In robotic radiotherapy, systematic latencies have to be compensated by prediction of external optical surrogates. We investigate possibilities to increase the prediction accuracy using multi-modal sensors. The measurement setup includes position, acceleration, strain and flow sensors. To select the most relevant and least redundant information from the sensors and to limit the size of the feature set, a sequential forward selection (SFS) method is proposed. The method is evaluated with three prediction algorithms - the least means square (LMS) algorithm, a wavelet-based LMS algorithm (wLMS) and an algorithm using relevance vector machines (RVM). We show that multi-modal inputs can easily be integrated into general algorithms. The relative root mean square error (RMSrel) of the best predictor, RVM, could be decreased from 60.5 % to 49.0 %. Furthermore, the results indicate that more complex algorithms can efficiently use different modalities like acceleration which are less correlated with the optical sensor to be predicted.
The data set consists of 18 subjects (11 male / 7 female, aged: 21 – 34 years). Each subject was asked to breathe normally for 20 minutes. The first and the last minutes of each recording were discarded to eliminate potential irregular breathing periods due to initialization or finalization of the measurement. Figure 1.a shows the placement of all six external sensors. As it is clinical standard for CyberKnife treatments, three optical markers (OM) were used. They were placed along the median line of the thorax and abdomen, starting with OM1 close to the areolas mammae, OM2 at the bottom end of the sternum and OM3 above the navel. The position was measured with an accuTrack 250 system (Atracsys LLC, Switzerland). The enlargement of the thorax was measured with a strain belt sensor (SleepSense Piezo Effort Sensor) which was placed between OM1 and OM2. The air flow was measured indirectly with a thermistor (SleepSense Airflow Thermistor). The strain belt and the flow sensor were connected to a g.tec USB amplifier (g.tec medical engineering GmbH, Austria). An acceleration (ACC) sensor was placed between OM1 and the strain belt, which measured the acceleration in all three directions with a range of ±2 g. All sensors were synchronized via strobe values and downsampled to a sample frequency of fs = 26 Hz, which is used in the current CyberKnife system. The 3D position and acceleration signals were reduced to their first principal component. More details about the setup are given in [3].
To compensate the latency error, the prospective true signal amplitude of an external surrogate yt+δ can be predicted. Here, t is the index of the current time step and δ is the prediction horizon, which was fixed to δ = 3 according to the latency of the CyberKnife system. The output of a prediction algorithm is denoted by . In general, the prediction is based on an input vector yt = {yt, yt-1, …, yt-p+1} of the current and previously observed data points, where p is the number of features per input vector. In recent years, several prediction algorithms have been proposed, which try to learn the underlying function f(yt). As many of these algorithms are general prediction algorithms, they are not restricted to a certain signal modality or to a certain size of yt like e.g. Kalman Filters. Therefore, to predict for example the signal of the second optical marker , yt can be extended by the input vectors of OM1 and ACC to ytOM2,OM1,ACC = {ytOM2, ytOM1, ytACC}. Assuming a constant p, the dimension of the input vector would increases by a factor of three. To evaluate our approach, we perform multi-modal prediction with three prediction algorithms. The first algorithm is the classical LMS algorithm which performs predictions according to = wTyt. The weight vector w is adaptively learned at each time step t by minimizing the current prediction error et = yt - wTyt. To increase the prediction accuracy and stability, the error of M points can be considered simultaneously at each time step t. To account for information beyond the signal history M, an averaging parameter µ Ԗ [0, 1] is added.
The second algorithm is the wLMS algorithm [5]. The algorithm decomposes a signal into J+1 scales using an à trous wavelet. A separate LMS predictor can be applied to each scale. The predicted point is the sum of all predicted points per scale. Ernst el al. [6] showed on a dataset of 304 motion traces that, using J = 3, M = 193 and µ = 0.0204, the wLMS algorithm can outperform support vector regression, LMS and Kalman Filter.
Finally, we used a predictor based on relevance vector machines (RVM). The RVM is a probabilistic approach using Bayesian inference. In [7], it has been shown that the RVM can outperform wLMS on average. Here, a multi-modal RVM with a linear function was implemented, to reduce the computational complexity.
To compare the results of N predicted points, irrespective of the patient-specific respiration amplitude, all results were evaluated with respect to the relative root mean square RMSrel = . A RMSrel = 100 % means that the prediction accuracy could not be improved compared to no prediction and for values above 100 % that the RMS error of the specific predictor is higher than for no prediction.
As in many classification and regression problems, the selection of the optimal feature set Sopt among all possible features F becomes essential to prevent overfitting and to reduce computation time, once the amount of input features increases. Feature selection methods can be divided into wrapper and filter methods [8]. Filter methods use information criteria like correlation coefficient or mutual information to estimate the relevance of a feature to the output and the redundancy between features.
In contrast, wrapper methods use a specific prediction algorithm and evaluate the relevance and redundancy of a feature depending on the prediction accuracy. Even though wrapper methods are often computationally expensive, they find the optimal features set for the specific algorithm. They can roughly be divided into forward selection and backa)
LMS wLMS
RVM b)
0 ] [%l Sre -500 M R -1000 ward elimination [8].
