A comparison between amplitude sorting and phase-angle sorting
using external respiratory measurement for 4D CT
Wei Lu, Parag J. Parikh, James P. Hubenschmidt, Jeffrey D. Bradley, and Daniel A. Lowa兲
Department of Radiation Oncology, Washington University School of Medicine, St. Louis,
Missouri 63110
共Received 19 September 2005; revised 21 May 2006; accepted for publication 13 June 2006;
published 27 July 2006兲
Respiratory motion can cause significant dose delivery errors in conformal radiation therapy for
thoracic and upper abdominal tumors. Four-dimensional computed tomography 共4D CT兲 has been
proposed to provide the image data necessary to model tumor motion and consequently reduce
these errors. The purpose of this work was to compare 4D CT reconstruction methods using
amplitude sorting and phase angle sorting. A 16-slice CT scanner was operated in ciné mode to
acquire 25 scans consecutively at each couch position through the thorax. The patient underwent
synchronized external respiratory measurements. The scans were sorted into 12 phases based,
respectively, on the amplitude and direction 共inhalation or exhalation兲 or on the phase angle
共0 – 360° 兲 of the external respiratory signal. With the assumption that lung motion is largely proportional to the measured respiratory amplitude, the variation in amplitude corresponds to the
variation in motion for each phase. A smaller variation in amplitude would associate with an
improved reconstructed image. Air content, defined as the amount of air within the lungs, bronchi,
and trachea in a 16-slice CT segment and used by our group as a surrogate for internal motion, was
correlated to the respiratory amplitude and phase angle throughout the lungs. For the 35 patients
who underwent quiet breathing, images 共similar to those used for treatment planning兲 and animations 共used to display respiratory motion兲 generated using amplitude sorting displayed fewer reconstruction artifacts than those generated using phase angle sorting. The variations in respiratory
amplitude were significantly smaller 共P ⬍ 0.001兲 with amplitude sorting than those with phase angle
sorting. The subdivision of the breathing cycle into more 共finer兲 phases improved the consistency in
respiratory amplitude for amplitude sorting, but not for phase angle sorting. For 33 of the 35
patients, the air content showed significantly improved 共P ⬍ 0.001兲 correlation with the respiratory
amplitude than with the phase angle, suggesting a stronger relationship between internal motion and
amplitude. Overall, amplitude sorting performed better than phase angle sorting for 33 of the 35
patients and equally well for two patients who were immobilized with a stereotactic body frame and
an abdominal compression plate. © 2006 American Association of Physicists in Medicine.
关DOI: 10.1118/1.2219772兴
Key words: 4D CT, respiratory motion, radiotherapy, phase, amplitude
I. INTRODUCTION
Four-dimensional computed tomography 共4D CT兲 has been
proposed as an imaging technique to support improving the
accuracy of radiation therapy delivery in the presence of respiratory motion.1–8 A 4D CT dataset consists of a set of 3D
images reconstructed at selected phases of the respiratory
cycle, e.g., at the end of exhalation 共EE兲, middle inhalation
共MI兲, end of inhalation 共EI兲, and middle exhalation 共ME兲.
CT scans are typically sorted into different respiratory phases
based on either the amplitude or the phase angle of a respiratory trace, which is usually obtained with a synchronized
external respiratory measurement. 共Phase angle is defined
here as the fraction of time between user-specified phases of
breathing, typically renormalized between the canonical
angles of 0° to 360°. The term “phase” when used alone is
reserved to describe a portion of the breathing cycle such as
the end of inhalation.兲 Many groups have attempted to generate 4D CT datasets by using the phase angle as a sorting
criterion.1–6,8 However, the respiratory cycle is often insuffi2964
Med. Phys. 33 „8…, August 2006
ciently reproducible so that using phase-angle sorting causes
large inconsistencies in the image reconstruction. For
respiration-gated radiotherapy, Vedam et al.9 stated that amplitude gating is better than phase angle gating because the
amplitude is more accurately related to the target position.
