180cGy is prescribed to a depth of 12cm at a point 5cm off the central axis. Compute the required monitor units for a 6MV beam delivered 105SSD with a field size of 12x12cm². Here... 180cGy is prescribed to a depth of 12cm at a point 5cm off the central axis. Compute the required monitor units for a 6MV beam delivered 105SSD with a field size of 12x12cm². Here %DD = 75.3, Sc = 1.008, Sp = 1.009, TMR = 0.82, and OAF = 1.023.
Understand the Problem
The question is asking for the calculation of required monitor units for a prescribed dose of radiation, given specific parameters related to a radiation beam. It involves applying formulas related to radiation therapy to derive the answer.
Answer
The required monitor units (MU) is approximately $189$.
Answer for screen readers
The required monitor units (MU) is calculated as follows:
- Output Factor (OF):
$$ OF = 1.008 \times 1.009 \times 1.023 \approx 1.0402 $$
- Dose at reference point ( D_{ref} ):
$$ D_{ref} = 180 \times \left(\frac{100}{75.3}\right) \times 0.82 \approx 180 \times 1.327 \times 0.82 \approx 180 \times 1.0874 \approx 195.7 , \text{cGy} $$
- Monitor Units (MU):
$$ MU = \frac{195.7 , \text{cGy}}{1.0402} \approx 188.5 $$
So, the required monitor units is approximately 189 (rounding to nearest whole number).
Steps to Solve
-
Calculate the dose required at the reference point The prescribed dose is 180 cGy, which we need to deliver at a depth of 12 cm.
-
Calculate the output factor (OF) based on the parameters Using the given data, compute the overall output factor (OF) as follows:
$$ OF = Sc \times Sp \times OAF $$
Substituting the values:
$$ OF = 1.008 \times 1.009 \times 1.023 $$
- Find the dose at the reference point using %DD and TMR To find the dose where the prescription was made, we adjust:
$$ D_{ref} = \text{prescribed dose} \times \left(\frac{100}{%DD}\right) \times TMR $$
Substituting the values:
$$ D_{ref} = 180 , \text{cGy} \times \left(\frac{100}{75.3}\right) \times 0.82 $$
- Calculate the required monitor units (MU) To find the monitor units, use the formula:
$$ MU = \frac{D_{ref}}{OF} $$
- Substituting values to find the monitor units Using the computed value of ( D_{ref} ) from step 3 and the ( OF ) from step 2, calculate the final required monitor units.
The required monitor units (MU) is calculated as follows:
- Output Factor (OF):
$$ OF = 1.008 \times 1.009 \times 1.023 \approx 1.0402 $$
- Dose at reference point ( D_{ref} ):
$$ D_{ref} = 180 \times \left(\frac{100}{75.3}\right) \times 0.82 \approx 180 \times 1.327 \times 0.82 \approx 180 \times 1.0874 \approx 195.7 , \text{cGy} $$
- Monitor Units (MU):
$$ MU = \frac{195.7 , \text{cGy}}{1.0402} \approx 188.5 $$
So, the required monitor units is approximately 189 (rounding to nearest whole number).
More Information
In radiation therapy, monitor units are a measure of the amount of radiation to be delivered to a target. Calculating these correctly ensures that patients receive the prescribed doses effectively while minimizing exposure to surrounding tissues.
Tips
- Miscalculating the output factor (OF) by not multiplying all components together.
- Failing to correctly apply the %DD and TMR in the determination of ( D_{ref} ).
- Not rounding the final answer properly for practical applications in treatment planning.
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