From Univariate to Multivariate Respiratory Motion Compensation - A Bayesian Way to Increase Treatment Accuracy in Robotic Radiotherapy

Cancer is one of the most prevalent causes of death worldwide. Even though intense research effort has been dedicated to advance diagnostic and treatment techniques, statistics indicate that the five year survival rates especially for lung, liver and pancreas tumours are still very low. Radiotherapy is a relevant treatment option beside surgical and chemotherapeutic approaches. One treatment option for tumours located in the breast and abdominal regions is robotic radiotherapy. The advantage is that tumour motion caused by respiratory or cardiac motion of patients can be compensated which increases the treatment accuracy. Clinically used systems are the CyberKnife or multileaf collimators (MLCs). To perform an adaptive motion compensation (MC), two problems have to be addressed. First, time latencies of the specific treatment system (due to data processing and kinematic limitations) have to be compensated. Second, real-time acquisition of the internal tumour position is not possible without exposing the patient to an additional radiation dose. To overcome these problems, prediction and correlation models are used, which both depend on data of univariate external optical surrogates. The problem of respiratory motion compensation is relevant for various medical applications. In general, a diverse number of techniques has been developed to measure respiratory activity including different sensor modalities and measurement positions. However, data of a single sensor covers only information of a specific aspect of the more complex underlying process of respiration. Motivated by this observation, the first and main focus of this work is to develop multivariate extensions of current prediction and correlation models. The aim is to efficiently combine information of multiple sensors to further increase treatment accuracy. In particular, probabilistic algorithms will be applied for this purpose. Due to the increased power of modern computers, these computationally more demanding models have become applicable for real-time applications. In contrast to non-probabilistic models, the output of these algorithms is a probability distribution with predicted mean and variance. The variance contains relevant information about the “certainty” of the algorithm in the current output. Such information might be useful to control the prediction error during the treatment, which is the second main focus of this work. An extensive literature review confirms the initial assumptions that primarily optical surrogates were investigated in the literature. Furthermore, only one probabilistic algorithm was evaluated for the purpose of respiratory motion compensation - with controversial results. As a consequence, two new MC algorithms were developed, namely Gaussian process (GP) models and relevance vector machines (RVMs). Before applying these in a multivariate setting, the performance of these algorithms was examined for the purpose of standard univariate prediction models. The influence of model specific parameters such as the number of training pairs (in case of RVM) and covariance function (in case of GP) was studied on selected motion traces. Furthermore, a comprehensive evaluation was performed on a dataset consisting of 304 motion traces. They were compared to six previously published algorithms including support vector regression (SVR), Kalman Filter, and wavelet-based least mean square (wLMS) methods for four different prediction latencies. On average, the RVM model with a linear basis function had a superior accuracy and outperformed all previous algorithms independently of the prediction latencies. The result of the best GP model indicates a superior accuracy for shorter prediction horizons (h = 77, 115, 154 ms) compared to the previously published algorithms. For h = 115 ms, the GP approach predicts 78.62 % and the RVM model 92.43 % of the data more accurately or equally good as the wLMS method (which had been the best algorithm so far). The benefit of monitoring the variance was investigated on the same dataset for the RVM model, exemplarily. Applying a simple variance threshold, to interrupt the treatment if exceeded, confirmed that the prediction error can be controlled by the variance. Further experiments showed that the variance can be exploited as a criterion to design hybrid algorithms. A practically relevant approach (as it does not require further parameters) is the combination of three RVM models with different basis functions (HYBRVM), which could even predict 94.74 % of the data more accurately or equally good as the wLMS method. In contrast to alternative real-time measures such as the current prediction error, the variance is only based on the input features x and not on the output y. This allows an error control for applications where the true output cannot be constantly observed as in the case of correlation algorithms. To investigate multivariate motion compensation techniques, a human study with 18 subjects was performed. Data of six external modalities such as acceleration, respiratory flow, or surface electromyography (sEMG) were acquired for two measurement phases; focussing on either normal or irregular breathing. Internal data were recorded by 4D-ultrasound (US) of the liver. An initial analysis of the correlation between the data of external, and external and internal signals revealed high correlation coefficients (0.54 ≤ r ≤ 0.93) between non-optical and optical surrogates or the internal motion, respectively. In the following, multivariate prediction algorithms were investigated. The input data of three non-probabilistic algorithms (nLMS, wLMS, SVR) and the RVM model were extended to incorporate multivariate data. To prevent overfitting, a sequential forward selection (SFS) method was used to select the most relevant and least redundant sensor combination. Using a multivariate instead of a univariate setting, the mean root mean square error (RMSE) of RVM (which outperformed all other approaches) decreased by 20% in the case of normal breathing and by 12% in the case of irregular breathing. In order to extend GP models to multivariate data, an alternative approach was investigated. Instead of extending the input data, a multi-output model was examined. We refer to this approach as multi-task Gaussian Process (MTGP) models. These models are capable of learning the correlation between and within sensors and offer several distinct advantages such as • prediction of arbitrary latencies independent of the sampling frequency, • incorporation of prior knowledge of the signal characteristics, and • use of signal-specific training observations. The latter is particularly relevant for motion compensation algorithms. With the MTGP approach, unified prediction and correlation models can be constructed which make use of all available training data. The properties of this new approach was intensively studied on synthetic examples and led to the development of an open-access toolbox2. Further, the approach was evaluated as uni- and multivariate correlation as well as a unified prediction and correlation algorithm. The comparison to alternative correlation approaches based on polynomial models or SVR revealed a superior performance of MTGPs. By using multivariate data, the mean RMSE of an MTGP based correlation algorithm could be decreased by 0.2 mm (≈ 10. Similar results were observed for a unified MTGP prediction and correlation model for different prediction latencies. The results of this work show that probabilistic prediction algorithms can predict over 95% of the data more accurately compared to previous results. Furthermore, the overall accuracy of adaptive motion compensation can be increased by on average 0.2 mm when using multivariate data. Most of the applied sensors are already used in clinical practise which allows a fast and cost-efficient integration into current radiotherapy systems.