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The Effect of Transponder Motion on the Accuracy of the Calypso Electromagnetic Localization System
Int. J. Radiation Oncology Biol. Phys., Vol. 72, No. 1, pp. 295–299, 2008 Copyright Ó 2008 Elsevier Inc. Printed in the USA. All rights reserved 0360-3016/08/$–see front matter
doi:10.1016/j.ijrobp.2008.05.036
PHYSICS CONTRIBUTION
THE EFFECT OF TRANSPONDER MOTION ON THE ACCURACY OF THE CALYPSO ELECTROMAGNETIC LOCALIZATION SYSTEM MARTIN J. MURPHY, PH.D.,* RICHARD EIDENS, PH.D.,y EDWARD VERTATSCHITSCH, PH.D.,y y AND J. NELSON WRIGHT, M.S. * Department of Radiation Oncology, Virginia Commonwealth University, Richmond, VA; and y Calypso Medical Technologies, Seattle, WA Purpose: To determine position and velocity-dependent effects in the overall accuracy of the Calypso Electromagnetic localization system, under conditions that emulate transponder motion during normal free breathing. Methods and Materials: Three localization transponders were mounted on a remote-controlled turntable that could move the transponders along a circular trajectory at speeds up to 3 cm/s. A stationary calibration established the coordinates of multiple points on each transponder’s circular path. Position measurements taken while the transponders were in motion at a constant speed were then compared with the stationary coordinates. Results: No statistically significant changes in the transponder positions in (x,y,z) were detected when the transponders were in motion. Conclusions: The accuracy of the localization system is unaffected by transponder motion. Ó 2008 Elsevier Inc. External beam radiotherapy, Respiratory motion tracking, Electromagnetic localization.
INTRODUCTION
setup imaging). The system is capable of continuously reporting the position of the implanted transponders throughout the fraction. This has been demonstrated in measurements that have recorded the changing position of the prostate during a typical treatment fraction (1, 3) and suggests the possibility of using the system in an adaptive targeting role to continuously track and correct for tumor motion in real time. However, the Calypso system requires a finite amount of time to complete each transponder location measurement, which raises the question of how transponder motion might affect the measurement accuracy. The paradigm for continuous tumor motion tracking is to follow a target site as it moves with respiration (5). We have made laboratory measurements to look for position and velocity-dependent effects in the overall accuracy of the system, under motion conditions that emulate normal free breathing.
The electromagnetic localization system developed by Calypso Medical Technologies (Seattle, WA) is intended for the targeting of tumors during external beam radiotherapy. The system uses miniature radiofrequency (RF) coils (henceforth called transponders) encased in glass capsules and implanted in or near the target tumor. An external panel containing an array of transmitting and receiving antennae alternately excites each transponder to its resonant frequency and then receives a radiated signal back from the transponder. By distributing receiver antennae over an area of approximately 20 20 cm in a plane above and parallel to the patient, the system can triangulate each transponder’s position. Each transponder has a characteristic resonant frequency, which allows them to be distinguished individually. The Calypso system has initially been used for prostate localization (1). Its accuracy and anatomic stability have been measured in several laboratory and clinical investigations that have shown approximately 0.03–0.05-cm random localization uncertainty (2) and little or no migration of the transponders within the target anatomy (3, 4). The present clinical application is for patient setup at the beginning of each fraction (in lieu of portal or kilovoltage
METHODS AND MATERIALS Our task was to look for changes in the accuracy of localizing individual transponders when they were moving at speeds comparable to anatomy during respiration. We considered the possible effect of changes in transponder position, as well as the effect of transponder speed. Conflict of interest: R.E., E.V., and J.N.W. are employees of Calypso Medical Technologies. Acknowledgment—The authors thank Dr. Zhong Su for assisting with some of the measurements. Received Feb 20, 2008, and in revised form May 12, 2008. Accepted for publication May 14, 2008.
Reprint requests to: Martin J. Murphy, Ph.D., Department of Radiation Oncology, Virginia Commonwealth University Health System, 401 College Street, P.O. Box 980058, Richmond, VA 23298-0058. Tel: (804) 628-7777; Fax: (804) 628-4709; E-mail: [email protected] Supported in part by National Cancer Institute grant R21CA119143. 295
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was repeated to verify the stability and reproducibility of the experimental setup.
Motion measurements
Fig. 1. The experimental configuration used to test for motion effects, showing the turntable with three transponders, the antenna array, and the radiofrequency (RF) interference coil used to signal that the table was passing 0 .
Experimental setup Our measurements were made with three transponders mounted to a turntable with programmable positions and speeds (Fig. 1). The transponders were at three different radii from the center of rotation. To test for motion effects in the same plane as the antenna array the turntable was positioned parallel to and at a distance of 19.3 cm from the antenna, which is within the recommended distance for optimal accuracy. The table moved the transponders in a circular trajectory parallel to the antenna array (i.e., in the x–y plane). When the table passed 0 an RF noise pulse could be injected into the position data to provide a reference point. To test for motion effects in the direction normal to the antenna the turntable was turned 90 to be perpendicular with and at a distance of 15 cm from the array (i.e., the transponders moved in the y–z plane). The variable angular velocity of the table produced transponder speeds from 0.1 to 3.0 cm/s, which is the range of lung tumor speeds observed in most freely breathing patients (6). The Calypso system was operated in its standard mode of sequential 100-ms readout periods for each transponder. This provided a new position measurement for each transponder at 300-ms intervals.
