Purpose: This study provides a simple protocol for validation of the gamma passing rates and to identify the optimum values of % dose and mm criteria for dose distributions measured with a detector array. Methods: We chose ArcCHECK detector array to illustrate the concepts. We used plans with uniform or quasi-uniform dose distributions along the detector array for testing in the presence of dose errors. For testing sensitivity to spatial shift we employed a plan with approximately constant dose gradient along the axis of the instrument. Results: We identified a representative set of parameters which describe performance of a detector array. We determined the minimum gamma-index acceptance criteria allowing the passing rates to reach 100% in the absence of errors, and identified the minimum fully detectable errors for such criteria. For our baseline plans delivered to ArcCHECK, 100% passing rates were obtained for 1.5% dose criterion together with ±3% minimum error detectable at 100% rate, and for 1.5 mm criterion together with the minimum fully detectable error of ±3 mm. We inspected the impact of selected program options on the passing rates. Conclusions: The protocol we developed provides a simple method of commissioning-style analysis of a detector array without a need for analysis of a large number of clinical plans.
A number of detector arrays have been developed for quality assurance (QA) of complex radiation treatment plans. Early-generation systems contained a set of detectors arranged in a line, e.g. Profiler 2, (Sun Nuclear Inc., Melbourne, FL) or in a plane, e.g. MatriXX (IBA Dosimetry GmbH, Schwarzenbruck, Germany). The latest instruments evolved to allow measuring the dose distribution in 3D space. Delta 4 (ScandiDos Inc., Uppsala, Sweden) consists of two planes of detectors arranged in “X” configuration and ArcCHECK (Sun Nuclear Inc., Melbourne, FL) consists of an array of detectors located on a cylindrical surface.
Several papers have been published to validate performance of each of these instruments. In particular, Feygelman et al. [
Historically, comparing multi-detector data to treatment planning system (TPS) data relied on calculations of the dose difference in flat portions of the dose distribution and of the distance to agreement (DTA) in regions of steep dose gradient. In 1998 Low et al. [
Examples of the gamma passing rates in clinical scenarios have been published e.g. by Létourneau et al. 2009 [
The gamma analysis acceptance criteria are often established through analysis of the passing rates in a large number of clinical plans, but this is a labour-intensive approach. Moreover, it is implied that the linac is capable of delivering these plans at a satisfactory level no matter how complex the plans are. In spite of availability of many publications employing gamma analysis, there is no consensus on the choice of the % dose and mm crite- ria in the gamma index. We designed a protocol that addresses these problems, as well as we compared simple- case results to the theoretical prediction. We applied this protocol to measurements performed with ArcCHECK.
We designed separate plans for testing for dose errors and testing for spatial errors. In the absolute-dose mode we used a uniform-dose plan for the former. The uniform dose distribution was approximated by combining ex- posure from 5 rectangular fields (87 MU each, 400 MU/min) aiming at the ArcCHECK from different directions (gantry equal 216˚, 288˚, 0˚, 72˚ and 144˚). The center of ArcCHECK was set to the isocenter, and its axis was aligned with the longitudinal direction of the (non-rotated) couch. Each field delivered 87 MU, and was collimated to 24 cm along the axis of ArcCHECK to minimize exposure to the electronics, and 25 cm across. The calculated longitudinal dose profile passing through the central detector is shown in
sured, not in the calculated dose, renormalizing the calculated plan provides equivalent passing rates under understanding that the sign of the error is opposite.
In the relative-dose mode we modified the plan described above by adding a small subfield (at gantry equal zero, and collimated to X = 1.2 cm and Y = 2 cm). The two central detectors irradiated under this subfield were used for normalization (to the maximum value), and the errors in the dose were simulated by changing the ratio of the weights between the subfield and the other fields. Subsequently, this plan will be referred to as the quasi-uniform plan, and the renormalization procedure as quasi-renormalization. The dose profile passing through the central detector for the quasi-uniform plan is plotted in
We used an approximately constant dose gradient plan for testing in the presence of spatial errors. We accomplished this by replacing the open fields in the uniform plan with 60˚ (enhanced dynamic) wedges, for which the dynamic jaw was moving along the axis of ArcCHECK. The dose profile passing through the central detector is plotted in
All plans were calculated in Varian’s Eclipse (Varian Medical Systems, Palo Alto, CA) using anisotropic analytical algorithm (AAA) ver. 11.0.31, under 1 mm grid and with heterogeneity correction on. The plans were delivered with Varian TrueBeam 1.6 linac using 6 MV flat beams.
