IMRT Treatment Planning Under Dose Uncertainty: A Polyhedral and Quadratic Programming Optimization Model

Cancer stands as a significant global mortality factor. Timely detection and proper treatment, such as intensity-modulated radiation therapy (IMRT), can hinder cancer progression. IMRT is crucial for targeting tumors while safeguarding healthy tissues. This study proposes a robust mathematical model addressing uncertainties in the dose delivered to the tumor as treatment sessions progress, using a polyhedral uncertainty set. The model employs linear constraints and a quadratic objective function derived from dose calculations. Variations of Newton-barrier and reduced gradient algorithms are utilized to solve the problem using real patient data, particularly from a prostate cancer case. Notably, the proposed method reduces penalties for healthy organs by approximately nine percent while maintaining an adequate dose delivered to the tumor.