Evaluation of the dosimetric impact of manufacturing variations for the INTRABEAM x‐ray source

Abstract Introduction INTRABEAM x‐ray sources (XRSs) have distinct output characteristics due to subtle variations between the ideal and manufactured products. The objective of this study is to intercompare 15 XRSs and to dosimetrically quantify the impact of manufacturing variations on the delivered dose. Methods and Materials The normality of the XRS datasets was evaluated with the Shapiro–Wilk test, the accuracy of the calibrated depth–dose curves (DDCs) was validated with ionization chamber measurements, and the shape of each DDC was evaluated using depth–dose ratios (DDRs). For 20 Gy prescribed to the spherical applicator surface, the dose was computed at 5‐mm and 10‐mm depths from the spherical applicator surface for all XRSs. Results At 5‐, 10‐, 20‐, and 30‐mm depths from the source, the coefficient of variation (CV) of the XRS output for 40 kVp was 4.4%, 2.8%, 2.0%, and 3.1% and for 50 kVp was 4.2%, 3.8%, 3.8%, and 3.4%, respectively. At a 20‐mm depth from the source, the 40‐kVp energy had a mean output in Gy/Minute = 0.36, standard deviation (SD) = 0.0072, minimum output = 0.34, and maximum output = 0.37 and a 50‐kVp energy had a mean output = 0.56, SD = 0.021, minimum output = 0.52, and maximum output = 0.60. We noted the maximum DRR values of 2.8% and 2.5% for 40 kVp and 50 kVp, respectively. For all XRSs, the maximum dosimetric effect of these variations within a 10‐mm depth of the applicator surface is ≤ 2.5%. The CV increased as depth increased and as applicator size decreased. Conclusion The American Association of Physicist in Medicine Task Group‐167 requires that the impurities in radionuclides used for brachytherapy produce ≤ 5.0% dosimetric variations. Because of differences in an XRS output and DDC, we have demonstrated the dosimetric variations within a 10‐mm depth of the applicator surface to be ≤ 2.5%.


| INTRODUCTION
The INTRABEAM ® (Carl Zeiss Meditec AG, Oberkochen, Germany) x-ray source (XRS) is an innovative electronic brachytherapy device used for intraoperative radiation therapy (IORT) delivery in clinical trials such as the TARGeted Intraoperative radioTherapy (TARGIT) for breast cancer or the INTRAoperative radiotherapy for glioblastoma multiforme (INTRAGO). 1 This XRS produces 40-kVp and 50-kVp energy x-rays at the tip of a needle-like probe, which may be used with a sterile catheter for kypho-IORT to treat spinal metastasis or with spherical applicators to treat the inner surface of the breast lumpectomy cavity or brain tumor bed. These rigid spherical applicators have 7.5-to 25.0-mm radiuses with 2.5-mm increments. After removing the tumor, an appropriately sized spherical applicator is placed in the tumor bed and secured into position using a pursestring suture. Radiation is delivered to the tissue surrounding the spherical applicator to treat neoplastic cells and reduce the risk of recurrence. 1 Although each INTRABEAM XRS has the same design, the output and the shape of the depth-dose curve (DDC) for each XRS can vary because of manufacturing variances in the thickness of the gold x-ray target and electron source. 2, 3 INTRABEAM system users commented on source-to-source variations using sample sizes of 2-4 XRSs, [3][4][5] but no report has estimated the dosimetric impact to the patient resulting from these variations. Armoogun et al. 5 presented a functional inter-source comparison of four photon radiosurgery system XRSs, the predecessor design to the current INTRABEAM 500. Their study used an in-house water phantom and a Physikalisch Technische Werkstaetten (PTW) model 23342 parallel-plate ionization chamber to acquire a DDC for these four XRSs. Given the small sample size and lack of measurement uncertainty analysis, no meaningful statistical analysis was performed.
Since the publication of the Armoogun et al. 5  Because radionuclides and electronic XRSs are manufactured to perform brachytherapy, we seek to evaluate if manufacturing variations of XRSs can produce ˃ 5% dosimetric variations.
The objective of this study is to perform an intercomparison of 15 INTRABEAM XRSs to understand output variations of the manufactured product and to dosimetrically characterize the impact that these variations have on the tumor bed dose. First, a parallel-plate ionization chamber was used to perform a calibration consistency check of the vendor-provided DDC. Once validated, the DDC was used to evaluate variations in the output at 5-, 10-, 20-, and 30-mm depths from the XRS, and variations in the shape of the DDCs were evaluated using D 3/5 , D 5/10 , D 10/20 , and D 20/30 depth-dose ratios (DDRs) .

