Interval Analysis-Based Optimization: A Robust Model for Intensity-Modulated Radiotherapy (IMRT)

Background: Cancer remains one of the leading causes of mortality worldwide, with radiotherapy playing a crucial role in its treatment. Intensity-modulated radiotherapy (IMRT) enables precise dose delivery to tumors while sparing healthy tissues. However, geometric uncertainties such as patient positioning errors and anatomical deformations can compromise treatment accuracy. Traditional methods use safety margins, which may lead to excessive irradiation of healthy organs or insufficient tumor coverage. Robust optimization techniques, such as minimax approaches, attempt to address these uncertainties but can result in overly conservative treatment plans. This study introduces an interval analysis-based optimization model for IMRT, offering a more flexible approach to uncertainty management. Methods: The proposed model represents geometric uncertainties using interval dose influence matrices and incorporates Bertoluzza's metric to balance tumor coverage and organ-at-risk (OAR) protection. The θ parameter allows controlled robustness modulation. The model was implemented in matRad, an open-source treatment planning system, and evaluated on five prostate cancer cases. Results were compared against traditional Planning Target Volume (PTV) and minimax robust optimization approaches. Results: The interval-based model improved tumor coverage by 5.8% while reducing bladder dose by 4.2% compared to PTV. In contrast, minimax robust optimization improved tumor coverage by 25.8% but increased bladder dose by 23.2%. The interval-based approach provided a better balance between tumor coverage and OAR protection, demonstrating its potential to enhance treatment effectiveness without excessive conservatism. Conclusions: This study presents a novel framework for IMRT planning that improves uncertainty management through interval analysis. By allowing adjustable robustness modulation, the proposed model enables more personalized and clinically adaptable treatment plans. These findings highlight the potential of interval analysis as a powerful tool for optimizing radiotherapy outcomes, balancing treatment efficacy and patient safety.