A novel and effective method for validation and measurement of output factors for Leksell Gamma Knife® Icon™ using TRS 483 protocol

Abstract The objective of this work was to identify the exact location of the effective point of measurement (EPM) of four different active detectors to compare the relative collimator output factors (ROF) of Leksell Gamma Knife (LGK) according to IAEA TRS‐483 recommendations. ROF was measured at the center of the spherical LGK‐Solid Water (LGK‐SW) Phantom for three (4‐, 8‐, and 16‐mm in diameter) collimators using four (PTW‐TN60008, PTW‐TN60016, PTW‐TN60017, and PTW‐60019 diode/diamond) detectors. Since diode detectors have a much smaller sensitive volume than the PTW‐31010 ion chamber used for reference dosimetry, its EPM might not be at the center of the phantom, or (100, 100, 100) of the Leksell Coordinate System, particularly in the z‐direction. Hence for each diode detector, a CBCT image was acquired after it was inserted into the phantom, from which the z‐Leksell coordinate of EPM was determined. Relative collimator output factors was then measured by focusing GK beams on the determined EPM of each diode. Measured ROFs were compared with the vendor‐provided values in GK treatment planning system. For validation, a plan was generated to measure the output of 4‐mm collimator for PTW‐TN60017 at various couch locations along the z‐axis. For PTW‐TN60008, the percentage variations were 0.6 ± 0.4%, and −0.8 ± 0.2% for 4 and 8‐mm collimators, respectively. For PTW‐TN60016, the percentage variations were 0.8 ± 0.0%, and 0.2 ± 0.1%, respectively. The percentage variations were −3.3 ± 0.0% and −0.9 ± 0.1%, respectively, for PTW‐TN60017, and −0.5 ± 0.0% and −0.8 ± 0.2%, respectively, for PTW‐TN60019. Center of the measured profile for PTW‐TN60017 was only 0.1 mm different from that identified using the CBCT. In conclusion, we have developed a simple and effective method to determine the EPMs of diode detectors when inserted into the existing LGK‐SW phantom. With the acquired positional information and using TRS‐483 protocol, good agreements were obtained between the measured ROFs and manufacturer recommended values.

Water (LGK-SW) Phantom for three (4-, 8-, and 16-mm in diameter) collimators using four (PTW-TN60008, PTW-TN60016, PTW-TN60017, and PTW-60019 diode/diamond) detectors. Since diode detectors have a much smaller sensitive volume than the PTW-31010 ion chamber used for reference dosimetry, its EPM might not be at the center of the phantom, or (100, 100, 100) of the Leksell Coordinate System, particularly in the z-direction. Hence for each diode detector, a CBCT image was acquired after it was inserted into the phantom, from which the z-Leksell coordinate of EPM was determined. Relative collimator output factors was then measured by focusing GK beams on the determined EPM of each diode. Measured ROFs were compared with the vendor-provided values in GK treatment planning system. For validation, a plan was generated to measure the output of 4-mm collimator for PTW-TN60017 at various couch locations along the z-axis. For PTW-TN60008, the percentage variations were 0.6 AE 0.4%, and −0.8 AE 0.2% for 4 and 8-mm collimators, respectively. For PTW-TN60016, the percentage variations were 0.8 AE 0.0%, and 0.2 AE 0.1%, respectively. The percentage variations were −3.3 AE 0.0% and −0.9 AE 0.1%, respectively, for PTW-TN60017, and −0.5 AE 0.0% and −0.8 AE 0.2%, respectively, for PTW-TN60019. Center of the measured profile for PTW-TN60017 was only 0.1 mm different from that identified using the CBCT. In conclusion, we have developed a simple and effective method to determine the EPMs of diode detectors when inserted into the existing LGK-SW phantom. With the acquired positional information and using TRS-483 protocol, good agreements were obtained between the measured ROFs and manufacturer recommended values.

