Lexicographic ordering: intuitive multicriteria optimization for IMRT

Abstract

Optimization problems in IMRT inverse planning are inherently multicriterial since they involve multiple planning goals for targets and their neighbouring critical tissue structures. Clinical decisions are generally required, based on tradeoffs among these goals. Since the tradeoffs cannot be quantitatively determined prior to optimization, the decision-making process is usually indirect and iterative, requiring many repetitive optimizations. This situation becomes even more challenging for cases with a large number of planning goals. To address this challenge, a multicriteria optimization strategy called lexicographic ordering (LO) has been implemented and evaluated for IMRT planning. The LO approach is a hierarchical method in which the planning goals are categorized into different priority levels and a sequence of sub-optimization problems is solved in order of priority. This prioritization concept is demonstrated using two clinical cases (a simple prostate case and a relatively complex head and neck case). In addition, a unique feature of LO in a decision support role is discussed. We demonstrate that a comprehensive list of planning goals (e.g., ∼23 for the head and neck case) can be optimized using only a few priority levels. Tradeoffs between different levels have been successfully prohibited using the LO method, making the large size problem representations simpler and more manageable. Optimization time needed for each level was practical, ranging from ∼26 s to ∼217 s. Using prioritization, the LO approach mimics the mental process often used by physicians as they make decisions handling the various conflicting planning goals. This method produces encouraging results for difficult IMRT planning cases in a highly intuitive manner.