A novel method to determine linac mechanical isocenter position and size and examples of specific QA applications

Abstract The most important geometric characteristic of stereotactic treatment is the accuracy of positioning the target at the treatment isocenter and the accuracy of directing the radiation beam at the treatment isocenter. Commonly, the radiation isocenter is used as the reference for the treatment isocenter, but its method of localization is not strictly defined, and it depends on the linac‐specific beam steering parameters. A novel method is presented for determining the linac mechanical isocenter position and size based on the localization of the collimator axis of rotation at arbitrary gantry angle. The collimator axis of rotation position is determined from the radiation beam center position corrected for the focal spot offset. The focal spot offset is determined using the image center shift method with a custom‐design rigid phantom with two sets of ball‐bearings. Three specific quality assurance (QA) applications and assessment methods are also presented to demonstrate the functionality of linac mechanical isocenter position and size determination in clinical practice. The first is a mechanical and radiation isocenters coincidence test suitable for quick congruence assessment of these two isocenters for a selected energy, usually required after a nonroutine linac repair and/or energy adjustment. The second is a stereotactic beam isocentricity assessment suitable for pretreatment stereotactic QA. The third is a comprehensive linac geometrical performance test suitable for routine linac QA. The uncertainties of the method for determining mechanical isocenter position and size were measured to be 0.05 mm and 0.04 mm, respectively, using four available photon energies, and were significantly smaller than those of determining the radiation isocenter position and size, which were 0.36 mm and 0.12 mm respectively. It is therefore recommended that the mechanical isocenter position and size be used as the reference linac treatment isocenter and a linac mechanical characteristic parameter respectively.

isocenter position and size based on the localization of the collimator axis of rotation at arbitrary gantry angle. The collimator axis of rotation position is determined from the radiation beam center position corrected for the focal spot offset. The focal spot offset is determined using the image center shift method with a customdesign rigid phantom with two sets of ball-bearings. Three specific quality assurance (QA) applications and assessment methods are also presented to demonstrate the functionality of linac mechanical isocenter position and size determination in clinical practice. The first is a mechanical and radiation isocenters coincidence test suitable for quick congruence assessment of these two isocenters for a selected energy, usually required after a nonroutine linac repair and/or energy adjustment. The second is a stereotactic beam isocentricity assessment suitable for pretreatment stereotactic QA. The third is a comprehensive linac geometrical performance test suitable for routine linac QA. The uncertainties of the method for determining mechanical isocenter position and size were measured to be 0.05 mm and 0.04 mm, respectively, using four available photon energies, and were significantly smaller than those of determining the radiation isocenter position and size, which were 0.36 mm and 0.12 mm respectively. It is therefore recommended that the mechanical isocenter position and size be used as the reference linac treatment isocenter and a linac mechanical characteristic parameter respectively.

