# Previous Treatment EQD2 Practice Questions

Given Information 1:

• A patient is simulated for whole brain radiation treatment.
• The doctor has indicated a prescription of 300 cGy/fx * 10 fx = 3000 cGy.

Question 1: While reviewing the patient’s history of present illness, you learn that the patient has received previous radiation treatment to the brain. When evaluating the DVH of the current plan, what additional metrics should you consider on top of normal OAR constraints?

Answer: While normal constraints should still apply, your particular institution or the doctor may have their own specific re-treatment constraints that should also be considered.

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Given Information 2:

• You find the following information in the patient’s previous treatment records:

Question 2: While the optic chiasm receives 643 cGy in each previous treatment plan, are these two value quantities equal in the context of radiobiology? That is, is 643 cGy from 128.6 cGy/fx * 5 fx, equivalent to 643 cGy from 643 cGy/fx * 1 fx?

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Given Information 3:

Plan doses can be converted to their 2 Gy equivalent forms (EQD2), which allows these values to have the same “unit of measurement.” Historically, radiobiological data has been gathered in EQD2 and by extension, the thresholds to constrain OAR doses to. It may also be clearer to express re-treatment constraints in EQD2 when previous and current treatments are expected to vary in fractionation.

Question 3: What are the optic chiasm max point doses of previous treatment plans 1 and 2 in EQD2, respectively (optic chiasm a/b = 2 Gy)?

Answer: 5.28 Gy and 13.55 Gy, respectively.
Solution: Solve manually using the following equation: EQD2 = D * ((d + a/b) / (2 Gy + a/b)), where:

• D = Total plan dose (to OAR) (Gy).
• d = Fractional plan dose (to OAR) (Gy).
• a/b = alpha/beta (generally 2 or 3 Gy for healthy tissue).
• EQD2 = Equivalent dose in 2 Gy fractions.

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Question 4: If the re-treatment constraint for the optic chiasm is 54 Gy EQD2, how much dose in EQD2 can the current plan give to the optic chiasm?

Solution: 54 – (13.55 + 5.28) = 35.17 Gy EQD2.

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Question 5: If the current treatment technique is VMAT, how much plan dose can the optic chiasm receive?

Solution: Using the EQD2 equation, substitute ‘d’ for ‘D/10’ and then rearrange, to arrive at the following quadratic equation: 0 = 0.025D2 + 0.5D – 35.17. Solve for the positive value of ‘x’ manually or using a calculator: https://www.calculatorsoup.com/calculators/algebra/quadratic-formula-calculator.php

Comment: Note that you might consider which direction to round. The unrounded value using the calculator above was 28.8175. While convention would suggest rounding up to 28.82, we should evaluate the context of this value, which is the maximum dose the current plan can give without overdosing the optic chiasm. If the optic chiasm received a maximum dose greater than 28.8175 Gy, but less than 28.82 Gy, it would falsely satisfy re-treatment limits on paper. Rounding down to 28.81 would be the “conservative” decision, especially when further calculations may be made using this value. While this example may seem extreme, this concept will have more relevance if, for example, you are rounding to tenths place.

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Question 6: If the current treatment technique is 3D, at what fraction should the fields “cone-down.” That is, at what fraction should the treatment fields switch from open fields (open field with OAR fully exposed), to partially closed fields (open field, but OAR blocked)?

1. Each fraction delivers exactly 300 cGy.
2. The optic chiasm receives 0 cGy when blocked.

Solution:

• 100% of RX/fx: 300 cGy/fx * 9 fx → 3375 cGy EQD2.
• 33.75 Gy EQD2 < 35.17 Gy EQD2.

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Question 7: Question 6 asked that you make your calculations under two assumptions. In actual practice, are these assumptions realistic (& conservative) and why?

1. The dose distribution at any slice will be heterogeneous.
2. Transmission and scatter still occur despite MLC blocking.

Solution:

1. The max dose of the optic chiasm may be 103-104% of the prescription. Therefore, calculations may be made using a certain percentage greater than the prescription:
• 105% of RX/fx: 315 cGy/fx * 9 fx → 3650 cGy EQD2
2. Even when the optic chiasm is blocked by MLCs, it may still receive a notable percentage of the prescription fractional dose:
• 20% of RX/fx: 60 cGy/fx * 1 fx → 39 cGy EQD2
• 36.50 Gy EQD2 + 0.39 Gy EQD2 = 36.89 Gy EQD2.
• 36.89 Gy EQD2 > 35.17 Gy EQD2 .

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Question 8: Based on your response to Question 7, does this change the fraction at which treatment fields are switched from open fields to partially closed fields in Question 6?

Answer: Yes, at fraction 9 (or 8 depending on conservativeness).

Solution:

• 105% of RX/fx: 315 cGy/fx * 8 fx → 3245 cGy EQD2
• 20% of RX/fx: 60 cGy/fx * 2 fx  → 78 cGy EQD2
• 32.45 Gy EQD2 + 0.78 Gy EQD2 = 33.23 Gy EQD2.33.23 Gy EQD2 < 35.17 Gy EQD2.

Comment: Note that while 20% of RX/fx is used for the max point dose to the blocked optic chiasm, the extent of MLC blocking in the plan will actually reflect this percentage value. Additionally, there is still around 1.94 Gy EQD2 of room left, meaning that optic chiasm blocking can be slightly loosened in order to calculate closer to the re-treatment limit, particularly relevant if you needed to slightly improve coverage around the optic chiasm.

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