Using eigenstructure of the Hessian to reduce the dimension of the intensity modulated radiation therapy optimization problem |
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Authors: | Fredrik Carlsson Anders Forsgren Henrik Rehbinder Kjell Eriksson |
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Institution: | 1. Optimization and Systems Theory, Department of Mathematics, Royal Institute of Technology (KTH), SE-100 44, Stockholm, Sweden 2. RaySearch Laboratories, Sveav?gen 25, SE-111 34, Stockholm, Sweden
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Abstract: | Optimization is of vital importance when performing intensity modulated radiation therapy to treat cancer tumors. The optimization
problem is typically large-scale with a nonlinear objective function and bounds on the variables, and we solve it using a
quasi-Newton sequential quadratic programming method. This study investigates the effect on the optimal solution, and hence
treatment outcome, when solving an approximate optimization problem of lower dimension. Through a spectral decompostion, eigenvectors
and eigenvalues of an approximation to the Hessian are computed. An approximate optimization problem of reduced dimension
is formulated by introducing eigenvector weights as optimization parameters, where only eigenvectors corresponding to large
eigenvalues are included.
The approach is evaluated on a clinical prostate case. Compared to bixel weight optimization, eigenvector weight optimization
with few parameters results in faster initial decline in the objective function, but with inferior final solution. Another
approach, which combines eigenvector weights and bixel weights as variables, gives lower final objective values than what
bixel weight optimization does. However, this advantage comes at the expense of the pre-computational time for the spectral
decomposition.
A preliminary version of this paper was presented at the AAPM 46th annual meeting, held July 25–29, 2004 in Pittsburgh, PA. |
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Keywords: | IMRT Optimization Sequential quadratic programming Quasi-Newton method |
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