Calibration of the motion trajectories and stationary localization uncertainty We first calibrated the circular paths for each transponder in the plane parallel to the antenna and measured the localization uncertainty for stationary transponders. The motion table was programmed to move to and stop at 60 intervals. At each stop, 100 position measurements were made for each transponder, and then the table was advanced to the next stop. This was repeated for five complete revolutions. From these measurements we obtained the mean position of each transponder at each stopping position and the standard deviation of the individual transponder measurements around each position. This established our baseline localization precision for stationary transponders and the absolute ground truth transponder coordinates for specific table positions. By making multiple revolutions we could detect whether there was any systematic or random variation in the stopping position of the table. We found no systematic or random changes in table position at our detection level of 0.01 cm. We then fit the stationary position data for each transponder to a circle to obtain its center and radius of rotation. The entire process
For the measurements of motion parallel to the antenna (i.e., in the x–y plane), we made three runs at angular turntable speeds of 10 , 20 , and 30 per second and looked for any change in the individual transponder localization accuracy that could be associated with transponder motion. Before each run we repeated the static calibration test to monitor measurement stability and reproducibility. Each run lasted for approximately 3 min, during which the table oscillated between 30 around the 0 position defined in the calibration runs. Thus, in Run 1 the transponders passed the 0 position approximately 30 times, whereas at the fastest speed the transponders passed zero 90 times. Except when reversing direction, the table moved at a constant angular speed. Transponder positions were recorded continuously at the conventional readout rate of 100 ms per transponder. To mark the point in the sequence of position measurements at which the table passed a known point, an RF coil was placed near the antenna array (apart from the turntable) and triggered by a switch on the table controller to generate a noise interference pulse at the moment that the table passed the 0 position moving in the clockwise direction (Fig. 1). The interference pulse was initiated at precisely 0 and lasted 0.163 s. If a transponder was in the process of readout, the noise pulse corrupted that particular measurement, resulting in an anomalous position in the otherwise smoothly continuous arc trajectory. Each outlier point was used as a synchronization mark to relate the position reported by the Calypso system at that moment to the true location of the transponder. Any systematic discrepancy between the measured and actual position, outside the stationary error bounds established in the calibration, would be evidence of motion-related effects on localization accuracy. For motion perpendicular to the antenna array (i.e., in the y–z plane, where the z-axis was normal to the antenna plane) the transponders were moved closer to the axis of rotation to reduce the range of motion. We acquired three stationary positions for each transponder and then recorded their positions continuously while systematically increasing the table rotation from 0.1 cm/s to 3.0 cm/s and then back to zero.
RESULTS Table calibration and baseline localization accuracy for stationary transponders in the x–y plane The center of rotation in the x–y plane for each transponder was the same to within 0.005 cm for all the calibration runs, which verified the mechanical stability of the measurement apparatus. The root mean square variation of the table stopping positions at 60 intervals ranged from 0.003 cm to 0.012 cm, which showed that the table’s programmed positions were reproducible to within 0.01 cm. Table 1 summarizes the standard deviations in the 100 (x,y) position measurements for each transponder at each stationary position. The stationary localization uncertainty varied from 0.02 to 0.06 cm per axis in the (x–y) plane, which is consistent with the observations of Balter et al. (2). Synchronization of the transponder and table positions and transponder motion measurements in the x–y plane Figure 2a illustrates the position record for Transponder 1 moving parallel to the antenna array at an angular velocity of 10 /s, which corresponded to a linear speed of 0.98 cm/s.
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Table 1. Standard deviation (in centimeters) of 100 (x,y) position measurements vs. position for stationary transponders Angular table position Axis x-axis SD Transponder 1 Transponder 2 Transponder 3 y-axis SD Transponder 1 Transponder 2 Transponder 3
0
60
120
180
240
300
0.032 0.027 0.041
0.044 0.041 0.051
0.040 0.034 0.038
0.035 0.024 0.029
0.028 0.021 0.028
0.024 0.017 0.026
0.023 0.023 0.029
0.022 0.021 0.025
0.028 0.022 0.030
0.037 0.026 0.033
0.048 0.037 0.058
0.036 0.028 0.039
Abbreviation: SD = standard deviation.