We used ArcCHECK in all measurements of the dose distributions. The polymethyl methacrylate (PMMA) plug was inserted at all times. The instrument was levelled on the couch, and its center was aligned with the linac’s isocenter during all measurements. SNC Patient ver. 6.2.3 software (Sun Nuclear Corporation, Melbourne, FL, 2013) was used to control the instrument and to analyze the data. We used a virtual phantom in the shape of a cylinder matching the outline of ArcCHECK to calculate the dose distributions, and assigned uniform density with the CT# of 160 HU. Use of a uniform-density virtual phantom instead of an actual CT scan is recommended by the manufacturer. The CT# specified above was chosen to comply with a requirement of using the effective electron density of 1.150 g/cm3, and was adjusted by modifying the CT# of the virtual phantom until the ratio of the effective distance to the geometrical distance was 1.150. The plastic rails, which are a part of the mechanical support of the instrument, were included in the virtual phantom, as well as the couch (Varian Exact Couch Top with Flat Panel, using CT# = −300 HU for the surface and −1000 HU for the interior; no couch rails). We verified consistency of setting the CT# in the virtual phantom by measuring the ratio of the dose along the CAX in the upstream detector to the dose in the downstream detector. Strictly speaking, due to the lack of a detector along the CAX, an average of the doses in the two detectors nearest to the CAX was used. The measured ratio was 3.62, and was only 0.7% higher than the ratio calculated in the plan (the manufacturer allows up to 1% discrepancy).
We initially calibrated the dose in ArcCHECK by irradiating the instrument (positioned with its center at the linac’s isocenter) with 6 MV flat beam (10 cm × 10 cm, 200 MU), and assigning the dose of 262.1 cGy, which is the dose calculated at the depth of 3.3 cm in a virtual flat-water phantom on the CAX at the SSD = 86.3 cm. In order to refine the calibration, we recalibrated the instrument by assigning the dose of 263.6 cGy, which is the calculated dose at the depth of 2.8 cm in the virtual cylindrical phantom mimicking ArcCHECK placed at the isocenter. We subsequently performed a closed-loop type verification of this refined calibration by comparing the dose measured with ArcCHECK on the CAX at the depth of 2.8 cm to the calculated dose of 263.6 cGy. We averaged the measured dose based on the readings in six detectors placed within no more than 1 cm from the CAX on the upstream portion of the detector array. To eliminate the effect of the output instabilities of the linac on our results, we performed the dose calibration during each session.
The passing rates calculated by SNC Patient software employ an algorithm based on, but slightly different from the original algorithm introduce by Low et al. [
where
Dm and Dc are the measured and the calculated doses at the measured and the calculated position, rm and rc, respectively. Dmax is the maximum dose, ∆dM is the distance criterion and ∆DM is the dose difference criterion in %.
Due to the lack of spatial dependency in the uniform-dose plan, the theoretical passing rates (upon plan renormalization) were calculated through evaluating the dose difference only. In the theoretical prediction, 100% passing rate was assigned when the theoretical dose (same for every detector) did not differ from the planned value by more than the % dose criterion in the gamma index, and 0% otherwise. The detection rates for the true negative events (failure to detect the error in dose of the given % value) was calculated by subtracting the passing rate from 100%.
For the dose-gradient plan (using the “global % difference” = ON) we analyzed the passing rates upon shifting (in SNC Patient software) the planned dose distribution along the direction of the gradient. We used two methods to calculate the theoretical passing rates following the multi-step protocol employed by the SNC Patient software. We assigned 0% or 100% passing rates based on the dose-to-agreement check when using the % dose criterion of 0.01% (which approximates 0%, the value not allowed in the software). When the % dose was set to larger number, we proceeded as follows: we converted the dose profile into unitless space, where the shift divided by the distance criterion of the gamma index is used as the abscissa, and the dose * 100, divided by the maximum dose and the % dose criterion of the gamma index is used as the ordinate, see
where s is the mm shift along the gradient direction and α is the angular tilt of the profile line, see
The detection rates for the true negative events in the presence of a spatial error were calculated in a similar manner as for the dose error, i.e. 100%-passing rate, except now it is a function of the shift in mm instead of the error in the dose.
Unless specified otherwise, we used the following software options to compute the passing rates: absolute dose, Van Dyk (Global % Difference) = ON, Apply Measurement Uncertainty = OFF, Use 3D DTA for ArcCHECK = OFF, dose threshold (TH) = 10%.
