Off‐axis dose distribution with stand‐in and stand‐off configurations for superficial radiotherapy treatments

Abstract Current practice when delivering dose for superficial skin radiotherapy is to adjust the monitor units so that the prescribed dose is delivered to the central axis of the superficial unit applicator. Variations of source‐to‐surface distance due to patient’s anatomy protruding into the applicator or extending away from the applicator require adjustments to the monitor units using the inverse square law. Off‐axis dose distribution varies significantly from the central axis dose and is not currently being quantified. The dose falloff at the periphery of the field is not symmetrical in the anode–cathode axis due to the heel effect. This study was conducted to quantify the variation of dose across the surface being treated and model a simple geometric shape to estimate a patient’s surface with stand‐in and stand‐off. Isodose plots and color‐coded dose distribution maps were produced from scans of GAFChromic EBT‐3 film irradiated by a Gulmay D3300 orthovoltage x‐ray therapy system. It was clear that larger applicators show a greater dose falloff toward the periphery than smaller applicators. Larger applicators were found to have a lower percentage of points above 90% of central axis dose (SA90). Current clinical practice does not take this field variation into account. Stand‐in can result in significant dose falloff off‐axis depending on the depth and width of the protrusion, while stand‐off can result in a flatter field due to the high‐dose region near the central axis being further from the source than the peripheral regions. The central axis also received a 7% increased or decreased dose for stand‐in or stand‐off, respectively.

anode-cathode axis, but the reduction is asymmetrical due to the heel effect. Therefore, there is variation in dose distribution across the treatment field which should be quantified.

Stand-in occurs when some part of a patient's anatomy pro-
trudes inside an open-ended applicator. Stand-off is a situation where the shape of the patient's anatomy results in a cavity between the reference plane at the end of the applicator and the patient's surface. Surface area of 90% (SA90) dose is a parameter defined in this study to describe the percentage of surface area inside an applicator which exceeds 90% of the dose at the central axis. This is useful as it allows a sense of what proportion of the treatment field is being underdosed. Figure 1 displays the patient geometry and surface area dose parameter graphically.
Previous studies [3][4][5][6][7][8] have almost exclusively focused on dose variation with stand-off at the central axis. While this shows that dose varies with stand-off, it neglects the additional dose variation off-axis which is compounded by the loss of dose due to increased source to surface distance (SSD). Also, many studies such as Gerig et al. 3

and
Gräfe et al. 4  both open-ended and closed-ended applicators but did not investigate stand-in. Li et al. 5 used two open-ended applicators, a 4 cm circular cone and an 8 × 8 cm 2 square cone, at 100 and 300 kVp. The closed-ended applicators were square cones of 10 × 10, 12 × 12, and 20 × 20 cm 2 . Dose was measured at certain stand-off distances for each energy and applicator combination. Their findings suggest that open-ended applicators show no clinically significant variation from dose calculated by adjusting for the inverse square law (ISL) up to 15 cm stand-off. For closed-ended applicators, exceeding 1 cm stand-off at 100 kVp results in clinically significant dose variation from that calculated with the ISL. Here, clinically significant is deemed as variance exceeding 5%, as stated by the International Commission of Radiation Units and Measurements. 9 Evans et al. 7  In vivo measurements were taken by Palmer et al. 8 using micro silica beads as thermoluminescent detectors (TLDs). They found that in half of the patient treatments investigated, off-axis dose exceeded 5% variance relative to the central axis dose. To the best of the author's knowledge, this study is the only previous study in the literature that has any investigation of dose off-axis, highlighting the need for investigation into dose off-axis relative to the central axis in kilovoltage radiotherapy. This is the closest study found in the literature to the investigation undertaken in this paper. This study aims to quantify the variability of dose off-axis and produce isodose plots similar to those produced for megavoltage photons and electrons.
This dose quantification will further knowledge of superficial treatment fields in order to determine if adjustments to current treatment planning practice are required for superficial treatments.

2.A | Superficial treatment unit
The treatment unit used in this study was a Gulmay D3300 orthovoltage x-ray therapy system which can produce beam energies from 40 to 300 kVp. Two beam energies, 100 and 140 kVp, and seven

2.B | Film calibration
Before performing measurements, it is necessary to calibrate the GAF-Chromic EBT-3 film 10 at the kilovoltage beam energies in use. It was decided to calibrate at 100 kV only as previous studies established that the energy dependence of GAFChromic EBT-3 film between 100 and 140 kVp was negligible. 11,12 The calibration required a range of dose values which was achieved by irradiating from 10 to 1000 MU. The absolute dose delivered was then calculated by multiplying the delivered dose by the applicator factor determined during commissioning. Next, the scanned film was imported into the FilmQA Pro 10 software as a "Film Calibration (Ordinary)" file. The exposed regions and an unexposed region were selected as regions of interest and a dose value was assigned to each region. This produced a calibration curve in the red, green, and blue channels. A graph produced with this calibration data is shown in Fig. 2. This file was then saved in FilmQA Pro and applied as a calibration for all the film measurements.

