A general optimization procedure for stereotactic small‐beam multi‐isocentric radiotherapy

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Abstract
Clinical experience in single‐dose stereotactic radiotherapy of irregular complex lesions has shown that new developments in optimization procedures were necessary to improve dose distribution, making this conformal technique more efficient. We propose a conformal procedure for stereotactic radiotherapy of complex lesions treated with multiple isocenters based on the associated targets methodology. The successive steps of this conformal procedure are: (a) the determination of the number of subvolumes; (b) the choice of collimator diameters using a dosimetric data basis; (c) the search by the inverse SVD optimizer algorithm for the optimal irradiation space and the minibeam weights for each subvolume using singular value decomposition; (d) the basis of quantitative evaluation criteria for the choice of satisfactory solutions on dose‐volume histograms and clinical considerations. The efficiency of the SVD optimizer to planify multi‐isocentric treatments was examined in the case of an irregular lesion planified with two isocenters. The condition number of this dual isocentric configuration showed a more ill‐conditioned problem than in the monoisocentric case. Examining different reconstructed weighting vectors, we observed that optimal solutions are obtained with the first singular components and an important healthy tissue overdosage occurs when the number of singular components used in the SVD expansion increases. Our SVD optimization approach is a general procedure which can be applied to different radiotherapy techniques.