Impact of sampling interval in training data acquisition on intrafractional predictive accuracy of indirect dynamic tumor-tracking radiotherapy*

Transcription

1 Impact of sampling interval in training data acquisition on intrafractional predictive accuracy of indirect dynamic tumor-tracking radiotherapy* Nobutaka Mukumoto a), Mitsuhiro Nakamura, Mami Akimoto, Yuki Miyabe, Kenji Yokota, Yukinori Matsuo, Takashi Mizowaki, and Masahiro Hiraoka Department of Radiation Oncology and Image-applied Therapy, Graduate School of Medicine, Kyoto University, Kyoto, Japan (Received 31 October 2016; revised 5 May 2017; accepted for publication 10 May 2017; published 10 July 2017) Purpose: To explore the effect of sampling interval of training data acquisition on the intrafractional prediction error of surrogate signal-based dynamic tumor-tracking using a gimbal-mounted linac. Materials and methods: Twenty pairs of respiratory motions were acquired from 20 patients (ten lung, five liver, and five pancreatic cancer patients) who underwent dynamic tumor-tracking with the Vero4DRT. First, respiratory motions were acquired as training data for an initial construction of the prediction model before the irradiation. Next, additional respiratory motions were acquired for an update of the prediction model due to the change of the respiratory pattern during the irradiation. The time elapsed prior to the second acquisition of the respiratory motion was min. A four-axis moving phantom reproduced patients three dimensional (3D) target motions and one dimensional surrogate motions. To predict the future internal target motion from the external surrogate motion, prediction models were constructed by minimizing residual prediction errors for training data acquired at 80 and 320 ms sampling intervals for 20 s, and at 500, 1,000, and 2,000 ms sampling intervals for 60 s using orthogonal kv x-ray imaging systems. The accuracies of prediction models trained with various sampling intervals were estimated based on training data with each sampling interval during the training process. The intrafractional prediction errors for various prediction models were then calculated on intrafractional monitoring images taken for 30 s at the constant sampling interval of a 500 ms fairly to evaluate the prediction accuracy for the same motion pattern. In addition, the first respiratory motion was used for the training and the second respiratory motion was used for the evaluation of the intrafractional prediction errors for the changed respiratory motion to evaluate the robustness of the prediction models. Results: The training error of the prediction model was mm in 3D for all sampling intervals. The intrafractional prediction error for the same motion pattern was mm in 3D for an 80 ms sampling interval, which increased larger than 1 mm in 10.0% of prediction models trained at a 2,000 ms sampling interval with a significant difference (P < 0.01) and up to 2.5% for the other sampling intervals without a significant difference (P > 0.05). The intrafractional prediction error for the changed respiratory motion pattern increased to mm in 3D for an 80 ms sampling interval; however, there was not a significant difference in the robustness of the prediction model between the 80 ms sampling interval and other sampling intervals (P > 0.05). Conclusions: Although the training error of the prediction model was consistent for the all sampling intervals, the prediction model using the larger sampling interval of the 2,000 ms increased the intrafractional prediction error for the same motion pattern. The realistic accuracy of the prediction model was difficult to estimate using the larger sampling interval during the training process. It is recommended to construct the prediction model at sampling interval 1,000 ms and to reconstruct the model during treatment The Authors. Medical Physics published by Wiley periodicals, Inc. on behalf of American Association of Physicists in Medicine. [ Key words: dynamic tumor-tracking irradiation, four-dimensional image-guided radiotherapy, intrafractional respiratory motion, motion management, prediction model 1. INTRODUCTION Respiratory-induced tumor motion creates uncertainties during beam delivery; this is particularly true for thoracic and abdominal tumors such as lung, liver, and pancreatic cancer. 