimetry and Applications. Annual Book of ASTM Standards, Vol 12.02.
Current edition approved Sept. 10, 2002. Published November 2002. DOI: Available from International Commission on Radiation Units and Measure-
10.1520/E2232-02. ments, 7910 Woodmont Ave., Suite 800, Bethesda, MD 20814 USA.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
E2232–02
RayswithMaximumPhotonEnergiesBetween0.6and50 3.1.4 deterministic method—a method using mathematical
MeV equations (transport equations) to directly calculate the radia-
tion field over all space as a function of radiation source and
ICRU Report 17, Radiation Dosimetry: X-Rays Generated
boundary conditions.
at Potentials of 5 to 150 kV
3.1.4.1 Discussion—The point kernel and discrete ordinate
ICRU Report 34, The Dosimetry of Pulsed Radiation
methods are examples of deterministic methods.
ICRU Report 35, Radiation Dosimetry: Electron Beams
3.1.5 discrete ordinates—a deterministic method for ap-
with Energies Between 1 and 50 MeV
proximate numerical solution of the transport equation in
ICRU Report 37, Stopping Powers for Electrons and
which the direction of motion is divided into a finite number of
Positrons
discrete ordinate angles.
ICRU Report 51, Quantities and Units in Radiation Protec-
3.1.5.1 Discussion—In the discrete ordinates approxima-
tion Dosimetry
tion,thetransportequationbecomesasetofcoupledequations,
ICRU Report 60, Fundamental Quantities and Units for
one for each discrete ordinate. Particle behaviors along paths
Ionizing Radiation, 1998
intermediate to described paths are approximated by a
2.4 International Organization for Standardization:
weighted average (numerical quadrature) of adjacent paths
ISO 9001 Quality Systems—Model for Quality Assurance (1). The method is useful for both electron and photon beam
in Design/Development, Production, Installation and Ser-
sources when appropriate assumptions can be made.
vicing 3.1.6 empirical model—a method derived from fitting an
approximating function to experimental data or Monte Carlo
ISO 9002 Quality Systems—Model for Quality Assurance
calculation result.
in Production and Installation
3.1.6.1 Discussion—Empirical models are generally devel-
ISO 11137 Sterilization of Health Care Products—
oped by fitting equations (for example, polynomial) to experi-
Requirements for Validation and Routine Control - Radia-
mental data or simulation output derived from another math-
tion Sterilization
ematical method.
3.1.7 histories—a particle history is the record of all simu-
3. Terminology
lated interactions along its track as used in stochastic or Monte
3.1 Definitions:
Carlo simulations.
3.1.1 benchmarking—comparing model predictions to inde-
3.1.7.1 Discussion—A history begins with the starting po-
pendent measurements or calculations under similar conditions
sition, energy and direction of a particle, follows all its
using established criteria of uncertainty.
interactions, and terminates in one of several outcomes such as
3.1.2 biasing—in a Monte Carlo simulation, an adjustment
absorption, escape from the boundary of the problem, or
of the source particle selection and/or the transported particle
reaching a cut-off limit (such as a cut-off energy). A particle
weight in a statistically valid manner so as to increase the
history is the systematic generation of a random, simulated
particles in a region where the detector response is most
particle track that is obtained according to the known physical
important.
interactions of either electrons or photons with the material
3.1.2.1 Discussion—Biasing is a method used to reduce the
being traversed.
estimated uncertainty or computer run times of Monte Carlo
3.1.8 mathematical method—a method of solution of an
simulations. Monte Carlo simulations using the natural prob-
electron and/or photon transport problem using algebraic
abilities of physical events may require unacceptably long run
relations and mathematical operations to represent the system
times to accumulate statistics for rare events. The simulated
and its dynamics.
probabilitiesmaybealteredtoachievetheuncertaintygoalsfor
3.1.9 mathematical model—a mathematical description of a
the simulation in acceptable run times by biasing the sampling
physical problem based on physical laws and/or empirical
from the probability distributions. The number of particles
correlation.
tracked and the particle weights may be adjusted so as to
3.1.10 Monte Carlo method—a simulation method used for
ensure a statistically valid sample from the probability distri-
calculating absorbed dose, energy spectra, charge, fluence and
butions. Appropriate biasing requires a detailed knowledge of
fluence rate in a volume of interest using a statistical summary
the model and the influence of rare events. As with all
of the radiation interactions. A Monte Carlo calculation con-
simulations, results should be compared with benchmark
sists of running a large number of particle histories (simula-
measurements or simulation results originated by a different
tions) until some acceptable statistical uncertainty in the
code.
desired calculated quantity (such as dose) has been reached.
