Approaches for the reference dosimetry of msr fields

The preferred approach for the reference dosimetry is to obtain a calibration coefficient directly in the msr field (  f_msr), provided the standards laboratory is able to supply such a calibration coefficient. In this case, the absorbed dose to water at the reference depth z_ref in water in the absence of the ionization chamber is given by:

msr msr msr

msr msr msr

w,^f_Q = _Q^f _D^f,w,_Q

D M N (7)

where Q_msr is the beam quality of the msr field (note that this can be different from the beam quality of a conventional reference field owing to the influence of the field size on the particle spectrum); ^M_Q^fmsr_msr is the reading of the dosimeter in the msr field f_msr corrected for influence quantities, such as pressure, temperature, incomplete charge collection, polarity effects, etc.; and ^msr

,w, msr f D Q

N is the calibration coefficient in terms of absorbed dose to water of the ionization chamber measured by the standards laboratory for the msr field f_msr of quality Q_msr.

Although it is not widely available yet, some standards laboratories provide calibrations of ionization chambers in the hospital’s msr field. A calibration coefficient could also be available via a cross-calibration, a procedure that will be described in Section 5.5.

3.2.1.2. Chamber calibrated for a conventional reference field, with generic beam quality correction factors available

In most cases, the ionization chamber calibration coefficient is measured in a calibration beam of quality Q₀ for a conventional 10 cm × 10 cm reference field f_ref. In that case, a beam quality correction factor is required for the use of the calibration coefficient in a beam of a different quality than the one used for the chamber calibration. The absorbed dose to water for the msr field is then given by: influence quantities, such as pressure, temperature, incomplete charge collection, polarity effects, etc.; ND^fref_,w,Q₀ is the calibration coefficient in terms of absorbed dose to water of the ionization chamber measured at the standards laboratory for a conventional 10 cm × 10 cm reference calibration field f_ref with beam quality

Q₀; and kQ^{fmsr ref}_msr^,_,^fQ₀ is a factor to correct for the difference between the response of the ionization chamber in a conventional reference calibration field f_ref with beam quality Q₀ at the standards laboratory and the response of the ionization chamber in the msr field f_msr with beam quality Q_msr.

The beam quality correction factor kQ^{fmsr ref}_msr^,_,^fQ₀ is defined as the ratio of the ionization chamber’s calibration coefficients in the machine specific and conventional reference fields: high energy X ray beam. Ideally, the beam quality correction factor is determined directly by calibration of the ionization chamber in the calibration reference and msr fields. A few standards laboratories have developed the capability of performing such calibrations for clinical machines, but such services are not widely available. However, given the increased uniformity in physical characteristics of series of treatment machines of the same type, generic experimental values for the beam quality correction factors may be available. For the same reason, generic Monte Carlo calculated beam quality correction factors may be determined for a particular ionization chamber type in such machines as:

msr msr

where all quantities on the right hand side of the equation are calculated in the Monte Carlo simulation, D_w is the absorbed dose to water at the measurement point, which, in practice, is calculated as the mean absorbed dose to water over a small volume around the measurement point (the suitable size of which depends on the field size) and D_air is the mean absorbed dose to air in the cavity of the ionization chamber.

Where generic experimental or Monte Carlo calculated beam quality correction factors are available for particular treatment machine/ionization chamber combinations, they are tabulated in Section 5. Machines for which such data are available are Gamma Knife, CyberKnife and TomoTherapy for a limited number of chamber types.

Note that a standards laboratory may be able to provide a calibration coefficient ND^fmsr_,w,Q₀ for an msr field that does not have exactly the same beam quality as the clinical msr field. In that case:

msr msr msr msr msr

msr msr 0 msr 0

, w,^f_Q = _Q^f _D^f,w,_{Q Q}^f ,^f_Q

D M N k (11)

3.2.1.3. Chamber calibrated for the conventional reference field, without generic beam quality correction factors available

In the case that no generic beam quality correction factors for the calibration field with reference to the msr field are available, a third approach has to be followed. In this case, the absorbed dose to water for the msr field is given by:

msr msr ref ref msr ref

msr msr 0 0 msr

, w,^f_Q = _Q^f _D^f,w,_{Q Q Q}^f, _Q^f ,^f_Q

D M N k k (12)

where ^M_Q^fmsr_msr is the reading of the dosimeter in the msr field f_msr corrected for influence quantities, such as pressure, temperature, incomplete charge collection, polarity effects, etc., ND^fref_,w,Q₀ is the calibration coefficient in terms of absorbed dose to water of the ionization chamber measured at the standards laboratory for a conventional 10 cm × 10 cm reference calibration field f_ref with beam quality Q₀, kQ Q^fref_{, 0} is a factor to correct for the difference between the response of the ionization chamber in a conventional calibration field f_ref with beam quality Q₀ at the standards laboratory and the response of the ionization chamber in a conventional 10 cm × 10 cm reference field f_ref with a beam quality Q using the same machine as the msr field f_msr, and kQ^{fmsr ref}_msr^,_,^fQ is a factor to correct for the difference between the response of the ionization chamber in a conventional 10 cm × 10 cm reference field f_ref with beam quality Q using the same machine as the machine specific reference field f_msr and the response of the ionization chamber in the msr field f_msr with beam quality Q_msr.