The RF interference points are visible as outliers on the arc. Figure 2b shows the same trajectory when Transponder 1 was moving at 30 /s (2.97 cm/s). The transponder coordinates at 0 measured in the stationary calibration run are superimposed on the arcs. These two figures show that transponder motion had no effect on their measured coordinates in the radial direction (i.e., perpendicular to the direction of motion). We used the noise interference signals to look for motion effects on the measured tangential position of the moving transponders (i.e., in the direction of motion) as they passed 0 . Each transponder’s position record was analyzed to find the noise-corrupted signals. At each corrupted measurement point the preceding three and the following three measurements were rotated back to overlap at the interference point and averaged to interpolate the transponder’s uncorrupted coordinates at that point. The relationship between each transponder readout cycle and the turntable oscillation cycle was asynchronous, which meant that the overlap between each 100-ms readout interval and the 163-ms noise pulse was variable. Any degree of overlap between a readout interval and the noise pulse could potentially corrupt that particular measurement. Therefore a particular corrupted position measurement could be at any point along the arc of length R = 0.363 vt cm, extending from 0.100 vt cm to +0.263 vt cm around the 0 point, where vt is the linear velocity of the transponder in centimeters per second. The expected centroid of this arc (i.e., the expected average of all the interference points along the arc) would be at a distance m = (0.163/2) vt cm beyond the 0 point. Thus, in the absence of motion-related systematic errors, one would expect the average of the measured interference points for a particular run to be displaced 0.082 vt cm in the clockwise direction from the 0 point. When the positions of all the RF interference points observed for Transponder 2 (moving at 20 /s) were interpolated from the positions of the six neighboring points on either side (as described above), they fell along the arc segment illustrated in Fig. 3. Transponder motion was clockwise from upper left to lower right. Figure 3 also shows the transponder’s calibrated position at 0 . Similar plots were made for the other transponders for each of the three runs. From each tran-
Fig. 2. (a) The positions in the plane parallel to the antenna array (as in Fig. 1) recorded for Transponder 1 moving at 0.99 cm/s between 30 ; (b) the same for Transponder 1 moving at 2.97 cm/s. The outlier points mark the transponder’s position overlap with the noise pulse that was used to signal that it was passing the 0 position (the spread corresponds to the finite duration of the interference noise pulse). The stationary coordinates of the transponder at precisely 0 are also shown.
sponder’s distribution of interference points we calculated the centroid, compared it with the expected coordinates of the point 0.082 vt cm beyond 0 , and looked for a systematic offset. Table 2 summarizes the observed and expected mean interference points and the differences between them. Because of the asynchronous timing, not every pass of 0 caused interference in a transponder readout. Thus, each transponder’s moving position record contained anywhere from 3 to 10 corrupted points. Because we have only a small number of observations of the interference point for each
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Table 3. Tangential deviation of the measured mean interference point from the expected mean interference point, compared with the standard deviation when the mean point is calculated from N measurements (in centimeters)
Run 1 1 1 2 2 2 3 3 3
Fig. 3. The interference points in the plane parallel to the antenna array observed for Transponder 2 moving at 1.77 cm/s, along with the ground truth position of the transponder at 0 . Because the interference signal could be picked up anywhere within a window of 0.363 s, the noisy points are distributed randomly along an arc 0.64 cm long.
transponder and table speed, we cannot expect the mean (centroid) of the observations to coincide exactly with the expected mean interference point; we can only expect it to be within one or two standard deviations. If we make N random observations of points distributed along an arc segment of length R and average them, we will get an observed mean position m. If we repeat this experiment many times, then the observed mean positions m will be distributed around the expected mean position m with a variance of R2/(12 N). The standard deviation of m will thus be R/O(12 N). In Table 3 we summarize for each run the transponder speeds, the number N of interference points detected, the distance between the observed and expected mean interference points, and the standard deviation of these observed means around the expected mean. We observe that for all three table speeds the discrepancy between each of our observed and expected average in-
Transponder
Speed (cm/s)
R (cm)
1 2 3 1 2 3 1 2 3
0.99 0.88 0.76 1.98 1.77 1.53 2.96 2.65 2.29
0.36 0.32 0.28 0.72 0.64 0.56 1.08 0.96 0.83
N
Standard deviation (cm)
Actual deviation (cm)
10 10 4 5 8 3 6 9 5
0.033 0.029 0.040 0.093 0.065 0.093 0.120 0.093 0.107
0.02 0.03 0.01 0.09 0.02 0.08 0.02 0.06 0.00
terference points is within 1 standard deviation. Our observed transponder positions therefore show no statistically significant deviations in the tangential direction due to motion. Motion measurements in the y–z plane No systematic velocity-dependent change in the transponder positions was detected for motion in the plane parallel to the antenna. Therefore, to detect motion effects perpendicular to the antenna it was sufficient to look for a velocity-dependent change in the z-coordinate for each (y,z) position when the transponders moved in the y–z plane (the z-axis being normal to the plane of the antenna array). This would manifest itself as a smearing out or distortion of the y–z trajectory in the z-direction while the transponders were in motion. Figure 4
Table 2. Observed centroid of the radiofrequency interference points, the expected centroid, and the difference (in centimeters) Measured mean Expected mean interference interference Run Transponder point (x,y) point (x,y)
Difference (x,y)
1 1 1 2 2 2 3 3 3
(0.00, 0.02) (0.01, 0.03) (0.01, 0.00) (0.04, 0.08) (0.01, 0.02) (0.03, 0.08) (0.01, 0.02) (0.06, 0.10) (0.00, 0.00)
1 2 3 1 2 3 1 2 3
(5.52, 1.36) (4.55, 2.25) (4.26, 0.98) (5.46, 1.50) (4.52, 2.29) (4.22, 1.10) (5.55, 1.19) (4.56, 2.19) (4.30, 0.85)
(5.52, 1.38) (4.56, 2.22) (4.25, 0.98) (5.50, 1.42) (4.53, 2.27) (4.25, 1.02) (5.56, 1.21) (4.62, 2.09) (4.30, 0.85)
Fig. 4. The trajectories of the three transponders moving at velocities from 0.1 cm/s to 3.0 cm/s in the plane perpendicular to the antenna array (i.e., with the rotation table turned sideways relative to Fig. 1). Stationary calibration points are also shown. The negative z-direction is directed away from the antenna plane.
