Internal-external correlation investigations of ... - Semantic Scholar

Internal-external correlation investigations of respiratory induced motion of lung tumors Dan Ionascua兲 Department of Radiation Oncology, Division of Medical Physics, Dana-Farber/Brigham and Women’s Cancer Center and Harvard Medical School, 75 Francis Street, Boston, Massachusetts 02115

Steve B. Jiang Department of Radiation Oncology, University of California, San Diego Moores Cancer Center, 3855 Health Sciences Dr. #0843, La Jolla, California 92093-0843

Seiko Nishioka NTT East-Japan Sapporo Hospital, Sapporo, Japan

Hiroki Shirato Hokkaido University Graduate School of Medicine, Sapporo, Japan

Ross I. Berbeco Department of Radiation Oncology, Division of Medical Physics, Dana-Farber/Brigham and Women’s Cancer Center and Harvard Medical School, 75 Francis Street, Boston, Massachusetts 02115

共Received 14 December 2006; revised 7 August 2007; accepted for publication 14 August 2007; published 19 September 2007兲 In gated radiation therapy procedures, the lung tumor position is used directly 共by implanted radiopaque markers兲 or indirectly 共by external surrogate methods兲 to decrease the volume of irradiated healthy tissue. Due to a risk of pneumothorax, many clinics do not implant fiducials, and the gated treatment is primarily based on a respiratory induced external signal. The external surrogate method relies upon the assumption that the internal tumor motion is well correlated with the external respiratory induced motion, and that this correlation is constant in time. Using a set of data that contains synchronous internal and external motion traces, we have developed a dynamic data analysis technique to study the internal-external correlation, and to quantitatively estimate its underlying time behavior. The work presented here quantifies the time dependent behavior of the correlation between external respiratory signals and lung implanted fiducial motion. The corresponding amplitude mismatch is also reported for the lung patients studied. The information obtained can be used to improve the accuracy of tumor tracking. For the ten patients in this study, the SI internal-external motion is well correlated, with small time shifts and corresponding amplitude mismatches. Although the AP internal-external motion reveals larger time shifts than along the SI direction, the corresponding amplitude mismatches are below 5 mm. © 2007 American Association of Physicists in Medicine. 关DOI: 10.1118/1.2779941兴 Key words: respiratory tumor motion, implanted fiducial, external suroggate, correlation, time shift, amplitude mismatch, lung cancer I. INTRODUCTION In gated radiotherapy, healthy tissue is spared by only turning on the treatment beam when the tumor is within a certain region.1–5 The accuracy of respiratory-gated treatments based on external body monitoring usually relies upon the assumption of a strong correlation between the external motion and the internal tumor motion. Ideally, the internal-external motion correlation should be investigated by synchronously monitoring fiducials implanted in or near the tumor 共internal tracking兲 and the external breathing motion 共external tracking兲. This type of investigation has been difficult to perform for the following reasons: 共1兲 Due to the increased risk of pneumothorax,6–9 lung implanted fiducials are not readily available in many clinics in the United States. 3893

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共2兲 The tumor is difficult to see in x-ray fluoroscopy10 without the aid of implanted fiducials. 共3兲 To obtain a large data set, long periods of x-ray fluoroscopy are needed.10 This is hard to justify clinically. There have been several notable attempts to monitor and to quantify the internal/external correlation.11–20 Vedam et al.11 measured the correlation between the abdominal wall and the SI location of the diaphragm. This only gives onedimensional internal information and it leaves out the correlative relationship between the diaphragm and the lung tumor itself. Moreover, investigations of the surrogate internal structures done by Iwasawa et al.12 reported paradoxical diaphragm motion in patients with emphysema. Plathow et al.13 used dynamic MRI to study the correlation between the lung tumor motion and the chest wall motion. However, most external surrogate gating systems21–23 use abdominal motion rather than chest wall motion. Studies by Gierga et al.14 have

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Ionascu et al.: Correlation of respiratory induced motion of lung tumors

