Experimental verification of Advanced Collapsed‐cone Engine for use with a multichannel vaginal cylinder applicator

Abstract Model‐based dose calculation algorithms have recently been incorporated into brachytherapy treatment planning systems, and their introduction requires critical evaluation before clinical implementation. Here, we present an experimental evaluation of Oncentra® Brachy Advanced Collapsed‐cone Engine (ACE) for a multichannel vaginal cylinder (MCVC) applicator using radiochromic film. A uniform dose of 500 cGy was specified to the surface of the MCVC using the TG‐43 dose formalism under two conditions: (a) with only the central channel loaded or (b) only the peripheral channels loaded. Film measurements were made at the applicator surface and compared to the doses calculated using TG‐43, standard accuracy ACE (sACE), and high accuracy ACE (hACE). When the central channel of the applicator was used, the film measurements showed a dose increase of (11 ± 8)% (k = 2) above the two outer grooves on the applicator surface. This increase in dose was confirmed with the hACE calculations, but was not confirmed with the sACE calculations at the applicator surface. When the peripheral channels were used, a periodic azimuthal variation in measured dose was observed around the applicator. The sACE and hACE calculations confirmed this variation and agreed within 1% of each other at the applicator surface. Additionally for the film measurements with the central channel used, a baseline dose variation of (10 ± 4)% (k = 2) of the mean dose was observed azimuthally around the applicator surface, which can be explained by offset source positioning in the central channel.

and BrachyVision (Varian, Palo Alto, CA, USA), which uses the grid based Boltzmann solver Acuros TM . 5 For gynecological cancer treatments, the present clinical situation that assumes all materials are composed of water has the potential to introduce errors in dose calculations. [6][7][8][9][10] These errors can potentially cause an undesired increase in radiation dose delivered to organs at risk (OARs: rectum, bladder, and sigmoid colon) or reduced dose to the tumor. In clinical practice it is common for OAR doses to approach their upper limit while trying to achieve acceptable target coverage.
Consequently, calculating OAR doses accurately might be the difference between successful OAR sparing and a radiation-related OAR complication. Furthermore, neglecting attenuation when using applicators with OAR shielding has been shown to overestimate D 2cc rectum and D 2cc bladder by 6.2% and 3.4%, respectively. 8 In addition, Hyer et al. reported that Acuros TM yielded a dose difference of approximately 2% relative to TG-43 when both tissue and applicator heterogeneities were considered based on planning CT images. 9 The prospect of bringing brachytherapy dose calculation accuracy up to the level of that of EBRT is very appealing. However, improved dose calculation accuracy does not necessarily equate to clinical benefits, and also requires longer calculation times. Therefore, it is important to critically evaluate and commission the MBDCAs both computationally and experimentally until their performance and contribution is established for a given treatment procedure. 11 As stated above, the use of MDBCAs has been investigated for some gynecological applicator models; e.g., tandem-ovoid [6][7][8][9] and tandemring applicators. 10 However, the performance of MDBCAs has not yet been reported for a multichannel vaginal cylinder (MCVC). Therefore, we present an experimental evaluation of OcB ACE v4.5 for a MCVC applicator using radiochromic film measurements. This evaluation focuses on ACE's ability to predict dose variations at the applicator surface caused by applicator-based heterogeneities. Differences between ACE calculated doses and the current clinical standard (TG-43) are used to evaluate the clinical implications of using ACE to predict heterogeneity-induced dose variances. The thorough and valid evaluation of ACE required confirmation that the expected MCVC dimensions corresponded to the physical MCVC applicator, which was performed using micro-CT imaging.

