The equivalence of multi-criteria methods for radiotherapy plan optimization

Area of Science:

• Medical Physics
• Radiation Oncology
• Computational Biology

Background:

• Multi-criteria optimization is crucial for radiation therapy planning, aiming for Pareto-optimal solutions where no objective improves without compromising another.
• Existing methods like weighted-sum and constrained optimization (e.g., 2-phase element-constraint) generate Pareto-optimal plans but lack flexibility for dynamic adjustments.

Purpose of the Study:

• To establish a theoretical framework for interconversion between constrained and weighted-sum optimization methods in radiation therapy planning.
• To demonstrate the utility of Lagrange multipliers for transitioning between these optimization approaches.

Main Methods:

• Utilized Lagrange multipliers derived from constrained optimization problems to formulate equivalent weighted-sum optimization problems.
• Developed a method to convert weighted-sum problems into constrained problems by setting appropriate constraints.
• Applied the 2-phase element-constraint method as the primary constrained optimization technique.

Main Results:

• Successfully demonstrated the theoretical equivalence and practical interchangeability of constrained and weighted-sum optimization methods.
• Showcased the ability to switch from a constrained method to a weighted-sum method using Lagrange multipliers.
• Validated the approach with an example of modifying an automated treatment plan to reduce dose in a specific structure.

Conclusions:

• The presented theory enables flexible adjustments to radiation therapy plans, particularly useful in online planning, handling anatomical changes, or refining automated plans.
• This interconversion capability enhances the adaptability of treatment planning systems to evolving clinical needs and patient-specific variations.