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FIG. 1. The Mitsubishi Real-Time Radiation Therapy system at NTT Hospital in Sapporo, Japan. The fluoroscopic x-ray imagers and the external respiratory tracking system are shown along with the corresponding synchronous motion amplitudes. AP—anteriorposterior; SI—superior inferior, and LR—lateral motion.

shown that even though the correlation between external markers and abdominal tumor motion is good, the potential of variations in tumor position for given marker positions may degrade the accuracy of the gating window. Furthermore, Ozhasoglu and Murphy15 and later Mageras et al.16 have shown that the phase of the organ motion does not necessarily match the phase of the surrogate motion, and their relationship can be time dependent. We will present a novel internal-external correlation study based on a unique data set.24 The three-dimensional internal fiducial-based tumor data were obtained in synchronization with one-dimensional abdominal motion as a function of time. This data is used to thoroughly investigate the correlations between the external abdominal surface motion and the internal lung tumor motion and to reveal and quantitatively estimate their nonstationary time behavior. The time behavior of the time shifts and their corresponding amplitude mismatches are consequently obtained. II. METHODS AND MATERIALS

recovery procedure, and algorithm used in this study are fully described elsewhere.10,25–27 Briefly, the treatment procedure28 consists of switching on the MV beam when a 1.5 mm diam gold ball-bearing is detected within a threedimensional predetermined window.10 Typically, the 3D window is given by a 5 mm edge cube centered on the planned position. The fluoroscopic images are recorded continuously, independent of the MV beam status 共on-off兲, with a sampling frequency of 30 Hz. In temporal synchronization with fluoroscopic imaging, the external respiratory motion of the patients’ abdominal surface was recorded. The external respiratory motion monitoring system used in this setup is the laser based AZ-733V “RespGate” made by Anzai Medical, Tokyo, Japan. The external monitoring system supplies onedimensional displacement data that reflects the abdominal motion induced by patient respiration. The internal threedimensional fiducial position and the external onedimensional abdominal position are recorded in a log file with the appropriate time stamp. The data is analyzed offline, after the treatment has been completed.

II.A. Real-time radiation therapy system

Radiopaque fiducial markers 共bbs兲 inside or near the target were implanted and visualized in real time by means of stereoscopic diagnostic x-ray fluoroscopy. For data collection, the recordings were made by a Mitsubishi Real-Time Radiation Therapy 共RTRT兲 system10 共Fig. 1兲 located at the Radiation Oncology Clinic at the Nippon Telegraph and Telephone Corporation 共NTT兲 Hospital in Sapporo, Japan. The details of the RTRT system at the NTT hospital, the data Medical Physics, Vol. 34, No. 10, October 2007

II.B. Patients

Ten lung patients with various tumor sites were studied for a maximum of 12 fractions and five beam configurations per fraction. These patients were selected from the general patient population to be treated with hypofractionated 共40 or 48 Gy in four or eight fractions兲 respiratory gated radiotherapy based on the tumor motion, size, and location, among other factors. The data for patient 5 was obtained

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TABLE I. Patient information. Patient 5 was treated twice, at the same site, with two months between treatments. The tumor site is indicated using the common anatomical notation for lung segmentation: S1-3 is upper lobe, S4-5 is middle lobe, S6-10 is lower lobe.

Patient 1 2 3 4 5 5 6 7 8 9 10

Gender

Age

Tumor pathology

Number of bbs

Tumor site

Prescribed dose 共Gy兲

Fractions

F F F F M

47 70 71 47 81

Adenocarcinoma Adenocarcinoma Adenocarcinoma Adenocarcinoma Squamous cell carcinoma

4 3 2 3 3

Rt. S7 Lt. S6 Rt. S5 Rt. S4 Rt. S2b

M M M M M

61 68 85 76 58

Small cell lung cancer Squamous cell carcinoma Adenocarcinoma Squamous cell carcinoma Adenocarcinoma

