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

To establish a new mathematical framework for IMRT treatment optimization with voxel-dependent optimization parameters.

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.

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.

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.