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A generic computer program for checking photon beam dose calculations

Department of Oncology Physics, Clinical Oncology Department, Lothian University NHS Trust, Crewe Road South, Edinburgh EH4 2XU, UK

	Abstract

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A computer program for checking photon external beam dose calculations is described. It provides a check of the treatment planning calculation by the use of machine data that are independent of that used in the initial calculation. Data required to specify any radiation beam are easily and rapidly set up and the program works for all the major manufacturers' machines. The user interface uses an interactive screen for machine data input and also for dose checking, where dose calculation is performed in real time as data are entered. The dose resulting from the planned field parameters is calculated and compared with the prescribed dose with a warning provided if the agreement is outside a set range (±5%). Its purpose is to act as a final quality assurance check to ensure that no significant errors occur in the monitor unit calculation.

	Introduction

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Treatment planning departments within radiotherapy centres are always very busy environments where staff have to work under pressure and perform their work quickly and accurately. Yet this is also the environment where complex calculations often have to be made and where accuracy is vital to ensure that patient treatment is delivered according to their prescription. It is understandable that mistakes are made and it is important that rigorous procedures are put in place to ensure that these are identified. One procedure that has been widely suggested is that of a final independent check on the calculated monitor units and computer programs providing the facility have been described by other workers [1, 2]. Commercial programs are also now available. This centre has used an in-house produced checking program for many years and its use has identified several errors that perhaps otherwise would have gone undetected. The principle involved in the checking program is that of a "reverse calculation" where the field parameters are used to calculate the dose they will deliver which is then compared with that prescribed. It is a worthwhile quality assurance tool for planning and the method should be available and used in all planning departments.

The purpose of this paper is to describe the rationale for and development of computer software that can be used as a quality assurance tool and can be very simply implemented in any planning department. It has several aims:

1) To work from a data set that is independent of that used for the initial planning calculation, whether performed manually or by computer. Using independent data is important to ensure that any systematic errors or inaccuracies in either data set do not go undetected.

2) To minimize any machine specific data required and ensure that any data required are readily available and easily used to set up a treatment machine. The requirement to produce large sets of depth dose data or output factors (that should be independent as previously argued) can be prohibitive to the implementation of the software.

3) To make the program "generic", in that it will operate for all manufacturers treatment machines without prejudice. It has been tested with Varian (Palo Alto, CA), Elekta (Crawley, UK) and Siemens (Erlangen, Germany) equipment.

4) To provide a user interface that facilitates data entry with calculation performed "on the fly" as input data is specified or altered.

5) To check the planning calculation with the aim of ensuring that significant treatment errors do not occur. If the checking level is set to ±5% then simplifications to the calculation can be made, which in turn simplifies the setting up and running of the software. This level is acceptable as initial planning calculations are always checked in detail using data available in the planning department.

It is not claimed that there is significant originality in the algorithms behind this work. Neither will the software provide much new to developed radiotherapy centres that will probably have written their own checking software or have bought a commercially available program. However, other centres may well find it useful especially when it can be implemented with little effort and a minimum amount of machine specific data.

	Materials and methods

Top Abstract Introduction Materials and methods Operation Conclusion References

 
Specification of machine parameters
Depth dose data
The central axis depth dose data supplied in BJR Supplement 25 [3] is stored for 10 tabulated radiation energies ranging from 4 MV to 25 MV. Each data set gives depth dose values at 100 cm source–skin distance (SSD) for square fields at depths from the reference depth up to 40 cm and field sides from 4 cm to 40 cm. The quality index (TPR₂₀/TPR₁₀) for each data set is also given and allows a data set for any beam energy to be interpolated from the knowledge of its quality index. The depth dose value at any depth and field size can then be determined by interpolation from this data set and converted to the required SSD by use of an inverse square law factor. Several measured depth dose data sets have been used to show that the method will predict depth dose values over the full range of field sizes at depths beyond the reference depth to within a maximum difference of 0.5% of the measured values. Quality index is therefore the only parameter that is required to specify depth dose data for any radiation beam. The approach has greater accuracy than required by the check program and provides an independent depth dose data set.

Field output
This centre still considers the reference point to be at the depth of maximum central axis dose and this is therefore where field outputs are specified. Consequently the program is written using this assumption but could easily be altered to operate for the reference point at some other depth. The variation in output with field size at the reference point is mainly dependent on radiation scattered from the head of the treatment machine. It therefore depends on the design of the head, which varies with manufacturer and may vary for the machines produced by one manufacturer. The variation depends to a lesser extent on radiation scattered within the patient (phantom scatter), which can be directly related to the irradiated area. Head scatter and phantom scatter correction factors can be determined separately and combined to give a total scatter correction factor (the output factor). This method is more accurate than simply considering output alone as it will take account of factors such as the jaw interchange effect. However, the result is that complex modelling of the head of the machine is required and therefore a significant increase in the work necessary to implement this program. The accuracy required can be achieved by considering only the output factor.

