Equivalent squares of circular electron fields.

Area of Science:

• Medical Physics
• Radiation Oncology
• Radiotherapy Physics

Background:

• Manual estimation of electron field output is crucial for verifying treatment planning system (TPS) calculations.
• Existing methods like the square root rule are suitable for rectangular fields but not ideal for circular ones.
• A need exists for a reliable method to determine the equivalent square of circular electron apertures.

Purpose of the Study:

• To develop and validate a simple, accurate method for calculating the equivalent square of circular electron fields.
• To provide a tool for physicists to manually check TPS-computed dose rates for shaped electron beams.
• To compare the accuracy of the proposed method with existing rules and experimental data.

Main Methods:

• Utilized Monte Carlo (MC) calculated output values for various circular and square field sizes, energies (6-15 MeV), and applicators.
• Derived an expression for the equivalent square of circular fields based on MC data.
• Validated the derived formula using an independent dataset of 104 parameter combinations.
• Compared MC results with measured output data and clinical treatment planning system (TPS) calculations.

Main Results:

• Established a simple and accurate relationship: Equivalent Square (X) = 1.83 * Radius (R).
• The formula demonstrated exceptional accuracy, with an average ratio of circular field output to equivalent square output of 1.000 and a standard deviation of 0.003.
• Accuracy was consistently better than 1%, often within 0.5%, aligning with MC statistical uncertainties.
• The equivalent square rule for circles proved more accurate than the square root rule for rectangular fields in tested scenarios.

Conclusions:

• The formula X = 1.83 R provides a highly accurate and practical method for estimating the equivalent square of circular electron fields.
• This method significantly enhances the ability to perform manual checks of TPS dose calculations in radiation therapy.
• The findings offer a valuable tool for quality assurance in electron beam radiotherapy, improving clinical dose verification.