3 3 3 2 1

Rt. S10 Rt.S6 Rt. S8 Lt. S3 Lt. S10

N/A N/A N/A 48 48 40 40 48 48 60 48

1 1 1 8 4 8 7 4 4 3 4

during two different sessions, but treatment was applied to the same site, with no isocenter shifts. Note that the patients studied do not represent a random sample of the general lung patient population. The patient selection for this study was based on the estimated amplitude of the internal marker motion greater than 10 mm, peak to peak, along any of the lateral 共LR兲, superior-inferior 共SI兲, and anterior-posterior 共AP兲 directions. The details of each patient are presented in Table I. If more than one marker was implanted, only one marker was picked and considered for analysis. The ten lung patients were treated by amplitude based threshold gating and the synchronized recordings were obtained from a study by Berbeco et al.24 II.C. Data analysis

We have developed a novel data analysis methodology to assess the dynamic correlation of the external breathing motion with the internal time dependent 3D position of the implanted fiducials. The technique is used to extract global correlation parameters as well as to reveal their time dependent behavior, that is, the dynamic correlation parameters. Subsequently, we quantify the time shifts 共if existent兲 and their time dependent variability. Using this information, we quantitatively assess the amplitude mismatch that is due to the time shift and its variation. We define the amplitude mismatch as the difference between the actual recorded internal motion and the internal motion predicted based on the external motion measurement. II.C.1. Motion traces In Fig. 1, we present the synchronous external 共onedimensional兲 breathing trace and the internal traces 共3D兲 of the implanted fiducials along the lateral, superior-inferior, and anterior-posterior coordinates. As demonstrated by the Fig. 1 insets, the signal-to-noise ratio 共SNR兲 is strongly dependent on the direction of the fiducial motion. This is due to the respiratory induced directionality of the fiducial/tumor Medical Physics, Vol. 34, No. 10, October 2007

motion that is manifested with large motion amplitudes along the SI direction and smaller motion amplitudes along the other directions. II.C.2. The global correlation coefficient and time shift The Pearson’s correlation coefficient 共R兲 is computed between the external signal 共Ext兲 and the coordinate components 共SI, AP, and LR兲 of the implanted fiducial internal trace as described by Eq. 共1兲: RExternal-Internal =

int n ext int 兺i=1 共Aext i − A 兲共Ai − A 兲 , 共n − 1兲␴Ext␴Int

共1兲

where Aext and Aint are the trace amplitudes for the external and internal traces, respectively, and ␴ is the standard deviation defined as

冑兺 N

␴=

1 共ai − ¯a兲2 . N i=1

For clarity purposes, the correlation coefficient computed using the entire available data set is called the global correlation coefficient 共GCC兲. For small motion amplitudes, where the signal is comparable with the detection system noise or with the heart induced motions,26 the global correlation coefficient could have values smaller than 0.7. This is the situation that we have observed for most of the patients along the LR direction. This situation is irreducible unless the SNR can be improved by means of improved detection accuracy or by means of filtering the higher frequencies out, as we will explain later. For a pair of internal-external motion traces with large signal-to-noise ratio, the global correlation coefficient can have small values 共poor internal-external correlation, R ⬍ 0.7兲 due to a time shift between the two motion traces. For clarity, to define time shift, let us consider two time series that are perfectly correlated. This corresponds to the correlation coefficient being close to 1 so that the two time series

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as the reference data making the correlation coefficient peak where the best correlation occurs 共Fig. 2兲. Because the time shift is not expected to exceed one-third of the breathing period, the induced time-shift values were set in the range 关−1.3 s , 1.3 s兴, where positive time-shift values imply that the external trace is lagging behind the internal tumor motion and vice versa for negative values. If the maximum correlation does not occur at zero time shift, then by shifting one time series versus the other one, the global correlation is maximized. The time shift between the motion of the implanted fiducials and the external breathing motion is consequently obtained as the time value where the correlation coefficient is maximized. Therefore, as shown in Fig. 2, the variable time-shift methodology described provides us with the following information: 共1兲 The value of global correlation coefficient R共tShift = 0兲. 共2兲 The maximum value of the global correlation coefficient Rmax ⬎ R共tshift = 0兲. 共3兲 The time shift, Tshift, where the R共Tshift兲 = Rmax.