TOCA-PET in glomus tumors d M. J. MURPHY et al.
shows the three transponder trajectories recorded while their speeds were continuously varied between 0 and 3 cm/s. The figure also shows three stationary measurements for each transponder (appearing as light-colored points on the trajectories). (The slight elliptical shape of the trajectories showed that the turntable plane was tilted a little from true perpendicular.) As the transponders moved further from the antenna the standard deviation in the position measurements increased as expected due to 1/r2 attenuation but did not exceed 0.05 cm for any transponder at its maximum distance, which is within the expected range for stationary position measurements. There was no change in the z-coordinates associated with the movement of the transponders perpendicular to the antenna (i.e., no distortion or broadening of the trajectories). DISCUSSION We detected a small but significant systematic trend in localization accuracy as a function of transponder position parallel to the antenna. This is displayed in Table 1 and arises from the internal calibration processes of the localization system. At the beginning of a tracking session the system goes through a ‘‘discovery’’ calibration based on the initial position of the transponders. The localization precision is optimal at this location. If the transponders move away from the ‘‘discovery’’ position, then the precision decreases somewhat, as shown in Table 1. In the plane parallel to the antenna the
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maximum displacement for Transponder 1 was 11.32 cm, for Transponder 2 it was 10.12 cm, and for Transponder 3 it was 8.8 cm. Over this distance the localization uncertainty increased approximately linearly from 0.02 to 0.06 cm per axis. When the transponders moved further away from the antenna in the z-direction by 3.0–4.5 cm the position uncertainty changed from 0.02 to 0.05 cm in the worst case. Lung tumors do not move more than approximately 3 cm in the most extreme cases. Therefore the Calypso system will have <0.03-cm systematic change in localization accuracy over the full range of tumor position. The moving transponder measurements showed no statistically significant systematic error in the (x,y,z) position coordinates due to transponder motion. We conclude that if the Calypso system is used for real-time respiratory motion tracking, then tracking accuracy will be unaffected by transponder motion, at least for the velocity range that will be encountered in most clinical applications. If the transponder is moving, its reported location corresponds precisely to its position at the midpoint of the readout interval, regardless of speed. In an adaptive motion correction system the tracking control loop will need to account for the time delay between the midpoint of the transponder readout cycle and the moment when the tracking device makes its alignment response. This can be done using the principles of predictive filtering that have been studied in this context (7, 8).
REFERENCES 1. Kupelian P, Willoughby T, Mahadevan A, et al. Multi-institutional clinical experience with the Calypso System in localization and continuous, real-time monitoring of the prostate gland during external radiotherapy. Int J Radiat Oncol Biol Phys 2007;67:1088–1098. 2. Balter JM, Wright JN, Newell LJ, et al. Accuracy of a wireless localization system for radiotherapy. Int J Radiat Oncol Biol Phys 2005;61:933–937. 3. Willoughby TR, Kupelian PA, Pouliot J, et al. Target localization and real-time tracking using the Calypso 4D localization system in patients with localized prostate cancer. Int J Radiat Oncol Biol Phys 2006;65:528–534. 4. Litzenberg DW, Willoughby TR, Balter JM, et al. Positional stability of electromagnetic transponders used for prostate localization and continuous real-time tracking. Int J Radiat Oncol Biol Phys 2007;68:1199–1206.
5. Murphy MJ. Tracking moving organs in real time. Semin Radiat Oncol 2004;14:91–100. 6. Shirato H, Suzuki K, Sharp GC, et al. Speed and amplitude of lung tumor motion precisely detected in four-dimensional setup and in real-time tumor-tracking radiotherapy. Int J Radiat Oncol Biol Phys 2006;64:1229–1236. 7. Murphy MJ, Jalden J, Isaksson M. Adaptive filtering to predict lung tumor breathing motion during image-guided radiation therapy. In: Lemke HU, Vannier MW, Inamura K, editors. CARS 2002. Computer-assisted radiology and surgery: Proceedings of the 16th International Congress and Exhibition, Paris, June 2629, 2002. Berlin: Springer Verlag; 2002. p. 539–544. 8. Sharp GC, Jiang SB, Shimizu S, et al. Prediction of respiratory tumour motion for real-time image-guided radiotherapy. Phys Med Biol 2004;49:425–440.
