From Roentgens to CentiGrays

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Exposure versus Absorbed Dose

The purpose of this discussion is to clarify the concepts of exposure and absorbed dose as used in radiological measurements. The difference is more than just two different units for the same quantity, but they are confused because the same instruments are used for their measurement.

In optical photography the concept of exposure, light energy per unit area incident on a film, is simplified by the fact that all the light is absorbed by the film or a measuring instrument. In radiography the image is produced by partial transmission through an absorbing object and we are concerned with the exposure to the object as well as the film. With such penetrating radiation most measuring instruments absorb only part of the energy incident on them, to produce a signal which can be used as a measure of either exposure or absorbed dose.

The Roentgen was conceived as a unit of exposure, to characterize the radiation incident on an absorbing material without regard to the character of the absorber. It was defined in terms of a measurement which requires the absorption of a negligible part of the incident energy, since complete absorption at a point is impossible. It was formalized in 1928 as "The amount of radiation which produces one electrostatic unit of ions, either positive or negative, per cubic centimeter of air at standard temperature and pressure." In modern units,

1 Roentgen = 2.58 x 10-4 Coulomb  = .3336 nC at  S. T. P.
                                           Kg air                  cc

The standard instrument used to characterize a radiation source at a standards laboratory for calibration of working instruments is called a free-air ionization chamber. It measures a narrow beam of radiation, defined by a diaphragm outside the sensitive volume, using electrodes designed to collect ions from a definite volume of air, at a sufficient distance from the source that a condition of equilibrium is achieved between secondary ionizing particles and the primary photons that produce them.

This system is not practical for most applications because it is bulky and sensitive to environmental conditions and because it is specialized for measuring a nearly-parallel beam of radiation from a distant point source, in the absence of scattering material other than air. However the standards laboratory uses it to provide measured calibration factors for a user's instrument, to convert an instrument reading to exposure in air at the point where the instrument was located, for the particular radiation quality that is calibrated.

An "air-wall" ionization chamber is an enclosed cavity with electrodes to collect charge from a definite volume of air which communicates to the outside so that atmospheric changes will affect the contents in a calculable way. The wall material is chosen to have an atomic composition that is similar to air so that the secondary particles emitted from the wall have the same number and energy distribution as in a free-air chamber, with a thickness sufficient to exclude secondary particles that may be produced in surrounding absorbing material. With this geometry the calibration is the same as a free-air chamber for a range of radiation qualities, and the chamber measures "exposure" even in the presence of nearby objects. Unfortunately this effort fails for photons above about 1 MeV because the range of secondary electrons is so great that the required wall thickness causes significant attenuation and scattering of the incident radiation and a measurement no longer characterizes "exposure" at a point.

In the 1940's and 1950's, with the advent of supervoltage therapy machines, telecurie sources, and energetic particle beams, the Roentgen was still the only recognized unit for radiation measurement. It was recognized that the same exposure gave different absorbed energy in different materials, and the observed differences in "relative biological effect" or RBE for different radiations were partly the result of different absorbed energy. The early efforts to account for this effect recognized that the Roentgen unit measured "Exposure Dose" and proposed the acronym RAD for "Roentgen-equivalent Absorbed Dose". With factors for energy absorption relative to air, to make air ionization measurements applicable to determining absorbed dose in other media, the RBE became the same for all but densely-ionizing particles.

In 1962 the RAD was formalized by the International Committee on Radiological Units and Measurements (ICRU), as a special unit of energy known as "Radiation Absorbed Dose" with a magnitude of 100 ergs per gram of absorbing material. It was thus defined as an independent physical standard which correlated well with chemical and biological effects of radiation and the ad-hoc definition of radiation exposure in terms of an air ionization measurement was abandoned for clinical dosimetry. The term "Exposure Dose" was disparaged as a confusing hybrid of the very different ideal concepts of radiation incident at a point and radiation absorbed at a point.

Unfortunately the U.S. standards laboratories do not yet maintain absolute determinations of absorbed dose in a standard medium such as water. The calibration they offer for use in supervoltage therapy beams uses a cobalt-60 beam with exposure rate as measured by a free-air ion chamber.(1994)   The burden is on the user to choose appropriate factors to calculate absorbed dose in water or another medium from the reading of an ion chamber in that medium which has been calibrated with its buildup cap in air to read exposure in Roentgens.

In the 1950's and 1960's the measurement of absorbed dose directly in various media was an active research interest, and chemical dosimeters, calorimeters, and cavity ionization chambers were developed to the point where appropriate correction factors could be applied to get absolute results that agreed within the experimental error of a fraction of a percent. For example, some of the energy absorbed in a calorimeter did not appear as heat but was stored as chemical change in the absorber, and the energy loss per ion pair produced by secondary electrons depends on the dielectric properties of the medium and the relativistic velocity of the particle. With suitable accounting for such effects any of these dosimeters could measure absorbed dose, but the cavity ion chamber was adopted for routine use because of its ease of use and availability.

The conceptual basis for relating absorbed dose in a medium to air ionization, in a chamber small enough that most of the ions are produced by secondary particles originating in the surrounding medium, is known as "Bragg-Gray cavity theory", published in 1912 and 1936. At the time the parameters were not known with precision but the theoretical development was used to justify the idealization that the exact composition and shape of a sufficiently small ion chamber did not affect its relative calibration factors for different modalities.

