Beam focal spot position: The forgotten linac QA parameter. An EPID‐based phantomless method for routine Stereotactic linac QA

Abstract Modern day Stereotactic treatments require high geometric accuracy of the delivered treatment. To achieve the required accuracy the IGRT imaging isocenter needs to closely coincide with the treatment beam isocenter. An influence on this isocenter coincidence and on the spatial positioning of the beam itself is the alignment of the treatment beam focal spot with collimator rotation axis. The positioning of the focal spot is dependent on the linac beam steering and on the stability of the monitor chamber and beam steering servo system. As such, there is the potential for focal spot misalignment and this should be checked on a regular basis. Traditional methods for measuring focal spot position are either indirect, inaccurate, or time consuming and hence impractical for routine use. In this study a novel, phantomless method has been developed using the EPID (Electronic Portal Imaging Device) that utilizes the different heights of the MLC and jaws. The method has been performed on four linear accelerators and benchmarked against an alternate ion chamber‐based method. The method has been found to be reproducible to within ±0.012 mm (1 SD) and in agreement with the ion chamber‐based method to within 0.001 ± 0.015 mm (1 SD). The method could easily be incorporated into a departmental routine linac QA (Quality Assurance) program.

focal spot is dependent on the linac beam steering and on the stability of the monitor chamber and beam steering servo system. As such, there is the potential for focal spot misalignment and this should be checked on a regular basis. Traditional methods for measuring focal spot position are either indirect, inaccurate, or time consuming and hence impractical for routine use. In this study a novel, phantomless method has been developed using the EPID (Electronic Portal Imaging Device) that utilizes the different heights of the MLC and jaws. The method has been performed on four linear accelerators and benchmarked against an alternate ion chamber-based method. The method has been found to be reproducible to within AE0.012 mm (1 SD) and in agreement with the ion chamber-based method to within 0.001 AE 0.015 mm (1 SD). The method could easily be incorporated into a departmental routine linac QA (Quality Assurance) program. The correct delivery of treatments requiring high spatial accuracy such as CSRS and SBRT means that the geometric accuracy of Recommendations for IGRT system QA are provided in AAPM TG-179 report. 4 This includes the recommendation for testing the imaging and treatment isocenters coincidence. This is often achieved using a Winston Lutz (WL) style measurement. 5 If the ball bearing to be imaged is placed at the imaging isocenter, then the imaged measured distance from collimator to ball bearing with gantry and collimator rotation can be used to provide a measure of imaging to treatment isocenter coincidence. This measurement provides an overall process type test with several influencing variables, which makes it difficult to diagnose the cause of an unacceptable result. Regular individual testing of each of the influencing variables should ensure stable WL results and provide a methodology for investigation of any WL fails that are observed. The variables that influence the treatment isocenter component of WL include mechanical isocenter size and shape, alignment of collimators and beam focal spot position relative to collimator rotation axis, 6 and their stability with gantry rotation.
Like the treatment isocenter; the imaging isocenter is also influenced by the mechanical isocenter as the axis of gantry rotation is shared. The geometric calibrations of the IGRT system account for the influences on imaging isocenter and TG-179 recommends updating these monthly. Of special mention is the Varian IsoCal geometric calibration, which Varian uses to help align the imaging and treatment isocenters. 7,8 Like the WL measurement, this geometric calibration is influenced by multiple variables and is only performed using the 6 MV beam. Because of potential variability in focal spot position between beam energies due to each beam being positioned and steered separately, 9 the IsoCal calibration may not ensure coincidence between treatment and imaging isocenters for all beam energies. This indicates the need for a regular check of beam focal spot position if beams other than 6 MV are to be used for CSRS or SBRT treatments.
Beam focal spot position is often not tested regularly in radiotherapy departments because it is not explicitly recommended in TG-142. However, in the interest of ensuring WL stability for CSRS and SBRT treatments and for ensuring coincidence of imaging and treatment isocenters for beams other than 6 MV, its testing is indicated. Furthermore, as an effect of a significant shift in beam focal spot position is a lateral shift of the beam 6 ( Fig. 1), correct focal spot alignment is required for geometric accuracy for all treatment types and is required for constancy of the beam profile, which is recom- Two accurate and independent methods of measuring focal spot position are described by Nyiri. 10 The first method, the corotational penumbra modulation measurement, uses an ionization chamber mounted on a jig attached to a collimator near the 50% beam edge position. A modified version of this method will be used in this study as the independent validation technique. The second method, the image center shift method, uses multiple EPID images of two opaque rods attached to a jig at two different geometric distances to the x-ray source. Both of those methods require a specially made jig which is not suitable for quick and routine measurements.
This study describes a first phantomless method of evaluating focal spot alignment to collimator rotation axis with no additional tools or assumptions necessary. The method presented is robust, accurate, and easy to perform.

2.A | Linear accelerators
All tests were conducted on four linear accelerators at the Crown Princess Mary Cancer Centre (Westmead, Australia), namely: two Varian Clinac â 6EX (Varian Medical Systems, Palo Alto, CA, USA) with the aS500 EPID, one Varian Clinac â 21iX with the aS1000 EPID, and one Varian Truebeam â with the IDU EPID. The sensitive area for all three panels is 40 cm 9 30 cm. The EPID aS500 has an array of 512 9 384 pixels and the EPID aS1000 and IDU has an array of 1024 9 768 pixels. Pixel size for the aS500 is 0.784 mm and for both the aS1000 and IDU panels is 0.392 mm, i.e., half the pixel size of the aS500. However, the images acquired on the Clinac â 21iX (in dosimetric mode) are of lower resolution with 512 9 384 pixels and a pixel size of 0.784 mm, the same as for the aS500.