doi:10.1016/j.ijrobp.2008.05.036
PHYSICS CONTRIBUTION
THE EFFECT OF TRANSPONDER MOTION ON THE ACCURACY OF THE CALYPSO ELECTROMAGNETIC LOCALIZATION SYSTEM MARTIN J. MURPHY, PH.D.,* RICHARD EIDENS, PH.D.,y EDWARD VERTATSCHITSCH, PH.D.,y y AND J. NELSON WRIGHT, M.S. * Department of Radiation Oncology, Virginia Commonwealth University, Richmond, VA; and y Calypso Medical Technologies, Seattle, WA Purpose: To determine position and velocity-dependent effects in the overall accuracy of the Calypso Electromagnetic localization system, under conditions that emulate transponder motion during normal free breathing. Methods and Materials: Three localization transponders were mounted on a remote-controlled turntable that could move the transponders along a circular trajectory at speeds up to 3 cm/s. A stationary calibration established the coordinates of multiple points on each transponder’s circular path. Position measurements taken while the transponders were in motion at a constant speed were then compared with the stationary coordinates. Results: No statistically significant changes in the transponder positions in (x,y,z) were detected when the transponders were in motion. Conclusions: The accuracy of the localization system is unaffected by transponder motion. Ó 2008 Elsevier Inc. External beam radiotherapy, Respiratory motion tracking, Electromagnetic localization.
INTRODUCTION
setup imaging). The system is capable of continuously reporting the position of the implanted transponders throughout the fraction. This has been demonstrated in measurements that have recorded the changing position of the prostate during a typical treatment fraction (1, 3) and suggests the possibility of using the system in an adaptive targeting role to continuously track and correct for tumor motion in real time. However, the Calypso system requires a finite amount of time to complete each transponder location measurement, which raises the question of how transponder motion might affect the measurement accuracy. The paradigm for continuous tumor motion tracking is to follow a target site as it moves with respiration (5). We have made laboratory measurements to look for position and velocity-dependent effects in the overall accuracy of the system, under motion conditions that emulate normal free breathing.
The electromagnetic localization system developed by Calypso Medical Technologies (Seattle, WA) is intended for the targeting of tumors during external beam radiotherapy. The system uses miniature radiofrequency (RF) coils (henceforth called transponders) encased in glass capsules and implanted in or near the target tumor. An external panel containing an array of transmitting and receiving antennae alternately excites each transponder to its resonant frequency and then receives a radiated signal back from the transponder. By distributing receiver antennae over an area of approximately 20 20 cm in a plane above and parallel to the patient, the system can triangulate each transponder’s position. Each transponder has a characteristic resonant frequency, which allows them to be distinguished individually. The Calypso system has initially been used for prostate localization (1). Its accuracy and anatomic stability have been measured in several laboratory and clinical investigations that have shown approximately 0.03–0.05-cm random localization uncertainty (2) and little or no migration of the transponders within the target anatomy (3, 4). The present clinical application is for patient setup at the beginning of each fraction (in lieu of portal or kilovoltage
METHODS AND MATERIALS Our task was to look for changes in the accuracy of localizing individual transponders when they were moving at speeds comparable to anatomy during respiration. We considered the possible effect of changes in transponder position, as well as the effect of transponder speed. Conflict of interest: R.E., E.V., and J.N.W. are employees of Calypso Medical Technologies. Acknowledgment—The authors thank Dr. Zhong Su for assisting with some of the measurements. Received Feb 20, 2008, and in revised form May 12, 2008. Accepted for publication May 14, 2008.
Reprint requests to: Martin J. Murphy, Ph.D., Department of Radiation Oncology, Virginia Commonwealth University Health System, 401 College Street, P.O. Box 980058, Richmond, VA 23298-0058. Tel: (804) 628-7777; Fax: (804) 628-4709; E-mail: [email protected] Supported in part by National Cancer Institute grant R21CA119143. 295
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was repeated to verify the stability and reproducibility of the experimental setup.
Motion measurements
Fig. 1. The experimental configuration used to test for motion effects, showing the turntable with three transponders, the antenna array, and the radiofrequency (RF) interference coil used to signal that the table was passing 0 .
Experimental setup Our measurements were made with three transponders mounted to a turntable with programmable positions and speeds (Fig. 1). The transponders were at three different radii from the center of rotation. To test for motion effects in the same plane as the antenna array the turntable was positioned parallel to and at a distance of 19.3 cm from the antenna, which is within the recommended distance for optimal accuracy. The table moved the transponders in a circular trajectory parallel to the antenna array (i.e., in the x–y plane). When the table passed 0 an RF noise pulse could be injected into the position data to provide a reference point. To test for motion effects in the direction normal to the antenna the turntable was turned 90 to be perpendicular with and at a distance of 15 cm from the array (i.e., the transponders moved in the y–z plane). The variable angular velocity of the table produced transponder speeds from 0.1 to 3.0 cm/s, which is the range of lung tumor speeds observed in most freely breathing patients (6). The Calypso system was operated in its standard mode of sequential 100-ms readout periods for each transponder. This provided a new position measurement for each transponder at 300-ms intervals.