| INTRODUCTION
Small photon fields are widely used in stereotactic radiosurgery (SRS) and radiotherapy (SRT). Dose measurements of small field sizes are challenging, due to many factors such as source occlusion, detectors size limitation, and lack of lateral electronic equilibrium. 1 In small fields, the precise and accurate determination of the effective relative output factor (ROF) of a Leksell Gamma Knife ( LGK. 9 The corrected ROFs for 14 and 8 mm collimator were in a very good agreement with the recommended values. However, for the 4-mm collimator, the diodes showed over response of maximum 2.8% and for the pinpoint chamber ROF was 25% lower than the vendor value. Thus, the size and type of detectors used for the ROF measurements are critical to the accuracy of measurement, and detectors with high spatial resolution, high precision, and good tissue equivalence are required. 10 In addition to detector response, identifying the EPM of each detector is necessary as the whole profile is a small field and the EPM is usually in the penumbra region. When the phantom is docked in the Gamma Knife for irradiation, the center of the phantom coincides with the focal point of the LGK unit, or (100, 100, 100) of the Leksell Coordinate System (LCS) in units of millimeters.
However, when a detector is inserted at this focal point, its reference point of measurement may not coincide with the focal point.
In this paper, we investigated how to determine the EPM of different diode detectors for accurate measurements of ROFs for LGK Icon™ unit. In addition, ROFs were measured using four different active detectors according to the recommendations of IAEA TRS-483 report. The results were compared with the vendor-recommended values in the Gamma Knife planning (GKP) system. The HDMM system consists of an IR camera, an IR reference tool and a patient marker. It is not used for initial setup of the patient but for monitoring the patient movements during the treatment. After the patient is aligned using the CBCT, the IR camera tracks the patient maker at a frequency of 20 Hz and measure its movement relative to the reference coordinate system defined by the IR reference tool. Treatment will be held off if the patient motion exceeds the preselected threshold, and resumed again when the patient returns to the initial position.
Both CBCT and HDMM systems have been introduced to provide LGK accuracy for fractionated stereotactic radio surgery (SRS) treatments that involve the replacement of the invasive coordinate frame with the use of thermoplastic masks. Different types of thermoplastic masks are commercially available from numerous vendors.
They are specially designed for SRS/SRT, which are stiffer, Kevlar reinforced, and have less shrinkage.

2.B | Gamma knife solid water (SW) phantom
Relative output factor (ROF) measurements were performed on the LGK Icon unit at the Center for Advanced Medicine (CFAM) of Northwell Health (New York, US) using the spherical Leksell Gamma Knife Solid Water (SW) Dosimetry Phantom provided by the manufacturer. When the phantom is docked to the machine, the Leksell coordinates of its center are (100, 100, 100) in millimeter. Figure 1 illustrates how the detector was inserted into the SW phantom and stabilized with tape for output measurements. The LGK SW phantom is designed for output measurement using PTW-31010 Semiflex ionization Chamber (sensitive volume: 0.125 cc, Dimension: radius 2.75 mm, length 6.5 mm). That is, when inserted into the phantom, the center of this ionization chamber, or effective point of CYRIAC ET AL.
| 81 measurement (EPM) is located at the phantom center with Leksell coordinates of (100,100,100). For routine output measurement, a treatment plan is executed to move the couch inside the GK unit to a location so that the planned location, that is, (100,100,100), coincides with the radiological focus of the machine known as the unit center point (UCP). The irradiation time can be controlled by the treatment plan or using the dose integration function of the electrometer, in which the user can specify a time (e.g., 1 min) for charge collection. Therefore, the holder customized for the PTW-31010 ionization chamber can potentially be used for the relative dosimetry measurements using the above four diode detectors if the EPM of each detector can be correctly identified. As stated in the previous section, when the PTW-31010 semiflex ion chamber is inserted into the sleeve of the holder of our Gamma Knife SW phantom, the center of the ion chamber or the EPM will be at Leksell coordinates of (100, 100, 100). However, (100,100,100) might not be the EPM for other detectors, particularly for diode detectors that have a much smaller sensitive volume than the PTW-31010 ion chamber.