For the two patients shown in Vedam et al.,9 amplitude gating was determined to be more effective than phase angle
gating for one patient and as effective for the other, who had
more reproducible breathing. For 4D CT, Rietzel et al.10
qualitatively examined amplitude sorting and phase angle
sorting for two patients. Phase angle sorting worked well for
the first patient who had more reproducible breathing. For
the second patient, it was found that phase angle did a poor
job of representing respiratory motion. To highlight this, Rietzel et al.10 showed that when replacing phase angle sorting
by amplitude sorting, a reconstruction artifact at the diaphragm was clearly reduced. It was not clear from the manuscript whether their amplitude sorting approach separated
scans based on the direction of respiration, e.g., inhalation
0094-2405/2006/33„8…/2964/11/$23.00
© 2006 Am. Assoc. Phys. Med.
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Lu et al.: Amplitude sorting and phase-angle sorting for 4D CT
and exhalation. Recently, Fitzpatrick et al. presented a
method to extract displacement 共amplitude兲 binned 共sorted兲
4D CT data from prospectively phase-binned image sets with
small phase intervals.11 They showed, in this one-patient
study, that the reconstructed image quality was improved
with amplitude sorting 共separating inhalation from exhalation for middle phases兲.
We have developed a 4D CT technique which sorts scans
based on the amplitude and direction 共inhalation or exhalation兲 of tidal breathing.7,12,13 The breathing direction is included to allow consideration of hysteresis 共the difference
between the inhalation and exhalation trajectories兲 in image
reconstruction.13,14 A quantitative study demonstrated that
4D datasets reconstructed using this technique were both accurate and precise.13 In this work we compare, using both
qualitative and quantitative tools, the effectiveness of amplitude sorting and phase-angle sorting in 4D CT during quiet,
natural breathing, for 35 patients.
II. METHODS AND MATERIALS
A. CT image acquisition with synchronized external
respiratory measurements
A brief description of the 4D CT process and internal air
content analysis is provided as follows:7,13 Transverse slices
are acquired with a 16-slice CT scanner 共Brilliance 16, Philips Medical Systems, Cleveland, OH兲 operated in ciné mode
共couch stationary during scanning兲. The scanned thickness
was 24 mm per couch position using 16 1.5 mm thick slices.
Each scan 共360° rotation兲 required 0.42 s to acquire followed
by a 0.30 s dead time. The CT scanner repeatedly acquired
and reconstructed 25 scans at each couch position for 18 s.
To keep the patient dose low, only a quarter of the clinical
mAs 共40 mAs兲 was used in the imaging process. The dose
per study was estimated to be about 8 cGy based on ion
chamber measurements. The data are acquired contiguously
in space, but there is a pause of approximately 4 s between
two adjacent couch acquisitions. This process is conducted
while the patient undergoes synchronized external respiratory measurements. The synchronization is provided by a
digital 共TTL兲 signal 共“X-Ray On” signal兲 from the CT scanner that indicates when an acquisition starts. Two respiratory
measurements—tidal volume from quantitative spirometry
and a digital voltage signal from a wraparound differential
pressure sensor 共“pneumo bellows”兲—are simultaneously acquired 共Fig. 1兲. The spirometry system measures the air flow
into the lungs and has been shown to be a useful, verifiable
physiologic measurement.13 The bellows system consists of
an accordionlike cylindrical bellows that is strapped around
the patient’s abdomen. The pressure within the bellows decreases as the patient inhales and consequently as the patient’s abdomen distends and their abdominal circumference
increases, with the opposite happening as the patient exhales.
This pressure change is measured by a remote pressure sensor that provides a direct-current voltage signal to an analogto-digital converter. Custom-written data acquisition software 共Labview, National Instruments, Dallas, TX兲 is used to
Medical Physics, Vol. 33, No. 8, August 2006
2965
FIG. 1. System setup for 4D CT scan and acquisitions of two respiratory
measurements: tidal volume from quantitative spirometry and a digital voltage signal from a wraparound differential pressure sensor “bellows.”