Calibration of the motion trajectories and stationary localization uncertainty We first calibrated the circular paths for each transponder in the plane parallel to the antenna and measured the localization uncertainty for stationary transponders. The motion table was programmed to move to and stop at 60 intervals. At each stop, 100 position measurements were made for each transponder, and then the table was advanced to the next stop. This was repeated for five complete revolutions. From these measurements we obtained the mean position of each transponder at each stopping position and the standard deviation of the individual transponder measurements around each position. This established our baseline localization precision for stationary transponders and the absolute ground truth transponder coordinates for specific table positions. By making multiple revolutions we could detect whether there was any systematic or random variation in the stopping position of the table. We found no systematic or random changes in table position at our detection level of 0.01 cm. We then fit the stationary position data for each transponder to a circle to obtain its center and radius of rotation. The entire process
For the measurements of motion parallel to the antenna (i.e., in the x–y plane), we made three runs at angular turntable speeds of 10 , 20 , and 30 per second and looked for any change in the individual transponder localization accuracy that could be associated with transponder motion. Before each run we repeated the static calibration test to monitor measurement stability and reproducibility. Each run lasted for approximately 3 min, during which the table oscillated between 30 around the 0 position defined in the calibration runs. Thus, in Run 1 the transponders passed the 0 position approximately 30 times, whereas at the fastest speed the transponders passed zero 90 times. Except when reversing direction, the table moved at a constant angular speed. Transponder positions were recorded continuously at the conventional readout rate of 100 ms per transponder. To mark the point in the sequence of position measurements at which the table passed a known point, an RF coil was placed near the antenna array (apart from the turntable) and triggered by a switch on the table controller to generate a noise interference pulse at the moment that the table passed the 0 position moving in the clockwise direction (Fig. 1). The interference pulse was initiated at precisely 0 and lasted 0.163 s. If a transponder was in the process of readout, the noise pulse corrupted that particular measurement, resulting in an anomalous position in the otherwise smoothly continuous arc trajectory. Each outlier point was used as a synchronization mark to relate the position reported by the Calypso system at that moment to the true location of the transponder. Any systematic discrepancy between the measured and actual position, outside the stationary error bounds established in the calibration, would be evidence of motion-related effects on localization accuracy. For motion perpendicular to the antenna array (i.e., in the y–z plane, where the z-axis was normal to the antenna plane) the transponders were moved closer to the axis of rotation to reduce the range of motion. We acquired three stationary positions for each transponder and then recorded their positions continuously while systematically increasing the table rotation from 0.1 cm/s to 3.0 cm/s and then back to zero.
RESULTS Table calibration and baseline localization accuracy for stationary transponders in the x–y plane The center of rotation in the x–y plane for each transponder was the same to within 0.005 cm for all the calibration runs, which verified the mechanical stability of the measurement apparatus. The root mean square variation of the table stopping positions at 60 intervals ranged from 0.003 cm to 0.012 cm, which showed that the table’s programmed positions were reproducible to within 0.01 cm. Table 1 summarizes the standard deviations in the 100 (x,y) position measurements for each transponder at each stationary position. The stationary localization uncertainty varied from 0.02 to 0.06 cm per axis in the (x–y) plane, which is consistent with the observations of Balter et al. (2). Synchronization of the transponder and table positions and transponder motion measurements in the x–y plane Figure 2a illustrates the position record for Transponder 1 moving parallel to the antenna array at an angular velocity of 10 /s, which corresponded to a linear speed of 0.98 cm/s.
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Table 1. Standard deviation (in centimeters) of 100 (x,y) position measurements vs. position for stationary transponders Angular table position Axis x-axis SD Transponder 1 Transponder 2 Transponder 3 y-axis SD Transponder 1 Transponder 2 Transponder 3
0
60
120
180
240
300
0.032 0.027 0.041
0.044 0.041 0.051
0.040 0.034 0.038
0.035 0.024 0.029
0.028 0.021 0.028
0.024 0.017 0.026
0.023 0.023 0.029
0.022 0.021 0.025
0.028 0.022 0.030
0.037 0.026 0.033
0.048 0.037 0.058
0.036 0.028 0.039
Abbreviation: SD = standard deviation.
