Reference Dosimetry for Ionizing Radiation

1.1 Introduction

The key to the accurate delivery of radiation is the ability to establish the absolute dose delivered. In radiation therapy clinical practice the primary tool used to measure absorbed dose is the ion chamber. The use of ion chambers has been well described by international codes of practice. While some of the details may differ slightly, the basic concepts of the various codes of practice are the same. The ionization measured by the chamber (typically filled with air) is converted to absorbed dose by applying a calibration factor (determined by an accredited calibration lab) and other correction factors based on the chamber design. The calibration factor may be a direct calibration in water (megavoltage (MV) photons, MV electrons, protons) or a calibration based on air kerma (kilovoltage (kV) photons, brachytherapy sources). The end goal is to determine absorbed dose to water in either case.

The starting point for these calibrations is the absorbed dose standard developed at a primary standard dosimetry laboratory (PSDL). End users obtain a calibration factor for their equipment at a secondary standard dosimetry laboratory (SSDL), also known as an accredited dosimetry calibration lab (ADCL). The SSDL applies the standard developed by the PSDL using the available radiation sources at that lab. All SSDLs have ⁶⁰ Co sources available for calibration but may not have linac-generated beams. Some labs do have other high energy photon beams available and can provide a calibration at multiple beam qualities. In the absence of this, correction factors must be applied to the calibration determined at ⁶⁰ Co energy to determine the calibration for the beam quality of interest. Further corrections are needed if the beam of interest is protons or other heavy ions. For a more complete discussion of the interaction between PSDLs, SSDLs, and the end user, the reader is referred to section 2.1 of International Atomic Energy Agency (IAEA) TRS-398, Absorbed Dose Determination in External Beam Radiotherapy: An International Code of Practice for Dosimetry Based on Standards of Absorbed Dose to Water.

The regulations on the frequency of a full calibration in water may vary from country to country but are generally required at least once per year. The suggested regulations by the Conference of Radiation Control Program Directors (CRCPD) and implemented by many states in the United States require full calibrations at intervals not to exceed 12 months (section X.7.iii). More frequent constancy checks are required but can be done using solid phantoms and dosimetry equipment that is not calibrated by a calibration laboratory. These constancy devices should be compared with the calibrated system immediately after the annual full calibration. The equipment used for the full calibration should be sent for recalibration every 2 years. A constancy check should be performed before sending equipment to the calibration lab and after receiving it back to ensure that nothing happened during the process to change the response of the chamber. For new radiation therapy treatment machines, a second check of the absolute dose calibration should be obtained prior to treating patients. This could be accomplished by using a mail-order reference dosimetry service or a second check by a colleague using an independent dosimetry system.

1.2 Standard Megavoltage Photon Beams

Several international codes of practice are used to determine absorbed dose for MV photon beams, the American Association of Physicists in Medicine (AAPM) TG-51, Protocol for Clinical Reference Dosimetry of High-Energy Photon and Electron Beams, IAEA TRS-398, Absorbed Dose Determination in External Beam Radiotherapy, Deutsche Industrie-Norm (DIN) 6800-2, Dosimetry Method for Photon and Electron Radiation—Part 2 Dosimetry of High Energy Photon and Electron Radiation with Ionization Chambers, Institute of Physics and Engineering in Medicine (IPEM) 1990, Code of Practice for High-Energy Photon Therapy Dosimetry, and others. An addendum to AAPM TG-51 has been published containing new k _Q values. They are all based on absorbed dose in water calibrations of cylindrical ion chambers. The charge reading obtained from the ion chamber is corrected for temperature, pressure, ion recombination, and polarity. Corrections are then made to account for the perturbation to the medium (water) caused by the presence of the ion chamber. The calibration factor is then used to convert charge to absorbed dose. All of the protocols use a reference field size of 10 cm × 10 cm but the depth and source-to-surface distance (SSD) can vary among them. It is important to note that the reference depth for the calibration protocol is likely not the depth of absorbed dose specification in the clinic. For example, the protocol may specify measurement at 10 cm depth but the output of the machine is adjusted to 1.0 cGy/MU at depth of dose maximum (d _max ). This will require the use of accurate percent depth dose to correct the readings taken at 10 cm depth to d _max depth. The general equation to calculate absorbed dose from a charge reading of an ion chamber measured with an electrometer is:

D_{w} (z) = {M N}_{D,w} k_{p} k_{s} k_{ρ} k_{Q} (z)