2.A | Film, applicator, and Oncentra â Brachy
All film measurements were performed using Gafchromic TM EBT3 film (Ashland Specialty Ingredients, Wayne, NJ, lot #03181303 and #04201501). EBT3 has a 28 lm thick active layer of lithium pentacosa-10,12-dyinoic acid, and has a total thickness of 0.27 mm. 12 The film calibration curves were determined using a tube may be inserted into the MCVC to provide a central channel.
There are two 5 mm deep grooves on the outside of the applicator where a perineal bar can be attached to provide fixation ( Fig. 1(b)).
The grooves begin 60 mm from the tip of the applicator. The majority of the applicator is composed of polyphenylsulfone (PPSU) plastic, which has a mass density of 1.29 g/cc.  4 A few of the key principles will be described here. ACE calculates dose as the sum of contributions from primary photons, once-scattered photons, and any residual scattering. The primary dose is calculated using a ray trace of the primary photons in a grid, which generates scatter energy that is input into the collapsed cone superposition convolution (CCSC) algorithm. CCSC utilizes angular discretization of radiation transport directions and pre-calculated dose deposition point kernels in water, scaled to reflect the influence of inhomogeneities. 13 The transport directions are a uniform spherical tessellation around each scattering center. [14][15][16] In ACE, high (hACE) and standard (sACE) accuracy calculation modes use different numbers of transport directions for first scatter and residual scatter components. 4,16 When a single dwell position is used, hACE calculates the scatter dose using 1620/320 first/residual scatter transport directions, and sACE uses 320/180 first/residual scatter transport directions. The number of transport directions decreases as the number of dwell positions increases. To speed up the calculations, multiple calculation grid resolutions are used. The white paper from Elekta 2 defines the grid resolution in terms of a voxel size, however, it will be referred to as the "grid size" in this paper. The grid sizes used in ACE calculations depend on the distance from each dwell position. To determine the grid size, ACE first defines a box that contains all the dwell positions. A margin is then added to that box, which contains a particular grid size. For example, hACE has a 1 mm grid size up to 80 mm from a dwell position in the x, y, and z directions, when more than one dwell position is used. Table 1 gives the margins and corresponding grid sizes for the hACE and sACE calculations, which also apply to the primary dose ray trace.

2.B.1 | Calibration of film
The radiochromic film calibration curves were determined using a 6 MV linac beam for each film batch. EBT3 film has been shown to be energy independent for photons with energy greater than 50 keV, therefore, the use of the 6 MV beam for calibration purposes is valid. 17,18 Pieces of film, 4 9 4 cm 2 in size, were irradiated at 13 dose levels between 0 and 10 Gy. The linac output was measured with an ion chamber (Capintec PR-06, Ramsey, NJ, USA) before and after the film irradiations, and the intended dose levels were corrected with a multiplicative factor equal to the measured output divided by the expected output. The irradiations were performed in a 10 9 10 cm 2 beam at 100 cm source-to-axis distance within 20 9 20 cm 2 slabs of solid water. The films were irradiated at the depth of maximum dose by placing a build-up of 1.5 cm of solid water above the film; 12 cm of solid water was placed below the film for backscatter. The film was scanned with an Epson Expression 10000 XL scanner (Seiko Epson Corp., Nagano, Japan) at 72 dpi, 48-bit RBG color (16-bit per color), and the scans were saved as tagged image file format images. For each color channel, fitting parameters a, b, and c in Eq. (1) were determined by the non-linear least squares effective variance method solved by direct optimization as described by Ramos and Azorin. 19 In Eq. (1), X(D) is the normalized film response in relative pixel values (PVs) (measured PV divided by maximum PV 65535) and D is the dose in cGy. The optical density (OD) was then determined by Eq. (2).
To perform measurements of unknown doses, triple channel analysis was used, wherein the dose determined from each channel was corrected for film thickness heterogeneities using an iterative approach.
Uncertainties in the film measurements follow from the uncertainty principles outlined in the NIST Technical Note 1297, 20 and implemented by Morrison et al. 21 and Chiu-Tsao et al. 22 The final dose was taken as a weighted mean using the relative uncertainties associated with each channel. Details pertaining to the uncertainty calculations are described in the Appendix. Film measurements were made at the surface of the MCVC applicator by wrapping a 20 cm long film piece around the outside of the applicator. The film was held in place with a 3 mm thick acrylic cylindrical sleeve whose inner radius was 0.5 mm larger than the applicator. Irradiations using the MCVC applicator were performed in a 30 9 30 9 30 cm 3 water tank with the applicator oriented vertically (Fig. 2). The dose was delivered to the film under two conditions: the applicator was either placed in the water prior to being inserted into the film and sleeve to ensure the applicator grooves were filled with water, which will be referred to as the "water-in-grooves" set-up in this paper, or the film and sleeve were applied to the applicator prior to insertion into the water and a tight waterproof latex sleeve was placed around the applicator to ensure water did not enter the grooves, which will be referred to as the "air-in-grooves" set-up.
For dose values obtained from the film measurements, an inverse square (IS) correction was applied to account for the thickness of When an average dose was calculated, the associated type A uncertainty was added in quadrature with the uncertainty arising from use of the derived calibration curve. 21,22 All uncertainties are stated with a coverage factor of 2 (k = 2). The averaged dose profiles were also used to obtain values for dose variations across the surface of the applicator: the maximum dose variation was calculated as the difference between the minimum and maximum doses; the size of the largest peak refers to the height of the dose difference observed at the surface of the two grooves in the applicator; and the baseline variation is the difference between the minimum and maximum doses at locations other than the peaks at the grooves or peripheral channels of the MCVC.

