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Biological optimization of tumor radiosurgery.

In tumor radiosurgery, a high dose of radiation is delivered in a single session. The question then naturally arises of selecting an irradiation strategy of high biological efficiency. In this study, the authors propose a mathematical framework to investigate the biological effects of heterogeneity and rate of dose delivery in radiosurgery. The authors simulate a target composed by proliferating and hypoxic tumor cells as well as by normal tissue. Treatment outcome is evaluated by a functional of the dose distribution that counts the LQ-surviving fractions of each cell type. Prescriptions on intensity, homogeneity, and duration of radiation delivery are incorporated as constraints. Biological optimization is performed by means of calculus of variation techniques. For a fixed dose, increasing heterogeneity considerably improved the biological performance. The dose peaks progressively concentrated in the hypoxic and proliferating areas, while damage to normal tissue was reduced. The duration of delivery, optimized in the range of 1-30 min and for various tumor/normal characteristic DNA repair time ratios, coincided with the maximum allowed value. It resulted in a poor therapeutic gain, which was positively correlated with the tumor/normal characteristic DNA repair time ratio. The mathematical framework described in this work allows one to design the dose distribution and dose rate of biologically based plans for tumor radiosurgery. It may be thus integrated into the available simulation softwares to assist in treatment planning.