Here, the features correspond to the used sensors. The complete feature set is F = {OM1, OM2, OM3, STRAIN, FLOW, ACC}. For the prediction of an external optical sensor, a sequential forward selection (SFS) method is very applicable compared to backward elimination, as within all possible features the optical sensor itself will have the highest relevance to the output. Therefore, the initial feature set S0 of the SFS method is not the empty set. Assuming that OM2 shall be predicted, the initial feature set is S0 = {OM2}. With this feature set a prediction error RMSrel-S0 can be achieved. In the next step, S0 will be expanded to S1 by one of the remaining features F\{OM2}. The feature that has the lowest RMSrel-S1 is selected. This procedure can be repeated up to a certain size d of the feature set S or until no features are found which further decrease RMSrel.
In our experiment, OM2 was exemplarily chosen to be the prediction target. We divided each measurement into a training set (ttrain = 1 min) and a test set (ttest = 17 min). The learning factor µ and the number of features per input vector p were optimized on the training set using exhaustive grid search. All wavelet scales of wLMS use the same p. The history length was set to MLMS = 1, MwLMS = 193 [5], MRVM = 1000 [7] and J = 3. The initial feature set was set to S0 = {OM2}.The maximum size of the feature set was set to d = 2, leading to two subset S1 and S2. For comparison, the RMSrel was also computed for the complete features set F. 3
The results of the experiment indicate that, in general, prediction accuracy can be increased using multi-modal sensors. However, using simply all features does not necessarily lead to the best RMSrel as shown in fig. 1.b for the wLMS algorithm. Using all features can lead to overfitting of the data. Even though not analyzed here, using the complete data set F also results in a strong increase of the computation time. Using a sequential forward selection of the features, an improved predictor-specific feature set can be found that uses multiple features and prevents overfitting of the data. The computational requirements and the size of the feature set can be limited with the factor d.
Comparing the three evaluated prediction algorithms reveals that RVM has the highest prediction accuracy, being in agreement with [7]. Furthermore, RVM can use the complete feature set F without overfitting of the data. However, the RMSrel difference between S2 and F is only 1.4 pp while the size of the features set is doubled. The high error of LMS was expected, as LMS is implemented in its simplest version with M = 1. With increasing M, the error would decrease. LMS serves here more as an example of a less complex algorithm. On average, the prediction performances of wLMS and RVM are worse compared to other publications [6], [7]. One reason is that even though, all subjects were asked to remain still, several movement artifacts could be identified in the measurements. The artifacts lead to the strong outliers.
S0 SFS, S1 SFS, S2
F
Mean RMSrel (standard deviation) in %
LMS wLMS RVM 251.6 (314.6) 63.3 (14.2) 60.5 (19.8) 104.3 (120.4) 57.1 (12.4) 51.3 (12.7) 103.0 (120.6) 58.3 (17.0) 49.0 (12.8) 97.2 (14.1) 60.4 (12.4) 47.6 (12.4) LMS wLMS RVM
Using SFS or the complete data set F, the RMSrel could be decreased strongly (crosses in fig. 2). Even though a real treatment would be interrupted at the occurrence of a strong motion artifact, these results indicate that also the effect of smaller motion artifacts could be better compensated using multi-modal sensors.
Table 2 illustrates that there is not only one optimal feature which could be added to decrease RMSrel in general. The features selected for S1 and S2 strongly depend on the prediction algorithm. Thereby, the complexity of the algorithm seems to be correlated to the selected features. The less complex LMS model uses basically only optical features. As shown in [3], these features have a high correlation to OM2 as they are measuring the same signal modality. More complex models can incorporate features based on different modalities which are less correlated to OM2 [3]. These features are potentially more relevant for the output and less redundant to the already selected features. This results also in the different numbers of nS1 and nS2. As the optical features are highly correlated to each other, they contain redundant information. As in the case of LMS, the expansion of S1 by another optical feature does not decrease the RMSrel as much of this information is already contained in the first two optical features. Consequently, the SFS method stops and nS2 is small for LMS. In contrast, RVM and wLMS can use features which are less redundant to each other leading to higher values of nS2. There is a strong variation of the added features for S1 and S2 in case of wLMS and RVM. This variation is most likely due to the heterogeneous subject group (male / female) and different breathing patterns which each subject has. The flow sensor is only selected in two cases. A probable reason could be the dead times of the airways and the thermistor, which lead to temporal delays between the mechanical movement of the torso / abdomen and the temperature difference of the air flow in front of the nose / mouth. Latter could be decreased by using an aeroplethysmograph. As mentioned in section 2, the SFS method itself can be computationally expensive depending on the algorithm and the training set. This could impede the use of this method in real time applications. An alternative feature selection method could be based on filter methods. However, it has to be further investigated how these methods could be used efficiently to find the optimal feature set. 5
In this paper, we used a multi-modal sensor setup to increase the prediction accuracy in respiratory motion prediction. We demonstrated that the most relevant and least redundant sensors can be selected by an SFS method, which lead to a decrease in RMSrel. We show that all evaluated algorithms can be easily adapted to use multi-modal inputs. As all sensors are relatively inexpensive, this technique could be easily integrated in treatment rooms. 6 [1] [2] [3] [4] [5] [6]