2.C | Micro-CT imaging
To fairly assess ACE using experimental film measurements, the

2.D | TG-43 and ACE dose calculations
The dose on the surface of the applicator was investigated with the same prescriptions points used to specify the dose in the experimental plans. The surface dose was averaged at nine locations along the length of the applicator for each angle, covering a span of 40 mm centered in the area that the dose was specified to. The uncertainty for individual dose points calculated using the TG-43 formalism was taken to be 3.4%. 23 The uncertainty associated with ACE calculated doses was estimated from analyses by others to be 5%. 24,25 When average doses were calculated from TG-43 or ACE data, the associated type A uncertainty was added in quadrature with the 3.4% or 5% type B uncertainty, respectively. All uncertainties are stated with a coverage factor of 2 (k = 2). These uncertainties are further described in the Appendix. The averaged dose profiles were also used to obtain values for dose variations across the surface of the applicator: the maximum dose variation was calculated as the difference between the minimum and maximum doses; peak dose increases were calculated by subtracting the average dose for dose points not at peaks from the dose at the peak.  loaded. For the measurement in Fig. 3(b), the outer grooves were filled with water, and no distinct dose increases are visible above the grooves. In contrast, Fig. 3(a) shows the film measurements with air in the grooves, where an (11 AE 8)% increase in dose (i.e., the size of the largest peak) is seen just above the two grooves on the outside of the applicator. Fig. 3(c) and 3(d) show the film results for the irradiations performed using the peripheral channels of the MCVC, with air and water in the grooves, respectively. The maximum dose variation for the air-in-grooves setup was 3% less than the variation produced when the central channel was loaded ( Fig. 3(a)). Additionally, the variation was more gradual. For the peripheral channel loading, the surface dose is very similar for the air-in-grooves and water-ingrooves set-ups.

3.B | Micro-CT imaging
The lCT images of the MCVC applicator (Fig. 4) Table 3. There was a measured increase of (11 AE 8)% of the mean dose at the surface of the applicator above the two outer grooves, when they were filled with air, and the central channel was loaded. This dose increase was also observed with hACE calculations and was (6 AE 8)% of the mean dose ( Fig. 6(a)). sACE did not predict a dose increase above the two outer grooves to points that are on the surface of the applicator, but did predict a dose increase of 6% at a distance of at least 1 mm off the surface of the applicator, as seen in Fig. 5(b). When the calculation was performed using sACE-20 mm, such that the grid size at the surface of the applicator is 1 mm, a (6 AE 8)% increase in dose was seen at the surface of the applicator (Fig. 6(a) ing may be desirable when the catheter diameter is significantly larger than the source. 26,27 T A B L E 3 Variations in the longitudinally averaged dose around the circumference of the MCVC applicator calculated using TG-43, sACE, sACE-20 mm, hACE, and measured using film. Percentages are relative to the mean dose and are given in parentheses. Expanded (k = 2) uncertainties are given.  Lastly, all of the film measurements and ACE calculations yielded average doses 3-7% less than the doses calculated using TG-43, but none of these differences were statistically significant.
The radiation oncologists at our clinic advise that a localized increase in dose of 11%, as observed above the two outer grooves when filled with air, would not constitute a significant clinical concern on its own. However, if the dose variation was greater than 20%, which is possible when combining the peak dose increase and baseline dose variation, it may necessitate adjustment of the plan.
Another consideration that may contribute to a larger dose variation is the presence of air pockets surrounding the applicator. [28][29][30] When considering TG-43 calculations alone, it was found that 11 of 174 (6.3%) patients were underdosed by an average of 6.1% of the prescribed dose due to displacement of the vaginal mucosa by air gaps. 28 A phantom study by Maxwell et al. 31 found that TG-43 slightly underestimates the dose due to the inhomogeneity caused by the presence of airthe dominant effect is a decreased dose to tissue due to increased distance from the source.