2.B | Method
The alignment of the focal spot with collimator rotation axes can be determined from beam center measurements from collimators at two different distances (Fig. 1).
Diagram of a Varian linac head (schematic and not to scale) and illustration of radiation focal spot position determination using the EPID. Vertical black line represents the collimator rotation axis. Red line represents center of jaw defined field with 180°collimator rotation. Blue line represents center of MLC defined field with 180°collimator rotation.
In this study the jaws and MLC were used as the collimators.
Firstly, the jaws were set to 10 9 10 cm 2 and 20 MU was delivered at collimator angles 90°and 270°. The beam was imaged using the EPID in integrated mode at the EPID source-imager distance equal to 100 cm for Varian Truebeam â and Clinac â 21iX and 105 cm for two Varian Clinacs â 6EX. From the image the edge of the field was determined as the position of the 50% intensity points. From these points the position of the center of field was calculated in both inplane (X jaws) and crossplane (Y jaws) directions. The whole process was then repeated with jaws retracted and 10 9 10 cm 2 MLC defined fields. By averaging the beam centers from the collimator symmetric measurements (i.e., 90°and 270°) the influence of MLC and jaw miscalibration is averaged out and the focal spot misalignment with collimator rotation axis isolated. The magnitude of the misalignment can then be calculated using eqs. 1 and 2 and Fig. 1. Where: D RFS = Radiation focal spot offset D EPI = Measured distance between field centers using the EPID a = machine-and procedure-specific proportionality factor.
Where: d epi = distance from the X-ray target (focal spot) to the EPID d jaw = distance from the X-ray target (focal spot) to the jaws d mlc = distance from the X-ray target (focal spot) to the MLC.

2.C | Image processing algorithm
All acquired EPID images were analyzed by a custom MATLAB â (The MathWorks, Inc., Natick, USA) script to determine the two radiation isocenter centroids defined by the jaws and MLC, respectively.
First, each image was filtered to remove noise using two-dimensional median filtering with a 3 9 3 size matrix. Each image was scaled to pixel values between 0 and 1, consequently the minimum value was assigned the value 0 and the maximum value was assigned the value 1. Each image was then resized, using bicubic interpolation, by a factor of 20 to increase the calculation resolution except for the Truebeam â linac, where each image was resized by a factor of 10, thus the output image pixel spacing was identical for all linacs. Next, each image was converted into a binary image with a threshold equal to 0.5 that relates to the Half-Value-Full-Width of the radiation field to determine the field edges. The center of each field was then calculated as the average point between field edges in both X and Y jaws directions. The radiation isocenter centroid defined by the jaws was then calculated as the average position of all field centers. The same process was performed with the aperture formed by the MLC only.
The distance between the two radiation isocenters defined by the jaws and the MLC at the EPID level was then calculated as the difference between the two isocenters expressed in pixels multiplied by pixel size for a given EPID panel and the resize factor used (10 for the Truebeam â and 20 for the other linacs).
To calculate radiation focal spot offset, the distance determined between the two isocenters was multiplied by the proportionality factor "a" (eq. 1) specific for the machine and the EPID source-imager distance. In this study the following parameters have been used: d mlc = 49 cm and d jaw distances are 40.6 cm and 31.9 cm for X and Y jaws, respectively. Therefore, the proportionality factor "a" defined in eq. 2 was equal to 2.368 and 2.2556 for X jaws and 0.9141 and 0.8706 for Y jaws with the EPID source-imager distance equal to 100 cm and 105 cm, respectively.

2.D | Reproducibility
The test was executed once per week on each linac over 3 weeks to observe reproducibility.

2.E | Independent validation
The validation of the phantomless method is based on the work published by Nyiri 10 with minor modification. The ionization chamber spatial sensitivity was determined by shifting the X and Y jaws, not the jig with the ionization chamber as in the original work.  The technique consisted of three distinctive steps: 1. Measurement of the sensitivity of a chamber to small changes in jaw position with a half-blocked field, i.e., changes in charge collected per 100MU per 1 mm change in either the half-blocked X or Y jaw position at the isocenter level.

Correlate geometrical shift of the jaw at the physical jaws level,
i.e., 1 mm shift of X and Y jaw at isocenter level equals 0.406 mm and 0.319 mm shift, respectively, at the physical X and Y jaws position (jaws X and Y are located 40.6 cm and 31.9 cm from the source, respectively).
The charge collected from the chamber depends on the amount the focal spot is obscured by the jaw [Fig. 2(b)]. Therefore, from the chamber point of view being half-blocked by the jaw, moving a jaw infinitesimally is equivalent to a shift of the source (a first-order linear approximation). Based on the geometric ratios of lengths of similar triangles, the position of the source is proportional to a shift of either X or Y jaws by: Where:

3.A | Reproducibility
Three linacs 1, 2, and 4 showed focal spot offsets less than 0.1 mm in each direction, but linac 3 had a significantly larger misalignment in the inplane direction, namely, 0.433 mm ( Table 1).
The average standard deviation (1 SD) of the focal spot offset for all linacs was 0.012 mm. However, high energy linacs (linac 2 and 4) showed increased relative uncertainty of source position offset in the inplane direction (Gun-Target) compared to the crossplane direction.

3.B | Independent validation
The ionization chamber validation method of the focal spot position agreed with the phantomless method with an average difference of 0.001 mm AE 0.015 mm (1 SD) ( Table 2).

| DISCUSSION
A phantomless method has been developed for measuring the colli-

ACKNOWLEDGMENTS
We thank the anonymous reviewers' scrutiny of the manuscript and insightful critique.

CONF LICT OF I NTEREST
The authors declare no conflict of interest.