Michel Pohl, Mitsuru Uesaka, Hiroyuki Takahashi, Kazuyuki Demachi, Ritu Bhusal Chhatkuli
During lung 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 RTRL and truncated BPTT 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. We used 9 observation records of the 3D position of 3 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 between 0.1s and 2.0s, using an RNN trained with UORO. We compare its performance with an RNN trained with RTRL, LMS, and offline linear regression. We provide closed-form expressions for quantities involved in the loss gradient calculation in UORO, thereby making its implementation efficient. Training and cross-validation were performed during the first minute of each sequence. On average over the horizon values considered and the 9 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.
| Task | Dataset | Metric | Value | Model |
|---|---|---|---|---|
| Time Series Forecasting | ExtMarker | Jitter | 0.9672 | UORO |
| Time Series Forecasting | ExtMarker | MAE | 0.845 | UORO |
| Time Series Forecasting | ExtMarker | Maximum error | 8.81 | UORO |
| Time Series Forecasting | ExtMarker | RMSE | 1.275 | UORO |
| Time Series Forecasting | ExtMarker | normalized RMSE | 0.2824 | UORO |
| Time Series Analysis | ExtMarker | Jitter | 0.9672 | UORO |
| Time Series Analysis | ExtMarker | MAE | 0.845 | UORO |
| Time Series Analysis | ExtMarker | Maximum error | 8.81 | UORO |
| Time Series Analysis | ExtMarker | RMSE | 1.275 | UORO |
| Time Series Analysis | ExtMarker | normalized RMSE | 0.2824 | UORO |
| Multivariate Time Series Forecasting | ExtMarker | Jitter | 0.9672 | UORO |
| Multivariate Time Series Forecasting | ExtMarker | MAE | 0.845 | UORO |
| Multivariate Time Series Forecasting | ExtMarker | Maximum error | 8.81 | UORO |
| Multivariate Time Series Forecasting | ExtMarker | RMSE | 1.275 | UORO |
| Multivariate Time Series Forecasting | ExtMarker | normalized RMSE | 0.2824 | UORO |