| INTRODUCTION
Quality control guideline TG142 1 recommends that the coincidence of radiation and mechanical isocenters, as well as imaging and treatment isocenters, should be verified annually. The assessment of coincidence of radiation and mechanical isocenters is difficult to perform directly since the mechanical isocenter is traditionally determined using gantry and couch-mounted mechanical pointers 2 and graph paper, and the radiation isocenter is determined by means of the Winston-Lutz (WL) test 3 with a ball-bearing (BB) phantom, historically with radiosensitive film and nowadays with the electronic portal imaging detector (EPID). 4 In the WL test, the BB phantom, representing a target, is attached to the patient support table and aligned to the treatment isocenter. EPID images of the BB phantom are then acquired with the collimated beam at various gantry and collimator angles and analysed in terms of deviations of the radiation field centers from the BB phantom (i.e. beam isocentricity).
Liu at al. 5 presented an improved version of the mechanical and radiation coincidence test, using a special EPID (BIS 710) sensitive to light and radiation that significantly reduces the measurement uncertainty. However, the mechanical isocenter was assumed to be represented by the optical isocenter (light and crosshair system), which might not be the case. An alternative and less complex method is to utilize the laser system (used for initial patient positioning) as the reference coordinate frame. In that case lasers are first aligned to the mechanical pointer adjusted to represent the mechanical isocenter. Rosca et al. 6 presented a high accuracy method of verifying the laser system alignment with the radiation isocenter using phosphor plates. The method also provides characteristics of the radiation isocenter geometry, similar to that achieved with the commonly used WL test and ball-bearing phantom. However, the method is still relatively time and resource intensive.
Letourneau et al. 7 discussed how to assess accurately the alignment of the radiation beam axis with the three independent mechanical axes of rotations of the collimator, the gantry and the couch based on an analytical model, custom-made phantoms and analysis software. However, the mechanical isocenter location was not defined, and therefore the coincidence of radiation and mechanical isocenters could not be unambiguously determined.
Zhang et al. 8 considered carefully the issues related to having various linac isocenters, commonly referred to as those for mechanical, radiation and imaging systems, depending on how the isocenter position is determined. They presented a theoretical framework of the linac isocenter starting from fundamental concepts of a definition expressed mathematically. They also recommended that the linac mechanical isocenter, called in brief 'linac isocenter', should be used as the reference isocenter and that the other isocenters should be aligned with it, including the treatment isocenter. Zhang et al. 8 asserted that there should be one 'center of collimation', that is common for all Beam Limiting Devices (BLD) (e.g. MLC, diaphragms, cones) since all BLDs can be calibrated against this reference 'center of collimation'. This approach is only effective when the focal spot position (point of the electrons hitting the target) is aligned with the collimator axis of rotation i.e. the focal spot offset (FSO) is zero.
The effect of FSO was first reported by Lutz et al. 9 They noticed that a transverse beam spot offset caused the radiation field positions to shift laterally, which resulted in two radiation fields at two opposed gantry angles to be misaligned ('FSO effect').
Sonke et al. 10  Nyiri et al. 12 considered the dependency of the x-ray shadows of radio opaque rods on the distance of the rod from the radiation source. They observed that when the focal spot is not aligned with the collimator axis of rotation the distance between the two centers of the images formed by projected x-ray shadows of two rods positioned at different distances from the radiation source is dependent on the collimator angle. They proposed the image center shift method to correlate geometrically the FSO (D FSO ) and the distance between the two image centers (Δ FSO ). The centers of the images were calculated as the average position of projected x-ray shadows of the two rods, respectively (placed at distances d 1 and d 2 from the radiation source), while rotating the collimator, and were measured using the EPID (placed at a distance d EPID from the radiation source): In practice, this means that the FSO effect causes the difference between radiation field centers to vary depending on the FSO value, the position of the BLD forming the field aperture and the position of the measurement plane (i.e., EPID). Chojnowski et al. 13  This study expands the work of Nyiri et al. 12 and Riis et al. 14 to localize the collimator CAX using radiation, utilizing a phantom of a different design and a modified method to guide the BB phantom to the mechanical isocenter. The mechanical isocenter position is defined in this study using the 'collimator axis trajectory' approach proposed by Skworcow et al., 16 which means that the mechanical pointer axis is utilized, instead of the mechanical pointer end, where the latter is common in standard approaches. It is important to emphasize that differences between mechanical isocenters determined using 'collimator axis trajectory' and standard approaches may be over 1 mm. The 'collimator axis trajectory' approach is more clinically relevant and conceptually similar to the radiation isocenter determination approach.
In this work, a method is proposed to localize the collimator CAX and the mechanical isocenter using radiation and was validated against varying radiation beam parameter settings of energy and MU. Based on the findings, three examples of procedures for specific linac quality assurance (QA) assessments were developed and presented, namely: • Coincidence assessment of mechanical and radiation isocenters

2.B.2 | FSO phantom
The FSO phantom was a specially designed and constructed phan-

2.B.3 | Validation phantom
The validation phantom [see Fig. 1(b)] was designed to validate the FSO and the collimator CAX determination methods at gantry 0°.
The phantom was similar in design to the FSO phantom, however, did not have four tightening screws and two BB sets were positioned at nominal distances to the radiation source of 70.5 cm and 100 cm (named BB 3 and BB 4 sets respectively).

2.C | Image processing and analysis software
Where: ᶱgantry angle. Dᶱ FSO  F I G .
2. An example of one EPID image (a) acquired for the comprehensive assessment and (b) processed by the IHD software. One central circle represents the BB phantom and four peripheral circles represent the FSO phantom. Two larger peripheral circles are related to the BBs located closer to the radiation source i.e. BB 1 set, and correspondingly two smaller peripheral circles are related to the BBs located further from the radiation source i.e. BB 2 set. BB 1 and BB 2 measured at the EPID level and for gantry angleᶱ.
Where: Mᶱ EPID -position of the mechanical collimator CAX at the EPID level and for gantry angleᶱ. Rᶱ BB1 -position of the radiation beam CAX defined by the ball-bearing set BB 1 at the EPID level and for gantry angleᶱ. Rᶱ BB2 -position of the radiation beam CAX defined by the ball-bearing set BB 2 at the EPID level and for gantry angleᶱ.
Where: Mᶱ REF -position of the reference mechanical collimator CAX at the EPID level and for gantry angleᶱ. d ISO == distance of the ballbearing BB WL from the radiation source: 100 cm.

