Sum signal dosimetry: A new approach for high dose quality assurance with Gafchromic EBT3

Abstract Gafchromic EBT3 film dosimetry in radiosurgery (RS) and hypofractionated radiotherapy (HRT) is complicated by the limited film accuracy at high fractional doses. The aim of this study is to develop and evaluate sum signal (SS) film dosimetry to increase dose resolution at high fractional doses, thus allowing for use of EBT3 for dose distribution verification of RS/HRT treatments. To characterize EBT3 dose–response, a calibration was performed in the dose range 0.44–26.43 Gy. Red (RC) and green (GC) channel net optical densities were linearly added to produce the SS. Dose resolution and overall accuracy of the dosimetric protocol were estimated and compared for SS,RC, and GC. A homemade Matlab software was developed to compare, in terms of gamma analysis, dose distributions delivered by a Cyberknife on EBT3 films to dose distributions calculated by the treatment planning system. The new SS and conventional single channel (SC) methods were compared, using 3%/1 and 4%/1 mm acceptance criteria, for 20 patient plans. Our analysis shows that the SS dose–response curve is characterized by a steeper trend in comparison with SC, with SS providing a higher dose resolution in the whole dose range investigated. Gamma analysis confirms that the percentage of points satisfying the agreement criteria is significantly higher for SS compared to SC: 95.03% vs. 88.41% (P = 0.014) for 3%/1 mm acceptance criteria and 97.24% vs. 93.58% (P = 0.048) for 4%/1 mm acceptance criteria. This study demonstrates that the SS approach is a new and effective method to improve dosimetric accuracy in the framework of the RS‐HRT patient‐specific quality assurance protocol.


| INTRODUCTION
The recent technological evolution in radiation therapy has led to the development of new techniques in the treatment of neoplastic lesions utilizing high doses with extremely steep dose gradients and sub-millimeter spatial accuracy. Although such progress has led to the reduction in the dose administered to healthy tissue, the clinical outcome relies heavily on the accordance between the dose calculated by the planning system and the dose actually delivered by the linear accelerator. The complexity of the new techniques thus makes it all the more necessary to evaluate such an accordance in doses.
Radiosurgery (RS) and hypofractionated radiotherapy (HRT) methods employ accurate imaging devices and dynamic delivery techniques to administer tightly conformed dose distributions while monitoring interfraction and intrafraction target positioning during the whole delivery process.
Gafchromic EBT3 films, thanks to their high spatial resolution, their near tissue equivalence, and their weak or absent energy and dose-rate dependence, nowadays represent a widespread tool to assess complex dose distributions in high-precision conformal radiotherapy where fractional doses of~2 Gy are delivered. [1][2][3] The use of Gafchromic EBT3 films in RS and HRT treatments (typical dose/fraction 5-21 Gy) is still under evaluation, as the EBT3 film response to high doses is characterized by a limited dose resolution. The characterization of the physical properties of EBT3 films has been described in detail in many studies for absorbed doses up to 40 Gy. 2,4 However, to our knowledge, the literature lacks information regarding patient dose distribution verification for doses higher than the red channel (RC) working range (~2-3 Gy).
Gafchromic EBT3 dosimetry is typically accomplished by the single channel (SC) method, which consists of using the RC data for doses below 10 Gy, and the green channel (GC) data for higher doses. 2  demonstrated that it produces the same level of accuracy as the RC with pre-irradiation film scan. 7 The aim of this study is to propose and validate a new and comprehensive dosimetric approach, by implementing the sum signal (SS) method in order to increase the film sensitivity at high doses, thus allowing the use of EBT3 for RS and HRT patient-specific quality assurance (QA).

2.A | IMAGE PROCE SSIN G
In order to use Gafchromic EBT3 films for absolute dosimetry, a preliminary dose calibration step was performed by irradiating 2.8 9 2.8 cm 2 film pieces (batch #AO40411301) with a 6 MV photon beam.
Films were arranged in a solid water slab phantom, 5 cm deep from the phantom surface with a 15 cm solid water layer placed to produce backscattered radiation, and exposed perpendicularly to the Cyberknife beam axis (isocentric setup, source to axis distance = 80 cm, collimator diameter = 6 cm). An absolute dose measurement during irradiation was contextually performed according to IAEA TRS 398 protocol. 8 An ionization chamber (Farmer FC65-P, Scanditronix Medical AB, Uppsala, Sweden) was located 7 cm deep from the phantom surface and the chamber reading was then scaled to the film depth by applying a previously measured conversion factor. Two different films were simultaneously irradiated for each dose value in a range of 0.44-26.43 Gy.
The calibration films were digitized with the commercial flatbed scanner EPSON Expression 10000XL (Seiko Epson Corp, Nagano, Japan) before and 1 day after irradiation, with an image resolution of 150 dots per inch according to published recommendations. 4,9,10 The scanner was always turned on at least 30 minutes before use and five preliminary scans without film on the scanner bed were performed in order to minimize the impacts of scanner noise and warmup effects of the scanner lamp. 9,11 Scans of the unirradiated and irradiated films were performed by positioning the film in the most uniform scanner region and acquiring the whole plate area in order to minimize the signal dispersion. 12 Digitized images were analyzed using the ImageJ software (v1.39, National Institutes of Health, Bethesda, MD, USA) to obtain the mean pixel values before (PV unexp ) and after irradiation (PV exp ) in a 1 9 1 cm 2 central region of interest (ROI). The obtained results were used to calculate the net optical density (netOD): In our new SS approach, the signal value to be associated with the corresponding calibration dose is given by the linear combination of the netOD values obtained for the red and green channels: Blue channel is not included in equation 2 because its variation in optical density is not dependent on the absorbed dose, a fact which has been widely demonstrated in the literature and confirmed in our preliminary studies. 2,5 The calibration and analysis procedures was repeated with EBT3 films belonging to a new batch (#AO4041203) in order to study the reproducibility of the proposed method. In the specific mathematical formalism of this study, the dose values will be hereafter considered as the dependent variable (y i ) and the signal values (as defined in eq. 1 for RC and GC; and in eq. 2 for SS) as the independent variable (x i ).

