The effects of cutouts on output, mean energy and percentage depth dose of 12 and 14 MeV electrons.

Electron field-shaping cerrobend cutouts on the linear accelerator applicator have some effects on the output and percentage depth dose. These effects which arise from the lateral scatter nonequilibrium are particularly evident in higher energies and in cutouts with smaller radius. Dose measurements for circular, square, and triangular cutouts as well as open field was performed in a 10 × 10 cm applicator, using plane parallel type ion chamber with a 100 cm source surface distance. The Percentage Depth Doses curves were drawn and the outputs were measured for each of these cutouts. The output factors, normalized to open 10 × 10 cm field, varied between 0.891 and 0.996 depending on the energy, cutout shape, and cavity area. With the use of cutouts, R(100) shifted toward the surface. The shifts ranged from 9 to 0 mm and from 13 to 0 mm for 12 and 14 MeV, respectively, depending on the shape and cavity area. For R(90), R(80), and R(50) the ranges for observed shifts narrowed down and practically no shifts were observed for R(20). We present these changes in the form of predictive formulas, which would be useful in clinical applications.

Introduction

In treatment of cancers using electron beams, depending on the type and the shape of tumor, cast cerrobend alloy cutouts are used. Cerrobend is a fusible alloy usually containing of Tin, Lead, Bismuth, and Cadmium. We used the cadmium-free type.

The cutouts change the percentage depth dose (PDD) and the output,[1-3] in a way that the slope of descending part of PDD curve increases. Therefore, the values for R100, R90, R80, and R50 in order show the highest decrease. Also E0(mean) and OPF decrease while the cutout cavity area decreases.[45]

These changes in higher energy and smaller diameter cutouts are more profound, which is arising from the lack of lateral scatter equilibrium. Req (minimum radius for the establishment of lateral scatter equilibrium) is calculated using the following equations:[6]

In this formula, Ep0 is the most probable energy at the phantom surface for the reference field size:[78]

In radius smaller than Req values of R100, R90, R80, R50, E0(mean), and OPF are expected to change.[2]

The main aim of this study was to fit the values of R100, R90, R80, R50, E0(mean), and OPF changes on a curve and formulizing these changes as a function of cutouts cavity area. There in this way there will be no need to carry on dosimetry for each patient individually.[29]

Materials and Methods

Dosimetry system

We used PTW (PTW Freiburg, Germany) hardware and software. The water phantom used had a 50 × 50 × 50 cm size and the model was MP3. A plane parallel-type chamber was used for absolute and relative dosimetry, and a thimble-type chamber was used as a reference chamber and was placed outside of the phantom near the radiation field corner. The plane parallel chamber model was PTW 34045 and its sensitive volume was 0.02 cm3. The cylindrical chamber model was PTW 31010. Controller software and collected data compiler was the MEPHYSTO® mc2. The IAEA TRS398 dosimetry protocol was used in this study.[10]

Dosimetry

Dosimetry was performed in 100 cm source surface distance (SSD) and using a 10 × 10 cm applicator. Dosimetry setup used for our work is shown in Figure 1. The PDD curve and output for the square, circle, and triangle cutouts and the 10 × 10 cm reference field was measured. The opening of X-ray jaws was 19 × 19 cm. Linear accelerator used was a Siemens Primus model and the results were for the 12 and 14 MeV energies. The circle cutout diameters were 3, 4, 5, 6, and 8 cm. Squares had side lengths of 2.66, 3.54, 4.43, 5.32, and 7.1 cm. Also the equilateral triangles had 4.05, 5.4, 6.75, 8.1, and 10.58 cm side lengths. The cavity areas from the smallest cutout to the largest one for each shape were 7.06, 12.56, 19.62, 28.26, and 50.24 cm2, respectively.

Figure 1

Dosimetry setup in Mahak Hospital Department of Radiation Therapy used for our work. (a) The thimble chamber was used as the reference chamber, (b) the plane parallel chamber moves along the central axis for PDD measurements, or would be fixed at dmax for output measurements, (c) bottom of the applicator, the place of cutout insertion, and (d) The water phantom

To obtain PDD both chambers were on. The obtained curves were the percentage depth ionization (PDI) and then converted to the PDD by MEPHYSTO® mc2 software. After the percentage depth dose curves were drawn, the information were extracted as R100, R90, R80, R50, R20, Rp, and E0(mean).