2.F.2 | Stereotactic beam isocentricity assessment
The stereotactic assessment was performed by comparing the rela-

2.F.3 | Comprehensive assessment
Comprehensive assessment of linac mechanical, radiation, and (additionally) imaging isocenters is possible by comparing relative positions of the stationary reference BB phantom to individually determined linac mechanical, radiation, and imaging isocenters.
Those relative positions are then normalized to a reference point, which is the average of mechanical isocenter position determined for all four energies.
The BB phantom was placed at the treatment isocenter using the IGRT system, which, in this study was the Cone Beam Computed Tomography (CBCT). The alignment of the BB phantom with the mechanical isocenter was reported, which characterizes the overall performance of the IGRT system. The radiation and mechanical isocenters determinations were described in the coincidence assessment, however, in this test all available energies were used.
The imaging isocenter in this study was defined for both MV

| RESULTS
An example of the EPID image acquired and processed by the IHD software with the FSO and the BB phantoms is shown in Figs. 2(a) and 2(b) with detected edges of the radiation field, four peripheral BBs, and one central BB.   Table 2).   Table 2).

3.B | Localizing collimator CAX for the BB phantom
3.C | Methods of assessment of linac mechanical, radiation, and imaging isocenters 3.C.1 | Coincidence assessment of mechanical and radiation isocenters An example of coincidence assessment is presented in Table 3

3.C.2 | Stereotactic beam isocentricity assessment
An example of the stereotactic beam isocentricity assessment of the 6MV FFF beam is presented in Fig. 7 and Table 4

| 51
The position deviation of the BB phantom from the mechanical isocenter shows the accuracy (of the day) of the image guidance system to align the target with the treatment isocenter, referred to commonly as the IGRT end-to-end test.
The uncertainty of the mechanical isocenter position determination (0.05 mm) with varying energies is observed to be significantly smaller than that for the radiation isocenter (0.36 mm).
It is also interesting to see the differences in mechanical and radiation isocenter sizes [see Fig. 8(b) and Table 5]. Radiation isocenter size is dependent on the transverse beam steering and varies from below 0.5 mm for 6MV beam to over 0.7 mm for 10MV FFF beam (1SD == 0.12 mm), whereas mechanical isocenter size is relatively constant, as expected, at 0.7 mm (1SD == 0.04 mm). It may be noted that, of course, the couch positioning, axes, limitations, and deviations are also an integral part of the overall geometric uncertainties of the system for the practical applications considered, e.g., stereotactic treatments. However, these can be assessed separately and are not evaluated here, since we are primarily concerned with the geometric behavior of the linac itself.

3.C.4 | Isocenters assessment uncertainty analysis
In the presented comprehensive assessment example, the uncer- The linac isocenter size is a very important linac specification parameter that is used for acceptance testing, especially if the linac is planned to be used for SRS/SBRT treatments. The mechanical isocenter size shows minimal variation with the energy and no variation with the BLD (see Table 5) and is therefore recommended to be used for linac acceptance testing, with other isocenters referenced to it.
Localizing mechanical isocenter position with the use of the BB phantom helps in setting-up or independently correcting linac radiation and imaging isocenters. Namely, the BB phantom should be positioned at the mechanical isocenter. All radiation isocenter posi-  8. An example of the comprehensive assessment of (a) positions of mechanical, radiation, and imaging isocenters and the BB phantom as well as (b) isocenters sizes.
alignment of mechanical and radiation isocenters. However, this might not be the optimal linac set-up since the gantry sag and the collimator tilt causes the mechanical and radiation isocenter sizes to be nonzero. Also, treatment planning systems assume that the radiation isocenter size is zero. Therefore, for linacs designated for SRS/ SBRT, it is advantageous to correct the transverse beam steering to minimize the radiation isocenter size at the cost of reintroducing a small FSO effect in the transverse direction. A practical guide for optimizing beam steering for SRS/SBRT linacs is the subject of future study.

| CONCLUSION
A new approach for localizing linac collimator CAX and mechanical isocenter using radiation has been presented. The mechanical isocenter position was proven not to depend on the beam energy, the beam collimating device or the beam MU settings, as expected, and it is therefore recommended to be used as a reference treatment isocenter for adjusting radiation and imaging isocenters positions.
Also, the mechanical isocenter size parameter was proven not to depend on the beam settings, as expected, as opposed to the radiation isocenter size, and it is therefore recommended to be the standard specification parameter in the linac customer acceptance procedure. The new methodology of localizing mechanical isocenter is efficient and effective and is presented in this study with three complementary practical applications of position and size assessment procedures of mechanical, radiation, and imaging isocenters combined with the patient positioning system.

ACKNOWLEDGMENTS
The authors thank Andrew Kovendy from the Department of Medical Physics, Mid North Coast Cancer Institute, for supplying materials for FSO and Validation phantoms.

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

D A T A A V A I L A B I L I T Y S T A T E M E N T
The data that support the findings of this study are available from the corresponding author upon reasonable request.