Beam focal spot position determination for an Elekta linac with the Agility® head; practical guide with a ready‐to‐go procedure

Abstract A novel phantomless, EPID‐based method of measuring the beam focal spot offset of a linear accelerator was proposed and validated for Varian machines. In this method, one set of jaws and the MLC were utilized to form a symmetric field and then a 180o collimator rotation was utilized to determine the radiation isocenter defined by the jaws and the MLC, respectively. The difference between these two isocentres is directly correlated with the beam focal spot offset of the linear accelerator. In the current work, the method has been considered for Elekta linacs. An Elekta linac with the Agility® head does not have two set of jaws, therefore, a modified method is presented making use of one set of diaphragms, the MLC and a full 360o collimator rotation. The modified method has been tested on two Elekta Synergy® linacs with Agility® heads and independently validated. A practical guide with instructions and a MATLAB ® code is attached for easy implementation.

isocentres is directly correlated with the beam focal spot offset of the linear accelerator. In the current work, the method has been considered for Elekta linacs. An Elekta linac with the Agility â head does not have two set of jaws, therefore, a modified method is presented making use of one set of diaphragms, the MLC and a full 360 o collimator rotation. The modified method has been tested on two Elekta Synergy â linacs with Agility â heads and independently validated. A practical guide with instructions and a MATLAB â code is attached for easy implementation.  3,4 Measurement of the beam focal spot offset is not explicitly advocated, because its measurement is impractical and timeconsuming. 5 However, beam focal spot position influences dosimetric and geometric properties of the beam (i.e., beam flatness and symmetry; radiation isocenter size and position). Ideally, it should be positioned at the collimator axis of rotation, so the size of the radiation isocenter is minimal and the propagation of the beam is along the collimator axis of rotation, as assumed and modeled by radiotherapy Treatment Planning Systems. A significant improvement of the beam focal spot offset measurement methodology proposed by Chojnowski et al. 6 using an EPID-based and phantom-less technique, has since been shown to produce quick and accurate measurements. The idea was developed from the fact that if the radiation source is aligned with the collimator axis then the radiation isocenter position determined by the collimator rotation is independent of the type of field collimation used: jaws (diaphragms) or MLC. However, if the radiation source is misaligned with the collimator axis of rotation then the radiation isocenter position depends on the type of collimation, (see Fig. 1.) because the physical position and distance of jaws and MLC are different in relation to the radiation source.
The procedure of measuring the beam focal spot offset as described by Chojnowski et al. 6 is specific to Varian machines. It uses four open fields; two of which use two sets of jaws (X and Y) to form the collimation aperture and the other two using the MLC.
While an Elekta machine with an Agility â head has only one set of diaphragms and MLC it is sufficient for determination of the beam focal spot offset when using a modified approach.
2 | ME TH ODS  The calculation formula for the beam focal spot offset (eq. 1.) is the same as previously published by Chojnowski et al. 6 but the schematic diagram (Fig. 1.) and proportionality factor "a" (eq. 2.) have been modified to reflect the geometry of the Elekta Agility â head.

2.A | Linear accelerators
The beam focal spot offset in any one direction is a product of the proportionality constant and the distance between beam centers, determined by the EPID: where: D BFSO = Beam focal spot offset D EPI = Measured distance between beam centers using the EPID a = machine and procedure specific proportionality factor where: d epi = distance from X-ray target (beam focal spot) to the EPID d dia = distance from X-ray target (beam focal spot) to the diaphragms d mlc = distance from X-ray target (beam focal spot) to the MLC. All acquired EPID images were analyzed by a custom MATLAB â (The MathWorks, Inc., Natick, USA) script to determine the two beam centroids defined by diaphragms and the MLC, respectively.
Only the central part of each image was analyzed. First, each image was filtered to remove noise using a two-dimensional median filtering with a 3 9 3 size matrix. Each image was normalized, with the minimum pixel value being assigned the value 0 and the maximum pixel value being assigned the value 1. Each image was then resized, using bicubic interpolation, by a factor of 10 to increase the calculation resolution. Next, each image was made binary, with a threshold of 0.5 representing the Full Width Half Maximum of the radiation field. The center of each radiation field was then calculated as the centroid of the binary object (field) in both inplane and cross-plane directions.
All four acquired images were visually inspected on the iView workstation for any signs of image artifacts that could potentially affect the result of the test. The filtering function in the code should help in removing single dead pixels, but otherwise all safeguards of detecting unsuitable images, that is, large panel shifts are removed from the code for simplicity.
The distance between the two beam centers defined by diaphragms and the MLC at the EPID level was then calculated as the difference between the two centers expressed in pixels multiplied by pixel size 0.4 mm and the resize factor 10.
To calculate beam focal spot offset (eq. 1), the distance determined between the two centers was multiplied by the proportionality factor "a" (eq. 2), which for the Elekta machine is equal to À0.9078 (eq. 2; d mlc = 35.54 cm, d dia = 47.05 cm and d epi = 160 cm).
The Agility â head has the MLC assembly closer to the radiation source compared to the diaphragms (in contrast to the Varian machines) therefore the proportionality factor is negative, which basically means that the beam focal spot position varies in the opposite way to the directional difference in radiation isocenters defined by diaphragms and the MLC.
A practical ready-to-go procedure and a MATLAB â script for the Elekta Linac with the Agility â head are attached in Appendices S1 and S2, respectively.

2.C | Validation
The validation of the modified, phantomless method is based on pre-

| RESULTS AND DISCUSSION
The mean difference of beam focal spot offset measured using EPID and ionization chamber was found to be 0.004 AE 0.052 mm (1 SD) (Table 1) and the beam focal spot offset reproducibility was on average AE0.045 mm ( Table 2).
Measurements were performed using both diaphragms and MLC at the four cardinal collimator angles. The difference in position of the centroids for each field in cross-plane and inplane directions can be used as a measure of the alignment of the beam focal spot. This is based on the principle that although the diaphragms and MLC share a common rotation axis their different distances from the effective radiation source position mean that their respective beam centers will project differently onto the EPID if the beam focal spot is misaligned with the collimator axis.
It is difficult to differentiate the accuracy of the method itself and the reproducibility of beam focal spot offset parameter. Some results were extremely accurate (i.e., Linac 1 15 MV cross-plane and Linac 2 6 MV cross-plane) and some less so (i.e., Linac 1 6 MV cross-plane and 15 MV inplane). The same procedure and analysis methodology was followed up for both linacs for both energies. Therefore, it can be concluded that the method is more precise than the uncertainty of the beam focal spot position for any given linac and energy.
It was found that changing the resize factor parameter in the software from 2 to 20 shows no significant difference in result with a magnitude of difference of AE0.002 mm (1 SD).
It was noticed that the mean discrepancy in validating beam focal spot offsets against the ionization chamber method was four times higher on Elekta linacs with the Agility â head (0.004 AE 0.052 mm) compared to published results for Varian linacs 6 (0.001 AE 0.015 mm). No specific reason for this was found other than the fact that the reproducibility of beam focal spot position is substantially higher on the Elekta machines.
The procedure presented in Appendix S1 can be automated as a

| CONCLUSION
An innovative phantom-less method of measuring beam focal spot offset using the EPID has been presented for Elekta linacs with the Agility â head. It is a modification of the method described previously for Varian linacs, 6 which have two sets of jaws as opposed to one for the Agility â head. It has the same advantages of being an accurate, practical and fast technique. It is recommended to include this test as part of the monthly linac QA.

CONFLI CT OF INTEREST
The authors declare no conflict of interest.