Custom-written software is run on the workstation to acquire and display
these signals 共bottom panel兲 as well as the “x-ray on” signal 共top panel兲.
acquire the “X-Ray On” signal from the CT scanner, the
spirometer readings 共via a serial interface兲, and the bellows
signal 共Fig. 1兲.
The spirometer signal has significant baseline level drift
caused by the instruments,12,13,15 while the bellows pressure
signal does not have such instrumental drift and is considered a drift-free measurement.16–18 However, the bellows signal was affected by sensor placement and patient positioning.
To diminish the affect of these nonphysiologic circumstances
on the relationship between the bellows signal and internal
motion, the bellows signal 共in V兲 was converted into a
pseudo tidal volume signal 共in ml兲 by multiplying the average ratio between a drift-corrected spirometer-measured tidal
volume and bellows signal during the scan session. The drift
correction along with a time offset correction was determined by maximizing a cross-correlation function between
the two measurements during 18 s 共time required for each
couch acquisition兲 segments as reported earlier.12 This generated a pseudo tidal volume measurement, which will be
shortened as tidal volume thereafter and used as the respiratory metric. In this paper, the respiratory amplitude or amplitude refers to the tidal volume value.
The internal air content analysis provides a measure of
how much air volume is within the CT volume in a single
couch position.19 The air content is determined by the
Hounsfield values in segmented air-containing tissues 共lungs,
trachea, bronchi兲.13 In a previous study, we showed that the
internal air content correlated with tissue motion in the lung
with a residual of less than 1 mm for 12 patients, and it
provided quantitative evaluations for the 4D CT process.13 In
this study, the internal air content was used as a surrogate for
internal motion and as an independent measurement for comparing the two sorting approaches.
A total of 39 sets of 4D CT data for 35 patients were
acquired while the patients underwent quiet, natural breathing. Among the 35 patients, 19 had lung cancer, while 16
were treated with radiation therapy for upper-abdomen cancers. Three of the patients were scanned more than once.
Four of the patients had stage I non-small-cell lung cancer
and were treated with stereotactic body radiation therapy
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Lu et al.: Amplitude sorting and phase-angle sorting for 4D CT
共SBRT兲,20,21 in which an Elekta stereotactic body frame
共SBF, Elekta Inc., Norcross, GA兲 was used to immobilize the
patient and an optional abdominal compression plate was
used to reduce the motion of the tumor if it was 5 mm or
more measured on a “short” 4D CT scan around the tumor
region.
phases. To determine the phase angle, first the peak and valley points in every breath were identified from the tidal volume trace with a semiautomatic method.22 Let t1, t2, and t3
be the times at the first peak, the following valley, and the
second peak, respectively. The phases at these three points
were defined as 0°, 180°, and 360°. The phase angle ␸ of a
point at ti was linearly interpolated in time as
B. 4D CT reconstruction using amplitude sorting
We have developed a 4D CT reconstruction technique
based on the amplitude and direction 共inhalation or exhalation兲 of tidal breathing.7,12,13 The direction was determined
using a semi-automatic peak and valley detection method.22
A breath consisted of two branches: exhalation 共a peak to the
following valley兲 and inhalation 共the valley to next peak兲. A
composite three-dimensional 共3D兲 image can be reconstructed at an arbitrary tidal volume during inhalation or exhalation. For example, to reconstruct at 300 ml during inhalation, we select at each couch position the inhalation scan
whose center tidal volume is nearest to 300 ml, repeating the
process throughout all couch positions to generate the 3D
image dataset.
The selection of tidal volumes used for reconstruction was
not arbitrary. Two of the 3D images were reconstructed at
end inhalation and end exhalation. However, there existed no
adequate definition for these two phases for sessions with
multiple breaths, so one was developed to support these imaging studies. Because breathing was inherently irreproducible, the tidal volume for each inhalation and exhalation varied. Reconstructing a composite 3D image at a selected tidal
volume required there to be CT scans acquired near that tidal
volume. The practical definition of exhalation/inhalation became the smallest/largest tidal volume for which a 3D image
could be reconstructed within 5% error 共in terms of the difference between mean tidal volume for selected scans to the
desired tidal volume兲. We used v1 and v95 tidal volumes for
EE and EI, respectively, where vx was the percentile tidal
volume.13,23 For example, the 95th percentile tidal volume,
v95, was the tidal volume at which the patient had that tidal
volume or less 95% of the time during the scanning session.