2.A | Device description
The system consists of a mobile floor stand, which is a counterbalanced arm designed to support a miniature x-ray generation unit.
Radiation is generated when the mobile x-ray unit accelerates a beam of electrons from the gun, down a drift tube, and then toward a thin hemispherical gold target of 1-µm (0.001 mm) thickness. 6 At the base of the drift tube are steering coils, which oscillate the beam around the tube axis in a process called "dithering" in order to create a "nearly isotropic" output. 7,8 High-voltage electronics and an internal radiation monitor, which tracks radiation output, are stored within the base of the XRS. An example of an INTRABEAM XRS is shown in Fig. 1. The output characteristics, spectrum, and features of the INTRABEAM system have been described. [9][10][11][12] 2.B | Calibration and specialized Zeiss water phantom Zeiss calibrates the INTRABEAM system using the setup published by Beatty et al. 11 Per this setup, a DDC is measured from the XRS for 3-to 45-mm depth in steps of 0.5 mm as shown in [ Fig. 2(A)]. The depth from the XRS is denoted z and the dose-rate in water from the XRS _ D w z ð Þ is expressed as shown in Eq. 1. ionization chamber calibration coefficient is N k . The conversion factor for differences between the T30 reference x-ray beam quality and the INTRABEAM XRS beam quality is K Q . The uncertainty in K Q was estimated by Watson et al. 13 by simulating the PTW model 34013 parallel-plate ionization chamber using reference kilovoltage photon beam qualities provided by the National Metrology Institute of Germany (PTB, Germany). They noted the difficulties in modeling the parallel-plate ionization chamber and the significant-measurement uncertainties. Thus, it is estimated that K Q = 1 ± 0.025, but a value of unity is used for K Q in this study to be consistent with the recommendations of the vendor. 14 Lastly, the conversion factor from air-kerma to dose to water is K Ka!Dw ¼ 1:054, which is reported on the chamber calibration certificate.
To estimate the perturbation to the x-ray beam and dose fall-off, when a spherical applicator is attached to the x-ray probe, the output of the source is multiplied by an applicator transfer function ATF (z). For depth z ≥ radius of the spherical applicator, the ATF (z) is a ratio of the dose-rate to water with the spherical applicator attached _ D wÀA z ð Þ; over the dose-rate to water without the spherical applicator _ D w z ð Þ as shown in Eq. 2.

2.C | Treatment time and dose
For the INTRABEAM system, treatment planning is performed using a manufacturer-provided calibration DDC. 11,18 This device is not characterized using either the AAPM TG-43 or AAPM TG-61 protocols. 2 Thus, the treatment time in minutes is calculated as shown in The dose at depth z is calculated with Eq. 4.
In this study, we compute the dose at 5-mm and 10-mm depths from the spherical applicator surface as shown in [ Fig. 2 Because the spherical applicators have a 7.5-to 25.0-mm radius, the z = the applicator radius plus the 5-mm or 10-mm depths.
For example, a 7.5-mm radius applicator would have z = 7.5 mm + 2.D | The shape of the depth-dose curve (DDC) The DDC of each XRS has a unique slope. The variability in slope is evaluated using the format D x=y , which is a ratio of dose-rate in Gy/minute at a depth x in mm divided by dose-rate in Gy/minute at a depth y in mm. In this study, we consider four different ratios:

2.E | Uncertainty of measured dose
The mean positional deviation in measurement for a single XRS at a depth Δ _ D w z ð Þ is calculated by Eq. 5.
The dose-rate in water at depth z is represented by _ D w z ð Þ; thus, the dosimeter readings more proximal and distal to the source can be represented by tively. The ± 0.1-mm chamber offset was chosen because it was consistent with the reported tolerance for the Zeiss water phantom. 13 In this study, the estimation and propagation of uncertainty followed the outline of the International Organization of Standardization (ISO) in their guide to the expression of uncertainty in measurement (GUM). The uncertainty in the measured dose σ for an XRS using the Zeiss method σ Zeiss k¼1 ð Þ can be expressed in Eq. 6.
The standard deviation (SD) of the mean σ rep is estimated from three chamber measurements. The chamber calibration factors (i.e.,

2.F | X-ray source (XRS) evaluation
The straightness of the probe influences the isotropy of the radiation field produced by the XRS. We evaluated the isotropy of an XRS with a fixed geometry attachment known as the photodiode array (PDA), which measures radiation output with five diodes. Deviations in output are corrected by fine-tuning the voltage applied to the steering coils during the dynamic offset check. 9 If the isotropy exceeds ± 6%, a mechanical hammer is used to straighten the probe.
The probe adjuster ion chamber holder (PAICH) attachment supports a thin-window parallel-plate ionization chamber to verify XRS output.

| RESULTS
The dose-rate as a function of the depth around the XRS is characterized to commission a new source in the clinical treatment planning system. Figure 4 presents the output characteristics for 15 XRSs on a logarithmic scale for 40-kVp and 50-kVp energies. The dose gradient near the XRS is very steep; thus, the separation between the parallel-plate ionization chamber and x-ray source must be known to high accuracy. The reported accuracy of the Zeiss water phantom is ± 0.1 mm. 13 Using the DDCs, we considered the change in measured dose-rate for a ± 0.1 mm chamber offset at 5-, 10-, 20-, and 30-mm depths from the source and for 40-kVp and T A B L E 1 Comparison of the change in measured dose-rate for a ± 0.1-mm chamber offset using the DDC.       Table 4.
We observed that the CV of the DDRs generally decreased as depth increased.
Because our dataset satisfied the Shapiro-Wilk normality conditions as demonstrated in Appendix B, the mean dose-rate, SD, and SE were reported in Table 5  When 20 Gy is prescribed to the surface of the applicator, the dose to the tumor bed (i.e., 5 mm and 10 mm from the applicator surface) will vary because of the shape of the DDC. Table 6 summarizes   Coefficient of variation (CV) reported to one decimal place per consensus guidelines.
c D x/y is the ratio of dose-rate in Gy/minute at depth x in mm divided by the dose-rate in Gy/minute at depth y in mm.
T A B L E 5 The mean dose-rate, SD, and SE for the DDC for the 3.0-to 45.0-mm depths from the source for the 40-KVp and 50-kVp energies.

| DISCUSSION
The primary purpose of this study was to investigate source-to-   Table 3. Unlike previous studies, this study has a larger sample size of 15 XRSs and presents novel DDRs. While it is beyond the scope of this paper to speculate on the reasons for the observed differences, it has been previously suggested that the dose-rate differences are attributed to the variability in target size, and small changes in other x-ray generation structures (i.e., electron source). 3

| CONCLUSION
The accuracy of the dose delivery influences both the benefits and the risks of radiotherapy. AAPM TG-167 requires that the impurities in radionuclides used for brachytherapy be limited to ≤ 5% dosimetric impact. This study demonstrated the variability in output characteristics of an XRS within a 10-mm depth from the applicator surface and that the maximum dosimetric effect of these variations was ≤ 2.5%. In general, the dosimetric impact of manufacturing variations increased as applicator size decreased and as the depth from the spherical applicator surface increased.

ACKNOWLEDG MENTS
The authors would like to offer a sincere thank you to Robin Scott, BS, CMD, RT(T) for diligently proofreading our paper.

CONFLI CT OF INTEREST
The authors declare no conflicts of interest.