2.C | Diode detectors for ROF measurements
Since all four detectors have the same external geometry, the Leksell coordinates of the flat face/tips are the same. However, as illustrated in Table 1, the reference point measured from the flat face/tips is different for the four diode detectors. Given that the central axis of these four detector is along the z-axis of Leksell coordinate system, the z coordinate is different for these four detectors while the x-and y-coordinates remain the same (100 and 100). It is therefore crucial to know the exact z-Leksell coordinate of EPM for each diode detector when inserted into the phantom; and position the phantom accordingly so that the EPM is located at UCP. Otherwise, the ROF measurements will not be accurate, particularly for the 4-mm collimator.

2.D | Determination of effective points of measurement
In this study, we developed a strategy for identifying the Leksell coordinates of EPM of a diode detector using the KV-CBCT of GKI unit. For each diode detector, a CBCT image was acquired after it was inserted into the phantom and fixed with duct tape. Once the CBCT scan was localized, the flat face/tip of the detector was first identified in the images and the Leksell coordinates of EPM of that detector was determined based on the distance between the reference point and the flat face/tip provided in Table 1. Once the EPM of the diode was determined, a GKI plan was generated that aimed the radiation at the EPM coordinates instead of (100,100,100).
When this new plan was executed, the couch would be moved to a location inside the GKI so that the Leksell coordinates of EPM, would coincide with the UCP. Sufficiently enough doses was prescribed for the plan so that the measurement time was set to one minute and were not controlled by the GKI plan but using the dose integration function (1 min integration) of the electrometer.
2.E | Measurement of relative output along the zaxis In order to validate the identified EPM of a diode using the abovementioned CBCT method, a GKI plan was generated to measure the outputs of the 4-mm collimator using PTW-TN60017 diode at various couch locations along its central axis. Starting by aligning the UCP with Leksell coordinates (100, 100, 103), the couch was moved out in steps (0.1 or 0.2 mm for the in-field and penumbra regions, and of 0.3 or 0.5 mm for the out-of-field region) along the z-axis until the UCP coincided with Leksell coordinates (100, 100, 92). A large dose (e.g., 50 Gy) was prescribed for the plan in order to have enough irradiation time (on the order of an hour). In each stop, output was measured by integrating the ionization charge for a specified time larger than 30 s. The measured sensitivity for different locations along the z axis of diode was then plotted and the center of the irradiation field identified as the center to the two 50% profile levels was identified and compared with the EPM of PTW-TN60017 identified using the CBCT method.

2.F | Measurement of relative output factors
Output in term of ionization charge in nC (nanocoulombs) was measured for each collimator size using all four diode detectors and a PTW UNIDOS E electrometer. The exposure time (controlled by using the dose integration function of the electrometer) was one minute for each irradiation, and three readings were obtained and averaged for each collimator size. The measured output for each collimator size was used to obtain the ROF according to the recommendations of IAEA TRS483 report, 3 particularly, Chapter 6 in that report for relative dosimetry of small fields. That is, the ROF was the ratio of the averaged readings for the 4-mm/8-mm collimator to that of 16-mm collimator, multiplied by a field output correction factor, k fclin,fmsr Q clin ,Q msr (given in table 25 of TRS483 for each detector) as a function of the collimator size, in order to correct for the side effects of small field sizes ( Table 2). The same experiment was performed twice for each detector from which the average and standard deviation of the measured ROFs were calculated and compared with the vendor provided ROF in the treatment planning system, which were generated using Monte Carlo simulation. is the PTW-31010 ionization chamber used for the reference dosimetry, which has almost the same outer geometry (diameter 6.9 mm). Therefore, the holder drilled for PTW-31010 ionization chamber can potentially be used for the relative dosimetry measurements using the above four detectors if the effective point of measurement (EPM) of each detector can be correctly identified.