The mean energy of the electron field in the phantom surface was calculated by Eq. (3).[78]

For measuring the output, the plane parallel chamber was placed at the depth of maximum dose. The maximum depth dose was calculated for each cutout using the PDD curve, because the cutouts’ dmax are different to a 10 × 10 cm field.

We measured the output after turning off the thimble chamber. The measurement was done four times for each field and the average was compared with the reference field (10 × 10 cm) output.

Results

Percentage depth dose curves

Percentage depth dose curve on the central axis for 12 MeV energy

We calculated Rp using PDD curve, which was equal to 5.7 cm and using the Eq. (2) the Ep0 was 11.53 MeV. Also the minimum radius required for lateral scatter equilibrium in 12 MeV electron energy by using Eq. (1) was about 3 cm. Meaning the minimum circular field diameter necessary for 12 MeV electron lateral scatter equilibrium establishment is about 6 cm, which means that changes in PDD for circular field with diameter of less than 6 cm are expected.[2]

As is clear from Table 1, shields cause more change in higher depth doses, especially R100, R90, and R80, and it has a little effect (up to 1 mm) on the R20, which is negligible. Triangular shields changed R100, R90, R80, and R50 more than the circular and square shields. The reduction in R100 in the triangle shield was from 27 to 18 mm, but for the circular and square shield it was from 27 to 19 mm. For circular and square fields larger than 28.26 cm2, due to the establishment of electron lateral scattering equilibrium effect there is no difference between the values of R100, R90, R80, and R50 compared to reference field. Also, the mean energy of the electron field in smaller fields is lower.

Table 1

Values obtained from percentage depth dose curve for each of the three field shapes (12 MeV)

By fitting these values on the curve, we devised Eq. (4) (8) formulas to calculate the parameter change based on cutouts area.

Dynamic fit curve was found to be the best method for matching above-mentioned values on a proper curve and attaining its computed formula. With formulization of these changes for R100, Eq. (4) was obtained:

This formula is a Polynomial type, where S is the area of the shield cavity.

Other methods, such as A/P[11] in which A is the area of the cavity and P is the periphery of the cutout hole, were not utilized due to the lack of favorable results in formulization.

For R90, R80, and R50 these equations were calculated:

In the formula for E0(mean), the fitted curve was a Sigmoidal (Gompertz) type.

Percentage depth dose curve on the central axis for 14 MeV energy

Here the Rp was equal to 6.2 cm and the Ep0 was 12.66 MeV. As a result Req = 3.2 cm.

PDD data for 14 MeV is demonstrated in Table 2.

Table 2

Values obtained from percentage depth dose curve for each of the three field shapes (14 MeV)

In this energy the highest change was observed in R100. Here again the decrease on R100, R90, R80, and R50 by the triangular shields is rather than circular and square shields. The R100 for the circular shape decreased from 30 to 20 mm in comparison with the reference field. For the square cutout it changed from 30 to 19 mm and for triangle cutout it changed from 30 to 17 mm. The R20 for the 7.06 cm2 area for all fields reduced from 59 to 57 mm.

In the largest area (50.24 cm2) for 14 MeV in the circular and triangle fields the change of R100 was 1 mm and for the square cutout it remained unchanged.

For 14 MeV similar to 12 MeV the mean energy for smaller fields was lower than the larger fields. The maximum reduction in mean energy was for the triangle shape, decreasing from 12.19 to 10.71 MeV.

Figures 2–4 are obtained by fitting the Mean values of Tables 1 and 2 on the curves. In these figures, the error bars represent plus and minus standard deviations for each point. Some points have same value in several measurements, for these points the standard deviations are zero and no error bar exists.

Figure 2

Central axis depth dose parameters changes as a function of the area for 12 MeV

Figure 4

E0(mean) change as a function of the area

Central axis depth dose parameters changes as a function of the area for 14 MeV

Output factor

Output factor in 12 MeV energy

Dose rates in Gy/min were measured at the depth of maximum for all fields and then calculated as a ratio of the reference dose rate value to obtain the OPF for each shield. The dose rates were measured 4 times for each field.

Averaging the output values in Table 3 can provide a more general formula for all forms:

Table 3

dmax and output factor for each of the three shapes and reference field for 12 MeV

As the cutout area becomes smaller the dose rate and consequently the OPF for the circle, square, and triangle are reduced from 0.993 to 0.907, from 0.995 to 0.895, and from 0.992 to 0.891, respectively. The lowest output was observed for the triangle. Eq. (14) is a more general formula and can be used for all shapes.

