Topics covered in this article include:
 Introduction
 Current Limitations

Calculation Notes
 Calculation of R50 values from I50 values
 TemperaturePressure Correction: PTP
 Polarity and Ion Recombination Correction Factors
 Corrected Readings
 Dose Delivered to Water at d=measurement depth (photons)
 Dose Delivered to Water at d =dmax (Photons, SAD)
 Dose Delivered to Water at d =dmax (Photons, SSD)
 Reference Depth dref (electrons)
 Gradient Effective Correction (electrons)
 Dose Delivered to Water at d =dref (electrons)
 Dose Delivered to Water at d = dmax (electrons)
 Target Reading for Adjustments
 Automatic Calculation of kQ
 Automatic Calculation of k'R50
 End Notes
Introduction
The TG51 capabilities built into the service are based on the original TG51 document^{1} and the later 2014 amendment^{2}.
The approach followed is to, as much as practical, integrate the workflow of the TG51 forms into the familiar TotalQA workflow to minimize the learning curve for existing users. Thus, TG51 prebuilt templates for photons (SAD and SSD) and Electrons can be scheduled for any Linac in a similar way that irregular QA templates are apple. The general workflow of completing, saving, commenting, and finalizing will be familiar to physicist users of the system.
The current focus of the TG51 system is for photon and electron TG51 reports using cylindrical and Farmer type chambers.
Many of our users gave generous and valuable feedback during the development of this project. Thank you. Many of your suggestions made it into the software already and rest assured that the others will guide us as we evolve the TG51 capabilities.
Current Limitations
Parallel plate chambers are not currently supported. We do plan on adding those as we gather more test data.
Calculation Notes
Calculation of R_{50} values from I_{50} values
Users may opt to enter I_{50} values and have the corresponding R_{50} values calculated.
R_{50 }= 1.029I_{50}  0.06 (cm) (for 2 ≤ I_{50} ≤ 10 cm)
or
R_{50 }= 1.059I_{50}  0.37 (cm) (for I_{50} > 10 cm)
See equations 16 and 17 in Almond et al(1999). I_{50} values < 2 cm are not permitted.
TemperaturePressure Correction: P_{TP}
The temperature  pressure corrections are calculated using the pressure units specified for the account.
P_{TP }= (T_{W }/ 295.15°K × (Reference Pressure/ Measured Pressure) where T_{W }= T(℃) + 273.15
Reference Pressure Unit 
Reference Pressure 
mmHg 
760 mmHg 
hPa 
1013.3 hPa 
kPa 
101.33 kPa 
Polarity and Ion Recombination Correction Factors
The polarity correction (P_{pol}) is based on equation 9 in Almond et al(1999). The value is calculated from the average raw electrometer readings entered in nC.
Note that the assumption is that Mh1 is the reading corresponding to the charge collected for the reference dosimetry measurements in the clinic and which should be the same as for the chamber calibration^{3}.
The ion recombination correction is based on equation 12 in Almond et al(1999).
Note the assumption is that the readings are in the range where P_{ion} < 1.05 where the linear form of the saturation curve holds^{4}.
Corrected Readings
Photon SAD and SSD
The fully corrected charge reading for the ion chamber reading is based on equation 8 in Almond et al(1999) with the addition of the P_{rp} factor to take account of the variation of the radial dose distribution that is averaged by the detector^{5}. This factor becomes important when measuring FFF fields
M = P_{TP}P_{elec}P_{pol}P_{rp}M_{raw}
Electron
The fully corrected charge reading for the ion chamber reading is based on equation 8 in Almond et al(1999) .
M = P_{TP}PionP_{elec}P_{pol}M_{raw}
Dose Delivered to Water at d=measurement depth (photons)
The dose delivered at the measured depth is calculated according to equation 3 in Almond et al(1999). Note that the N^{60Co}_{D,w} is recorded in units of cGy/nC within the system and the results of the equation are displayed in units of cGy.
D_{w}^{Q} at d_{measureddepth} = Mk_{Q}N^{60Co}_{D,w}
Dose Delivered to Water at d =d_{max} (Photons, SAD)
To calculate dose at d_{max} the dose at the measured depth is divided by the clinical TMR for the appropriate depth, field size, and energy entered for the Linac^{6}. Note that TMR is recorded in the system as a proportion (0 to 1).
D_{w}^{Q} at d_{max} = D_{w}^{Q} at d_{measureddepth} / TMR_{(depth, fieldsize)}
Dose Delivered to Water at d =d_{max} (Photons, SSD)
To calculate dose at d_{max} the dose at the measured depth is divided by the clinical percent depth dose for the appropriate depth, field size, and energy entered for the Linac^{7}. Note that percentage depth dose is recorded in the system as a percentage (0 to 100%).