1,2 If respiratory-induced uncertainties persist, the field size will enlarge, causing damage to healthy tissues surrounding the tumor. 3,4 Several techniques, including forced shallow breathing, breath-holding, respiratory gating and dynamic 3899 Med. Phys. 44 (8), August /2017/44(8)/3899/10 tumor-tracking, have been proposed to reduce respiratoryinduced uncertainties. 1,2 Recent interest has focused on the dynamic tumor-tracking technique, which can dynamically reposition the radiation field in line with the position of the moving target. 5 9 One advantage of dynamic tumor-tracking is minimization of internal uncertainties without burdening patient respiration or prolonging treatment time. 7,10 The Vero4DRT (Mitsubishi Heavy Industries, Ltd., Hiroshima, Japan; and Brainlab, Feldkirchen, Germany) has two 2017 The Authors. Medical Physics published by Wiley periodicals, Inc. on behalf of American Association of Physicists in Medicine. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. 3899

2 3900 Mukumoto et al.: Sampling intervals in prediction training 3900 special features allowing dynamic tumor-tracking with realtime monitoring. The platform has two sets of orthogonal kilovoltage (kv) X-ray imagers, which monitor the threedimensional (3D) position of the tumor in real-time via implanted fiducial markers. The detection accuracy is < 0.1 mm for a static target and < 0.4 mm for a moving target. 11,12 The other useful feature is a gimbal-mounted linear accelerator, enabling indirect dynamic tumor-tracking radiotherapy. 7,8,11 13 When such therapy is delivered using the Vero4DRT, it is necessary to build a prediction model [ fourdimensional (4D) model ] based on the correlation between the 3D internal target and the one-dimensional (1D) external surrogate positions during training data acquisition prior to beam delivery. The 4D model is expressed by a quadratic equation involving two variables: the position and the velocity of the infrared-reflective markers. 13 To compensate for the system delay of dynamic tumor-tracking, the future positions of the infrared-reflective markers are predicted linearly from the past motion of the infrared-reflective markers. Subsequently, the gimbal-mounted X-ray head tracks the moving target by predicting its future position from the displacements of infrared-reflective markers located on the abdominal wall. Therefore, predictive accuracies are dependent on the correlations between the positions of the internal target and the external surrogates. Such correlations usually change in the presence of phase shifts and intrafractional baseline drift, 14 increasing predictive uncertainties. 13,15 In clinical practice, re-modeling of the prediction model is required during dynamic tumor-tracking to minimize intrafractional uncertainties. 7,13 Recently, a new ExacTRAC software (version 3.5; Brainlab, Feldkirchen, Germany) running on the Vero4DRT was clinically released. The principal difference between the new and previous software versions is that the predefined sampling interval for the target position has increased from 80 to 320 ms during the training period, and the prediction model can be updated using intrafractional monitoring images taken over the last 60 s. Figure 1 shows a treatment workflow for dynamic tumor-tracking, with reconstruction or update of the prediction model. As kv X-ray imaging systems are fixed with respect to the MV X-ray head, the visibility of the fiducial markers depends on a gantry angle causing a change of the contrast between the fiducial and adjacent areas. An appropriate gantry angle can be optimized by minimizing the water equivalent path length passing the fiducial markers on a computed tomography image independently from the treatment beam angles, resulting in an additional gantry rotation for the 4D modelling. 