We used a subset of all detectors in the analysis. For the uniform-dose and the quasi-uniform dose plans we excluded the first and the last loop of detectors from the region of interest (ROI). This is because we chose to limit the field size in order not to irradiate the electronics of the device, and consequently the dose was less uniform at these detector locations. The detectors utilized in the analysis are marked in the dose profile in
We selected a smaller ROI, marked in
We repeated all measurements for the total of three or four times, each in a separate session, to estimate the uncertainties of the passing rates. As the setup was redone at the beginning of each session, the uncertainty of the setup is included in the error bars. The error bars plotted throughout this manuscript were calculated as the standard deviation of the mean.
The ratio of the measured to the calculated dose at the depth of 2.8 cm on the CAX in the closed-loop verification of the initial calibration was: 0.994 ± 0.003. The corresponding ratio for the refined calibration was 1.001 ± 0.003, which is better. We used the refined calibration in the subsequent measurements and analysis.
The passing rates as a function of the % dose criterion in the gamma index for ArcCHECK irradiated with the uniform-dose plan are shown in
Also shown in
The γ(1.5%, 1 mm) in the uniform-dose plan as a function of the plan renormalization, i.e. the dose error (shown in the top axis), is plotted in
The plot of the passing rates vs. the dose error is also useful in verifying the rate of detection of the true negative events for a given error. It should be noted that not all detectors of the array read the passing rates equal zero in the presence of the dose error equal the % dose criterion. In particular, the detection rate of the true negatives is only about 20% (100% - 80%) for −1.5% error, and 85% (100% - 15%) for 1.5% error. This is a consequence of system uncertainties. These rates are different for the positive and the negative error due to the presence of the (small) centroid shift. All true negatives are detected (i.e. 0% passing rate) only when the error is ±3% or larger. This value is significantly larger than the % dose criterion. Also plotted in
The passing rates as a function of the mm criterion in the gamma for the dose-gradient plan are plotted in
As the primary purpose of using the plan with a gradient is to validate the passing rates in the presence of spatial shifts, we examined the relation between the passing rates and the shift in the plan along the direction of the gradient. In
100% - 60%) of true negatives are detected for −1.5 mm shift, and about 70% (i.e. 100% - 30%) for 1.5 mm shift. All true negatives are detected for shifts equal or over ±3 mm, which is considerably more than the mm criterion of the gamma index.
The tests described in this manuscript are summarized in
The minimum % dose criterion and the minimum mm criterion listed in
We did not use MLC in our baseline plans, with the exception of the subfield in the quasi-uniform plan, in order to eliminate errors due to limitations in modeling of the MLC in Eclipse. After all, the shape of the penumbra measured with film differs slightly from the shape planned with Eclipse [
We opted not to include clinical plans in our protocol. After all, there are several publications listing gamma rates in clinical cases, including a multi-site review by Vieillevigne et al. [
Test | Test description | Result upon error in dose | Result upon shift error |
---|---|---|---|
1 | HWHM upon error | Measured-theory ≈ 0.01% | Measured-theory ≈ 0.4 mm |
2 | Centroid upon error | 99.6% (i.e. −0.4% off) | −0.2 mm |
3 | 90% - 10% penumbra upon error | 1.11% | 1.7 mm |
4 | Do the passing rates with no error reach 100%? | Yes | Yes |
5 | Minimum criterion allowing 100% passing rate (in absence of errors) | 1.5% | 1.5 mm |
6 | Minimum error detectable at 100% rate (for γ-index criterion allowing 100% passing rate in absence of errors) | 3.0% for γ(1.5%, 1 mm) | 3.0 mm for γ(0.01%, 1.5 mm) |
commissioning-style protocol that could be quickly performed, and would allow selecting % dose and mm criteria that are not specific to the technique (VMAT, IMRT, etc.) or the site. Arguably, it is better to select the gamma criteria from first principles, instead of inspecting numerous clinical plans and assuming that the linac delivers them perfectly. Consequently, we chose to use baseline-type plans instead, and we designed them in a way to make interpretation of the results straightforward. In particular, we constructed these plans to have the theoretical gamma index independent on the location of the detector. In such case the passing rate is either 0% or 100%. As the gamma index depends both on the dose error and the spatial error, it is desirable to test each type of error in a separate step. A uniform-dose plan is an appropriate plan for testing the sensitivity to errors in dose. We used the quasi-uniform plan in the relative-dose mode because it is impossible to introduce dose errors into a uniform-dose plan (in the ideal case, all detectors receive 100% dose independent on the actual value of the dose received). In the relative dose mode with normalization set to the maximum value, only underdose-like discrepancies can be obtained (and tested) by definition.
