Multi-Criteria Inverse Robustness in Radiotherapy Planning Using Semidefinite Programming

Area of Science:

• Medical Physics
• Optimization Theory
• Radiation Oncology

Background:

• Radiotherapy planning involves complex multi-criteria optimization.
• Uncertainty in treatment parameters poses significant challenges.
• Balancing objectives and robustness is crucial for effective treatment.

Purpose of the Study:

• To develop a quantitative approach for radiotherapy planning under uncertainty.
• To integrate robustness against uncertainty as an objective.
• To address practical challenges in treatment plan optimization.

Main Methods:

• Modeling uncertainty using interval matrices derived from dose-influence matrices.
• Introducing inverse robustness as an objective to maximize uncertainty set volume.
• Employing a multi-criteria optimization framework.
• Solving the quadratically constrained quadratic optimization problem (QCQP) via semidefinite programming (SDP) relaxation.

Main Results:

• Demonstrated a method to handle uncertainty in radiotherapy planning.
• Successfully integrated inverse robustness into the optimization process.
• Developed a technique to solve QCQP by transforming it into an SDP.

Conclusions:

• The proposed quantitative approach effectively balances multiple objectives and uncertainty in radiotherapy planning.
• Inverse robustness provides a novel way to manage uncertainty.
• The SDP relaxation method offers a viable solution for complex optimization problems in radiation oncology.