Using percentiles has the advantage over percentages in that
it takes into consideration the relative time a patient reached
a tidal amplitude level so that it is much less affected by the
few extreme breaths 共very deep inhalation or exhalation兲 often seen during the entire scan session.
For this study, we reconstructed 4D CT datasets at six
inhalation phases and six exhalation phases. The six phases
had the same amplitude levels for inhalation and exhalation:
v1 and v95 were the lowest and highest levels, and the other
four levels were evenly spaced between v1 and v95. Using
these definitions, v1 inhalation corresponded to start of inhalation 共SI兲, v95 inhalation EI, v95 exhalation start of exhalation 共SE兲, v1 exhalation EE, and 共v95 + v1兲 / 2 MI or ME.
C. 4D CT reconstruction using phase-angle
sorting
We adopted a phase-angle sorting technique used by
others3,5,6 to reconstruct 4D CT datasets at 12 respiratory
Medical Physics, Vol. 33, No. 8, August 2006
2966
␸i =
ti − t1
⫻ 180 ° ,
t2 − t1
if t1 ⱕ ti ⱕ t2 ,
共1兲
ti − t2
␸i = 180 ° +
⫻ 180 ° ,
t3 − t2
if t2 ⬍ ti ⱕ t3 .
This process was repeated for each breath. For example, using this method, the phase angle 210° corresponded to SI,
phase angle 270° MI, phase angles 0° and 360° EI, phase
angle 30° SE, phase angle 90° ME, and phase angle 180°
EE. For reconstruction, scans whose center phase angle is
closest to the user-specified phase angle were collected to
produce a composite 3D image dataset. This was done for
the 12 phases evenly spaced between 0° and 360° of a respiratory cycle.
D. Variations in tidal volume for each respiratory
phase with amplitude sorting and phase-angle sorting
An assumption of the variation analysis was that, for quiet
respiration, lung motion was largely proportional to the externally measured respiratory amplitude.13,24 Under this assumption, smaller variation in tidal volume would suggest
smaller residual motion or an improved reconstructed image
for a specific respiratory phase. The variations 共quantified by
the standard deviation, s.d.兲 in tidal volume for each phase
were computed and compared between amplitude sorting and
phase-angle sorting. This was done for 共1兲 the entire scan
session 共500– 1000 s兲 for the 12 respiratory phases, 共2兲 all
scans that were used in the reconstruction for the 12 3D
composite images, and 共3兲 the entire scan session for 8, 12,
24, and 48 respiratory phases.
E. Correlating air content with respiratory amplitude
and phase angle
As described in Sec. II A, the internal air content was
used as a surrogate for internal motion and as an independent
measurement for comparison of the two sorting metrics 共amplitude and phase angle兲. A smaller fitting residual 共root
mean squared error兲 between a metric and the air content
suggested a stronger relationship of the metric with internal
motion. We found that air content showed a strong linear
relationship with respiratory amplitude at each couch position within the lung.12,13 We observed that the air content
showed a quadratic relationship with phase angle at each
couch position within the lung. The residuals of a linear fitting between air content and respiratory amplitude were
compared to those of a quadratic fitting between air content
and phase angle throughout couch positions within the lung.
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Lu et al.: Amplitude sorting and phase-angle sorting for 4D CT
2967
TABLE I. Patient breathing characteristics. T and sdT are the mean and s.d.
of breathing period, v and sdv are the mean and s.d. of peak to peak tidal
volume amplitude.
Patient
no.
Dataset
no.
