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February 2, 2018

Andrew Edel

Transmission Factor Calculation for a Physical 45-degree Wedge

Objective: Calculate and implement the transmission factor in a monitor unit calculation for a

clinical situation requiring a wedge.

Purpose: Physical wedges are a devise the modify the profile of a beam by attenuation of photon

beam before it reaches the patient. The thick edge, or heel, attenuates more of the energy

resulting in less dose being passed to the patient’s tissue behind it. The amount of attenuation is

lowered on a gradient moving toward the thinner edge, or toe, of the wedge. The 45- degree

angle does not refer to the angle of the wedge itself but to the resulting angle of the dose

distribution.1 Because the wedge itself absorbs the beams energy, the amount of energy the linear

accelerator must produce, or monitor units (MU), must be increased to give the patient the same

dose. When calculating the increase in monitor units for a devise that attenuates a portion of the

beams energy we use a transmission factor. All transmission are ratios of the dose that is

transmitted through the device divided by the dose that would be transmitted if the device was

not present. It can be though of as the fraction of the dose that will pass through a device. The

wedge factor (WF) is a specific case of a transmission factor that relates to the dose transmission

on the central axis of a beam that passes through a wedge.

Method: The wedge factor can be calculated using empirical measurements of dose with and

without the wedge in place. Three trials were performed for open and wedged fields at 6

megavolt (MV) and 18 MV energy. The average dose for each category was used to calculate the

WF for each energy using the formula:

WF = Dose measurement with wedge / Dose measured without wedge.

Materials: The linear accelerator used was a Varian Trilogy. 100 MU were used in each trial

using a 600 MU per minute dose rate with a 10x10cm field size. Dose was measured using a

farmer chamber at the Isocenter or a source to axis distance (SAD) of 100cm. This chamber was

inserted into a plastic phantom that is tissue equivalent. This put the chamber at a depth of 10cm

of phantom material. This chamber was then connected an electrometer that displays the charge

that the photon beam delivered. The wedge being measured was a 45-degree Upper wedge that

was composed of steel.

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Image 1. Experimental setup of farmer chamber in plastic water phantom.

Image 2. 45-degree wedge in accessory rack.

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Image 3. Electrometer in control room.

Results:

Table 1. Measured doses with calculation of averages.

Energy Dose with wedge (x10^-8C) Dose without wedge (x10^-

8C)

6MV

Average (sum of trials dived

by number of trials)

.7439

.7442

.7433

(2.2314/3) = .7438

1.5248

1.5242

1.5234

(4.5902/3) = 1.5301

18MV

Average (sum of trials dived

by number of trials)

.9650

.9647

.9650

(2.8947/3) = .9649

1.8822

1.8825

1.8829

(5.6476/3) = 1.8825

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Table 2. Calculation of WF.

Energy Calculation (average dose with wedge/ average dose without

wedge)

Wedge

factor

6MV .7438 / 1.5301 .4861

18MV .9643 / 1.8825 .5122

Discussion: The wedge factors specified above show that when a wedge is in place then

approximately half the beams dose is attenuated, and half is transmitted. This means we will

need to approximately double the amount of monitor units for the patient to receive the same

dose at a given on axis point. It should be noted that the higher energy beam is attenuated

slightly less resulting in a slightly higher transmission factor than the lower energy beam.

Clinical Application: Most palliative spine treatments are performed with opposed beams

running anterior to posterior and posterior to anterior (APPA).2 However, sometimes because of

prior radiation this technique can not be used. In this case a previous breast treatment raised

concern about total dose to the anterior chest wall that an APPA setup would deliver. As an

alternative, a paired wedge technique was chosen. This paired wedge technique utilized two 45-

degree wedges heel to heel with a 80-degree hinge angle between fields. The 45-degree angles

are abutting providing a uniform dose deeper. Without the wedges there would be a hot spot

where the beams converge.

Image 4. Representation of how a paired wedge technique avoids overlap with previous fields.

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Image 5. Beam and wedge arrangement.

Image 6. Homogeneity of dose because of wedges.

Image 7. Treatment plan summary.

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Image 8. Independent MU hand calculation using experimental WF value.

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Conclusion: This exercise shows how using empirical measurements an accurate MU

calculation can be made by hand. It also demonstrated were all the information in the data books

originates. The importance of the transmission factor should be highlighted. When calculating

MU, the dose is divided by the transmission factor in this case the wedge factor. With the wedge

factors we calculated if this component was accidently left out of the MU calculation, the patient

would only receive approximately half the dose prescribed. Similarly, if radiation therapists

forget to put in the wedge for treatment, the dose at isocenter would be approximately doubled.

Even worse without wedges reshaping the beam profile there would be an extremely hot spot

where the beams converge.

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References

1. Khan FM, Gibbons JP. Treatment Planning 1: Isodose Distributions. In: Kahn’s The Physics of

Radiation Therapy. 5th ed. Philadelphia: Wolters Kluwer Health; 2014: 185-188.

2. Chao KSC, Perez CA, Brady LW. Palliation: Brain, Spinal Cord, Bone, and Visceral Metastases.

In: Radiation Oncology Management Decisions. 3rd ed. Philadelphia: Wolters Kluwer Health;

2011: 798-799.