II.C.3. The dynamic correlation coefficient and time shift FIG. 2. The time-shift methodology. A pair of simulated synchronous internal 共tumor motion 共b兲兲 and external 共breathing motion 共a兲兲 traces are shown as continuous lines. The Pearsons’ correlation coefficient is computed as a function of an induced variable time shift applied to the internal trace, whereas the external trace is kept as a reference 共a兲. The R共0兲 represents the zero shift correlation coefficient and the Rmax is the maximum correlation coefficient obtained at the corresponding time shift, Tshift 共c兲. The obtained time shift, Tshift quantifies the phase shift that is present between the internal tumor motion and external breathing motion. The corresponding shifted internal trace where the correlation is maximized is shown by the dashed line 共b兲. The presence of the time shift has, as a direct result, an amplitude mismatch between the original internal motion trace and internal motion trace that has been corrected for the time shift 共b兲.

can be considered to be “in phase.” By shifting, in time, one series versus the other one 共i.e., by inducing a positive or negative time shift as shown in Fig. 2兲, the global correlation coefficient is gradually decreased as the absolute value of the time shift becomes larger. This is a simple mathematical exercise for an analytically defined time series. However, for a time series similar to the internal tumor motion induced by the breathing process, where the baseline, amplitude, and period are variable within a limit, the phase concept becomes ill defined. Therefore, we prefer to call this effect “time shift.” To investigate the possibility of time shifts in our data, the developed methodology is based on the dynamic computation of the Pearson’s correlation coefficient between the external breathing motion and the implanted fiducial motion. This is achieved by computing the global correlation coefficient as a function of a variable time shift induced on the internal motion time series 共Fig. 2共b兲兲. The induced variable time shift is set to be symmetrical around a reference time. The external breathing motion is set Medical Physics, Vol. 34, No. 10, October 2007

Due to the variability of the breathing motion 共amplitude and frequency changes兲, it is important to find out if the correlation coefficient and the corresponding time shift are constant during the treatment. Even though the global correlation ensures a robust way to recover the internal-external time shift, it does not offer any insights regarding the time evolution of the correlation coefficient and the associated instantaneous time shift. To study the time behavior and obtain the variability of these parameters, we have applied the dynamic correlation methodology to a sliding time window of short time duration. The window time duration is chosen based on the average period of the time series and is typically set at 2.5 to 3 breathing periods 共Fig. 3共a兲兲. We have found that this value is optimal to preserve the local periodic character of the time series within the sliding time window, and to keep the window time duration to a minimum. For each sliding window time position, the correlation coefficient, the maximum of the correlation coefficient and its corresponding time shift were computed by using the method described in Sec. II C 2 where the entire duration of data set is considered for analysis. The global values obtained for the correlation parameters are shown in Figs. 3共b兲 and 3共c兲. The window was set to gradually slide with the smallest available time step 共tstep = 0.033 s兲 for the entire time range of the data sets, hence providing the time evolution of the correlation parameters. The time dependent parameters R共t兲, Rmax共t兲 and Tshift共t兲 are depicted in Figs. 3共b兲 and 3共c兲 along with their average and standard deviation. In Eq. 共1兲, the correlation coefficient becomes a function of time. The time variable is now defined by the sliding window position on the time axis. Therefore, the summation limits in Eq. 共1兲 become

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FIG. 3. The sliding window methodology is used to reveal the nonstationary 共dynamic兲 character of the correlation coefficient and time shift. The correlation parameters 共R共t兲, Rmax共t兲, 共b兲 and the time-shift TS共t兲, 共c兲兲 are computed as a function of the window time position 共gray rectangle兲. The time average of the dynamic correlation parameters is compared with the global correlation parameters 共where the entire available data set is used兲 and presented at the right side of b and c panels. The error bars represent the standard deviation of the corresponding averaged dynamic parameter over the duration of the time series. Note that different scales are used for clarity. The data shows a significant nonstationary time shift along the AP direction 共c兲 and a very good correlation along the SI direction. The lateral direction has small SNR and poor correlation with the external breathing trace.