Output factor in 14 MeV energy

Here again, the average of OPF values for Table 4 can be used to make a more general formula for all forms in 14 MeV:

Table 4

dmax and output factor for each of the three shapes and reference field for 14 MeV

Eqs (14) and (15) are the formulas for the Figure 5 curves, which were obtained from Tables 3 and 4 data. The curves in Figure 5 are very close together; hence the error bars have had overlap, so the error bars are omitted. However, the standard deviations are available in Tables 3 and 4.

Figure 5

Output factor changes for cutouts with different areas

Discussion

The chart of changes for R100, R90, R80, and R50 shows that while increasing the shield cavity area, after a certain area the values of these parameters reach a saturation status. This means that there is a threshold for the field size influence on R100, R90, R80 and R50. This threshold is close to the Req.[26]

Su et al. measured the cutout OPF for 6 MeV electron beam by radiographic film and 2D small volume ion chamber array. The aim of their study was not about the cutout effects on the output, but in their research this effect can also be observed.[1]

Xu et al. have demonstrated that for 6 MeV beam and circular cutout, reducing the diameter reduces the amount of R100, R50, and OPF.[2] Besides, Sharma et al. observed similar changes in R100, R90, and R50 for quadrangular cutouts and 6 MeV energy, due to the changes of R100, they propose using of bolus to decrease the skin dose arisen by the reduction of dmax.[12] Zhang et al. found that the OPF in 6, 12, 20, 30, and 40 MeV for circular cutouts is reduced when the field radius is smaller than the minimum needed radius for the establishment of lateral scatter equilibrium.[13]

Sharma et al. instead of Req did their measurements for several cutouts with a radius less or more than Rp. For 6 MeV electron beam the difference between the amount of Rp and Req is about 9 mm, however, in their study the exact threshold of change had not been investigated.[12] Other researchers got the same result for other energies in different methods.[34911]

Our findings are in line with the mentioned studies except that these studies have been limited to a particular shape (circular or square) and mostly for one energy level, and none of them have formulized the changes caused by using different cutouts.

In 12 MeV and 50.24 cm2 area for circular, square, and triangle shapes the values of R100, R90, R80, R50, and R20 are equal to the values of the 10 × 10 cm field. The most changes in PDD parameters was observed for the triangle shape, so that R100 and R90 for 7.06 cm2 area were changed 1 mm more in comparison with circle and square shapes.

In 14 MeV, the minimum radius for establishment of lateral scatter equilibrium was increased. So, in the 50.24 cm2 area, which had the largest radius, the R100 for both the circular and the triangle shapes was different to the 10 × 10 cm field. For the triangle the R90, R80, and R50 values were different from the 10 × 10 cm field. Here again the most changes in the values of R100, R90, R80, R50, and R20 were observed with the triangle.

E0(mean) will decrease, if the cutout size is reducing. Whereas E0(mean) is related to the R50, the reduction of R50 would cause reduction in E0(mean) as well.

The minimum value of E0(mean) in 12 and 14 MeV was achieved by using 7.06 cm2 square and 7.06 cm2 triangle cutouts, respectively, which was equal to 10.05 MeV for 12 MeV and 10.71 MeV for 14 MeV.

The reason why the output and percentage depth dose for triangle are different to circular and square shapes is arising from the nature of the triangle which has smaller width of field in the corners in comparison to square and circle fields, which prevents the establishment of lateral scatter equilibrium more than circular and square shapes.

Conclusions

It is clear that if we use smaller cutouts, in higher depth doses (R100, R90, R80, and R50), more reduction of depth would be seen.[212] However, this reduction is much more tangible in the depth of R100 and R90.

Considering the dmax changes due to the small cutouts, it is obvious that the chamber should be placed at the correct dmax in output measurements.[12]

The output of the machine which is one of the most important factors in treatment, decreases with reducing the diameter of cutout.[12912] This reduction is more pronounced for triangles rather than circle or square. Also, the changes in PDD and outputs in clinical cases must be considered. For example, to compensate the changes of dmax, the bolus might be used[12] and output changes should be considered in the treatment calculation.

The formulas presented in this study, are clinically useful to calculate the changes of PDD and OPF for each regular and semi-regular geometry cutouts on the central axis.

Knowledge of these variations might be effective in having an accurate dosimetry and treatment.