The RF interference points are visible as outliers on the arc. Figure 2b shows the same trajectory when Transponder 1 was moving at 30 /s (2.97 cm/s). The transponder coordinates at 0 measured in the stationary calibration run are superimposed on the arcs. These two figures show that transponder motion had no effect on their measured coordinates in the radial direction (i.e., perpendicular to the direction of motion). We used the noise interference signals to look for motion effects on the measured tangential position of the moving transponders (i.e., in the direction of motion) as they passed 0 . Each transponder’s position record was analyzed to find the noise-corrupted signals. At each corrupted measurement point the preceding three and the following three measurements were rotated back to overlap at the interference point and averaged to interpolate the transponder’s uncorrupted coordinates at that point. The relationship between each transponder readout cycle and the turntable oscillation cycle was asynchronous, which meant that the overlap between each 100-ms readout interval and the 163-ms noise pulse was variable. Any degree of overlap between a readout interval and the noise pulse could potentially corrupt that particular measurement. Therefore a particular corrupted position measurement could be at any point along the arc of length R = 0.363 vt cm, extending from 0.100 vt cm to +0.263 vt cm around the 0 point, where vt is the linear velocity of the transponder in centimeters per second. The expected centroid of this arc (i.e., the expected average of all the interference points along the arc) would be at a distance m = (0.163/2) vt cm beyond the 0 point. Thus, in the absence of motion-related systematic errors, one would expect the average of the measured interference points for a particular run to be displaced 0.082 vt cm in the clockwise direction from the 0 point. When the positions of all the RF interference points observed for Transponder 2 (moving at 20 /s) were interpolated from the positions of the six neighboring points on either side (as described above), they fell along the arc segment illustrated in Fig. 3. Transponder motion was clockwise from upper left to lower right. Figure 3 also shows the transponder’s calibrated position at 0 . Similar plots were made for the other transponders for each of the three runs. From each tran-
Fig. 2. (a) The positions in the plane parallel to the antenna array (as in Fig. 1) recorded for Transponder 1 moving at 0.99 cm/s between 30 ; (b) the same for Transponder 1 moving at 2.97 cm/s. The outlier points mark the transponder’s position overlap with the noise pulse that was used to signal that it was passing the 0 position (the spread corresponds to the finite duration of the interference noise pulse). The stationary coordinates of the transponder at precisely 0 are also shown.
sponder’s distribution of interference points we calculated the centroid, compared it with the expected coordinates of the point 0.082 vt cm beyond 0 , and looked for a systematic offset. Table 2 summarizes the observed and expected mean interference points and the differences between them. Because of the asynchronous timing, not every pass of 0 caused interference in a transponder readout. Thus, each transponder’s moving position record contained anywhere from 3 to 10 corrupted points. Because we have only a small number of observations of the interference point for each
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Table 3. Tangential deviation of the measured mean interference point from the expected mean interference point, compared with the standard deviation when the mean point is calculated from N measurements (in centimeters)
Run 1 1 1 2 2 2 3 3 3
Fig. 3. The interference points in the plane parallel to the antenna array observed for Transponder 2 moving at 1.77 cm/s, along with the ground truth position of the transponder at 0 . Because the interference signal could be picked up anywhere within a window of 0.363 s, the noisy points are distributed randomly along an arc 0.64 cm long.
transponder and table speed, we cannot expect the mean (centroid) of the observations to coincide exactly with the expected mean interference point; we can only expect it to be within one or two standard deviations. If we make N random observations of points distributed along an arc segment of length R and average them, we will get an observed mean position m. If we repeat this experiment many times, then the observed mean positions m will be distributed around the expected mean position m with a variance of R2/(12 N). The standard deviation of m will thus be R/O(12 N). In Table 3 we summarize for each run the transponder speeds, the number N of interference points detected, the distance between the observed and expected mean interference points, and the standard deviation of these observed means around the expected mean. We observe that for all three table speeds the discrepancy between each of our observed and expected average in-
Transponder
Speed (cm/s)
R (cm)
1 2 3 1 2 3 1 2 3
0.99 0.88 0.76 1.98 1.77 1.53 2.96 2.65 2.29
0.36 0.32 0.28 0.72 0.64 0.56 1.08 0.96 0.83
N
Standard deviation (cm)
Actual deviation (cm)
10 10 4 5 8 3 6 9 5
0.033 0.029 0.040 0.093 0.065 0.093 0.120 0.093 0.107
0.02 0.03 0.01 0.09 0.02 0.08 0.02 0.06 0.00
terference points is within 1 standard deviation. Our observed transponder positions therefore show no statistically significant deviations in the tangential direction due to motion. Motion measurements in the y–z plane No systematic velocity-dependent change in the transponder positions was detected for motion in the plane parallel to the antenna. Therefore, to detect motion effects perpendicular to the antenna it was sufficient to look for a velocity-dependent change in the z-coordinate for each (y,z) position when the transponders moved in the y–z plane (the z-axis being normal to the plane of the antenna array). This would manifest itself as a smearing out or distortion of the y–z trajectory in the z-direction while the transponders were in motion. Figure 4
Table 2. Observed centroid of the radiofrequency interference points, the expected centroid, and the difference (in centimeters) Measured mean Expected mean interference interference Run Transponder point (x,y) point (x,y)
Difference (x,y)
1 1 1 2 2 2 3 3 3
(0.00, 0.02) (0.01, 0.03) (0.01, 0.00) (0.04, 0.08) (0.01, 0.02) (0.03, 0.08) (0.01, 0.02) (0.06, 0.10) (0.00, 0.00)
1 2 3 1 2 3 1 2 3
(5.52, 1.36) (4.55, 2.25) (4.26, 0.98) (5.46, 1.50) (4.52, 2.29) (4.22, 1.10) (5.55, 1.19) (4.56, 2.19) (4.30, 0.85)
(5.52, 1.38) (4.56, 2.22) (4.25, 0.98) (5.50, 1.42) (4.53, 2.27) (4.25, 1.02) (5.56, 1.21) (4.62, 2.09) (4.30, 0.85)
Fig. 4. The trajectories of the three transponders moving at velocities from 0.1 cm/s to 3.0 cm/s in the plane perpendicular to the antenna array (i.e., with the rotation table turned sideways relative to Fig. 1). Stationary calibration points are also shown. The negative z-direction is directed away from the antenna plane.
