Impact of the breathing motion prediction horizon on the performance of bidirectional classical recurrent neural and temporal Kolmogorov-Arnold networks

Objective: For breathing motion prediction, which is essential to overcome inherent system latencies of active motion management strategies in radiotherapy, long short-term memory (LSTM) networks have shown promise, primarily for a prediction horizon of 500ms. The related architectures bidirectional LSTMs (BiLSTM), gated recurrent units (GRUs), temporal Kolmogorov-Arnold networks (TKANs), BiGRUs, and BiTKANs remain unexplored for this application. Therefore, this study aimed at assessing the performance of the above six networks for different prediction horizons up to 1000ms. Approach: C-Rad Sentinel (C-Rad AB, Sweden) breathing signals were retrospectively collected for 207 patients. Signals from 41 patients were used for model testing, while the remaining data sets were 90:10 split for training and validation. Pre-processing included cropping, low-pass filtering, re-sampling, and scaling. Signals were cut into 8s segments as input for the prediction models with a corresponding true label. A grid search was performed to optimize hyperparameters for each of the six network types using a prediction horizon of 500ms. Subsequently, each network was trained ten times with these parameters across various training:validation splits, evaluating ten prediction horizons between 100ms and 1000ms. Root mean square errors (RMSEs) between the predicted breathing amplitudes and the true labels as well as inference times were calculated on the test set. Main results: The hyperparameter-tuning resulted in a lowest mean RMSE of 57±39μm for the LSTM, while a mean RMSE of 88±35μm was obtained for the TKAN. TKANs were fastest to infer, averaging 10.2ms per prediction. Increasing prediction horizons resulted in moderate increases of RMSEs up to 113μm for horizons below 600ms. RMSEs remained below 500μm for horizons up to 1000ms. Significance: The LSTM outperforms newer networks for most prediction horizons. All models showed feasibility for a wide range of prediction horizons and the effect of the prediction horizon on the RMSE was assessed.