PURPOSE: The stereotactic irradiation of intracranial lesions constitutes an excellent example of conformational therapy whose purpose is to adapt the dose envelope to the target volume with great precision and at the same time to deliver as low a dose as possible to the healthy tissues. We propose the mathematical analysis of the singular values decomposition (SVD) as an inverse planning process to find the optimal minibeam weightings that permit the calculation of the most conformational dose distribution. METHODS: For the radiosurgical treatment of complex lesions, we realize a division of the lesion into several elliptic volumes using the "Associated Target Methodology." This division allows the definition of an irradiation configuration: the number of isocenters, the position of the isocenters, and the diameter of each collimator. For this defined irradiation configuration, we use SVD to find the optimal minibeam weightings. This analysis enables us to understand better the ill-conditioning of the multi-isocentric irradiation and the influence of irradiation parameters on the process of reconstruction minibeam weightings. RESULTS: In this paper, the SVD analysis and the reconstruction technique have been evaluated for the first time on practical cases. We present, as an example, a complex lesion compartmentalized into 3 subvolumes according to our Associated Target Methodology. This analysis allows us to study the ill-conditioning of the example and proposes a large number of solutions from among which we have to choose the most conformational physical solution. This choice is based on the dose-volume histograms. CONCLUSION: We use the SVD procedure as a computer-aided planning system and obtain good solutions, i.e., healthy tissue protection and lesion coverage similar to or better than an experimented planner solution.
PURPOSE: The stereotactic irradiation of intracranial lesions constitutes an excellent example of conformational therapy whose purpose is to adapt the dose envelope to the target volume with great precision and at the same time to deliver as low a dose as possible to the healthy tissues. We propose the mathematical analysis of the singular values decomposition (SVD) as an inverse planning process to find the optimal minibeam weightings that permit the calculation of the most conformational dose distribution. METHODS: For the radiosurgical treatment of complex lesions, we realize a division of the lesion into several elliptic volumes using the "Associated Target Methodology." This division allows the definition of an irradiation configuration: the number of isocenters, the position of the isocenters, and the diameter of each collimator. For this defined irradiation configuration, we use SVD to find the optimal minibeam weightings. This analysis enables us to understand better the ill-conditioning of the multi-isocentric irradiation and the influence of irradiation parameters on the process of reconstruction minibeam weightings. RESULTS: In this paper, the SVD analysis and the reconstruction technique have been evaluated for the first time on practical cases. We present, as an example, a complex lesion compartmentalized into 3 subvolumes according to our Associated Target Methodology. This analysis allows us to study the ill-conditioning of the example and proposes a large number of solutions from among which we have to choose the most conformational physical solution. This choice is based on the dose-volume histograms. CONCLUSION: We use the SVD procedure as a computer-aided planning system and obtain good solutions, i.e., healthy tissue protection and lesion coverage similar to or better than an experimented planner solution.