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Solution to treatment planning problems using coordinate transformations

R L Siddon

    Medical Physics
    |November 1, 1981
    PubMed
    Summary
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    This study introduces a mathematical method for complex 3D radiation therapy planning. It simplifies intricate problems involving gantry, collimator, and turntable rotations for improved treatment accuracy.

    Area of Science:

    • Medical Physics
    • Radiation Oncology
    • Computational Geometry

    Background:

    • Standard radiation therapy planning often uses fixed gantry angles.
    • Complex 3D planning requires coordinated rotation of gantry, collimator, and turntable.
    • Existing methods for complex 3D planning are often cumbersome or rely on trial-and-error.

    Purpose of the Study:

    • To present a systematic mathematical method for solving complex 3D radiation therapy planning problems.
    • To provide a unified framework for diverse clinical scenarios requiring non-coplanar beams or oblique planes.

    Main Methods:

    • The method models the gantry, collimator, and turntable as interconnected coordinate systems.
    • Coordinate transformations incorporating rotation angles are used to define relationships between these systems.

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  • Treatment planning problems are categorized into two general types within this framework.

    • Main Results:

    • The proposed mathematical method is applicable to a wide range of complex 3D treatment planning challenges.
    • It offers a systematic alternative to tedious analytical solutions or trial-and-error simulations.
    • The framework simplifies the understanding and solution of problems like 3D field matching and tangential breast treatments.

    Conclusions:

    • A novel mathematical approach simplifies complex 3D radiation therapy planning.
    • This method provides a systematic and easily applicable solution for intricate treatment geometries.
    • The coordinate transformation framework facilitates efficient planning for advanced radiation oncology cases.