3.1.3 build-up factor—the ratio of the total dose, particle
3.1.10.1 Discussion—This calculation method is suitable
fluence, exposure or other quantity due to primary and second-
for problems involving either electrons or photons or both.
ary (scattered) radiation, at a target (or field point) location to
This technique produces a probabilistic approximation to the
the dose due to primary radiation at that location. The concept
solution of a problem by using statistical sampling techniques.
of build-up applies to the transport of photons.
See also stochastic and history.
4 5
Available fromAmerican National Standards Institute (ANSI), 25 W. 43rd St., The boldface numbers in parentheses refer to the list of references at the end of
4th Floor, New York, NY 10036 USA. this standard.
E2232–02
3.1.11 numerical convergence—the process in which the 3.1.19 uncertainty—a parameter associated with the result
iterative solution of an equation or set of equations changes by of a measurement, that characterises the spread of values that
could reasonably be attributed to the measurand or derived
less than some defined value.
quantity.
3.1.11.1 Discussion—The mathematical equations describ-
3.1.20 validation—accumulation of documented experi-
ing a problem are often so complex that an analytical (alge-
mental evidence, used to demonstrate that the mathematical
braic) solution is not possible. The solution of the equations
method is a reliable prediction technique.
can be estimated by an iterative process of progressively
3.1.20.1 Discussion—Validation compares a code or theory
refining approximate solutions at a grid of discrete locations.A
with results of an appropriate experiment.
consistent set of solutions arrived at by this method achieves
numerical convergence. Convergence may not be obtained if
3.1.21 verification—confirmation by examination of evi-
the discrete locations are too widely separated (that is, the grid dence that the mathematical method has been properly and
is too coarse). successfully applied to the problem.
3.1.12 point kernel method—a deterministic method for 3.1.21.1 Discussion—It is important to know the type of
radiation sources, geometries, energies, etc. for which a code
calculating dose based on integrating the contributions from
has been validated. The calculated results will also depend on
point sources.
quantities at the user’s disposal such as cutoff energy (for
3.1.12.1 Discussion—The point kernel method is typically
Monte Carlo) or mesh size (for discrete ordinate methods).
used for photon transport applications. The radiation source is
Verification demonstrates that theory was implemented in the
modeled as a large set of point sources. The absorbed dose,
way intended, and that the simulation was performed in
dose equivalent or exposure is estimated at a dose point by
accordance with its requirements and specifications.
integrating the contribution from each of the point sources. A
3.1.22 zoning—The geometric description used to break up
multiplicative value (the semi-empirical build-up factor) is
a larger region into smaller segments in which to calculate the
used to account for the contribution from scattered (indirect)
dose.Partitioningazoneintosmallersegmentsisreferredtoas
radiationfromregionsnotinthedirectpathbetweenthesource
subzoning.
point and field point.
3.2 Definitions of other terms used in this standard that
3.1.13 radiation field—a function describing the particle
pertain to radiation measurement and dosimetry may be found
density and the distributions of energy, direction and particle
in Terminology E170. Definitions in Terminology E170 are
type at any point.
compatible with ICRU 51 and 60; those documents, therefore,
3.1.14 radiation transport theory—an analytical description
may be used as alternative references.
of the propagation of a radiation field according to the physical
laws governing the interactions of the radiation.
4. Significance and Use
3.1.14.1 Discussion—In its most general form, transport
4.1 Use as an Analytical Tool—Mathematical methods pro-
theory is a special branch of statistical mechanics, which deals
vide an analytical tool to be employed for many applications
with the interaction of the radiation field with matter.
related to absorbed dose determinations in radiation process-
3.1.15 semi-empirical model—an empirical model in which
ing. Mathematical calculations may not be used as a substitute
thefittingparametersareconstrainedsothatthemodelsatisfies
for routine dosimetry in some applications (for example,
one or more physical laws or rules.
medical device sterilization, food irradiation).
3.1.15.1 Discussion—The satisfaction of such physical
4.2 Dose Calculation—Absorbed-dose calculations may be
rules may enable the model to be applicable over a wide range
performed for a variety of photon/electron environments and
of energies and materials.Agood example of a semi-empirical
irradiator geometries.
model for electron beam energy deposition is found in refer-
4.3 Evaluate Process Effectiveness—Mathematical models
ence (2).
may be u
...
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