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The formalism for the determination of absorbed dose to water in the msr field f_msr is detailed in Section 3.2.1. The measurement is performed using an ionization chamber with its reference point positioned at the reference depth z_ref in a water phantom⁸. Depending on the availability of a calibration coefficient

8 If a water equivalent plastic phantom is used, the expressions are modified according to the description given in Section 3.2.2.

for the ionization chamber, one of the three different methods outlined in Section 3.2.1 is used to determine the absorbed dose to water in a water phantom:

(a) A calibration coefficient, ^N_D^fmsr_,w,Qmsr, in terms of absorbed dose to water for the ionization chamber in a reference beam of quality Q_msr in the msr field  f_msr is available; this is the preferred option, although at present few standards laboratories offer this type of calibration. The absorbed dose to water for the f_msr field, in a beam of quality Q_msr, at the reference depth z_ref in water and 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 (24)

If the conventional reference field  f_ref = 10 cm × 10 cm can be established at the machine, in Eq. (24)  f_msr will be replaced by f_ref and the beam quality Q_msr by Q.

(b) A calibration coefficient, f^ref,w, ₀ D Q

N , in terms of absorbed dose to water for the ionization chamber in a standards laboratory’s reference beam of quality Q₀ in the conventional reference field  f_ref = 10 cm × 10 cm is available, as well as a beam quality correction factor kQ^{fmsr ref}_msr^,_,^fQ₀ to correct for the use of the calibration coefficient in the f_msr field. The absorbed dose to water for the f_msr field, in a beam of quality Q_msr, at the reference depth z_ref in water and in the absence of the ionization chamber is given by:

msr msr ref msr ref

msr msr 0 msr 0

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

D M N k (25)

When the calibration beam quality Q₀ is ⁶⁰Co, the generalized symbol for the beam quality correction factor kQ^{fmsr ref}_msr^,_,^fQ₀ can be simplified to kQ^fmsr_msr^,fref. If the conventional reference field  f_ref = 10 cm × 10 cm can be established at the machine, in Eq. (25) f_msr will be replaced by f_ref and the beam quality Q_msr by Q. In addition, as the resulting double superscript f_ref in k can be removed (there is no need to consider different types of reference fields), Eq. (25) reduces to the formalism given in conventional COPs, showing consistency between those and the present COP.

While Eq. (25) is meant to be applied using kQ^{fmsr ref}_msr^,_,^fQ₀ that are directly measured or calculated for the f_msr field, based on current knowledge and uncertainty estimates it can be assumed that kQ^{fmsr ref}_msr^,_,^fQ₀ = kQ Q^fref_{, 0}, where Q refers to the hypothetical conventional reference field of the machine. Data for the beam quality correction factor kQ^fref, short notation for kQ Q^fref_{, 0} with reference to Q₀ = ⁶⁰Co and f_ref = 10 cm × 10 cm, in WFF beams are given in Table 12 for a range of ionization chambers, consistent with the k_Q data in Refs [1, 2, 7].

TABLE 12. kQfref DATA FOR THE CONVENTIONALfref FIELD (10 cm × 10 cm) FOR REFERENCE IONIZATION CHAMBERS IN WFF LINACS, AS A FUNCTION OF THE BEAM QUALITY INDICES TPR20,10(10) AND %dd(10,10)x Ion chamber TPR

20,10(10) = %dd(10,10)x = 0.630 63.4 0.660 65.2 0.690 67.6 0.720 70.5 0.750 73.9

Capintec PR-06C/G Farmer0.9970.9940.9910.9880.982 Exradin A2 Spokas0.9980.9970.9950.9920.988 Exradin A12 Farmer0.9980.9960.9930.9900.984 Exradin A12S0.9960.9940.9910.9870.981 Exradin A190.9960.9930.9900.9850.980 Nuclear Assoc 30-751 Farmer0.9960.9930.9900.9850.979 Nuclear Assoc 30-752 Farmer0.9970.9950.9920.9890.983 NE 2505/3, 3A Farmer0.9960.9940.9920.9890.984 NE 2571 Farmer0.9970.9940.9920.9890.984 NE 26110.9960.9930.9910.9880.984 PTW 23331 rigid0.9960.9920.9890.9850.980

↓

TABLE 12. kQfref DATA FOR THE CONVENTIONALfref FIELD (10 cm × 10 cm) FOR REFERENCE IONIZATION CHAMBERS IN WFF LINACS, AS A FUNCTION OF THE BEAM QUALITY INDICES TPR20,10(10) AND %dd(10,10)x (cont.) Ion chamber TPR20,10(10) = %dd(10,10)x = 0.630 63.4 0.660 65.2 0.690 67.6 0.720 70.5 0.750 73.9