$D_{w} (z) = {M N}_{D,w} k_{p} k_{s} k_{ρ} k_{Q} (z)$

where D _w (z) = absorbed dose to water at depth z
M = the ion chamber reading corrected for the electrometer calibration
N _D,w = calibration factor for absorbed dose to water for ⁶⁰ Co energy
k _p = polarity correction. The value is generally less than 1% from unity. The value should be stable from year to year and any deviation greater than 0.5% from the running average should be investigated. For new chambers, it should be measured several times to establish consistency.
k _s = ion recombination factor. The value is generally less than 1.01 and AAPM TG-51 recommends not using a chamber if the correction is greater than 5%. The same recommendation regarding year-to-year stability applies.
k _ρ = air density correction factor (often formulated as a temperature/pressure correction)
k _Q (z) = beam quality correction factor for the measured beam versus the ⁶⁰ Co beam (in which N _w is determined). k _Q is specific to the beam energy being measured and the ion chamber used to make the measurement. Typical values range from 1 to approximately 0.96 for MV photon beams.

A comparison of the four codes of practice is shown in Tables 1.1 to 1.5 . Comparisons among the codes of practice show variations within the expected uncertainty levels of 1% to 1.5%. Standards labs are moving toward offering calibrations at beam qualities other than ⁶⁰ Co. This has the advantage that the k _Q factor determined will be for the specific chamber used in the clinic, not a generic k _Q for a given chamber model. There are two possibilities for implementing this strategy:

1.
The calibration lab determines N _D,w for the chamber along with a series of k _Q values across the range of beam qualities including electrons. This has the advantage that because the beam energy dependence for the chamber is not expected to change, future calibrations will only require determination of N _D,w at the reference quality, Q ₀ .
2.
The calibration lab determines a series of N _D,w values, eliminating the need for k _Q .

TABLE 1.1

Polarity Correction (k _p ) Determination for the Various Protocols

AAPM TG-51	$\| \frac{(M_{raw}^{+} - M_{raw}^{-})}{2 M_{raw}} \|$ $\| \frac{(M_{raw}^{+} - M_{raw}^{-})}{2 M_{raw}} \|$
IAEA TRS-398	$\| \frac{(M_{raw}^{+} - M_{raw}^{-})}{2 M_{raw}} \|$ $\| \frac{(M_{raw}^{+} - M_{raw}^{-})}{2 M_{raw}} \|$
DIN 6800-2	$(M_{1} + M_{2}) {/M}_{1} / {[(M_{1} + M_{2}) {/M}_{1}]}_{Co}$ $(M_{1} + M_{2}) {/M}_{1} / {[(M_{1} + M_{2}) {/M}_{1}]}_{Co}$
IPEM 1990	none

When determining polarity corrections and comparing among systems, care should be taken to understand the bias configuration used. This can vary among manufacturers. The value can either be less than or greater than 1 depending on which polarity is used for the final output determination but should not exceed 1%. In general k _p is a smaller effect with increasing energy. It should be noted that if k _p is known for the calibration beam quality (Q ₀ ), k _p will then be determined as k _p = k _p,Q /k _pQ0 . It follows from this that if the user beam quality (Q) is the same as the calibration beam quality (Q ₀ ), k _p = 1. This must be done if k _p exceeds 0.3% for 6 MV or ⁶⁰ Co energies.

TABLE 1.2

Ion Recombination (k _s ) Determination for the Various Protocols for Pulsed Beams

AAPM TG-51	$\frac{1 - V_{H} / V_{L}}{M_{raw}^{H} / M_{raw}^{L} - V_{H} / V_{L}}$ $\frac{1 - V_{H} / V_{L}}{M_{raw}^{H} / M_{raw}^{L} - V_{H} / V_{L}}$
IAEA TRS-398	$\begin{matrix} k_{s} = \frac{M_{1} {/M}_{2} - 1}{U_{1} {/U}_{2} - 1} \\ or \\ k_{s} = a_{0} + a_{1} \frac{M_{1}}{M_{2}} + a_{2} {(\frac{M_{1}}{M_{2}})}^{2} \end{matrix}$ $\begin{matrix} k_{s} = \frac{M_{1} {/M}_{2} - 1}{U_{1} {/U}_{2} - 1} \\ or \\ k_{s} = a_{0} + a_{1} \frac{M_{1}}{M_{2}} + a_{2} {(\frac{M_{1}}{M_{2}})}^{2} \end{matrix}$
DIN 6800-2	$\frac{U_{1} {/U}_{2} - 1}{U_{1} {/U}_{2} - {[(M - M_{0}) k_{p} k_{ρ}]}_{1} / {[(M - M_{0}) k_{p} k_{ρ}]}_{2}}$ $\frac{U_{1} {/U}_{2} - 1}{U_{1} {/U}_{2} - {[(M - M_{0}) k_{p} k_{ρ}]}_{1} / {[(M - M_{0}) k_{p} k_{ρ}]}_{2}}$
IPEM 1990	1+X% for an X% decrease in reading when chamber voltage is halved

Since

, the value is always >1. It should be noted that ion recombination is mostly dependent on dose per pulse and therefore will be different for flattening filter free beams.