iwindow =

冋册 t

tstep

and

n=

冋

1 tstep

册

· 共t + k · Tbreathing兲 ,

where k · Tbreathing is the duration of the sliding time window, typically set at 2.5 to 3 times the patient breathing period 共Tbreathing兲. II.C.4. Amplitude mismatch The amplitude mismatch is a direct consequence of the time shift and it represents the difference in internal position between a motion trace and itself after the appropriate time shift has been induced. Practically, if the external motion trace is to be used for tumor position prediction 共assuming a near perfect internal-external correlation兲, the amplitude mismatch value is the amount the implanted fiducial is displaced from the position predicted by the external signal. The amplitude difference between a periodic signal and the identical signal shifted in time varies from zero 共where the two signals coincide兲 to a maximum value that is a function of the time shift. The pattern of the amplitude mismatch for a periodic signal is periodic itself, as can be seen in Fig. 2共b兲. Depending on the speed of the internal motion, for a given time shift, the amplitude mismatch will vary from a minimum value 共close to zero兲 that occurs during end-ofexhale 共where the motion speed is the smallest兲 to a maximum value that corresponds to the inhale region where the gradient of the motion is the largest. The amplitude mismatch reported here is the maximum value that the amplitude mismatch can take for the specific patient day, beam, and motion direction. Based on the time shift variability, we can determine the corresponding range of the amplitude mismatch for each paMedical Physics, Vol. 34, No. 10, October 2007

tient. Whereas the average time shift is used to calculate the amplitude mismatch, the standard deviations of the time shift are used to compute the range of the amplitude mismatch. The amplitude mismatch range is computed using the upper and lower limit given by the time shift standard deviation 共i.e., Ts共t兲 ± ⌬Ts兲. Using these time shift values, the maximum amplitude mismatch is computed for the upper and lower limit, respectively. However, in order to reduce local effects, the amplitude mismatch range is calculated based on the average of the largest 10% of the amplitude mismatch values for the entire duration of the time series. In addition, to reduce the noise, we apply our methodology after the time series was processed with a low pass Gaussian filter 共1.5 Hz HWHM兲. The determination of the time shift and its corresponding standard deviation translates into the amplitude mismatch and its daily variability. III. RESULTS The characteristics of the internal tumor motion 共amplitude and period兲, specifically for each patient and motion direction, are shown in Fig. 4. As expected, the amplitude of the implanted fiducial motion is decreasing as a function of the direction of the motion projection, SI, AP, and LR, respectively. The variability of tumor motion amplitude and period during the entire treatment was observed. For patients that have large interfractional amplitude variations, the standard deviation shows large values, especially along the SI direction. The lung tumor implanted fiducials move predominantly along the SI direction with peak to peak amplitudes in the range of 6 mm to 20 mm, depending on the patient/tumor location. This effect is expected because of the respiration mechanics, where most of the changes are manifested along

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FIG. 4. The amplitude and period of the implanted fiducials motion during the entire treatment are shown specifically for each patient. The error bars represent the amplitude and period standard deviations determined over the entire treatment duration.

the SI direction where the amplitude is the largest. The effect is also observed for fiducial motion along the AP direction, however, smaller than observed on the SI direction, with amplitudes that range from 1 mm to 11 mm. Similarly, the effect is furthermore diminished along the LR direction where the internal fiducial motion is the smallest in amplitude accounting for less than 4 mm. For robustness, the internal fiducial motion amplitude and the period were obtained after a low pass Gaussian filter was applied to the motion traces. The filter HWHM was set to 1.5 Hz. The amplitude and period were extracted within a time moving window that scanned the motion traces. The duration of the time window was set to span approximately three breathing periods. This method allowed us to obtain the internal amplitude and period intrafractional variation 共not shown兲 and finally recover the variation over the entire treatment 共Fig. 4兲. The robust recovery of the correlation coefficient requires that the tumor motion trace has a large SNR. If the SNR is small, then the subsequent recovery of the time shift is compromised. If the signal is comparable to the noise, then the noise is transferred to the correlation values making the time shift recovery hard to perform. Therefore, the extent of the tumor motion affects the SNR and, subsequently, the global correlation coefficient 共GCC兲. For robustness, we have applied our technique to motion along LR direction, but our study has revealed that even when the internal-external correlation was sufficiently large, in general, no time shift was recovered. To check the validity of this conclusion, we have tried to improve the signal-to-noise ratio by applying a low pass Gaussian filter with a HWHM ranging from 0.5 Hz to 1.5 Hz. In general, the internal-external LR correlation was poor, with values below 0.5, and our methodology was not able to recover time shifts between external and internal motion. This situation could be due to the fact that there is no time shift between the external motion and the internal LR Medical Physics, Vol. 34, No. 10, October 2007