2.C | Surface and depth measurements
Measurements with the GAFChromic EBT-3 film were taken on the surface of 10 cm of backscatter material as well as at 5 and 10 mm depth underneath Bart's water tissue equivalent plastic (Barts Health NHS Trust, Clinical Physics CSS CAG, The Royal London Hospital, UK).
The applicator end was placed on top of the film and backscatter material, and where necessary, shims were used to eliminate any air gaps between the applicator end and the film. The film pieces were cut such that each piece was 1.5-2 cm longer and wider in each direction than the field size being measured. Each film was exposed to 200 MUs due to the linearity of the response between 150 and 250 cGy. Measurements were taken at the 100 and 140 kVp beam energies, and thus, a total of six sets of measurements were taken. Each applicator, energy, and depth combination film were carefully scanned following the procedure described above and imported in the FilmQA Pro software as "Dose Map (single scan)" files. A square region of interest was selected around the irradiated area, and the dimensions of the selected region noted. The dimensions are important to note to enable conversion of the scale into millimeters. The "Surface Plot" option was selected on the right-hand side of the FilmQA Pro window and the plot data imported into a spreadsheet. It is important to note that FilmQA Pro exports the data as a 51 by 51 grid of points within the region of interest. This has the effect of restricting the spatial resolution depending on the field size. That is, larger field sizes will have a worse spatial resolution than smaller field sizes. An Octave script (GNU Octave, version 4.2.2) was written by the author to extract the data from the spreadsheet and to perform analysis to produce isodose plots and color-coded dose distribution maps. For all applicators, every dose point inside the applicator was compared to the dose at the central axis. The applicator size was approximated by selecting points above 50% of the central axis dose, which gave appropriate shapes and sizes for each applicator. The SA90 was calculated by finding the number of data points above 90% of the central axis dose and calculating the percentage of those points compared to the total.

2.E | Case simulation
A GNU Octave script was written which created a geometric shape in the form of a Gaussian of adjustable height and thickness and calculated the ISL correction factor for each data point. The correction was applied to the data from flat surface measurements and isodose plots and dose distribution maps created to highlight the variation of dose with a shape replicating the nonuniformity of the surface of a patient. The aim was to discover if the effect of a nonuniformity on a patient could be modeled by taking the inverse square law into account for each data point. By inverting the direction of the Gaussian, stand-off was also simulated. For the same two cases, color-coded dose distribution maps were produced (Fig. 6). This highlights the variation in dose across the field even for flat surfaces. Figure 7 shows that the SA90 decreases with increasing applicator size for the 100 and 140 kVp beam energies, respectively. As the imported data from the scans were in the form of a square grid, circular fields were selected by comparing data points inside a circle with a radius equal to the distance to the 50% dose values. For the square and rectangular fields, a similar approach was taken but with appropriate shapes for the field selected.    Table 1 shows that there is general agreement between the two, confirming the use of the GAFChromic EBT-3 film for use with the beam energies in question. The largest percentage difference between the GAFChromic EBT-3 Film and PTW LA-48 Linear Chamber Array measurements was 2%, with standard errors ranging from 1% to 3%.

3.A | Surface measurements
Overall, Table 1 shows that there is generally agreement between the GAFChromic EBT-3 Film and PTW LA-48 Linear Chamber Array measurements. Figure 8 Figure 7 shows that this is most feasible for circular applicators and at the 100 kVp beam energy in particular, as the SA90 does not decrease significantly with increasing circular field size at that beam energy. Another option is to use a larger applicator if there is a concern that disease could extend into the periphery of the field where the dose decreases. This method increases coverage but will increase the amount of healthy tissue being irradiated.

3.B | Wax stand-in and stand-off
The measured stand-in shows that when the dose across the surface is made relative to the central axis which has a reduced SSD, the periphery of the field receives a significantly reduced dose, dropping to around 75% of the prescribed dose (Fig. 9). To compare calculated dose from the flat surface data to the measured stand-in data, the datasets had to be matched to the correct coordinates and positioning for accurate comparisons using GNU Octave. The location of the wax block was then determined by subtracting the flat surface data from the stand-in data, and the coordinates of the position of the block were used to apply the inverse square law correction. The calculated and measured data were then compared by finding the average percentage difference between dose at the same coordinates in each case. For the area of stand-in, the average percentage difference between the dose values was found to be 2 ± 4%. 10 × 10 1.5 ± 0.5% 0.2 ± 0.8% The physical measurements of the simulated stand-off scenario using wax implied that the reduction of dose at the central axis due to increased SSD and the increase in dose relative to the central axis at the periphery due to decreased SSD resulted in a flatter field

| CONCLUSION
Isodose plots and dose distribution maps were produced for a flat surface using seven applicator sizes and two superficial beam energies. For flat surfaces, increasing field size decreases the SA90. Some potential practice adjustments have been described, such as increasing the delivered MUs or using larger applicators to alleviate the issue of dose falloff at the periphery of a field.
Utilization of the inverse square law to predict dose distribution in a superficial field for stand-in and stand-off was verified by comparing computed dose to dose measured using a simple wax block to simulate stand-in and stand-off. A GNU Octave script was written that applies an ISL correction for stand-in or stand-off situations across the dataset of a flat surface in the shape of a Gaussian of adjustable height and thickness. The methodology outlined in this study could be followed to allow users to produce baseline flat surface films and simulate patient stand-in and standoff using simple Gaussian shapes of varying height and thickness.
The study highlights the need for more extensive knowledge of superficial field dose distribution than is currently employed in clinical settings. Acquisition of this knowledge would allow clinicians and physicists to make more informed decisions during planning of patient treatments.

ACKNOWLEDG MENTS
The first author acknowledges support from a research publication scholarship funded by the CAMPEP accredited MSc in Medical Physics, NUI Galway. The author thanks the staff of both NUI Galway and the Radiotherapy Department of the University Hospital Galway for all of their assistance.

CONFLI CTS OF INTEREST
There are no conflict of interest to report.