TU‐G‐BRB‐02: A New Mathematical Framework for IMRT Inverse Planning with Voxel‐Dependent Optimization Parameters

Purpose: To establish a new mathematical framework for IMRT treatment optimization with voxel‐dependent optimization parameters. Methods: In IMRT inverse treatment planning, a physician seeks for a plan to deliver a prescribed dose to the target while sparing the nearby healthy tissues. The conflict between these objectives makes the multi‐criteria optimization an appropriate tool. Traditionally, a clinically acceptable plan can be generated by fine‐tuning organ‐based parameters. We establish a new mathematical framework by using voxel‐based parameters for optimization. We introduce three different Pareto surfaces, prove the relationship between those surfaces, and compare voxel‐based and organ‐based methods. We prove some new theorems providing conditions under which the Pareto optimality is guaranteed. Results: The new mathematical framework has shown that: 1) Using an increasing voxel penalty function with an increasing derivative, in particular the popular power function, it is possible to explore the entire Pareto surface by changing voxel‐based weighting factors, which increases the chances of getting more desirable plan. 2) The Pareto optimality is always guaranteed by adjusting voxel‐based weighting factors. 3) If the plan is initially produced by adjusting organ‐based weighting factors, it is impossible to improve all the DVH curves at the same time by adjusting voxel‐based weighting factors. 4) A larger Pareto surface is explored by changing voxel‐based weighting factors than by changing organ‐based weighting factors, possibly leading to a plan with better trade‐offs. 5) The Pareto optimality is not necessarily guaranteed while we are adjusting the voxel reference doses, and hence, adjusting voxel‐based weighting factors is preferred in terms of preserving the Pareto optimality. Conclusions: We have developed a mathematical framework for IMRT optimization using voxel‐based parameters. We can improve the plan quality by adjusting voxel‐based weighting factors after organ‐based parameter adjustment. This work is supported by Varian Medical Systems through a Master Research Agreement.