The variation in output with ln(beam area), measured in dose per monitor unit (MU) at the reference point and 100 cm SSD for square fields, produces a relationship that is very close to linear. If break points at field sizes of 4, 10, 20 and 30 cm² are chosen, then a piecewise linear fit can predict output to better than 0.5% and the relationship holds for machines from all the manufacturers considered. The consequence is that field outputs are required at 3 field sizes if the output is normalized to unity for a 10 cm² field. Equivalent square field size is used for calculation of output and takes account of field blocking including multileaf collimation.

Change in field output from 100 cm SSD to any other SSD can be accounted for by the use of an inverse square law (ISL) correction. The correction is usually adequate, but if not, it tends to break down at the extreme limits of SSD and field area. Using a virtual SSD instead of the 100 cm value at which the data are measured, can correct for deviations from ISL. The virtual SSD (V) is used to convert output factors (OF) from 100 cm SSD to any SSD (S) by Where and d_max is the reference depth on the central axis for the beam energy. If V=100 cm the conventional ISL conversion is applied.

Wedges
Varian
Varian linear accelerators utilize dynamic wedges where the wedge effect is produced by sweeping one of the upper (Y) collimators across the field during irradiation. The generation of the movement pattern for the collimator is specified by a segmented treatment table (STT) describing the relationship between the cumulative dose in MU and the collimator position Y necessary to produce the desired wedge angle. A full description of STTs can be found in Varian literature (C-Series Clinic (1996)) [4]. An STT for a 60° wedge is provided by Varian and the STT for any other wedge angle ° can be calculated at each position in the table from:

where STT(0°,Y) is for an open field and is constant with respect to collimator position Y.

A wedge factor can be calculated rapidly and with sufficient accuracy from knowledge of the appropriate STT table for the wedge. A wedged field can be simulated by a summation of a large number N of asymmetric fields where the moving collimator travels from its start position to its stop position at a distance of 0.5 cm from the static collimator. For every asymmetric field used in the simulation the fraction MU to be given of the total monitor units MU can be interpolated from the STT table. MU is multiplied by a weighting factor W and summed over all simulating fields, where W=1.0 if the calculation point is within the field and W=T if outside the field. T can be considered to be the fraction of the unshielded dose at the calculation point when shielded by the collimator. T will of course vary according to the position of the calculation point relative to the edge of the collimator, but in practice it is possible to assign a constant value to T and achieve more than acceptable accuracy in the calculation of the wedge factor. The wedge factor W can be calculated from:

The value of T is optimized to give the best fit to experimentally obtained wedge factors over the full range of field sizes and is set to 0.013. This gives agreement to within 0.2% and is independent of the machine and energy used.

STT tables are available for the 7 energies (4, 6, 8, 10, 15, 18 and 20 MV) that are available on Varian accelerators. In this centre, wedge angles in 5° steps from 10° to 60° are provided by the manufacturer, but in others some of the higher value angles may not be available. In summary, no input data are required for Varian wedges as wedge factors can be calculated from STT tables.

Elekta
Elekta linear accelerators use a motorized wedge where a 60° physical wedge is remotely driven into position in the treatment field. Any wedge angle ° can be produced by the appropriate combination of an unwedged and a wedged field using the tan relationship described in Equation 1. It is therefore necessary to know the wedge factor WF for the motorized wedge and to account for variations in WF with field size. The relationship between wedge factor and equivalent square field size F is linear over the range of field sides from 4 cm to at least 20 cm and can be approximated to within an accuracy of better than 0.5% by the equation where WF₁₀ is the wedge factor for an equivalent square field of side 10 cm and W_slp is the change in wedge factor for a 1 cm change in the side of the equivalent square field (the slope of the linear relationship). Both of these parameters must be supplied for Elekta machines.

Siemens
Siemens machines use dynamic wedging in a similar manner to Varian machines with wedge angles available in steps of 1° up to 60°. However Siemens have used a combination of dose rate and collimator drive speed to ensure that wedge factors are all unity regardless of field size and energy. Wedge factors do not therefore have to be considered for Siemens machines.

	Operation

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Machine data input
The screen for machine data input is shown in Figure 1 and requires one row of data with up to 12 parameters to be specified for any beam energy. The parameters are as follows:

View larger version (31K): [in this window] [in a new window]   Figure 1. Machine data input screen.

2) make — the machine manufacturer: V, Varian; E, Elekta; S, Siemens. Required to determine the wedge type and hence wedge factors

3) nominal energy, which is only required to identify the STT table to be used to calculate wedge factors on Varian machines. The allowed energies are 4, 6, 8, 10, 15, 18, 20 MV

4) quality index, which is used to interpolate depth dose data from BJR, Supplement 25 data. The value must be in the range 0.626 (4 MV) to 0.799 (25 MV)

5) d_max, the reference depth on the central axis for the beam energy

6) virtual SSD (V), used to convert field output factors (OF) from 100 cm SSD to the required SSD

7) field output factor (OF) for a 4 cm² field

8) OF for a 10 cm² field (normally=1.0)

9) OF for a 20 cm² field

10) OF for a 30 cm² field

Elekta machines require the following motorized wedge information:

11) wedge factor at the reference point for a 10 cm² field

12) Slope of the linear relationship between wedge factor and equivalent square field.

