Author: Peng Dong, Lei Xing 👨🔬
Affiliation: Department of Radiation Oncology, Stanford University, Stanford University 🌍
Purpose: Volumetric Modulated Arc Therapy (VMAT) optimization is a complex, non-convex problem with numerous variables and intricate constraints. Traditional optimization methods often lack efficiency. This study reformulates VMAT optimization as a neural network training task, leveraging differentiable programming to enhance performance and quality.
Methods: We developed a neural network model initializing three primary learnable parameters: MLC left leaf position, leaf opening, and monitor units for each control point. The forward pass involves matrix multiplications with beamlet position matrices, followed by a custom activation function using softsign/sigmoid operations to approximate the square function, ensuring contiguous beamlet constraints. The network outputs a weighted combination that modulates treatment plan parameters. The loss function captures VMAT optimization's multifaceted objectives by integrating mean squared errors and ReLU-based penalties targeting PTV, bladder, rectum, and femoral areas. Additionally, it incorporates constraints on maximum dose and DVH metrics like D95%. Optimization utilizes gradient descent and backpropagation with the Adamx optimizer for efficiency. The model was implemented in PyTorch, optimized for high-performance hardware.
Results: In a proof-of-concept experiment on a MacBook with an M2Max chip, the neural network-based VMAT optimization minimized the objective function in under five minutes and 2,500 iterations. Applied to a prostate cancer patient, the optimized plan showed favorable isodose distributions at 50%, 75%, and 100% levels, along with improved DVH metrics. The combination of the softsign activation function and the Adamx optimizer outperformed other configurations. The model effectively navigated the non-convex optimization landscape, achieving both target coverage and organ-at-risk constraints with high quality.
Conclusion: Integrating neural network training with differentiable programming and custom loss formulations presents a promising alternative to conventional VMAT optimization methods. This approach enables rapid, efficient optimization, overcoming local minima and enhancing quality. Preliminary results indicate significant potential for more robust and scalable optimization frameworks in radiation therapy planning, warranting further development.