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Study of the degree of III conditioning of the phase space of pencil‐beam radiotherapy using singular value decomposition
Author(s) -
Lefkopoulos D.,
Grandjean P.,
Laouar A.,
Schlienger M.
Publication year - 1995
Publication title -
international journal of imaging systems and technology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.359
H-Index - 47
eISSN - 1098-1098
pISSN - 0899-9457
DOI - 10.1002/ima.1850060113
Subject(s) - singular value decomposition , weighting , mathematical optimization , inverse , singular value , computer science , pencil (optics) , mathematics , algorithm , physics , optics , radiology , medicine , eigenvalues and eigenvectors , geometry , quantum mechanics
Dose distribution optimization algorithms are necessary in pencil‐beam radiotherapy to exploit efficiently the multiple parameters of this powerful irradiation technique. We propose as an optimization technique singular value decomposition (SVD) analysis, which allows the measurement of ill conditioning of the stereotactic radiotherapy inverse problem and yields optimal weights for conformal treatment. Our approach to dose distribution optimization is to recover estimates of the minibeams weights from well‐defined previsional dose matrices to study the influence of the different parameters on the stereotactic radiotherapy inverse procedure. The adjustment of the different parameters of the stereotactic irradiation to the “SVD optimizer” procedure is realized taking into account the ratio of the quality reconstruction to the calculation time. It will permit a more efficient use of the SVD optimizer in clinical applications with real three‐dimensional lesions. We show the efficiency of the SVD optimizer in analyzing and predicting ill conditioning in stereotactic radiotherapy and in recognizing the topography of the different beams to create an optimal vector containing the beam weights (reconstructed weighting vector).