The objectives of radiotherapy treatment is to kill cancerous cells while minimizing damage to surrounding healthy tissues. The tumour location uncertainty "forces" oncologists to prescribe a larger treatment area than required in order to ensure that the whole tumour is receiving the prescribed dose. The problem is more acute when a tumour can move during treatment, e.g., as a result of breathing. In this paper, we present an algorithm for computing the area covered by a tumor as a result of a cyclic motion during treatment. Our algorithm solves the following geometric problem: Given an n-vertices convex polygon P = {v 1 v 2,... v n}, a monotone chain C = {c 1, c 2..., c m}, compute a minimums area polygon Q that includes all the space covered by P as it is translated along C such that v 1 ∈ P touches C. Here, we present a simple algorithm when P is a convex polygon. Our algorithm takes O(mn + m log n log(m + n)) time in the worst case.

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Conference 3rd International Conference on Information Technology and Applications, ICITA 2005
Citation
Chen, J., Lanthier, M, MacPherson, M., & Nussbaum, D. (2005). Computing tumour coverage as a result of respiratory motion during radiotherapy treatment. Presented at the 3rd International Conference on Information Technology and Applications, ICITA 2005.