Respiratory motion forecasting with online learning of recurrent neural networks for safety enhancement in externally guided radiotherapy

In lung radiotherapy, infrared cameras can record the location of reflective objects on the chest to infer the position of the tumor moving due to breathing, but treatment system latencies hinder radiation beam precision. Real-time recurrent learning (RTRL), is a potential solution as it can learn patterns within non-stationary respiratory data but has high complexity. This study assesses the capabilities of resource-efficient online RNN algorithms, namely unbiased online recurrent optimization (UORO), sparse-1 step approximation (SnAp-1), and decoupled neural interfaces (DNI) to forecast respiratory motion during radiotherapy treatment accurately. We use time series containing the 3D position of external markers on the chest of healthy subjects. We propose efficient implementations for SnAp-1 and DNI based on compression of the influence and immediate Jacobian matrices and an accurate update of the linear coefficients used in credit assignment estimation, respectively. The original sampling frequency was 10Hz; we performed resampling at 3.33Hz and 30Hz. We use UORO, SnAp-1, and DNI to forecast each marker's 3D position with horizons (the time interval in advance for which the prediction is made) h<=2.1s and compare them with RTRL, least mean squares, and linear regression. RNNs trained online achieved similar or better accuracy than most previous works using larger training databases and deep learning, even though we used only the first minute of each sequence to predict motion within that exact sequence. SnAp-1 had the lowest normalized root mean square errors (nRMSE) averaged over the horizon values considered, equal to 0.335 and 0.157, at 3.33Hz and 10.0Hz, respectively. Similarly, UORO had the highest accuracy at 30Hz, with an nRMSE of 0.0897. DNI's inference time, equal to 6.8ms per time step at 30Hz (Intel Core i7-13700 CPU), was the lowest among the RNN methods examined.