Cancer
site
1
2
2
3
3
4
6
6
6
10
13
14
19
20
22
23
24
25
27
28
30
33
34
5
7
8
9
11
12
15
16
17
18
21
26
29
31
32
35
Mean
1
2
3
4
5
6
8
9
10
14
17
18
23
24
26
27
28
29
31
32
34
37
38
7
11
12
13
15
16
19
20
21
22
25
30
33
35
36
39
Lung
Lung
Lung
Lunga
Lunga
Lung
Lunga
Lunga
Lunga
Lung
Lung
Lung
Lungb
Lungb
Lung
Lung
Lung
Lung
Lung
Lung
Lung
Lung
Lung
Abdomen
Abdomen
Abdomen
Abdomen
Abdomen
Abdomen
Abdomen
Abdomen
Abdomen
Abdomen
Abdomen
Abdomen
Abdomen
Abdomen
Abdomen
Abdomen
T
共s兲
4.5
3.1
2.8
2.7
3.0
4.7
7.6
8.6
7.5
3.0
2.4
3.2
4.5
3.5
3.6
5.1
3.3
3.8
3.4
4.0
2.6
4.2
7.6
8.6
3.5
4.7
6.9
4.2
3.9
4.9
3.9
4.5
4.5
4.7
3.8
3.9
4.8
3.1
9.2
4.6
sdT
共s兲
1.1
0.7
0.5
0.3
0.2
0.8
1.1
1.2
0.8
0.5
0.7
0.5
0.8
0.3
0.5
2.5
0.3
1.8
0.3
0.5
0.5
0.6
1.2
1.5
0.6
0.7
1.4
0.4
0.7
1.4
1.3
1.8
1.0
0.5
0.3
0.5
0.7
0.6
2.4
0.9
v
共ml兲
sdv
共ml兲
680.3
532.2
527.2
377.1
346.4
343.9
731.2
649.1
566.4
415.6
263.2
734.5
745.0
424.1
314.7
379.2
136.7
436.0
612.1
448.4
373.1
529.8
1197.8
1073.7
479.4
707.8
531.3
565.4
506.9
496.7
518.5
595.2
745.0
459.5
323.9
643.0
430.0
348.8
1560.2
557.7
141.9
129.4
73.9
37.8
33.0
75.4
87.1
142.0
73.3
44.6
63.6
124.4
89.0
36.1
34.2
209.1
16.4
109.1
58.2
37.6
93.5
76.6
209.4
244.4
55.7
100.6
64.4
65.7
93.4
181.5
123.8
141.1
116.2
72.3
37.8
182.3
141.0
48.0
365.1
103.3
a
Patients underwent SBRT in a SBF with an abdominal compression plate.
Patients underwent SBRT in a SBF without abdominal compression plate.
b
III. RESULTS
A. Characterization of patient breathing period and
amplitude
In each of the 39 patient data sets, the respiratory trace
demonstrated variations in period and amplitude from breath
to breath and from patient to patient. Table I lists the mean
and s.d. of breathing period and peak to peak amplitude for
each patient data set. Data sets 2 and 3, 4 and 5, and 8, 9, and
10 were multiple scan sessions from three lung cancer patients. Data set 28 represented a lung-cancer patient with
only the left lung operating and had the smallest peak to peak
Medical Physics, Vol. 33, No. 8, August 2006
FIG. 2. Samples of the internal air content, tidal volume 共amplitude兲, and
phase angle for a couch position in the middle of lung and intercepting the
diaphragm 共patient data set 21兲. The data points indicate the tidal volume
and phase angle for each scan, respectively. Phase angles of 0° or 360°
corresponded to end of inhalation 共EI兲, 180° was the end of exhalation 共EE兲,
90° was the mid-exhalation 共ME兲, and 270° was mid-inhalation 共MI兲.
amplitude. The mean breathing period ranged from 2.4 to
9.2 s with an average of 4.6 s. The s.d. in the period ranged
from 0.2 to 2.5 s, or from 6.7% to 49.0% as a ratio over the
mean period. The mean peak to peak amplitude ranged from
263.2 ml 共excluding data set 28兲 to 1560.2 ml, with an average of 557.7 ml. The s.d. in the amplitude ranged from
33.0 ml 共excluding data set 28兲 to 365.1 ml, or from 8.4% to
55.1% as a ratio over the mean amplitude. There was no
significant difference in any of these variables between patients with lung cancers and patients with upper-abdomen
cancers 共all P ⬎ 0.05兲. Data set 21, with large variations, and
data set 5, with smallest variations 共as a ratio of the mean兲 in
breathing period and amplitude, were selected as example
patients.