As previously explained, the need for an msr field arose from the impossibility of realizing a 10 cm × 10 cm field using the treatment machine to perform dosimetry according to a conventional dosimetry protocol. Where a 10 cm × 10 cm field cannot be realised, f_ref is referred to as a hypothetical 10 cm × 10 cm reference field [8]. The beam quality correction factor kQ Q^fref_{, 0} can thus be obtained from Ref. [1] or Refs [2, 7], for which the beam quality Q of the hypothetical 10 cm × 10 cm reference field needs to be determined according to the guidance in Section 5.3.3.

Since the hypothetical reference field f_ref cannot be established experimentally, a direct measurement of kQ^{fmsr ref}_msr^,_,^fQ is not possible. If an experimental determination of kQ^{fmsr ref}_msr^,_,^fQ₀ were available (e.g. measured by a PSDL), a value could be inferred as:

msr ref

With a Monte Carlo simulation, it is possible to establish a 10 cm × 10 cm reference field virtually and calculate the beam quality correction factor as:

msr msr

In some cases, establishing the hypothetical reference field in the Monte Carlo simulation may not only require modification to the secondary and tertiary collimators, but also to the primary collimator (as for example is the case in CyberKnife), which could have a substantial influence on the beam quality.

For beams with a flattening filter providing a uniform lateral beam profile, the factor kQ^{fmsr ref}_msr^,_,^fQ equals unity in most cases for the detectors recommended in this COP. Comparing Eqs (12) and (11) shows that this is equivalent to assuming that kQ^{fmsr ref}_msr^,_,^fQ₀ equals kQ Q^fref_{, 0}. For practical implementation of these equations it may be sufficient to estimate an uncertainty on the assumption that kQ^{fmsr ref}_msr^,_,^fQ = 1.

Figure 12 summarizes the three approaches.

For the application to FFF beams, the complication arises that the value

ref , 0 f

kQ Q for the FFF beam may be different from those tabulated in existing COPs, such as Ref. [1] or Refs [2, 7]. For this reason, kQ Q^fref_{, 0} in Eq. (12) is replaced with the product of two factors to account for the difference between the response of the ionization chamber in the hypothetical FFF beam of quality Q^FFF = Q and that in a beam WFF with beam quality Q^WFF , for which the beam quality index is the same as for the beam quality Q⁵. For clarity, a superscript index ‘FFF’ has been included for all beam qualities of FFF beams and a superscript index ‘WFF’ has been included for all beam qualities of beams WFF:

msr msr ref ref ref msr ref

FFF FFF WFF FFF WFF FFF FFF

msr msr 0 0 msr

k is the beam quality correction factor obtained from Refs [1, 2, 7]

or an equivalent COP for a beam WFF with the same beam quality index as the one determined for the FFF beam and ^refFFF, WFF

f

Q Q

k is the factor that accounts for the

5 This condition means that TPR_20,10(10)[Q^WFF] = TPR_20,10(10)[Q] or %dd(10,10)_x[Q^WFF] =

%dd(10,10)_x[Q], but the beam qualities are not identical.

different response of the ionization chamber in the FFF and the WFF beam. Two effects contribute to the value of ^k_Q^frefFFF_,Q^WFF: one is the different response of the ionization chamber due to the different charged particle spectra of both beam qualities changing stopping-power ratios and perturbation correction factors, and the second one is the volume averaging because of the non-uniformity of the lateral beam profile in the FFF beam (the typical quasi-conical 2-D profile)⁶. The volume averaging correction factor can differ significantly from unity if there is substantial field non-uniformity as is the case in FFF beams. Details of the calculation of ^refFFF, WFF

f

Q Q

k are given in Appendix I.

6 Note that this approach is different from the one adopted in Ref. [7], where the volume averaging correction factor is not considered as a contribution to the beam quality correction factor but is included as a correction factor to the ionization chamber reading.

msr msr msr

FIG. 12. Schematic overview of the dosimetry of small static fields with reference to a machine specific reference field according to the formalism of this COP. The arrows and formulas labelled (1), (2) and (3) correspond with the approaches of Section 3.2.1.1, 3.2.1.2 and 3.2.1.3, respectively. (Reproduced from Ref. [8] with the permission of the American Association of Physicists in Medicine.)