16 Meanwhile, the visibility of fiducial markers from the treatment beam angles can be estimated using intrafractional monitoring images. In the case that fiducial markers can be detected from the treatment beam angle, the prediction model can be reconstructed or updated at the treatment beam angles instead of a predefined gantry angle. Nakamura et al. 16 explored the effects of training periods of 10, 20, and 40 s, and concluded that predictive accuracies derived from 20 s of training were almost identical to those obtained over 40 s of training, and superior to those obtained over 10 s of training. However, the relationship between the intrafractional prediction error and the sampling interval used to monitor the internal target position during training data acquisition has not yet been studied. We explored the effects of the sampling interval of training data acquisition on the intrafractional prediction error of indirect dynamic tumortracking using the Vero4DRT. 2. MATERIALS AND METHODS 2.A. Respiratory motions Twenty pairs of respiratory motions were acquired from patients who underwent dynamic tumor-tracking, including 10 lung, 5 liver, and 5 pancreatic cancer patients. All work was approved by our Institutional Review Board. We acquired two sets of respiratory motions from each patient during dynamic tumor-tracking treatment on the same day. The first respiratory motion was acquired prior to beam delivery and used to train a 4D model. The second motion was acquired during beam delivery to reconstruct the 4D model, improving predictive accuracy. 7,13 The interval between the first and second respiratory motion acquisitions was min. Table I shows characteristics of the first and second respiratory motions. There was no significant difference in peakto-peak amplitude and breathing period between the first and second respiratory motion, (paired Student s t-test, P > 0.05). 2.B. 4D modeling of dynamic tumor-tracking using the Vero4DRT During dynamic tumor-tracking using the Vero4DRT, the predicted target position is calculated from a 4D model expressed as a quadratic equation involving two variables. These are the positions and velocities of the infrared-reflective markers used as the surrogate signal, expressed as follows 13 : x y p A ¼ 1 z n p P n i¼1 P n i¼1 P n i¼1 1 ða x;i s 2 i þ b x;i s i þ c x;i þ d x;i v 2 i þ e x;i v i Þ ða y;i s 2 i þ b y;i s i þ c y;i þ d y;i v 2 i þ e y;i v i Þ ; C A ða z;i s 2 i þ b z;i s i þ c z;i þ d z;i v 2 i þ e z;i v i Þ where x p, y p, and z p are the predicted target positions in the LR, CC, and AP directions, n is the number of infraredreflective markers, and s and v are the predicted position and velocity of each infrared-reflective marker in the AP direction. The positions of the infrared-reflective markers were linearly predicted from past motion to compensate for the system delay of dynamic tumor-tracking. Parameters of the 4D model (a, b, c, d, and e) were optimized using a leastsquares algorithm so that residual training errors between the predicted and detected target positions during the training (1)

3 3901 Mukumoto et al.: Sampling intervals in prediction training 3901 FIG. 1. Treatment workflow for dynamic tumor-tracking with reconstruction or update of the prediction model of the three-dimensional (3D) target position using one-dimensional (1D) surrogate position [four-dimensional (4D) model]. (Left) Additional data acquisition of target position, and additional gantry rotation, will be required to reconstruct the 4D model due to the low contrast between the fiducial and adjacent areas. When the target positions are well detected on monitoring images, additional gantry rotation for the modeling will not be required (dashed arrow). (Right) The efficiency of workflow has been improved with update function. [Color figure can be viewed at wileyonlinelibrary.com] TABLE I. Characteristics of the first and second respiratory motions. Peak-to-peak amplitude of target motion (mm) Peak-to-peak amplitude of surrogate motion (mm) LR CC AP 3D AP Breathing period (s) First respiratory motions acquired before beam delivery Second respiratory motions acquired during beam delivery Abbreviations: LR, left-right; CC, cranio-caudal; AP, anterior-posterior; 3D, three dimension.

