Background and objective: During lung cancer radiotherapy, the position of infrared reflective objects on the chest can be recorded to estimate the tumor location. However, radiotherapy systems have a latency inherent to robot control limitations that impedes the radiation delivery precision. Prediction with online learning of recurrent neural networks (RNN) allows for adaptation to non-stationary respiratory signals, but classical methods such as real-time recurrent learning (RTRL) and truncated backpropagation through time are respectively slow and biased. This study investigates the capabilities of unbiased online recurrent optimization (UORO) to forecast respiratory motion and enhance safety in lung radiotherapy.
Methods: We used nine observation records of the three-dimensional (3D) position of three external markers on the chest and abdomen of healthy individuals breathing during intervals from 73s to 222s. The sampling frequency was 10Hz, and the amplitudes of the recorded trajectories range from 6mm to 40mm in the superior-inferior direction. We forecast the 3D location of each marker simultaneously with a horizon value (the time interval in advance for which the prediction is made) between 0.1s and 2.0s, using an RNN trained with UORO. We compare its performance with an RNN trained with RTRL, least mean squares (LMS), and offline linear regression. We provide closed-form expressions for quantities involved in the gradient loss calculation in UORO, thereby making its implementation efficient. Training and cross-validation were performed during the first minute of each sequence.
Results: On average over the horizon values considered and the nine sequences, UORO achieves the lowest root-mean-square (RMS) error and maximum error among the compared algorithms. These errors are respectively equal to 1.3mm and 8.8mm, and the prediction time per time step was lower than 2.8ms (Dell Intel core i9-9900K 3.60 GHz). Linear regression has the lowest RMS error for the horizon values 0.1s and 0.2s, followed by LMS for horizon values between 0.3s and 0.5s, and UORO for horizon values greater than 0.6s.
Conclusions: UORO can accurately predict the 3D position of external markers for intermediate to high response times with an acceptable time performance. This will help limit unwanted damage to healthy tissues caused by radiotherapy.
Keywords: Lung cancer; Online learning; Radiotherapy; Recurrent neural network; Respiratory motion management; Time series forecasting.
Copyright © 2022. Published by Elsevier B.V.