TABLE 1.3

kρ Determination for the Various Protocols

AAPM TG-51	where T = water temperature in °C and P = pressure in kPa. Humidity must be between 20% and 80%.
IAEA TRS-398 DIN 6800-2 IPEM 1990	Standard temperature is 20 instead of 22. Therefore the denominator is 273.2 + 20.0 in the temperature term.

TABLE 1.4

Photon Beam Quality Correction Factors for the Various Protocols

AAPM TG-51	Table of values for various ion chambers across a range of beam energies. Beam quality is specified by the percent depth dose (PDD) at 10 cm depth, 100 cm SSD with electron contamination removed or PDD(10) _x for energies ≥10 MV. To measure the photon component PDD, a thin lead foil (1 mm) is placed at 50 cm from the source to eliminate electron contamination from the beam at energies of 10 MV or greater. This lead foil is used for measurement of the PDD only and must be removed for the output measurement.
IAEA TRS-398	Table of values for various ion chambers across a range of beam energies. Beam quality is specified by the ratio of the TPR at 20 cm depth and the TPR at 10 cm depth for the reference field size or TPR _20,10 . This can be measured directly or calculated from PDD measurements using the equation 1.2661* (PDD(20)/PDD(10)) − 0.0595. Recommend using a measured value rather than a generic value.
DIN 6800-2	Same as IAEA.
IPEM 1990	Beam quality is specified by the ratio of the TPR at 20 cm depth and the TPR at 10 cm depth for the reference field size or TPR _20,10 .

TABLE 1.5

Ion Chamber Location for the Various Protocols

AAPM TG-51	Reference point (center of chamber) at measurement depth.
IAEA TRS-398	Reference point at measurement depth.
DIN 6800-2	Reference point 0.5 r below measurement depth. DIN 6800-2 also explicitly uses a perturbation correction to account for the difference in chamber position at the calibration lab (reference point at measurement depth) and the local dose measurement. Factor = 1 + \|δ\| r /2, where δ is the relative gradient of the depth dose curve at the point of measurement (about 0.006 mm ⁻¹ for ⁶⁰ Co) and r is the inner radius of the chamber.
IPEM 1990	Reference point at measurement depth.

1.3 Nonstandard Megavoltage Photon Beams

There are photon delivery machines that cannot produce the required 10 × 10 cm reference field and/or the SSD required by the codes of practice, including TomoTherapy, CyberKnife, Gamma Knife, and Vero. Furthermore, the geometry of some treatment units such as Gamma Knife do not readily accommodate the use of water phantoms for primary dose calibration, and so an air/medium protocol such as AAPM TG-21, A Protocol for the Determination of Absorbed Dose from High Energy Photon and Electron Beams, is sometimes used. The forthcoming AAPM TG-178, Gamma Stereotactic Radiosurgery Dosimetry and Quality Assurance, will address the topic of dose calibration of stereotactic radiosurgery beams for Gamma Knife. Some beams are not compliant with standard protocols because they do not have a flat dose profile (e.g., TomoTherapy or flattening filter free beams), which complicates reference dosimetry.

In addition, the size of the detector must be appropriate for the beam. The detector size should be small enough so that the gradient across detector volume is less than a few percent. Kawachi et al. showed that the relatively flat portion of the beam for a CyberKnife cone does not exceed 1 cm, as shown in Figure 1.1 . The gradient can be caused by the inherent gradient created by beams without flattening filters. References are available that describe the additional corrections that must be made for these units to accurately calculate absorbed dose. The corrections are made by adjusting the value of k _Q to account for the lack of charged particle equilibrium. The correction is about 1% for a TomoTherapy unit to as much as 10% for small cones on a CyberKnife unit. For flattening filter free beams there may be a slight correction needed for the quality factor if the Tissue-Phantom Ratio is used to specify beam quality. There are several treatment machines either in early clinical use or in development that use MR imaging. Ion chamber readings will need a correction factor that may depend on the magnetic field strength.