4 3902 Mukumoto et al.: Sampling intervals in prediction training 3902 period were minimized. The 4D model was built from training data acquired over 20 s. These training data contained 3D target positions and simultaneously acquired surrogate positions. The surrogate positions were acquired with the infrared camera of the ExacTRAC system using a 16.7 ms sampling interval. The 3D target positions were acquired using the orthogonal kv X-ray imaging systems at 80 ms and 320 ms sampling intervals in the old and new versions of ExacTRAC, respectively. During the training process, the sampling interval of the target position was automatically doubled, i.e., from 320 ms to 640 ms in the new Exactrac software when the velocity of the surrogate motion slowed down blow a predefined threshold; this feature is common to both the older and newer versions of the ExacTRAC software. The new version of ExacTRAC has a unique function that can update the 4D model using intrafractional monitoring images obtained over 60 s with various constant sampling intervals. The training data to construct the 4D model are replaced by the latest 60-s data set of target positions acquired from the intrafractional monitoring images. We assumed that the sampling intervals of monitoring affected the accuracy of the prediction model, and decided to employ sampling intervals of 500, 1,000, and 2,000 ms in the present study. After monitoring the target position for 60 s, the original 4D model is updated with the training data acquired at various sampling intervals. The residual training error is evaluated during the training process in each sampling interval. 2.C. Accuracy verification of the 4D models trained with the training data acquired at various sampling intervals First, we reproduced 3D target and 1D surrogate motions using a four-axis moving phantom, developed in-house and with a positional accuracy of < 0.05 mm. 17 Next, a 4D model was constructed using the training data of target positions acquired over 20 s, employing sampling intervals of 80 or 320 ms. Each target position was calculated by reference to the centroid of fiducials embedded in a homogeneous cube placed on the moving phantom. The peak-to-peak amplitude of the detected target motions, and mean and standard deviation (SD) of the residual training error, were automatically calculated during the training process. The training error was defined as the mean-plus-two SD of the absolute difference between the predicted and detected target positions during the training period. After 4D model construction, the moving target reproducing respiratory motion was irradiated with tracking. During beam delivery, the intrafractional target positions were identified on these images, taken for 30 s using a constant 500 ms sampling interval. The corresponding predicted positions were derived from the synchronously acquired log files. The mean + 2SD of each intrafractional prediction error between the detected and predicted target positions was calculated. The intrafractional prediction error for the same motion pattern was calculated with the same respiratory motion for training and evaluation using first respiratory motion or second respiratory motion. Meanwhile, the intrafractional prediction error for the changed respiratory motion was calculated using the first respiratory motion for training and second respiratory motion for evaluation. The training error and intrafractional prediction errors derived using 4D models updated with sampling intervals of 500, 1,000, and 2,000 ms were calculated similarly. In addition, the intrafractional prediction error of the 4D model trained at the 2,000 ms sampling interval was calculated at the same sampling interval with four different initial phases. The differences between the intrafractional prediction error for the 80 ms sampling interval and that for other sampling intervals were compared using the paired Student s t-test. The level of significance for all tests was set at a P-value of A total of 200 log files (1 file 9 5 models 9 20 patients 9 2 patterns) were analyzed for the training error. A total of 18,000 paired intrafractional monitoring images (60 paired images 9 5 models 9 20 patients 9 3 patterns), and corresponding 300 log files (1 file 9 5 models 9 20 patients 9 3 patterns), were analyzed for the intrafractional prediction error. 3. RESULTS Table II shows variations of training data compared to the 80 ms sampling interval. The largest variation was observed for 2,000 ms sampling interval with statistical significance TABLE II. Variations in training data compared to the 80 ms sampling interval. Sampling interval of target training data (ms) Periods of training data (s) Number of target training data Sampling interval of surrogate training data (ms) Number of surrogate training data Variation of peak-to-peak amplitude (mm) [vs. 80 ms sampling interval] 3D for target motion AP for surrogate motion , , , , , , , Abbreviations: 3D, three dimension; AP, anterior-posterior.

