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45 Degree Wedge Factor Calculation

Objective: To obtain the wedge transmission factor for a 45OUT dynamic wedge, for a 10x10

and 20x20 cm2 field size using a 6 megavotage (MV) beam, and to show the effect of the wedge

in a monitor unit calculation.

Purpose: Dynamic wedges (EDW) are a commonly used beam modifier in radiation therapy.

Wedges essentially attenuate the beam, decreasing intensity from the “toe” end to the “heel”

end.1 The isodose lines are tilted toward the thin “toe” end. Since a wedge is modifying the beam

by attenuation, it must be taken into account for a treatment’s monitor unit’s calculation.1 If a

wedge is not taken into account, the prescribed dose will not be accurately met.

Methods: The wedge transmission factor (WF) is defined as the ratio of dose with and without

the wedge along the central axis at a specified depth.1

WF= Dose with the wedge along the central axis at a depth

Dose without the wedge along the central axis at a depth

With the aid of a physics resident, the necessary data for the WF was obtained. An open air ion

chamber was placed in a water phantom. The water phantom was placed at 100 SSD and the ion

chamber was at a depth of 10 cm. Also, an energy of 6 MV was used. First, three trials were

conducted using 100 monitor units (MU) for a 10x10 cm2 field size without a wedge. The ion

chamber measured the total charge collected in nanoCoulombs (nC). Next, three trials were

performed for the same field size but with the 45OUT EDW. The same was repeated using a

20x20 cm2 field size, without and with the EDW. The values were recorded and the three trials

for each situation were averaged.

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Figure 1. Water phantom with ion chamber used to find the WF.

Results:

Table 1. Three measurements for the 10x10 cm2 with and without the 45OUT EDW, and three measurements for the 20x20 cm2 field with and without the 45OUT EDW for a 6 MV beam.

Field Size

(cm)

Measurements without wedge (nC) Measurements with wedge (nC)

10x10 2.500 1.864

2.502 1.860

2.503 1.865

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20x20 2.673 1.484

2.673 1.485

2.671 1.486

Table 2. Finding the average measurement of both fields with and without the 45OUT EDW for a 6 MV beam.

Field Size

(cm)

Measurements without wedge (nC) Measurements with wedge (nC)

10x10 2.500+2.502+2.503= 7.505 1.864+1.860+1.865= 5.589

Average 7.505/3= 2.502 5.589/3= 1.863

20x20 2.673+2.673+2.671= 8.017 1.484+1.485+1.486= 4.455

Average 8.017/3= 2.672 4.455/3 = 1.485

Table 3. Dividing the average measurement with a wedge by the average measurement without a wedge to find the 45OUT EDW transmission factor.

Field Size

(cm)

Measurement with wedge / Measurement

without wedge (nC)

Transmission Factor

10x10 1.863/2.502= 0.745 0.745

20x20 1.485/2.673= 0.556 0.556

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Discussion: It was initially expected that the output of the beam would be decreased when a

wedge was placed in the field. This expectation was reinforced by the measurements taken with

both field sizes. For the 10x10 cm2 field size, the average charge collected was 1.863 nC with the

EDW, compared to 2.502 nC without the EDW. The addition of the wedge caused attenuation of

the beam, thus leading to a smaller collection of charge in the ion chamber. For the 20x20 cm2

field size, an average charge of 1.485 nC was measured with the EDW compared to 2.672 nC

without the wedge. The transmission factor for the 20x20 cm2 field was 0.556. Essentially, the

WF is the percentage of the reduction in dose. The charge measured with the wedge is 55.6% of

the charge measured without the wedge. This significant reduction due to attenuation highlights

the importance of taking the WF into account when calculating monitor units.

Clinical Application: To start with a simple example, the 45OUT EDW will be compared to the

same field without the wedge in the treatment planning system, normalized to a 10 cm depth

with a 6 MV beam.

Figure 2. Normalized to a depth of 10 cm in a phantom without a wedge.

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In Figure 2, it takes 376 MU to deliver 300 cGy to a 10 cm depth.

Figure 3. Same field as figure 2, but with a 45OUT EDW.

In Figure 3, it takes 487 MU to deliver 300 cGy to a 10 cm depth with the 45OUT EDW. This

example highlights the difference in MU a dynamic wedge can make.

For an example of an actual clinical application, a prone rectum being treated to 45 Gy in 25

fractions will be used.2 A three field, isocentric technique will be used, and 45 degree dynamic

wedges will be used. The PA beam will be weighted at 50%, and the laterals will be weighted at

25% each. The isocenter will be at a depth of 9 cm for the PA beam and 19 cm for each lateral.

Each field will have an equivalent field size of 15x15 cm2. A 6 MV beam will be used. The

MU’s will be calculated using The James TPR and wedge factor library.

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Figure 4. MU calculation of the L Lateral beam.

The information used in the example was based off an actual prone rectum data set in the

treatment planning system. The depths to isocenter and field size for each field was fairly

accurate to the actual CT data set. The monitor units calculated in the treatment planning system

were close to the hand calculation in Figure 4.

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Figure 5. The CT data set used to compare with the hand calculation in Figure 4.

The treatment planning system calculated the monitor units for the lateral fields to be 112 MU

and 113 MU for the L lateral and R lateral respectively. The differences can be attributed to a

few different factors such as a more accurate equivalent square field size and use of density

corrections in the treatment planning system calculation. To further compare the monitor unit

hand calculation using a 45 degree EDW, it will be compared with a second check calculation

using the software RadCalc.

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Figure 6. The independent second check using RadCalc.

The second check using RadCalc produced similar monitor unit calculations for the lateral fields

with the EDW. The significant percent difference is likely to due to density corrections being

turned off when using RadCalc, as the calculation in the treatment planning system uses density

corrections.

Last, the calculation in Figure 4 will be compared to the result if for whatever reason the

dynamic wedge did not activate during a treatment.

Figure 7. The dose if the EDW fails.

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In Figure 7, it’s observed that the dose delivered from the L Lateral beam becomes 69 cGy if the

wedge fails, compared to the desired 45 cGy. Please not that one of the positives of a dynamic

wedge is that the therapists can’t accidentally forget to put the wedge in, so this situation is

extremely unlikely. It is simply an example to show what happens to the dose when a wedge is

forgotten.

Conclusion: The purpose of a wedge is to modify the beam for treatment planning purposes.

During the modification of the beam, it is attenuated by the wedge. This attenuation is decreasing

the output of the beam. Therefore, a wedge factor must be taken into account to deliver the

desired dose to a patient. If a WF is not considered, the patient can be significantly underdosed

or overdosed as seen in this paper.

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References

1. Khan FM. Treatment Planning I: Isodose Distributions. In: Khan FM, Gibbons JP, eds. The Physics of Radiation Therapy. 5th ed. Philadelphia, PA: Lippincott Williams & Wilkins; 2014:170-194.

2. Chao KSC. Colon and Rectum. In: Chao KSC, Perez CA, Brady LW, eds. Radiation Oncology Management Decisions. 3rd ed. Philadelphia, PA: Lippincott Williams & Wilkins; 2011:443-454.

3. Photos and data values were obtained at The James Cancer Hospital.