B. Phase angle calculation
Figure 2 shows samples of the internal air content, tidal
volume 共amplitude兲, and calculated phase angle for data set
21 at a couch position near the middle of the lung and intercepting the diaphragm. The phase angle was calculated with
Eq. 共1兲 on the tidal volume trace. Notice that due to the
asymmetrical inhalation and exhalation in time 共t2 − t1 ⫽ t3
− t2兲, the calculated phase angle for one cycle 共0 ° – 360° 兲
consisted of two line segments with a transition point at 180°
共EE兲. Also the slopes of the two line segments varied from
breath to breath.
C. Images reconstructed using amplitude sorting and
phase-angle sorting
Figure 3 compares sagittal lung images reconstructed using amplitude sorting and phase-angle sorting. A sagittal
view is chosen because motions in the craniocaudal and anteroposterior directions are generally larger than motions in
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FIG. 3. Images reconstructed using amplitude sorting 共top row兲 and phaseangle sorting 共bottom row兲. 共a兲 A patient 共data set 21兲 with relatively irreproducible breathing. 共b兲 A patient 共data set 5兲 with relatively reproducible
breathing. From left to right in each row: end exhalation, middle inhalation,
end inhalation, and middle exhalation. Arrows indicate significant reconstruction artifacts.
the lateral direction in the lung, so errors in reconstruction
are more easily detected. Images for 4 of the 12 respiratory
phases are shown: EE, MI, EI, and ME. For patient data set
21 关Fig. 3共a兲兴, the tumor is observable near the diaphragm
apex. Images generated using amplitude sorting display
smoother lung-diaphragm boundaries and minimal reconstruction artifacts. Images generated using phase-angle sorting, however, display distorted lung-diaphragm boundaries at
all four phases. The vessel in the middle of the lung appears
broken in the ME image with phase-angle sorting. For patient data set 5 关Fig. 3共b兲兴, images generated using both sorting approaches display similarly smooth lung-diaphragm
boundaries and minimal reconstruction artifacts for all four
phases except for ME, where one reconstruction artifact is
visible with phase-angle sorting. Animations of the lung motion during a respiratory cycle were generated with images at
all 12 phases. Animations for amplitude sorting were observed to show smoother lung motion, less tissue jumping
motion, and less distortion at the lung-diaphragm boundary
than those for phase-angle sorting. Similar results were observed for all 35 patients. In summary, amplitude sorting
provided better images and animations, as compared to
phase-angle sorting.
D. Variations in tidal volume with amplitude sorting
and phase-angle sorting
1. A visual comparison
Figure 4 shows the variation in tidal volume for two
breathing samples for MI and EI 共patient data set 21兲. The
period of the patient’s breathing varies appreciably among
breaths in Figs. 4共a兲 and 4共b兲. All data points classified by
Medical Physics, Vol. 33, No. 8, August 2006
FIG. 4. Variation in tidal volume with amplitude sorting 关共a兲 and 共c兲兴 and
phase-angle sorting 关共b兲 and 共d兲兴 for patient data set 21. Two breathing
samples are shown for middle inhalation 关共a兲 and 共b兲兴 and end inhalation 关共c兲
and 共d兲兴. Thicker segments indicate aggregated data points falling into each
respiratory phase.
amplitude sorting as MI correspond to a consistent intermediate tidal volume close to 共v95 + v1兲 / 2 关Fig. 4共a兲兴. On the
other hand, many data points classified by phase-angle sorting as MI clearly do not correspond to a consistent intermediate tidal volume 关Fig. 4共b兲兴. Particularly, data points classified as MI for two long breaths 共545– 555 s and
564– 577 s兲 have very small tidal volumes. In Figs. 4共c兲 and
4共d兲, the peak to peak tidal volume varies appreciably among
breaths. Data points from shallow breaths are excluded by
amplitude sorting for EI 关Fig. 4共c兲兴 but are classified as EI by
phase-angle sorting 关Fig. 4共d兲兴. Basically, phase-angle sorting regards a shallow breath 共⬃300 ml兲 the same as a normal
共⬃700 ml兲 and a deep breath 共⬃1000 ml兲. Clearly, the variation in tidal volume for either respiratory phase is smaller
with amplitude sorting than with phase-angle sorting.