| RESULTS
T A B L E 1 Characteristics of the diode detectors used in this study. All four detectors have the same external but different internal geometry. The geometric form of sensitive area is "disk" for all detectors. The last column lists the z eff , which is the z-Leksell coordinate in mm of effective measurement point (EMP) when it is inserted into the SW phantom. These values were derived in this study using the CBCT method.      Tables 3 and 4. As shown in Table 4, significant differences were observed between the measured and reference if the EPM of the diode is not positioned at machine UCP. Table 5 lists the mean and standard deviation of the ROFs of 4 and 8-mm collimators for the GKI relative to the 16-mm collimator, measured at the EPM of each detector determined using the CBCT method. The same data are plotted in Figure 6 to demonstrate the good agreement between the measured and reference ROFs. Even though the image quality of the CBCT scans in Fig. 2 is not optimal, it is observed in this figure that the internal structure is very different for these four detectors. This is particularly obvious when we compare the z-Leksell coordinates of the most superior part of the detector that can be identified from the scans of these four detectors: they are quite different ranging from 96.5 to 97.3 mm.
This large variation was attributed to the different internal structures, particularly the presence of air gaps in some of these four detectors. Therefore, even though these four detectors have the same external geometry (outer diameter 7 mm), the tip/front wall might not show in the CBCT scan if it is next to low attenuation material (e.g., air gaps).
Because the CBCT image quality was not optimal, we decided to perform an independent check by measuring the relative output of the 4-mm collimator using the PTW 60017 detector. The FWHM of the measured profile agreed very well with that determined during the commissioning and the z Leksell coordinate of the center measured profile was only 0.1 mm different from that determined using the CBCT method. It is noticed that the shape of the profile in Fig. 4 is not symmetrical around the center of the field but is slightly higher (~2%) toward the superior side. This was most likely because the beam was attenuated slightly more when the detector traveled The ROF measurements were performed following the recommendations of IAEA TRS-483 report 3 for relative dosimetry of small fields. In general, the differences in the measured ROFs were within 1% of the recommended OFs used by the treatment planning system, as shown in Tables 5 and 6 and Fig. 3. The only exception was the PTW-TN60017 diode which has underestimated the ROF by 3.3% for the 4-mm collimator. Even though the 3.3% accuracy is generally acceptable for validating GK collimator ROFs, particularly for the 4-mm collimator, we still repeated multiple CBCT images and measurements for this particular diode. The results in Fig. 4 showed that the EPM identified using the CBCT scan was correct but the deviations in the output factor were similar after multiple measurements. Therefore, we concluded that the deviations could be due to the fact that the k fclin,fmsr Q clin ,Q msr for PTW-TN60017 diode might not be sufficient enough to correct for the field output at 4mm collimator size.   (Table 1), z eff = 96.5 + 1.3 = 97.8 (mm) is the z-Leksell coordinate of the sensitive volume in the z direction.
T A B L E 3 Relative Output factors (ROFs, relative to the 16 mm collimator) for the Gamma Knife Icon uncorrected for the location of sensitive volume, that is, assuming the sensitive volume is located at z-Leksell coordinate z eff = 100 mm, or the geometric center of the phantom. All measurements were performed with the same plan. The reference ROFs are that used in Gamma Knife planning (GKP) system, which were calculated using Monte Carlo simulations. However several authors reported silicon detectors will over respond to lower energy scattered photons due to photo electric effect in the sensitive area of the silicon. 13 To reduce this effect in unshielded PTW-TN60017, a disk-shaped silicon chip surrounded by a polymer plastic is fixed to reduce the unwanted back scattering of electrons from the shield. 14 Hence the discrepancies could be possibly due to the increase of backscattered electrons from this inefficient shield as the angle of incident photon beam decreases. Further study is needed to identify the source of this discrepancy.
Alternate detectors such as polymer gels, radiographic film and radiochromic film can also be considered for the validation of ROF

| CONCLUSION
In this study, a novel and simple imaging method was developed to determine the EPMs of diode detectors when inserted into the existing LGK-SW phantom. With the acquired information, each diode could be positioned at the focal point of the machine for relative collimator OF measurements, without any modification or customization of the phantom. Following the recommendations of IAEA TRS-483 report 3 for relative dosimetry of small fields, the ROFs measured using this method showed a very good agreement with the values recommended by the manufacturer for all diode detectors used in this study. The only exception was the measurement of ROF for the 4-mm collimator using the PTW-TN60017 diode detector.
We suspect it was due to some unknown discrepancy of the output correction factor, k fclin,fmsr Q clin ,Q msr for that diode, and further investigation is needed.

ACKNOWLEDG MENT
The authors thank the financial support from the Union for Interna-   | 87