A plan with a steep dose gradient offers high sensitivity in testing the effect of geometrical errors on the passing rates. We used a plan where the dose gradient is set by 60˚ enhanced dynamic wedges. For simplicity, we only tested the axial direction for shift-type errors. The dose profile of the gradient plan plotted in
Our protocol relies on calculations of the passing rates constrained to the ROIs. When using software that does not allow such, to maintain the constant dose gradient during analysis of the dose gradient plan, one could increase the minimum dose threshold, TH, to about 60%, and shift the ArcCHECK such that the peak of the dose profile (see
Accurate calibration of ArcCHECK is very important in achieving satisfactory results, as any inaccuracy will introduce an error to the measured dose distribution. While our refined calibration procedure differed slightly from the manufacturer’s recommendation, the refined method is consistent with the instructions in the manufacturer's note (ArcCHECK TPS Phantom Setup and Calibration, Sun Nuclear Inc, Melbourne, FL), and is similar to the calibration described by Kozelka [
The results are not expected to be significantly affected by slight beam asymmetry, because field sizes much smaller than the maximum beam opening were used.
Use of “measurement uncertainty” option during calculations of the gamma indices has been discussed by Nelms et al. [
Use of fractional values for the criteria in the gamma index requires some clarification. According to the manual, there are no restrictions on the % dose criterion. For the mm‑criterion fractional values are permitted, but their interpretation is limited. Upon searching for the distance to agreement, the grid is interpolated, and the fractional values of the mm criterion are used. When the dose to agreement criterion fails, the full definition of the gamma index is used, and only dose points on the 1 mm square grid are inspected. Consequently, the well- defined values are: 1 mm, 1.5 mm, 2 mm, 2.3 mm, 2.9 mm, 3 mm, etc.
The formalism presented here is applicable to various detector arrays, not just ArcCHECK, as long as the passing rates are calculated based on the gamma index, e.g. film data or 2D data measured with MatriXX. The baseline plans need to be modified accordingly to provide dose distribution appropriate for the given geometry, e.g. the dose distributions need to be uniform or have constant gradient in a plane, not on a cylindrical surface, for measurements with 2D instruments like MatriXX. Use of the formalism in systems which calculate the dose distributions in entire 3D space, not just on a cylindrical surface, is possible too. Again, the plans need to be modified accordingly to provide uniform dose or dose gradient in a 3D structure corresponding to the investigated detector array. The parameters equivalent to those listed in
The recommended workflow for commissioning-style analysis (for ArcCHECK) is as follows: After calibration of the instrument (on the same day as the subsequent measurements), deliver the uniform-dose plan when absolute-dose measurements are desired for routine QA, or the quasi-uniform dose plan for relative-dose measurements. Decide which other program options will be used, and we recommend disabling the “measurement uncertainty”. Inspect the dependence of the passing rates on the %dose criterion (
Instead of analyzing a large number of clinical plans, we performed only two measurements with baseline-type plans to identify the optimum criteria for gamma analysis of dose distributions measured with a detector array (ArcCHECK), see the recommended workflow described in Discussion. We validated the corresponding passing rates against the theoretical prediction. We used a uniform (or quasi-uniform) dose plan to examine the influence of the dose error on the gamma rates, and a steep gradient plan to test the influence of shifts on the gamma rates. We identified a set of single-number parameters that quantify performance of detector arrays, and we identified optimum gamma-index criteria from the baseline plans. We observed that introduction of delivery errors equal in magnitude to the corresponding criterion (% or mm) did not guarantee detection of artificially introduced errors by all the detectors of the array. Instead, we determined the minimum errors that would be detected by all detectors of the array. We discussed the impact of selected program options (in SNC Patient) on the passing rates. This protocol can be applied to other detector arrays, provided the baseline plans are modified as dictated by the topology of the detector array.
Stanislaw Szpala,Kirpal Kohli, (2015) Gamma-Index Passing Rates in Baseline Plans Measured with a Detector Array. International Journal of Medical Physics, Clinical Engineering and Radiation Oncology,04,326-337. doi: 10.4236/ijmpcero.2015.44039