2. Entire scan session for 12 respiratory phases
Figure 5 shows scatter plots of the tidal volume and phase
angle during the entire scan session for the example patients.
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Lu et al.: Amplitude sorting and phase-angle sorting for 4D CT
FIG. 5. Scatter plot of tidal volume and phase angle. 共a兲 A patient 共data set
21兲 with relatively irreproducible breathing. 共b兲 A patient 共data set 5兲 with
reproducible breathing. One out of every 10 measured time points is shown
for the entire scan session.
The tidal volume values are spread out at any single phase
angle value, indicating that the amplitude at a phase angle
changes considerably from breath to breath. Figure 6 shows
the variation 共s.d.兲 in tidal volume at the 12 respiratory
phases for amplitude sorting and phase-angle sorting for the
entire scan session. For amplitude sorting, the variation in
tidal volume is close to a constant for the 12 phases since the
range of tidal volume was the same for each phase. The
variations at the breathing ends are slightly smaller than
those at the middle of breathing. This is because not every
breath had data points that covered the entire range of tidal
volume at those breathing ends. All patients had a similar
shape of the variation curve. For phase-angle sorting, the
variation was different at each phase. For both patients
shown, the variation is larger at greater tidal volumes 共MI,
EI, ME兲 than at lesser tidal volumes 共SI, EE兲, indicating that
the patients breathed less reproducibly at greater tidal volumes than at lesser tidal volumes. Also notice that this variation is different at ME 共phase angle 90°兲 from that at MI
Medical Physics, Vol. 33, No. 8, August 2006
2969
FIG. 6. Variation in tidal volume at 12 respiratory phases for amplitude
sorting and phase-angle sorting. 共a兲 A patient 共data set 21兲 with relatively
irreproducible breathing. The mean peak to peak amplitude is 595.2 ml. 共b兲
A patient 共data set 5兲 with reproducible breathing. The mean peak to peak
amplitude is 346.4 ml. Variation is taken for all data points in the entire scan
session.
共phase angle 270°兲. This change in the variation curve was
expected since the spread of tidal volume varied at each
phase as shown in Fig. 5. The shape of the tidal volume
variation curve was different for each patient. The mean
variation for the 12 phases was smaller with amplitude sorting than with phase-angle sorting for both patients. The mean
variation in tidal volume was significantly smaller 共P
⬍ 0.001兲 with amplitude sorting than with phase-angle sorting for all patients 共Table II兲. There was no significant difference in the mean variation for amplitude sorting or phaseangle sorting between patients with lung cancer and patients
with upper-abdomen cancers 共both P ⬎ 0.05兲.
3. Data points during CT scans used in the
reconstruction for the 12 respiratory phases
Figure 7 shows the variation in tidal volume of data points
during CT scans used in the reconstruction for each of the 12
3D composite images. For phase-angle sorting, every scan
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Lu et al.: Amplitude sorting and phase-angle sorting for 4D CT
2970
TABLE II. Comparison results. The mean variation in tidal volume, with
amplitude sorting 共A兲 and phase angle sorting 共P兲, respectively, for entire
scan session 共sdA1 , sdP1兲 and for data points during CT scans used in the
reconstruction for each of the 12 3D composite images 共sdA2 , sdP2兲. The
mean fitting residuals of air content to amplitude 共resA兲 and to phase angle
共resP兲, respectively.