2.B | DOSE RESOLUTION ANALYSIS
Considering two consecutive calibration dose values y1 and y2, which differ by the quantity D= |y1-y2|, the minimal detectable dose DΔp is defined as: where k p is a coverage factor equal to 1.96 for a 95% level of confidence and u c (y i ) is the combined standard uncertainty of the dose values, which in local approximation is simply given by 15 :

2.C | DOSE CALIBR ATION
In order to calibrate the film response to dose the choice of the functional form better able to ensure a high accuracy level in the whole dose range investigated is of the utmost importance. Considering the results of published works, five functional forms were compared in this section: one rational function, 5,6 one double exponential function, 16 and three polynomials. 16,17 The comparison was based on the use of the Akaike Information Criterion (AIC), a statistical method which allows to compare different non-nested models on the basis of the best balance between accuracy requirements and number of fit parameters used. 18 According to this criterion, the best fit function is the one showing the lowest AICc value: where k is the number of parameters in the fit function, y i,sper is the dose value measured during the film calibration step, y i,fit is the corresponding dose value obtained by the fit function investigated, and r eff (y i ) is the effective uncertainty: The effective uncertainty r eff (y i ) takes into account the experimental uncertainties r(y i ) associated with the dose values (equal to 1% of the measured value, according to the ionization chamber certificate) and the uncertainties r(x i ) associated to signal values.
For all functional forms investigated, the fit parameters were calculated using the effective variance method, 19 since that the experimental uncertainties r(x i ) and r(y i ) were similar in size.

DOSIMETRIC PROTOCOL
The overall accuracy of the dosimetric protocol developed was investigated for both the SC and SS methods taking into account the various sources for error. 11 In general, the uncertainties associated with the dose verification through the use of radiochromic films can be characterized into three main category sources 16,17 : 1. uncertainties related to the signal value determination (D meas ); 2. uncertainties related to intrafilm and interfilm uniformity (D film ); and 3. uncertainties related to the fit procedure (D fit ); The size of uncertainties for the three sources listed above was assessed and statistically included in this study to obtain and investigate their overall accuracy associated with the dosimetric procedure: The first type of uncertainty (D meas ) includes errors due to the scanning procedure (warm-up effects of the scanner lamp, uniformity and reproducibility in the scanner acquisition) and image analysis procedure (determination of net optical density starting from the pixel values).
In terms of mean percentage error, D meas is equal to: For the SC approach, r(x i ) is the uncertainty associated with the mean netOD value, which is obtained by averaging the netOD values of the two films exposed to the same dose: Each calibration film is affected by an indetermination dnetOD i obtained by applying the error propagation law to Eq. 1 20,21 : where dPV unexp and dPV exp are the uncertainties related to the pixel values for the calibration films before and after the irradiation, respectively. For both methods, this uncertainty is composed of two terms: 1. r A , the experimental uncertainty (type-A error) associated with the scanning measurement (uniformity and reproducibility in scanner acquisition, warming up effects); and 2. r B , the statistical error due to the fact that the pixel values obtained in the calibration step are averaged on 1 9 1 cm 2 ROIs (~160 points).
These two error types were statistically added to produce the pixel value indetermination: By scanning the films in accordance with the recommendations reported in paragraph A, it was possible to evaluate r A equal to 1% of the measured pixel value, 10,12 while r B was obtained by calculating the standard deviation on the 1 9 1 cm 2 ROI.
For the SS method, r(x i ) was obtained by applying the error propagation law to Equation 2: The covariance term r RC,GC (x i ), evaluated according to Equation 14, is present due to the fact that red and green channel values are derived from the same scan, so they have to be considered as correlated quantities. 20,21 where x RC and x GC represent the average net optical density values obtained for the red and green channel, and k is the number of film pieces exposed to the same dose during the calibration step.
The size of the uncertainties related to the interfilm uniformity Finally, the fit uncertainty r fit was determined by the mean percentage error method, namely by computing the average of percentage errors by which our fitting model y i,fit differs from actual values y i,sper : jy i;fit À y i;sper j y i;sper (14) where n is the total number of calibration dose points.