Dose check program
The output screen for the dose check program is shown in Figure 2. The program provides an independent calculation of the dose to the isocentre for a multifield treatment and will handle dynamic and motorized wedges, asymmetric collimation, lung inhomogeneities, blocked fields and the presence of tray attenuators.

View larger version (49K): [in this window] [in a new window]   Figure 2. Interactive screen for dose check program.

Wedge angle increases in 5° steps from 10° to 60° for Varian and in 1° steps for Siemens machines, whereas only 60° is allowed for Elekta machines. Although wedge angle can be set for Siemens machines, it has no effect on the calculation as the wedge factor is unity and is only included for annotation on the printout of the calculation. Setting the wedge angle to 0° specifies an unwedged field. It is assumed that machines with dynamic wedges use the Y jaws with Y1 as the moving jaw and Y2 as the fixed jaw, which applies for Varian machines. Y1 and Y2 may be interchanged should Y2 be the moving jaw and the X and Y jaw settings interchanged should the wedge operate on the X jaws. In both cases dose calculation will still be correct.

Most of the dimensional input data required is obvious with all dimensions in mm except for the field area (cm²). Area is calculated by an equivalent square calculation using the positions of the four jaws. Area may be reduced should blocking be used on any field, but may not be increased above the equivalent square area. X2 and Y2 jaw settings follow X1 and Y1 to allow ease of setting symmetric fields. Asymmetric fields are set using the independent movement of the X2 and Y2 jaws.

Changing the SSD will automatically change the depth of calculation (at the isocentre) to (100-SSD) cm although the depth is not allowed to be less than d_max for the beam energy. Lung thickness is measured along the central axis up to the depth of the isocentre. An effective depth calculation with ISL correction is applied to the depth dose to account for the thickness of lung tissue.

Total daily machine MU are always required regardless of whether the field is unwedged or wedged. The input of wedge daily MU is only enabled for Elekta machines with motorized wedges where the wedge angle required is determined by the MU given with and without the wedge. The wedge daily MU obviously cannot exceed the total daily MU. Tray attenuation factors must be greater than unity and the factor is applied to the field output.

Results give the field output in cGy MU^-1 to the reference point at d_max on the central axis according to whether the field is unwedged or wedged. Both values are supplied for wedged fields on Elekta machines. Given dose is the dose to the reference point for each field. Depth dose applies to the depth of the isocentre and the dose calculation also gives the dose to the isocentre for that field. Calculated total dose to the isocentre is shown together with the percentage difference from the prescribed dose.

The COPY FIELD 1 button will copy the parameters for field 1 into all other existing fields and can be used to speed up data input. The PRINT button provides a hardcopy of the calculation where an investigation prompt is evident should the percentage difference found exceed an action level.

	Conclusion

Top Abstract Introduction Materials and methods Operation Conclusion References

 
The program resides on a departmental server and can be run on any PC throughout the Radiation Oncology Department. It is mainly used by the treatment planning department and on the treatment machines. Treatment planning staff run the program on every external beam photon calculation as a final quality assurance check prior to the start of treatment and attach a hardcopy of the program results to the treatment sheet. Radiographers on the treatment machine use the program to check their calculation for emergency patients treated out of working hours when planning staff are not available.

The object of the program is to identify any significant errors that may have occurred as a result of the planning calculation. The agreement with planning calculations is in general better than 1% but may rise to 3% for calculations involving a large degree of field asymmetry or a significant amount of lung tissue. For that reason an action level of 5% is used as the prompt for further investigation of the calculation. That rarely happens but the use of the program provides an added confidence in the correctness of the planning calculation and for that reason alone, all staff readily accept its use.

The program is available on CD from the author on request or may be downloaded from www.oncphys.ed.ac.uk/downloads.

Received for publication April 22, 2003. Revision received August 4, 2003. Accepted for publication August 29, 2003.

	References

Top Abstract Introduction Materials and methods Operation Conclusion References

 

1. Morrey D, Smith CW. A radiotherapy treatment planning check program. Br J Radiol 1985;58:668–70.[Medline]
2. Williams JR, Bradnam MS, McCurrach GM, Deehan C, Johnston S. A system for the quality audit of treatment dose delivery in radiotherapy. Radiat Oncol 1991;20:197–202.
3. Jordan TJ. Central axis depth dose data for use in radiotherapy. Br J Radiol 1996;(Suppl. 25)5:62–109.
4. C-Series Clinac: Enhanced dynamic wedge implementation guide 1996; Varian Oncology Systems (1103580-01).

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