motion or due to the fact that our methodology breaks down when analyzing very low SNR time series. The only exception when we were able to recover the time shift, was for patient 4, where a time shift of approximately 0.15 s ± 0.10 s was recovered. Furthermore, the Gaussian filter was applied to internal-external motion pairs for the SI and AP directions and the global correlation parameters were recomputed. Even though the SNR of the motion time traces was increased, the correlation and time shift results were relatively unchanged 共±5 % 兲, compared to the unfiltered results. We attribute this to the large amount of data points contained in a time series. In Fig. 5, we present the results for patient 4 during 10 days of treatment and with four MV beam configurations. The beam configurations represent four LINAC gantry angles that do not affect the imaging. In Fig. 5共a兲, along the SI direction, the internal-external correlation is very high, with values larger than 0.97. Because of this high correlation, the Rmax values are practically overlapping with the global correlation coefficient R values, and are not shown for clarity of the data plot. Subsequently, the obtained time shift, Tshift is very small 共⬃0.07 s兲 and approaching the smallest sampling time interval 共⌬t = 0.033 s兲 as seen in Fig. 5共c兲. For the motion along the AP direction, the internal-external correlation for this patient is not as good as in the case of the SI direction 共Fig. 5共b兲兲. The GCC values are in the range 0.77–0.88, depending on the day when data were recorded. Based on our technique, as shown in Fig. 5共b兲, it can be seen that the GCC is improved by approximately 20%, depending on the treatment day. The corresponding time shift is ⬃0.25 s 关Fig. 5共d兲兴. These results can also be seen as a function of treatment day in Figs. 6 共SI兲 and 7 共AP兲 where the correlation, time shifts, and their variability are presented.

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FIG. 5. The global correlation and the time-shift parameters computed for patient 4 during 10 days of treatment and with four beam configurations are presented for the SI direction 共a兲 and for the AP direction 共b兲. The SI internal-external correlation shows values very close to 1 and with negligible time shifts 共a,c兲 with good intrafraction and interfraction repeatability. The AP direction 共b兲 shows a discrepancy 共⬃20% 兲 between the zero shift correlation coefficient 共R共0兲兲 and its maximized value 共Rmax兲 that translates into a time shift of ⬃0.25 seconds 共d兲. The repeatability is preserved intrafractionally 共along the “beam” coordinate兲 but is lost interfractionally.

Medical Physics, Vol. 34, No. 10, October 2007

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FIG. 6. The global and dynamic correlation coefficient and the corresponding time shift per patient, per day, along the SI direction are shown. The error bars represent the standard deviation of the dynamic correlation coefficient and time shift over a specific treatment day. Except for patients 3 and 5 共days 8 and 9兲, and 10 共day 1兲 no larger than 0.15 s time shifts are observed.