5 3903 Mukumoto et al.: Sampling intervals in prediction training 3903 (P < ). The mean SD of the training error in the 3D direction was mm for all sampling intervals. The intrafractional prediction error for the same motion pattern was mm in 3D for the 80 ms sampling interval. Compared to the 80 ms sampling interval, the proportions of the variations larger than 1 mm in the intrafractional prediction error were 10% for the 2,000 ms sampling interval and within 2.5% for others. There was a significant difference in the intrafractional prediction error between the 80 ms and the 2,000 ms sampling intervals (P = 0.006), and not for others (P > 0.05). The training error and intrafractional prediction error differed by more than 1 mm for 12.5% of motion patterns for the 2,000 ms sampling interval and within 2.5% for others. There were very strong correlations (r) between the training error and intrafractional prediction error using the prediction models trained with the 80 ms, 320 ms, 500 ms, and 1,000 ms sampling intervals (r = 0.89, 0.92, 0.95, and 0.96, respectively), and a relatively weak correlation for the 2,000 ms sampling interval (r = 0.73). The intrafractional prediction error was increased by up to 2.3 mm from the training error for the 2,000 ms sampling interval. Figure 2 shows the variations of the intrafractional prediction error calculated at ms sampling interval with various initial phases. The initial phase difference caused a variation of the intrafractional prediction error up to 3.6 mm. The training error was almost equivalent to the minimum intrafractional prediction error without a statistical significant difference (P = 0.173) and different from maximum intrafractional prediction error with a statistical significant (P < ). The intrafractional prediction error for changed respiratory motion was mm in 3D for the 80 ms sampling interval. Compared to the 80 ms sampling interval, the proportions of the variations larger than 1 mm were within 2.5% for all sampling intervals. There was no significant difference between the 80 ms sampling interval and other sampling intervals (P > 0.05). The largest deviations in peak-to-peak amplitude and intrafractional prediction error for the same motion pattern (compared to those acquired using the 80 ms sampling interval) were observed for 2,000 ms sampling interval at the second respiratory cycle of the liver cancer patient. Table III shows the representative peak-to-peak amplitude for the largest variation case. The variations of the peak-to-peak amplitude in the 3D direction compared to the 80 sampling interval were within 0.5 mm for 320 ms and 500 ms sampling intervals, which enlarged to 1.9 mm for 1,000 ms sampling interval and 5.4 mm for 2,000 ms sampling interval. There were no differences in surrogate motion for all sampling intervals. Table IV shows the representative training error and intrafractional prediction error for the same motion pattern as Table III. The variations of training error in the 3D target motion compared to the 80 ms sampling interval was within 0.2 mm for all sampling intervals. The variations of intrafractional prediction error for the same motion pattern in the 3D direction compared to the 80 ms sampling interval was 1.9 mm for 2,000 ms sampling interval and within 0.1 mm for others. Figure 3 shows the representative training data and residual training error for the prediction models trained with various sampling intervals. The residual training error was equivalent for the all prediction models with various sampling intervals. However, the training data with a 2,000 ms sampling interval caused the underestimation for the motion amplitude of the target at the end-inhalation phase due to a lack of target detection frequency. Figure 4 shows the representative intrafractional prediction error for the same motion pattern using the prediction models trained with various sampling intervals. The deviations larger than 3 mm between predicted and detected target positions were observed at the end-inhale phase using the prediction model trained with the 2,000 ms sampling interval. FIG. 2. Scatter plot between the residual training errors of the prediction models and intrafractional prediction errors with the different initial phases. The training errors and intrafractional prediction errors were calculated at the 2,000 ms sampling interval. The mean + 2SD of the errors are shown. Solid line represents a reference line on which the training error and the intrafractional prediction error is equivalent. [Color figure can be viewed at wileyonlinelibrary.com] 4. DISCUSSION Recently, various dynamic tumor-tracking techniques have been developed. 5 9 Two basic approaches have been taken: direct and indirect tracking methods. 5 Direct tracking methods detect the target motion, whereas indirect tracking methods assess surrogate quantities and predict target motion based on surrogate motion. The CyberKnife (Accuray, Sunnyvale, CA, USA) features both tracking options. Dynamic tumor-tracking may be achieved by continuously monitoring internal target motion using two sets of fixed kv X-ray imaging subsystems (Xsight) or by monitoring three respiratory surrogate markers attached to a form-fitting vest using a stereo camera system (Synchrony). 6,18,19 The dynamic multileaf collimator (DMLC) tumor-tracking method using the Calypso system (Calypso Medical, Seattle, WA, USA), another direct tracking method, is now clinically available. 9 With either approach, the lookahead time for the future target