4.B | sACE and hACE calculations
The difference between sACE and hACE calculations for the MCVC was dependent on whether the central channel or peripheral channels were loaded. As previously stated in section 4.A, the hACE calculation predicted an increase in dose above the two grooves on the surface of the applicator, whereas the sACE calculation did not due to the larger calculation grid size. In general, sACE was observed to compute lower doses than hACE, for the majority of the dose points, relative to TG-43 (Fig. 5). The lower doses computed by sACE can be explained by the "ray effect", which was investigated for ACE by Ma et al. 32 In collapsed-cone convolution algorithms, energy is transported along the axis of a cone-shaped scatter kernel. When the radius of the kernel is larger than the grid size, too much energy is deposited along the central axis, thereby overestimating the dose to those grid points, and underestimating the dose to the majority of the grid points lying between the axes. The ray effect is less pronounced in the hACE calculation because the number of transport directions for primary scatter is 720 whereas sACE uses 320. Therefore, sACE has a tessellation triangle that covers an area over twice the size of the hACE triangle, but the grid size of sACE is exactly twice the size of hACE on the surface of the applicator, resulting in the sACE cone containing relatively more grid elements than the hACE cone. When the peripheral channels of the applicator are used, sACE and hACE have a 1 mm grid size at the surface of the applicator and predict similar doses to the surface of the applicator that are less than 1% different. The peripheral channels are also much closer to the surface of the applicator; therefore the opening area of the cone is smaller, which will reduce the ray effect. Additionally when the peripheral channels are used, and despite the hACE calculation having approximately twice the number of primary scatter transport lines than sACE, the numerous dwell positions "wash-out" the ray effect for the sACE calculation. This occurs due to overlapping transport lines from the many dwell positions. 32

| CONCLUSION
Triple channel radiochromic film dosimetry was performed to verify Oncentra â Brachy ACE v4.5 calculations for a multichannel vaginal cylinder applicator, and comparisons between TG-43 and ACE dose calculations were used to evaluate the clinical significance of applicator-heterogeneity-induced dose variations. High accuracy ACE dose calculations were found to agree with film measurements when just the central channel of the applicator was loaded and when just the peripheral channels of the applicator were loaded.
Standard accuracy ACE dose calculations did not predict an increase in dose to the applicator surface above two outer applicator grooves when they were filled with air, and TG-43 calculations cannot predict this increase, therefore high accuracy ACE is recom-

ACKNOWLEDG MENTS
The authors would like to acknowledge Dr. Hans-S€ onke Jans for his assistance in obtaining the micro-CT images, the Wuest group at the Cross Cancer Institute for providing access to the micro-CT scanner, the staff of the Cross Cancer Institute machine shop for construction of the applicator mount and sleeve, and Yury Niatsetski and Bob van Veelen from Elekta for their advice on the use of ACE.

CONFLI CT OF INTEREST
The authors have no relevant conflicts of interest to disclose. Morrison et al. 21 The combined uncertainty from the measured optical density (r OD ), the calibration curve parameters (r A , r B , r C ), and the reference linac doses (r Dref ), gives the total uncertainty for a single dose measurement (D) and a single color channel (C1): Propagation of calibration curve uncertainty by weighting the dose with uncertainties associated with each color channel, and using triple channel analysis Let r D,C1 , r D,C2, and r D,C3 be r i for i = 1, 2, 3 = C1, C2, C3.
Let k = single color channel.
The weight (w) for the dose (D), determined by the calibration curve for each color channel, is given by Eq. (A2). The total weighted dose (D w ) is given by Eq. (A3).
The uncertainty of the weighted dose is given by: The uncertainty from the triple channel analysis is given by: The total uncertainty for the weighted dose determined from the calibration curves and triple channel analysis is the quadrature sum of the triple channel uncertainty and weighted dose uncertainty. The total uncertainty for a single film pixel will henceforth be referred to as the type B film uncertainty: Resulting uncertainty in average value of dose made from multiple dosimetric measurements The type A uncertainty associated with averaging N pixels that have a standard deviation in dose r D :