Abstract
In this study, we introduce a novel approach employing sphere placement with controlled overlaps to strategically position radiation shots within a three-dimensional tumor characterized as a convex polyhedral set. Our primary goal is to ensure optimal radiation dosage by managing sphere overlaps. We present a method that guides a systematic sphere placement procedure, utilizing predetermined sizes, to achieve a heightened filling coefficient within the tumor volume. Through the dense arrangement of these spheres, we effectively minimize uncovered regions, contributing to improved radiation coverage. The iterative packing process concludes upon reaching the threshold where no additional spheres can be accommodated, accounting for permissible overlaps. The proposed methodology embodies principles of an intelligent system, orchestrating the placement sequence to enhance treatment efficacy. A practical illustration is included to demonstrate the application of our approach
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