D_{w}^{Q} at d_{max} = D_{w}^{Q} at d_{measureddepth} / (%ddR_{(depth, fieldsize)} / 100%)
Reference Depth d_{ref }(electrons)
The reference depth is based on equation 18 in Almond et al. (1999).
d_{ref} = 0.6R_{50 } 0.1 (cm)
Gradient Effective Correction (electrons)
The correction for the gradient effect is based on equation 21 in Almond et al(1999).
Dose Delivered to Water at d =d_{ref} (electrons)
The dose delivered at the reference depth is based on equation 6 in Almond et al.(1999) . Note that the depth dose is recorded in units of cGy/nC within the system and the results of the equation are displayed in units of cGy.
D_{w}^{Q} at d_{ref} = MP^{Q}_{gr}k'_{R50}k_{ecal}N^{60Co}_{D,w}
Dose Delivered to Water at d = d_{max} (electrons)
The dose at d_{max} is derived by dividing the dose at the reference depth by the PDD value for the field size and measurement depth and then by the MUs delivered^{8}. Note that percentage depth dose is recorded in the system as a percentage.
D_{w}^{Q} at d_{max} = D_{w}^{Q} at d_{ref} / (Clinical %dd / 100%) / MUs
Target Reading for Adjustments
The target reading attempts to predict the electrometer reading required to achieve a dose at d_{max} of 1 cGy/MU.
Automatic Calculation of k_{Q}
To calculate k_{Q}, the method must be determined by answering a number of questions in the calculation form shown below.
The flow chart below shows the three main routes to calculating %dd(10)x. The main differentiator is the beam energy. For beams below 10 MV, electron contamination is negligible.
For photon beams at or above 10MV electron contamination becomes large enough to be considered. The recommended method to deal with the contamination is to insert a 1mm lead foil into the beam’s path. Note that the procedure requires the lead sheet to be at approximately 30cm or 50cm from the solid water phantom’s surface and provides formulas for the %dd(10) x calculation for either case.
Alternatively, Tg51 provides an “interim” calculation method to determine the %dd(10)x where the lead foil is not employed.
All FFF beams, regardless of energy, require lead foil in the beam path.
It is essential to remove the lead foil before doing the actual T51 dose measurement procedure performed with an open beam that takes the electron contribution into account.
The method and calculation determination are show below. Note that you may need enlarge your browser window or change the text size if the chart is not clear. Ctrl+ will make the text size larger and Ctrl will make text size smaller on most operating systems.
Once %dd(10)x is determined, two alternate, established methods of calculating the final k_{Q } value are used. The first method is a linear interpolation from a lookup table for each chamber of k_{Q } values vs %dd(10) . The second method was introduced in the 2014 TG51 addendum. The addendum provided curvefit parameters for %dd(10)x between 63 and 86%.
Method 1: Linear Interpolation from a Lookup Table^{2}
This method uses a linear interpolation of a measured %dd(10)x to a lookup table of k_{Q } for given %dd(10).
Example:
The user has an average electrometer reading using an Exradin A12 chamber at d_{max} of 20.54nC and an average reading at d=10cm of 13.64nC.
The measured %dd(10)x = 13.64/20.54*100 = 66.41%
The nearest table values (from McEwen, 2014) are 63%(k_{Q } = 0.997) and 67%(k_{Q } = 0.992)
The linear interpolation between the table values is calculated:
k_{Q } = (66.41  63)(6763)x (0.9920.997) + 0.997 = 0.9927
Method 2: Calculate k_{Q} values from curve fit parameters^{2}
This method uses curvefit parameters from Table 1 in McEwen(2014) to calculate k_{Q } factors. Use equation 1 in McEwen (page 0415014) to calculate kQ.
Example:
The user has an average electrometer reading using an Exradin A12 chamber at Dmax of 20.54nC and an average reading at D=10cm of 13.64nC.
The measured %dd(10)x = 13.64/20.54*100 = 66.41%
The curve fit parameters for the A12 chamber are: A = 1.0146, B = 0.777, C= −1.666
dd = 66.41;
A = 1.0146;
B = 0.777;
C= 1.666;
k_{Q }= A+(1e3)*B*dd +(1e5)*C*dd^2
k_{Q } = 0.9927
Automatic Calculation of k'R_{50 }
The prerequisites for the calculation are:
 The user must be using a Farmerlike cylindrical chamber. Note there is an equation for parallel plate chambers that we will support when we bring those into Tg51.
 The R_{50} value must be between >= 2cm and <= to 9cm.
Under those conditions, the factor is calculated using the equation shown below.
k'R_{50} (cyl) = 0.9905+0.0710e^{(R50/3.67)}
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