6 3904 Mukumoto et al.: Sampling intervals in prediction training 3904 TABLE III. Representative peak-to-peak amplitude for the largest variation case compared to the 80 ms sampling interval. Sampling interval of target training data (ms) Periods of training data (s) Number of target training data Peak-to-peak amplitude of target motion (mm) Peak-to-peak amplitude of surrogate motion (mm) LR CC AP 3D AP , , Abbreviations: LR, left-right; CC, cranio-caudal; AP, anterior-posterior; 3D, three dimension. TABLE IV. Representative mean + 2SD values for the training error and intrafractional prediction error for the same motion pattern as Table III. Sampling interval of target training data (ms) Training error (mm) Intrafractional prediction error (mm) LR CC AP 3D LR CC AP 3D , , Abbreviations: LR, left-right; CC, cranio-caudal; AP, anterior-posterior; 3D, three dimension. position depends on system latency, and the frequency of prediction depends on the sampling interval of respiratory motion. 20 With direct tracking methods, baseline respiratory drift can be compensated for by reference to an adjacent position. However, the lookahead time is longer than with indirect tracking methods. 21 Thus, large variations in respiratory motion cause predictive uncertainty because instantaneous predictive feedback is lacking. The latter methods have the advantage that predictive assessments are made at a high frequency without invasion, such as exposure to radiation from kv imaging. However, long-term predictive accuracy can be degraded by baseline drift of the target or surrogate motion, or changes in the correlations between target and surrogate motion during beam delivery if re-modeling is not appropriately performed. 14 In the present study, it was shown that the amplitude of respiratory motion did not change significantly after 12.6 min on average has elapsed; however, long-term prediction accuracy decreased. The Synchrony system of the CyberKnife updates the correlation model every minute, on average, by adding a new target position to the training dataset. During clinical use of the earlier Vero4DRT platform, remodeling of the correlation model (by training the model using changes in respiratory motion) is required. However, this requires delivery of additional imaging doses to the skin surface and prolongs treatment time. 7,8,13 The new version of the ExacTRAC software on the current Vero4DRT platform allows dynamic tumor-tracking to be performed using fewer sampling data than before for initial training, and updates the correlation model employing intrafractional monitoring images. In the present study, we examined the effects of various sampling intervals used to acquire training data on intrafractional predictive accuracy. The sampling interval for initial training was 80 ms in the earlier software and is 320 ms in the new ExacTRAC. The minimum monitoring interval was 1,000 ms for the earlier software, and 500 ms for the new ExacTRAC. A sampling interval of 320 ms afforded a predictive accuracy comparable to that obtained using an 80 ms sampling interval [Figs. 3(a), 3(b), 4(a), 4(b)]. A similar tendency was evident when a sampling interval of 500 ms was used [Figs. 3(c), 4(c)]. However, peak-to-peak amplitude was underestimated for the 1,000 ms sampling interval and further for the 2,000 ms sampling interval, in 3D target motion [Figs. 3(d), 3(e)]. The intrafractional prediction error for the same motion pattern increased for the 2,000 ms sampling interval [Figs. 4(d), 4(e)], although the training errors were not different for the 1,000 and 2,000 ms sampling intervals [Figs. 3(d), 3(e)]. The mean difference in peak-to-peak amplitude of surrogate AP motion was 0.3 mm for the 500, 1,000 and 2,000 ms sampling intervals, which was identical to the detection accuracy of the infrared camera (0.3 mm). Compared to an 80 ms sampling interval, the proportions of training error variations larger than 1 mm were within 2.5% for all sampling intervals. Therefore, the accuracies of correlation models built with the aid of acquired training data were nearly identical for all tested sampling intervals. Meanwhile, the proportions for variations of intrafractional prediction error for the same motion pattern that were larger than 1 mm (compared to those obtained using an 80 ms sampling interval) were 10% for a 2,000 ms sampling interval and within 2.5% for all other sampling intervals, indicating that use of a 2,000 ms sampling interval during training degraded predictive accuracy. Use of a 2,000 ms sampling interval caused peak-to-peak amplitude to be underestimated, because of mis-sampling of peak positions by up to 1,000 ms, creating large values of intrafractional prediction error [Figs. 3(e), 4(e)]. We previously showed that the intrafractional prediction errors in overall treatment were nearly identical to the training error for various respiratory motions. 13 However, in the present study, we found large differences between the

