Mathematical modeling of anatomical structures by means of spherical harmonics

Abstract

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.

LAPACK library for mathematical modeling used in 3D object reconstruction

“…Due to the improvements made to our implementation we obtained a much better computation time than the results obtained by [6], which was possible with the help of LAPACK library.…”

“…As shown in [6], using the least square method we obtained a linear system of equations with (L max + 1) 2 equations and (L max + 1) 2 unknowns given by:…”

“…We gave special importance to the time in which the reconstruction of an object was carried out, as we tried to bring it as close as possible to real time. To make all this possible we decided to use parallel computation to solve linear systems [7], [1], [6] for problems such as enriching the image scanned by CT [2].…”