| The goal of radiotherapy treatment is to kill a cancerous tumor while minimizing the damage to the surrounding healthy tissues. Several factors affect the ability to achieve this goal. One of the factors is tumor motion (e.g., as a result of breathing). In this thesis, we introduced a new solution to compensate for respiratory movement both for treatment planning and for treatment during radiation therapy. We also presented an algorithm which computes tumor coverage due to a patient's respiratory cycle. This algorithm solves the following problem: Given an n-vertex convex polygon P = {lcub}v1, v2,..., vn{rcub} and a monotone chain C = {lcub} c1, c2,..., c m{rcub}, compute a minimal area polygon Q that includes all the space covered by P as it is translated along C such that C is the trajectory of a vertex vi ∈ P. Our algorithm takes O(mn+m log n log( m+n)) time in the worst case. By applying this algorithm, individual tumor coverage can be computed and used to optimize treatment planning. |