7 3905 Mukumoto et al.: Sampling intervals in prediction training 3905 (a) (b) (c) (d) (e) FIG. 3. Representative training data and residual training errors of prediction models trained with various sampling intervals, for the case exhibiting the largest deviations in the peak-to-peak amplitude compared to those acquired using an 80 ms sampling interval. The residual training errors during the training period are shown for prediction models trained with (a) 80 and (b) 320 ms sampling intervals over 20 s; and (c) 500, (d) 1,000, and (e) 2,000 ms sampling intervals over 60 s. The linearly interpolated detected and predicted target positions of the prediction models trained with various sampling intervals are shown in each sampling interval. The linearly interpolated detected surrogate positions with 16.7 ms sampling interval are shown. The residual training error defined as the difference between detected and predicted target positions of the prediction models trained with various sampling intervals were consistent. However, the training data with a 2,000 ms sampling interval caused the underestimation for the amplitude of the target at the end-inhalation phase due to a lack of target detection frequency. [Color figure can be viewed at wileyonlinelibrary.com] training error and the intrafractional prediction error when a 2,000 ms sampling interval was employed. The prediction error evaluated at the 2,000 ms sampling interval was varied with initial phase differences (Fig. 2). Prediction models trained at a large sampling interval only fitted to a particular phase contained in the training data and failed to predict a tumor position at the other phase. The intrafractional prediction error differed from the training error by more than 3.5 mm in two patients due to the suboptimal prediction model. In clinical practice, it is important to estimate the intrafractional prediction error from the training error before irradiation, which was difficult when a large sampling interval was used for training. Therefore, the prediction model should be trained with the 1,000 ms sampling interval or less,

8 3906 Mukumoto et al.: Sampling intervals in prediction training 3906 (a) (b) (c) (d) (e) Detected target position in LR direction Predicted target position in LR direction Detected target position in CC direction Predicted target position in CC direction Detected target position in AP direction Predicted target position in AP direction Absolute prediction error in LR direction Absolute prediction error in CC direction Absolute prediction error in AP direction Absolute prediction error in 3D direction FIG. 4. Representative intrafractional prediction error for the same motion pattern as Figure 3. The intrafractional prediction errors using prediction models trained with (a) 80, (b) 320, (c) 500, (d) 1,000, and (e) 2,000 ms sampling intervals are shown. The intrafractional prediction error was evaluated using intrafractional monitoring images obtained over 30 s with the 500 ms sampling interval for the prediction models trained with various sampling intervals. The linearly interpolated detected and predicted target positions using the prediction model trained with various sampling intervals are shown. Deviations larger than 3 mm between predicted and detected target positions were observed at the end-inhale phase using the prediction model trained with a 2,000 ms sampling interval. [Color figure can be viewed at wileyonlinelibrary.com] or need to be re-modeled if the training data fails to contain the peak position of the respiration. In addition, the proportions of variations in the intrafractional prediction error for the changed respiratory motion that differed by more than 1 mm from those afforded by an 80 ms sampling interval were within 2.5% for all sampling intervals. The robustness of prediction models for the changed respiratory motion due to the long treatment time was nearly identical for all tested sampling intervals. In other words, any effect of sampling interval on long-term predictive accuracy was small. Therefore, we suggest that the prediction model should be updated frequently to ensure long-term predictive accuracy. As a limitation in the present study, periods of the original respiratory motions were 20 s, which repeated three times to train the prediction model using the update function with 500 ms, 1,000 ms, and 2,000 ms sampling intervals. Without