GAMMA ANALYSIS
The new SS method and the conventional SC method were com-

3.A | Calibration curves
The calibration curves obtained simultaneously irradiating the two films belonging to the batch #AO40411301 are shown in Fig. 1 for RC, GC and SS.
The error bars associated with the dose values were calculated using Eq.4.
In Fig. 2, the reproducibility of the curve trends displayed in

3.B | Dose resolution analysis
In Fig. 3  The same conclusion was drawn also from the AICc values deriving from the validation batch. The double exponential function was consequently used to fit the calibration data into our high-dose verification protocol. The addition of the covariance term [see eq. (14)] to the D meas calculation results in the increment of D meas value from 1.12% to 1.30%.

3.E | Film QA verification and gamma analysis
In Table 3 Table 4 shows the mean percentage of c values < 1, between 1 and 1.5, and > 1.5 obtained for the 20 lesions analyzed in this study.
The percentage of dose distribution points with c < 1 is higher for the SS method compared to the SC method: 95.03% vs. 88.41% for 3%/1 mm acceptance criteria, 97.24% vs 93.58% for 4%/1 mm acceptance criteria, respectively. The statistical significance of these differences is confirmed by a P value equal to 0.014 for 3%/1 mm and 0.049 for 4%/1 mm acceptance criteria. Table 5 reports the results obtained for the 20 cGy/1mm gamma analysis limiting film doses from 0 to a threshold value of 4 Gy and considering doses greater than 4 Gy.
The difference between the two methods is statistically significant only for doses greater than 4 Gy. Table 6     Film sensitivity at high doses using the SC approach therefore seems very limited.
In general, signal values for the SS curve are widely spaced, producing a steeper trend and suggesting improved film sensitivity at higher doses with respect to the SC method.
Also, reproducibility was observed in the behavior of films belonging to different batches.
The spillover effect of this increase in sensitivity on the minimal separation of two contiguous doses, at which their most probable values are different within a given level of confidence, is quantified by the dose resolution analysis in the following paragraph.

4.B | Dose resolution analysis
The resolution values illustrated in Figs. 3 and 4 confirm the published data reporting about the red and green channel responses to radiation exposure. In particular, the GC resolution was confirmed to be higher than the RC resolution for doses above 8-10 Gy. 1,4 Provided that dose resolution worsening is taken into consideration, the use of the SS method can be extended to higher dose levels, until saturation effects are observed. These effects were found by Borca et al. to occur from a dose level which varied for each specific channel (38 Gy for RC and above 40 Gy for GC). 4

4.C | Curve fitting
The AIC was chosen in particular as an alternative to the sum of residuals because it also takes into account the effective uncertainties r eff (y i ) and the number of parameters used in the fit function.
It demonstrates that, provided the most appropriate functional form is chosen, four parameters are sufficient to fit the whole film dose-response object of this study. It is therefore possible to adopt the SS method using only four calibration points, as advocated by the film vendor. 5

4.D | Accuracy estimation of the dosimetric protocol
The results obtained in terms of overall accuracy for individual chan- This behavior is confirmed also if we apply the experimental uncertainties reported in Table II to the measured dose distributions (AE 1.98% for the RC, AE 2.45% for the GC, AE 1.79% for the SS), in fact the percentage of c points < 1 decreases by the same quantity (equal to~5% in the 3%/1 mm case and equal to~3% in the 4%/ 1 mm case) for sum signal and single channel.
Furthermore, the analysis of the 20 cGy/1 mm gamma results contained in Table V leads to the conclusion that SS and SC can be considered equivalent at doses lower than 4 Gy, while the SS performs better for doses higher than 4 Gy. The superiority of SS at high doses is confirmed also by the ion chamber measurements in the center of the PTV. In fact, from the data contained in Table VI it can be appreciated that the percentage difference with respect to the estimated dose values is generally smaller for the SS method.

| CONCLUSIONS
In recent years, several protocols have been developed to improve SC film dosimetry accuracy. 2,17 Some focus on the digitization procedures 16,24 while others deal with the assessment of the different uncertainty sources affecting the measurements. 23,27,28 However, the SC reduced sensitivity still limits the accuracy of the resulting dosimetric analyses for high-dose treatment plans.
A different approach to high-dose verifications is to apply a scaling factor to the delivered dose, and reduce it to a value that falls in the film's sensitive range. The problem with this approach lies in the fact that for dosimetry of complex delivery techniques it does not assure the administration of the minimum number of MU needed for the accelerator to achieve a stable output during treatment irradiation. 29 The results of this study confirm the suitability of the SS method applied to EBT3 films for the dosimetry of state-of-the-art precision RS/HRT treatments where multiple beams, delivery angles and LINAC movement are used for optimal dose conformation to the target, and overcoming the limitations of dose scaling or color channel switching procedures.
The concept of dose resolution, used to compare the effectiveness of the SS to the SC approach, also gives valuable information about the accuracy of dose distribution verifications as a function of delivered dose in the clinical evaluation of patient dose distribution QA.
The SS method can thus be considered an effective and promising method to improve dosimetric accuracy in the framework of the RS-HRT patient-specific QA protocol.