PTW 23332 rigid0.9960.9930.9890.9840.978 PTW 23333 (3 mm cap)0.9960.9930.9890.9850.979 PTW 30001 Farmer0.9960.9930.9890.9850.979 PTW 30010 Farmer0.9960.9930.9890.9850.979 PTW 30002/30011 Farmer0.9960.9930.9910.9870.982 PTW 30004/30012 Farmer0.9980.9950.9930.9890.984 PTW 30006/30013 Farmer0.9960.9930.9890.9840.978 PTW 31003/31013 Semiflex0.9960.9930.9890.9840.978 SNC 100700-0 Farmer0.9970.9940.9910.9860.979 SNC 100700-1 Farmer0.9980.9960.9940.9900.984

↓

TABLE 12. kQfref DATA FOR THE CONVENTIONALfref FIELD (10 cm × 10 cm) FOR REFERENCE IONIZATION CHAMBERS IN WFF LINACS, AS A FUNCTION OF THE BEAM QUALITY INDICES TPR20,10(10) AND %dd(10,10)x (cont.) Ion chamber TPR20,10(10) = %dd(10,10)x = 0.630 63.4 0.660 65.2 0.690 67.6 0.720 70.5 0.750 73.9

Victoreen Radocon III 5550.9930.9890.9850.9790.973 Victoreen 30-3480.9950.9910.9880.9820.976 Victoreen 30-3510.9950.9910.9880.9830.977 Victoreen 30-3490.9950.9910.9880.9830.978 Victoreen 30-3610.9950.9910.9880.9830.977 IBA FC-65P (Wellhöfer IC 69) Farmer0.9970.9940.9920.9860.979 IBA FC-65G (Wellhöfer IC 70) Farmer0.9980.9970.9940.9890.983 Note: See Appendix I for details.

↓

If the calibration beam quality Q₀ is not ⁶⁰Co, the beam quality correction factor can be derived from the ratio of values for Q and Q₀, as both are relative to ⁶⁰Co. Hence, kQ Q^fref_{, 0} is obtained from the values in Table 12 as follows:

ref ref

0 ref

0

, =

f

f Q

Q Q f

Q

k k

k (26)

(c) A calibration coefficient, f^ref,w, ₀ D Q

N , in terms of absorbed dose to water for the ionization chamber in a standards laboratory’s reference beam of quality Q₀ in the conventional reference field f_ref = 10 cm × 10 cm is available, but there is no beam quality correction factor available to correct for the use of the calibration coefficient in the f_msr field. The absorbed dose to water for the f_msr field, in a beam of quality Q_msr, at the reference depth z_ref in water and in the absence of the ionization chamber 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 (27)

This requires that the beam quality Q of the hypothetical conventional reference field of the machine (see Section 3.2.1.3) be estimated in order to adopt beam quality correction factors kQ^fref from Ref. [1] or from Refs [2, 7].

The determination of the beam quality index is detailed in Section 5.3.3, and the values of kQ^fref for a range of ionization chambers for generic WFF beams are given in Table 12. Based on current knowledge and uncertainty estimates, it can be assumed that kQ^{fmsr ref}_msr^,_,^fQ = 1, which is consistent with the assumption kQ^{fmsr ref}_msr^,_,^fQ₀ = kQ Q^fref_{, 0} in Eq. (25); note that these equalities hold only within the uncertainty estimates discussed in Appendix I.

In Eqs (24–27), MQ^fmsr_msr is the reading of the ionization chamber in the field f_msr corrected for influence quantities, such as pressure, temperature, incomplete charge collection, polarity effects, etc. (see Section 5.4).

5.3.2.2. FFF high energy X ray beams

For FFF high energy X ray beams, the formalism is essentially the same;

in particular, options (a) and (b) in the previous section remain unaltered. For the application of option (c), values of kQ^fref (the short notation for kQ Q^fref_{, 0} when Q₀ = ⁶⁰Co) for a range of ionization chambers for FFF photon beams as well as

for the two specific machine types CyberKnife and TomoTherapy are given in Table 13. These data include a generic volume averaging correction factor⁹. 5.3.2.3. ⁶⁰Co gamma ray beams

For ⁶⁰Co gamma ray beams such as in the Gamma Knife, only option (b) is considered (see Eq. (25)). The factor kQ^{fmsr ref}_msr^,_,^fQ₀ with reference to a chamber calibration f^ref,w, ₀

D Q

N with Q₀ = ⁶⁰Co is close to unity for most chambers suitable for reference dosimetry in these treatment machines. Note, however, that as reference dosimetry in Gamma Knife beams is usually performed in plastic phantoms (ABS or Solid Water), the correction factors include the conversion to absorbed dose to water. Values of kQ^{fmsr ref}_msr^,_,^fQ₀ for the Gamma Knife models Perfexion and 4C are given in Table 14.

5.3.3. Determination of the beam quality when the conventional f_ref cannot