Prediction of the motion of chest internal points using a recurrent neural network trained with real-time recurrent learning for latency compensation in lung cancer radiotherapy

During the radiotherapy treatment of patients with lung cancer, the radiation delivered to healthy tissue around the tumor needs to be minimized, which is difficult because of respiratory motion and the latency of linear accelerator (LINAC) systems. In the proposed study, we first use the Lucas-Kanade pyramidal optical flow algorithm to perform deformable image registration (DIR) of chest computed tomography (CT) scan images of four patients with lung cancer. We then track three internal points close to the lung tumor based on the previously computed deformation field and predict their position with a recurrent neural network (RNN) trained using real-time recurrent learning (RTRL) and gradient clipping. The breathing data is quite regular, sampled at approximately 2.5 Hz, and includes artificially added drift in the spine direction. The amplitude of the motion of the tracked points ranged from 12.0 mm to 22.7 mm. Finally, we propose a simple method for recovering and predicting three-dimensional (3D) tumor images from the tracked points and the initial tumor image, based on a linear correspondence model and the Nadaraya-Watson non-linear regression. The root-mean-square (RMS) error, maximum error and jitter corresponding to the RNN prediction on the test set were smaller than the same performance measures obtained with linear prediction and least mean squares (LMS). In particular, the maximum prediction error associated with the RNN, equal to 1.51 mm, is respectively 16.1% and 5.0% lower than the error given by a linear predictor and LMS. The average prediction time per time step with RTRL is equal to 119 ms, which is less than the 400 ms marker position sampling time. The tumor position in the predicted images appears visually correct, which is confirmed by the high mean cross-correlation between the original and predicted images, equal to 0.955. The standard deviation of the Gaussian kernel and the number of layers in the optical flow algorithm were the parameters having the most significant impact on registration performance. Their optimization led respectively to a 31.3% and 36.2% decrease in the registration error. Using only a single layer proved to be detrimental to the registration quality because tissue motion in the lower part of the lung has a high amplitude relative to the resolution of the CT scan images. The random initialization of the hidden units and the number of these hidden units were found to be the most important factors affecting the performance of the RNN. Increasing the number of hidden units from 15 to 250 led to a 56.3% decrease in the prediction error on the cross-validation data. Similarly, optimizing the standard deviation of the initial Gaussian distribution of the synaptic weights sigma(RNN)(init) led to a 28.4% decrease in the prediction error on the cross-validation data, with the error minimized for sigma(RNN)(init) = 0.02 with the four patients.