The mathematical description of moving anatomical structures is of increasing importance when dealing with tumor irradiation by particle beams. A mathematical description of the orientation of anatomical structures by principal inertia axes and of the shape by spherical harmonics is given. Structures of convex and concave shape are decomposed and reconstructed with index numbers L max = 10. Conformity of decomposed and reconstructed shape is measured by a similarity index. For irradiation therapy the influence of a security margin is considered. No significant improvement of conformity was found by using different coordinate systems for decomposition and reconstruction.

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