A unified approach for inversion problems in intensity-modulated radiation therapy.

Area of Science:

• Medical Physics
• Radiation Oncology
• Optimization Theory

Background:

• Radiation therapy planning involves complex dose and source constraints.
• Existing models may require separate handling of different constraint types.
• A unified framework can streamline optimization and improve treatment efficacy.

Purpose of the Study:

• To develop a unified mathematical model for handling dose and radiation source constraints.
• To implement an optimization algorithm based on the split feasibility problem.
• To evaluate the model's performance in achieving feasible or near-feasible solutions.

Main Methods:

• Formulated a unified model using the split feasibility problem framework.
• Developed an optimization algorithm minimizing a weighted proximity function to constraint sets.
• Tested the model with computational results to demonstrate validity.

Main Results:

• The model successfully integrates physical dose, equivalent uniform dose (EUD), and radiation source constraints.
• The algorithm converges to feasible solutions when the problem is consistent.
• For inconsistent problems, the algorithm converges to solutions with minimal constraint violations.

Conclusions:

• The proposed unified model offers a robust mathematical framework for radiation therapy optimization.
• The split feasibility problem approach provides an effective algorithmic scheme for handling complex constraints.
• This method enhances treatment planning by ensuring feasible or minimally violated dose and source constraints.