An equivalent square field formula for determining head scatter factors of rectangular fields

Area of Science:

• Medical Physics
• Radiation Oncology
• Radiotherapy Physics

Background:

• Accurate calculation of radiation beam output is crucial in radiotherapy.
• Head scatter factors (HSF) are essential for accurate dose calculations, especially for non-square fields.
• Existing methods for determining equivalent square fields can be complex or require extensive data.

Purpose of the Study:

• To derive a simple, geometrically based formula for calculating an equivalent square field.
• To ensure the equivalent square field yields the same head scatter factor as a given rectangular field.
• To validate the formula's accuracy and applicability to medical linear accelerator treatment heads.

Main Methods:

• Derived a formula based on geometric parameters of the linear accelerator treatment head.
• The formula utilizes distances between the target and field-defining apertures.
• The method accounts for field elongation and collimator exchange effects.

Main Results:

• A simple formula was derived for calculating equivalent square fields.
• The formula accurately predicts output (within 1%) for both open and wedged fields.
• No new measured data are required beyond field size dependence of HSF for square fields.

Conclusions:

• The derived formula provides a simple and accurate method for determining equivalent square fields.
• This approach simplifies head scatter factor calculations in radiotherapy planning.
• The formula's format is consistent with previously empirically derived methods.