However, the correlation enhancement is unattainable by our technique along the LR direction, therefore, no time shift was recovered 共Fig. 3兲. Denoted with an upper bar, the time average of the dynamic correlation parameters are shown at the end of the time dependent plots. Specifically, the parameters presented are: the mean dynamic correlation, R共t兲 and the mean dynamic time shift, Ts共t兲 and their corresponding standard deviations, next to their global values, global R and global Ts. For example, in Fig. 3共b兲, we see that for patient 1, the internal-external correlation along the SI direction is exSI ⬃ 0.98. In contrast, the LR direction corcellent with RExt-Int LR ⬃ 0.3– 0.4. Of course, less morelation is poor with RExt-Int tion also means less need for tracking in that direction, so the poor SNR is not problematic. As seen in Figs. 3 and 5 for the AP direction, our methodology allows us to improve the internal-external correlation for tumor motion traces with good SNR, provided there is a fundamental time shift between the internal and external motions. Due to the patient setup and treatment procedure, we expect the intrafractional correlation to be preserved. Indeed, upon visual inspection, Fig. 5 demonstrates that for patient 4, this is true and there is small intrafraction variability. This can be seen even better in Fig. 6, where for patient 4, the correlation coefficient intrafraction variability 共the error bar兲 is smaller than 2%. Along the AP direction, the intrafraction variability is below 6% 共Figs. 5 and 7兲. However, interfractionally, the correlation is preserved for the SI direction with values below 6% variation, but it becomes poor for AP 共10%兲 and lateral coordinates 共not shown兲. This is even more evident for patient 5 共Figs. 6 and 7兲. Medical Physics, Vol. 34, No. 10, October 2007

In some cases, the time shift is the clear cause for poor correlation. Figure 5 shows that by applying our methodology, the correlation is improved substantially and the corresponding time shift is obtained. The large spectrum of values obtained for the time shift 共up to 0.55 s兲 may have to do with the specific position of the tumor29 and with the mechanical coupling between the respiratory motion and the tumor motion.17,18,20 Using the sliding window methodology, we observe that the internal-external motion coupling may change in time 共Figs. 3共b兲 and 3共c兲兲. For example, in Fig. 3共c兲 along the AP direction, the time shift jumps from Ts共t兲 ⬃ 0.3 s to values larger than Ts共t兲 ⬃ 0.6 s. This translates into a maximum amplitude mismatch of approximately 2 mm. What this means is that if the external motion trace is to be used for tracking with the assumption of a close to 1 internal-external correlation coefficient, there are moments when the implanted fiducial/tumor is at maximum 2 mm away from where predicted, based on the external signal. In Fig. 6, we present the overall results for the global and dynamic correlation coefficient with their corresponding time shift per patient, per day, along the SI direction. The tumor motion along the SI direction is very well correlated with the external abdominal motion. Consequently, the obtained time shift is very small, with values below 0.2 s and with good day to day reproducibility. However, patient 3 represents an exception and shows the largest discrepancy between the maximized correlation coefficient Rmax and the correlation coefficient R, computed statically. This discrepancy is the consequence of a time shift of ⬃0.3 s. The cor-

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FIG. 7. The anterior-posterior 共AP兲 overall results for the global and dynamic correlation coefficient and the corresponding time shift per patient, per day, along the AP direction are shown. The error bars represent the standard deviation of the dynamic correlation coefficient and time shift over a specific treatment day. Patients 1, 3, 4, 5, and 10 show large time shifts.

responding maximum of the amplitude mismatch is approximately 3.3 mm. It is noteworthy to observe that the correlation cannot be improved by our methodology 共e.g., patient 9兲, unless there is a time shift 共e.g., patients 3 and 5兲. This is more evident along the AP direction, shown in Fig. 7. In general, the discrepancies between R and its maximized value Rmax are larger along the AP direction with time shifts as large as 0.55 s. We observe that for patient 4, the day to day correlation variability along the AP direction is very low. The corresponding 0.2 s time shift is also nearly constant over the entire treatment period. In addition, there is very little intrafraction variability, as shown by the relatively small error bar values. However, we must point out that there are situations when the day-to-day predictability may become problematic, even along the generally well correlated SI direction, as seen for patient 5 during the treatment days 8 and 9 共Fig. 6兲. In this case, the time shift obtained at the beginning of the treatment 共less than 0.1 s兲 increases to 0.2 s on the eighth treatment day. This corresponds to a jump in the maximal amplitude mismatch from 1.5 mm on the first treatment day to larger than 3 mm on the eighth treatment day 共Fig. 8共a兲兲. Moreover, the amplitude mismatch along the AP direction can be even greater, reaching values as large as 4.7 mm. Relatively large amplitude mismatches 共larger than 2.5 mm兲 in the SI direction are observed for patients 3, 10, and 5 共days 8 and 9兲. This shows that even with the global time shift accounted for, internal fiducial/tumor localization is not guaranteed. Medical Physics, Vol. 34, No. 10, October 2007

