STUDY OF THE DEGREE OF ILL CONDITIONING OF THE PHASE-SPACE OF PENCIL-BEAM RADIOTHERAPY USING SINGULAR-VALUE DECOMPOSITION

Dose distribution optimization algorithms are necessary in pencil-beam radiotherapy to exploit efficiently the multiple parameters of this p owerful irradiation technique. We propose as an optimization technique singular value decomposition (SVD) analysis, which allows the measure ment of ill conditioning of the stereotactic radiotherapy inverse prob lem and yields optimal weights for conformal treatment. Our approach t o dose distribution optimization is to recover estimates of the minibe ams weights from well-defined previsional dose matrices to study the i nfluence of the different parameters on the stereotactic radiotherapy inverse procedure. The adjustment of the different parameters of the s tereotactic irradiation to the ''SVD optimizer'' procedure is realized taking into account the ratio of the quality reconstruction to the ca lculation time. It will permit a more efficient use of the SVD optimiz er in clinical applications with real three-dimensional lesions. We sh ow the efficiency of the SVD optimizer in analyzing and predicting ill conditioning in stereotactic radiotherapy and in recognizing the topo graphy of the different beams to create an optimal vector containing t he beam weights (reconstructed weighting vector). (C) 1995 John Wiley and Sons, Inc.