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shows the three transponder trajectories recorded while their speeds were continuously varied between 0 and 3 cm/s. The figure also shows three stationary measurements for each transponder (appearing as light-colored points on the trajectories). (The slight elliptical shape of the trajectories showed that the turntable plane was tilted a little from true perpendicular.) As the transponders moved further from the antenna the standard deviation in the position measurements increased as expected due to 1/r2 attenuation but did not exceed 0.05 cm for any transponder at its maximum distance, which is within the expected range for stationary position measurements. There was no change in the z-coordinates associated with the movement of the transponders perpendicular to the antenna (i.e., no distortion or broadening of the trajectories). DISCUSSION We detected a small but significant systematic trend in localization accuracy as a function of transponder position parallel to the antenna. This is displayed in Table 1 and arises from the internal calibration processes of the localization system. At the beginning of a tracking session the system goes through a ‘‘discovery’’ calibration based on the initial position of the transponders. The localization precision is optimal at this location. If the transponders move away from the ‘‘discovery’’ position, then the precision decreases somewhat, as shown in Table 1. In the plane parallel to the antenna the
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maximum displacement for Transponder 1 was 11.32 cm, for Transponder 2 it was 10.12 cm, and for Transponder 3 it was 8.8 cm. Over this distance the localization uncertainty increased approximately linearly from 0.02 to 0.06 cm per axis. When the transponders moved further away from the antenna in the z-direction by 3.0–4.5 cm the position uncertainty changed from 0.02 to 0.05 cm in the worst case. Lung tumors do not move more than approximately 3 cm in the most extreme cases. Therefore the Calypso system will have <0.03-cm systematic change in localization accuracy over the full range of tumor position. The moving transponder measurements showed no statistically significant systematic error in the (x,y,z) position coordinates due to transponder motion. We conclude that if the Calypso system is used for real-time respiratory motion tracking, then tracking accuracy will be unaffected by transponder motion, at least for the velocity range that will be encountered in most clinical applications. If the transponder is moving, its reported location corresponds precisely to its position at the midpoint of the readout interval, regardless of speed. In an adaptive motion correction system the tracking control loop will need to account for the time delay between the midpoint of the transponder readout cycle and the moment when the tracking device makes its alignment response. This can be done using the principles of predictive filtering that have been studied in this context (7, 8).
REFERENCES 1. Kupelian P, Willoughby T, Mahadevan A, et al. Multi-institutional clinical experience with the Calypso System in localization and continuous, real-time monitoring of the prostate gland during external radiotherapy. Int J Radiat Oncol Biol Phys 2007;67:1088–1098. 2. Balter JM, Wright JN, Newell LJ, et al. Accuracy of a wireless localization system for radiotherapy. Int J Radiat Oncol Biol Phys 2005;61:933–937. 3. Willoughby TR, Kupelian PA, Pouliot J, et al. Target localization and real-time tracking using the Calypso 4D localization system in patients with localized prostate cancer. Int J Radiat Oncol Biol Phys 2006;65:528–534. 4. Litzenberg DW, Willoughby TR, Balter JM, et al. Positional stability of electromagnetic transponders used for prostate localization and continuous real-time tracking. Int J Radiat Oncol Biol Phys 2007;68:1199–1206.
5. Murphy MJ. Tracking moving organs in real time. Semin Radiat Oncol 2004;14:91–100. 6. Shirato H, Suzuki K, Sharp GC, et al. Speed and amplitude of lung tumor motion precisely detected in four-dimensional setup and in real-time tumor-tracking radiotherapy. Int J Radiat Oncol Biol Phys 2006;64:1229–1236. 7. Murphy MJ, Jalden J, Isaksson M. Adaptive filtering to predict lung tumor breathing motion during image-guided radiation therapy. In: Lemke HU, Vannier MW, Inamura K, editors. CARS 2002. Computer-assisted radiology and surgery: Proceedings of the 16th International Congress and Exhibition, Paris, June 2629, 2002. Berlin: Springer Verlag; 2002. p. 539–544. 8. Sharp GC, Jiang SB, Shimizu S, et al. Prediction of respiratory tumour motion for real-time image-guided radiotherapy. Phys Med Biol 2004;49:425–440.