IV. DISCUSSION External surrogate based gating and tracking algorithms are based on the assumption that there is a strong and constant correlation between the internal tumor motion and the external abdominal motion, at all times. For most patients, intrafraction variation of SI correlation and time shift is small, as shown by the relatively small error bars in Fig. 6. However, for some patients, such as patient 3 共SI兲 and patient 6 共AP兲, the error bars are large, indicating that they ought not to be treated based solely on external surrogates. Although extra care was exercised in consistent positioning of the external monitoring system relative to the patient’s surface, change from day to day is possible. This may introduce interfractional changes of the internal-external correlation 共as seen for patient 5 during the treatment days 8 and 9, Figs. 6 and 8共a兲. In addition, during the treatment, patients may lose weight, affecting the shape of their body, possibly changing the day-to-day internal-external correlation. The state of the patient’s gastrointestinal tract 共mostly induced by the organs within the diaphragm proximity, the stomach and large intestine兲 may change due to filling or gas, and could generate additional day-to-day variations of the internalexternal correlation. A study of the relationship between the patient’s state and the day-to-day internal-external correlation would be extremely beneficial for the medical physics community. For the patients studied, an increase of the treatment margins by 5 mm in the SI and AP directions would ensure that

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FIG. 8. The maximal amplitude mismatch between the surrogate external motion trace used to predict the tumor position and the implanted fiducial position are shown for all the patients along the SI 共a兲 and AP 共b兲 directions. The error bars represent the maximal variability range of the amplitude mismatch computed from the standard deviation of the dynamic time shift for the corresponding patient and day of treatment.

the amplitude mismatch between the external surrogate motion and the internal tumor motion is fully compensated 共Fig. 8兲. If a similar analysis could be done in a clinic prior to the treatment, one could statistically assess the confidence interval of the correlation coefficient, time shift, and amplitude mismatch, hence allowing for pretreatment adjustments. This can be simply done, as mentioned above, by incorporating the amplitude mismatch into the treatment margins. However, the amplitude mismatches obtained in this paper were revealed by using the RTRT system, which can be considered because of the fast rate synchronous system, lag time free. This situation can change for a different gating system and each system needs to be evaluated separately. A possible approach to compensate for the time shift during the time of a gated treatment would be to use the standard amplitude gating technique,30,31 combined with an additional time shift that has been determined according to the method described here 共or perhaps with a 4DCT兲. This can be done by having separate amplitude levels for the beam on/off, so that the time shift is taken into account. For example, the beam is turned on 0.5 s after it has reached a predetermined amplitude level, and it is turned off after it has reached the preset threshold. A situation similar to that of patients 4 and 5 共Fig. 7兲 would be perfect for the inclusion of a constant time shift into the amplitude gating technique. This idea will be examined further in a future study. V. CONCLUSION We have found good internal-external correlation along the superior-inferior direction with small or no internalMedical Physics, Vol. 34, No. 10, October 2007

external time shifts and amplitude mismatches. Along the anterior-posterior direction, we have found relatively large time shifts and amplitude mismatches. Our dynamic technique can inform us of the underlying time dependence of the internal-external correlation coefficient, time-shift, and amplitude mismatch. This methodology reveals that there can be significant and unpredictable time shifts and amplitude mismatches that have never been quantified before. We have found that these effects could be caused by 0.4– 0.6 s instantaneous time shifts that induce amplitude mismatches in the range of 2.5– 4.7 mm. The time dependency of the correlation parameters could be used to increase the confidence region of a gated treatment by incorporating them into the gating algorithm or treatment margin. a兲

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