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A note on equivalent circles, squares, and rectangles

B E Bjärngard, R L Siddon

    Medical Physics
    |March 1, 1982
    PubMed
    Summary
    This summary is machine-generated.

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    The scatter dose in photon beams can be simplified using a linear approximation. This method accurately estimates scatter across various field shapes, including squares and rectangles.

    Area of Science:

    • Medical Physics
    • Radiation Oncology
    • Radiotherapy Physics

    Background:

    • Accurate dosimetry is crucial for effective radiotherapy.
    • Calculating scatter dose in photon beams is complex due to varying field shapes.
    • Existing methods may require extensive computation for different geometries.

    Purpose of the Study:

    • To develop a simplified method for estimating scatter dose in the center of photon beams.
    • To evaluate the accuracy of a linear approximation for scatter integration.
    • To determine the relationship between circular and non-circular fields for scatter calculation.

    Main Methods:

    • Representing scatter dose using a serial expansion.
    • Utilizing the first term of the expansion, proportional to the radius.

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  • Integrating scatter based on the average radius of the field contour.
  • Analyzing square and rectangular field shapes.

    • Main Results:

    • The scatter dose approximation is proportional to the average radius (r) for any field shape.
    • For square fields, the ratio of side to average diameter (s/d) is 0.891.
    • A formula for rectangular fields incorporates area-to-perimeter ratio and elongation.
    • The error from the linear approximation remains small across conditions.

    Conclusions:

    • A linear approximation provides a robust method for estimating central scatter dose in photon beams.
    • This simplified approach is applicable to various field shapes, aiding in treatment planning.
    • The method offers a computationally efficient alternative for dosimetric calculations in radiotherapy.