Conventional direct aperture optimization (DAO) in intensity-modulated radiation therapy uses a gradient map to directly generate an aperture, which is considered the fastest descent method to solve the optimization problem. We derived conjugate- and momentum-gradient descent directions to resolve the problem of convergence oscillation when the fastest descent method approaches the optimal value, while simultaneously solving the optimization problem. However, these improvements do not consider the independent controllability of the beamlet.

Considering previous studies, an aperture shape generation based on AdaGrad is proposed. During optimization, according to the original aperture gradient map obtained, the AdaGrad descent direction is calculated for DAO, and a clinically acceptable aperture shape is generated. The performance of the proposed method was verified via 10 cancer cases. Compared with the generic method, the proposed method reduces the normal tissue complication probability by up to 2.07% and the optimization time by up to 10.17%.

The proposed method demonstrated a significant statistical significance in shortening the optimization time and improving the dose distribution on ipsilateral parotid gland, bladder, and rectum (P < 0.05). The experimental results demonstrated that the proposed method guarantees the dose distribution of the planning target volume and effectively protects the organs at risk. Furthermore, this AdaGrad-based method achieved optimized results that meet the clinical requirements in a shorter time.

Based on theoretical derivation and experimental verification, the proposed method combines the advantages of the AdaGrad gradient concept in deep learning and can effectively and stably obtain optimization results that meet the clinical requirements compared with the generic DAO. The proposed method is applicable to aperture shape generation on different types of cancer.