In the 1960's and 1970's the practice of deriving a conversion coefficient called the "f-factor" to relate the reading of an air-wall ionization chamber calibrated to read roentgens in air, when immersed in an absorbing medium, to absorbed dose at that point in the medium, was extended to apply to the situation where the calibration in air was done with a standard modality, usually Co-60 gamma rays, and the absorbed dose measurement would be in a different modality. Lists of recommended values were compiled, called Clambda or CE for photon or electron beams respectively, which represented a consensus of published experimental results that were deemed applicable to any ionization chamber that was small enough to cause negligible perturbation of the absorbed dose distribution.

In 1983 the American Association of Physicists in Medicine published its "TG-21 Protocol", named after the Task Group 21 of its Radiation Therapy Committee. This landmark effort analyzes and systematizes the procedures required to take account of the composition of the ion chamber wall and buildup cap used in its "in-air" Co-60 calibration to derive a measure of its effective volume called "Ngas". This measure, essentially a calibration factor for measuring absorbed dose to air in the free-air calibration geometry, is then used to derive a calibration factor for the ion chamber used as a Bragg-Gray cavity in an absorbing medium when exposed to a different high-energy radiation beam, to measure absorbed dose at that point in the medium, in the absence of the chamber. Worksheets and tables of empirical data are provided to facilitate the task in a standardized way.

The TG-21 protocol resulted in differences from the earlier ICRU recommendations of as much as 1.5% for some modalities; this was soon largely offset by a 1% change in calibration of the U.S. standard cobalt source due to reconsideration by NIST of their derivation of free-air exposure from measurements with a standard series of spherical graphite ion chambers. Later publications have shown errors in the TG-21 equations which the committee has accepted as valid which might result in differences under 0.5%. The current recommendation is to use the protocol as published, for the sake of consistency between institutions, until a new version is available with these corrections as well as improved values for the tabulated data. Current work is in progress by the Task Group 51 of the AAPM Radiation Therapy Committee.

Another line of development is to rely on a national standard of absorbed dose in a standard medium such as water, which has been promised but is not yet available in the U.S. The ICRU and the AAPM TG-51 both are currently considering new protocols which will rely on calibrations with absorbed dose standards and which will provide recommendations for calculating relative calibration factors for other modalities and absorbing media. Canadian, British, and German standards of absorbed dose are now available. (1994)

Exposure versus Air Kerma

The acronym KERMA, Kinetic Energy Released in absorbing Material, has been used to conceptualize the energy deposition by ionizing radiation, in J/kg or Gray. It is defined to include the kinetic energy which is locally absorbed from products of interaction with the particular medium such as Compton electrons, photoelectrons, and pair production while excluding the energy which is not locally absorbed, from Compton-scattered photons, characteristic radiation, and annihilation photons. It is a measure of radiation incident at a point, in energy units suitable for dosimetry in an absorbing medium, where the effects of interest are due to ionization and the penetrating scattered radiation will be included as input from the surrounding irradiated volume when appropriate.

The concept of kerma in air is very close to the practical definition of the roentgen as a unit of exposure, times a factor for energy per ion pair. However bremsstrahlung photons are lost in the secondary-particle equilibrium condition assumed in defining the roentgen and they represent a small fraction of the energy given to charged secondary particles which becomes significant at supervoltage energies. It is necessary to include a factor that accounts for this fraction of energy deposition that is not locally absorbed when using ionization to measure kerma.

Fluence versus Flux

The term fluence is used in particle diffusion contexts in a way that seems analogous to the term flux in fluid flow and electromagnetic field problems. To define radiation exposure at a point we need a limiting process to conceptualize the ratio of incident photons to area without regard to their direction in space. Fluence is defined as the limiting ratio of the number of particles impinging on a sphere to its cross sectional area, and it implies an integral over time analogous to exposure as well as integration over solid angle. Flux is the integral of fluid flow rate over a given area so flux density is analogous to fluence rate as the intensity at a point of two different kinds of flow.

The term energy fluence is used to signify the radiation incident at a point in an absorbing medium, sometimes including scattered radiation from all directions, but sometimes used to mean only a particular class of photons such as those in the primary beam from a distant point source. Likewise kerma can be used to conceptualize all or a particular part of the energy deposition processes at a point in an actual radiation field.

Primary versus Scattered Radiation

The absorbed dose distribution in a radiation therapy field is the result of a statistical aggregate of energy deposition events which are each well understood, at least in terms of probability functions for their various outcomes. The best calculations have been done with Monte Carlo type computer programs which follow many thousands of event histories and tally the energy deposition into an array of memory locations which represent the spatial distribution of absorbed dose. However the time necessary to achieve clinically useful accuracy and resolution is prohibitive except for research applications to test theoretical assumptions.

Computer program systems are used for routine calculation of dose distributions in a patient cross section which access stored data from measurements in a water phantom. They draw isodose curves on a plot of the patient cross section under consideration, for a proposed arrangement of external beams. For intelligent use of these programs the user must be aware of the assumptions and idealizations inherent in each program system.

For example the ADAC system uses depth-dose and off-axis ratio data measured in a square field central plane, interpolated for an equivalent depth of overlying tissue at each data point of a rectangular array. A lookup table prepared from scans across the edge of a 20x20 cm field is used for points within 2 cm of a beam margin due to collimator or beam blocks. Thus this system and many others pretend that the patient has a cylindrical shape that is the same above and below the plane represented by an outline. If the plane is calculated as an off-axis plane the resulting dose values will be "normalized", that is scaled to a measured beam profile value.

Many commercial treatment planning systems facilitate visualizing proposed treatment plans with sophisticated 3-D graphics of the patient anatomy derived from C-T or MRI data. However they do not necessarily use that data in calculating dose distributions.

GS23DEC90:\RTTEACH\R_TO_CGY.DOC v.894 ==> RtocGy.htm
Posted 6 August 1998 by  Glen Sandberg

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