The motion of thoracic and abdominal tumours induced by respiratory motion often exceeds 20 mm, and can significantly compromise dose conformality. Motion-adaptive radiotherapy aims to deliver a conformal dose distribution to the tumour with minimal normal tissue exposure by compensating for the tumour motion. This adaptive radiotherapy, however, requires the prediction of the tumour movement that can occur over the system latency period. In general, motion prediction approaches can be classified into two groups: model-based and model-free. Model-based approaches utilize a motion model in predicting respiratory motion. These approaches are computationally efficient and responsive to irregular changes in respiratory motion. Model-free approaches do not assume an explicit model of motion dynamics, and predict future positions by learning from previous observations. Artificial neural networks (ANNs) and support vector regression (SVR) are examples of model-free approaches. In this article, we present a prediction algorithm that combines a model-based and a model-free approach in a cascade structure. The algorithm, which we call EKF-SVR, first employs a model-based algorithm (named LCM-EKF) to predict the respiratory motion, and then uses a model-free SVR algorithm to estimate and correct the error of the LCM-EKF prediction. Extensive numerical experiments based on a large database of 304 respiratory motion traces are performed. The experimental results demonstrate that the EKF-SVR algorithm successfully reduces the prediction error of the LCM-EKF, and outperforms the model-free ANN and SVR algorithms in terms of prediction accuracy across lookahead lengths of 192, 384, and 576 ms.

Motion-adaptive radiotherapy aims to deliver a conformal dose to the target tumour with minimal normal tissue exposure by compensating for tumour motion in real time. The prediction as well as the gating of respiratory motion have received much attention over the last two decades for reducing the targeting error of the treatment beam due to respiratory motion. In this article, we present a real-time algorithm for predicting and gating respiratory motion that utilizes a model-based and a model-free Bayesian framework by combining them in a cascade structure. The algorithm, named EKF-GPR(+), implements a gating function without pre-specifying a particular region of the patient's breathing cycle. The algorithm first employs an extended Kalman filter (LCM-EKF) to predict the respiratory motion and then uses a model-free Gaussian process regression (GPR) to correct the error of the LCM-EKF prediction. The GPR is a non-parametric Bayesian algorithm that yields predictive variance under Gaussian assumptions. The EKF-GPR(+) algorithm utilizes the predictive variance from the GPR component to capture the uncertainty in the LCM-EKF prediction error and systematically identify breathing points with a higher probability of large prediction error in advance. This identification allows us to pause the treatment beam over such instances. EKF-GPR(+) implements the gating function by using simple calculations based on the predictive variance with no additional detection mechanism. A sparse approximation of the GPR algorithm is employed to realize EKF-GPR(+) in real time. Extensive numerical experiments are performed based on a large database of 304 respiratory motion traces to evaluate EKF-GPR(+). The experimental results show that the EKF-GPR(+) algorithm effectively reduces the prediction error in a root-mean-square (RMS) sense by employing the gating function, albeit at the cost of a reduced duty cycle. As an example, EKF-GPR(+) reduces the patient-wise RMS error to 37%, 39% and 42% in percent ratios relative to no prediction for a duty cycle of 80% at lookahead lengths of 192 ms, 384 ms and 576 ms, respectively. The experiments also confirm that EKF-GPR(+) controls the duty cycle with reasonable accuracy.

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The prediction as well as the gating of respiratory motion have received much attention over the last two decades for reducing the targeting error of the radiation treatment beam due to respiratory motion. In this article, we present a real-time algorithm for predicting respiratory motion in 3D space and realizing a gating function without pre-specifying a particular phase of the patient's breathing cycle. The algorithm, named EKF-GPRN(+) , first employs an extended Kalman filter (EKF) independently along each coordinate to predict the respiratory motion and then uses a Gaussian process regression network (GPRN) to correct the prediction error of the EKF in 3D space. The GPRN is a nonparametric Bayesian algorithm for modeling input-dependent correlations between the output variables in multi-output regression. Inference in GPRN is intractable and we employ variational inference with mean field approximation to compute an approximate predictive mean and predictive covariance matrix. The approximate predictive mean is used to correct the prediction error of the EKF. The trace of the approximate predictive covariance matrix is utilized to capture the uncertainty in EKF-GPRN(+) prediction error and systematically identify breathing points with a higher probability of large prediction error in advance. This identification enables us to pause the treatment beam over such instances. EKF-GPRN(+) implements a gating function by using simple calculations based on the trace of the predictive covariance matrix. Extensive numerical experiments are performed based on a large database of 304 respiratory motion traces to evaluate EKF-GPRN(+) . The experimental results show that the EKF-GPRN(+) algorithm reduces the patient-wise prediction error to 38%, 40% and 40% in root-mean-square, compared to no prediction, at lookahead lengths of 192 ms, 384 ms and 576 ms, respectively. The EKF-GPRN(+) algorithm can further reduce the prediction error by employing the gating function, albeit at the cost of reduced duty cycle. The error reduction allows the clinical target volume to planning target volume (CTV-PTV) margin to be reduced, leading to decreased normal-tissue toxicity and possible dose escalation. The CTV-PTV margin is also evaluated to quantify clinical benefits of EKF-GPRN(+) prediction.