Future frame prediction in chest cine MR imaging using the PCA respiratory motion model and dynamically trained recurrent neural networks

Lung radiotherapy treatment systems are subject to a latency that leads to uncertainty in the estimated tumor location and high irradiation of healthy tissue. This work addresses future frame prediction in chest dynamic MRI sequences to compensate for that delay using RNNs trained with online learning algorithms. The latter enable networks to mitigate irregular movements, as they update synaptic weights with each new training example. Experiments were conducted using four publicly available 2D thoracic cine-MRI sequences. PCA decomposes the time-varying deformation vector field (DVF), computed with the Lucas-Kanade optical flow algorithm, into static deformation fields and low-dimensional time-dependent weights. We compare various algorithms to forecast the latter: linear regression, least mean squares (LMS), and RNNs trained with real-time recurrent learning (RTRL), unbiased online recurrent optimization, decoupled neural interfaces and sparse 1-step approximation (SnAp-1). That enables estimating the future DVFs and, in turn, the next frames by warping the initial image. Linear regression led to the lowest mean DVF error at a horizon h = 0.32s (the time interval in advance for which the prediction is made), equal to 1.30mm, followed by SnAp-1 and RTRL, whose error increased from 1.37mm to 1.44mm as h increased from 0.62s to 2.20s. Similarly, the structural similarity index measure (SSIM) of LMS decreased from 0.904 to 0.898 as h increased from 0.31s to 1.57s and was the highest among the algorithms compared for the latter horizons. SnAp-1 attained the highest SSIM for h $\geq$ 1.88s, with values of less than 0.898. The predicted images look similar to the original ones, and the highest errors occurred at challenging areas such as the diaphragm boundary at the end-of-inhale phase, where motion variability is more prominent, and regions where out-of-plane motion was more prevalent.