Aperture Shape Generation Based on Gradient Descent With Momentum

Liyuan Zhang,Zhiguo Gui,Jie Yang,Pengcheng Zhang,Jie Li

doi:10.1109/access.2019.2949871

Abstract

Direct aperture optimization (DAO) is an effective method to generate high-quality intensity-modulated radiation therapy treatment plans. In generic DAO, the direction of negative gradient descent is generally used to determine the aperture shape. However, this strategy can reduce the convergence rate, especially near the optimal value. We propose aperture shape generation based on the direction of gradient descent with momentum, where column generation is implemented as carrier. During aperture shape generation of column generation, the current aperture gradient map is first calculated. Then, the gradient with momentum is calculated based on the existing gradient information. Finally, the direction of gradient descent with momentum is constructed for obtaining the deliverable aperture shape by solving the pricing problem. To verify the effectiveness of the proposed method, we conducted comparative experiments on two head and neck and two prostate tumor cases. Compared with generic column generation, the proposed method can effectively protect the organs at risk while ensuring the required dose distribution to the target. Using the proposed method, the number of apertures and optimization time can be reduced by up to 30.95 and 32.96%, respectively, compared to the conventional approach. The experimental results suggest that the proposed method can accelerate the search speed and improve the quality of treatment plans.

Highlights

Direct aperture optimization (DAO) [1]–[4] usually considers three approaches: stochastic search [5]–[8], local gradient-based method [9], and column generation [10]–[13]
We propose aperture shape generation based on the direction of gradient descent with momentum, where column generation is used as carrier for implementation
EXPERIMENTS AND RESULTS We evaluated two cases of head and neck tumors and two cases of prostate tumors to experimentally verify the proposed aperture shape generation based on gradient descent with momentum in comparison to generic column generation

Summary

Introduction

Direct aperture optimization (DAO) [1]–[4] usually considers three approaches: stochastic search [5]–[8], local gradient-based method [9], and column generation [10]–[13]. The optimization strategies of these three approaches differ, aperture shape generation consists of selecting an appropriate gradient descent direction for the improvement of the objective function. Many studies are available on aperture shape generation. The genetic algorithm to optimize aperture shape has been proposed in [7], [8]. Simulated annealing based on the gradient has been employed for optimization [14], and subsequently, aperture shape optimizations based on fuzzy enhancement [15] and region growth [16] have been proposed.

Objectives

Methods

Results

Discussion

Conclusion