9 3907 Mukumoto et al.: Sampling intervals in prediction training 3907 such intentional repetition, the accuracy of the updated prediction model would differ from the results of the present study, depending on the respiratory motion in clinical practice. Several investigators have derived methods for updating the model. 13,15,21 24 Kanoulas et al. 22 presented two aggressive, and two conservative, update methods for a simple linear correlation model, and showed that the aggressive methods afforded better results when the update frequency was high (2 15 Hz). However, conservative methods running at low update frequencies ( Hz) appeared to be more appropriate. The Synchrony system of the CyberKnife uses a correlation model derived from comparison of internal and external motions; 15 training data points are employed. During treatment, a new data point is added to the training dataset every minute on average, with deletion of an older data point. 6,17,18 Poels et al. 23 compared the accuracy of the correlation models derived for the CyberKnife and the Vero4DRT, and found no significant differences between the predictive accuracies when training was performed using high sampling intervals. In addition, the same authors in a different study developed an update method similar to that employed in the CyberKnife. 24 Some training data derived from a total of 220 points were randomly replaced with new data acquired in the breathing phase. In the conservative model, 5 points were replaced each 500 ms, and the aggressive model replaced 15 points. Workflow efficiency and tracking accuracy were improved by using the update methods. Akimoto et al. 15 modified model parameters by monitoring the respiratory motion baseline over 10 s. We have previously taken another approach to reduce intrafractional prediction errors and found that correction of systematic prediction errors in the previous field over 30 s, on average, was effective. 13 The ExacTRAC software (version 3.5) enables updating of prediction models using the latest 60 s of data, with an accuracy comparable to that found in previous studies. It should be noted, however, that training data acquired using a sampling interval larger than 2,000 ms may unexpectedly underestimate the accuracy of the prediction model. Apart from improving predictive accuracy, this update function reduces both imaging dose and treatment time. Depuytdt et al. 8 showed that avoidance of conventional remodeling procedures reduced treatment time by 3.2 min on average, and the imaging dose to the skin was estimated to be only 30 mgy; these data were supported by the work of Garibaldi et al. 25 Another valuable feature of the ExacTRAC software (version 3.5) is the automatic beam off function triggered when the 3D intrafractional prediction error deviates from a predefined threshold. Garibaldi et al. 25 explored the ability of the new function to manage sinusoidal patterns of change, including variation in baseline drift, changes in amplitude and period, and phase shifts between internal and external movement. These new functions of automatic beam off and updating of the correlation model have improved tracking accuracy. Thus, the efficiency of workflow and tracking accuracy during dynamic tumor-tracking, using the Vero4DRT running the new ExacTRAC software, has been improved. 5. CONCLUSION We explored the impact of a range of sampling intervals on the predictive accuracy of surrogate-signal based dynamic tumor-tracking. Model updating using intrafractional monitoring images effectively improved predictive accuracy by replacing initial training data with newer positional data acquired during beam delivery. However, a sampling interval of 2,000 ms caused larger intrafractional prediction errors than other sampling intervals, due to fewer sampling data during the training process. ACKNOWLEDGMENTS This research was partially supported by JSPS KAKENHI Grant Number 15K21102, Practical Research for Innovative Cancer Control (17ck h0001), and Development of Medical Devices and Systems for Advanced Medical Services (16he h0002) from the Japan Agency for Medical Research and Development, AMED. CONFLICT OF INTEREST This research was in part sponsored by Mitsubishi Heavy Industries, Ltd., Japan. Masahiro Hiraoka has a consultancy agreement with Mitsubishi Heavy Industries, Ltd., Japan. *This work was presented in part at the 57th Annual Meeting of the American Society for Radiation Oncology in San Antonio, Texas, October 18 21, a) Author to whom correspondence should be addressed. Electronic mail: mukumoto@kuhp.kyoto-u.ac.jp; Tel.: REFERENCES 1. Keall PJ, Mageras GS, Balter RS, et al. The management of respiratory motion in radiation oncology: report of AAPM radiation therapy committee task group no. 76. Med Phys. 2006;33: Korreman SS. Motion in radiotherapy: photon therapy. Phys Med Biol. 2012;57:R161 R Matsuo Y, Shibuya K, Nakamura M, et al. Dose-volume metrics associated with radiation pneumonitis after stereotactic body radiation therapy for lung cancer. Int J Radiat Oncol Biol Phys. 2012;83:e545 e Nakamura A, Shibuya K, Matsuo Y, et al. 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