Patient Dataset Cancer
no.
no.
site
1
2
2
3
3
4
6
6
6
10
13
14
19
20
22
23
24
25
27
28
30
33
34
5
7
8
9
11
12
15
16
17
18
21
26
29
31
32
35
Mean
1
2
3
4
5
6
8
9
10
14
17
18
23
24
26
27
28
29
31
32
34
37
38
7
11
12
13
15
16
19
20
21
22
25
30
33
35
36
39
Lung
Lung
Lung
Lunga
Lunga
Lung
Lunga
Lunga
Lunga
Lung
Lung
Lung
Lungb
Lungb
Lung
Lung
Lung
Lung
Lung
Lung
Lung
Lung
Lung
Abdomen
Abdomen
Abdomen
Abdomen
Abdomen
Abdomen
Abdomen
Abdomen
Abdomen
Abdomen
Abdomen
Abdomen
Abdomen
Abdomen
Abdomen
Abdomen
resA
共ml兲
resP
共ml兲
sdA1
共ml兲
11.8
3.9
4.5
4.0
4.2
4.9
5.1
5.6
6.7
2.7
3.6
5.9
4.0
4.3
5.3
5.9
5.3
3.2
3.1
3.9
4.9
3.5
6.1
7.5
4.1
2.3
5.0
4.0
2.6
4.3
3.4
3.9
3.7
4.1
3.1
2.1
3.7
3.3
6.0
4.5
13.3
6.3
6.0
3.3
3.0
4.9
4.5
5.0
4.5
3.8
5.9
8.5
6.4
5.0
6.6
9.4
6.6
5.2
5.0
5.3
5.9
5.2
11.8
10.0
5.0
4.0
6.5
4.3
4.3
5.8
7.3
6.7
4.3
5.3
4.5
5.4
6.2
4.6
12.2
6.1
43.8
38.4
35.2
22.7
18.8
19.9
43.4
40.6
36.3
23.8
18.8
45.5
45.7
29.4
17.5
39.9
17.5
31.9
37.5
24.9
24.4
32.7
79.8
69.5
31.1
45.2
31.1
32.6
35.5
44.2
39.5
41.6
43.6
27.5
20.0
40.3
31.6
21.5
99.1
36.5
sdP1
共ml兲
sdA2
共ml兲
sdP2
共ml兲
106.0 51.5
105.5 46.0
81.1 39.2
40.2 28.8
27.8 30.5
42.3 23.3
79.2 55.0
92.1 50.0
80.6 55.6
41.4 22.1
44.1 20.5
102.2 50.6
100.9 45.0
65.8 35.3
27.6 20.6
191.2 71.0
27.6 20.6
118.7 38.5
72.0 36.3
40.7 26.7
56.5 29.8
68.6 32.7
193.1 80.0
154.6 67.8
65.9 42.1
97.7 52.1
54.5 30.8
54.3 35.2
93.3 39.8
148.8 35.8
120.2 52.9
127.9 61.7
106.0 50.3
65.6 31.0
41.7 22.6
101.0 45.2
98.6 43.1
40.6 21.5
219.7 103.3
87.1 42.2
111.8
99.0
74.6
39.2
30.5
40.0
81.8
96.8
92.9
39.5
43.5
97.6
100.1
68.6
28.5
183.7
28.5
105.6
72.4
42.1
53.1
67.0
193.0
159.8
66.4
99.7
55.5
57.9
94.9
78.1
123.8
130.5
113.9
59.3
43.0
99.2
98.7
40.8
207.2
85.1
a
Patients underwent SBRT in a SBF with an abdominal compression plate.
Patients underwent SBRT in a SBF without abdominal compression plate.
b
used in the reconstruction for a respiratory phase belonged to
that phase. The shape of the variation curves were, therefore,
similar to those in Fig. 6. For amplitude sorting, not all of the
scans used in the reconstruction for a specific respiratory
phase belonged to that phase. For example, if a patient
breathed shallowly at a couch position so that none of the 25
scans fell into the EI phase, an inhalation scan with tidal
volume closest to but less than the lower limit of EI would
be selected in the reconstruction for the 3D EI image. This
Medical Physics, Vol. 33, No. 8, August 2006
FIG. 7. Variation in tidal volume at 12 respiratory phases for amplitude
sorting and phase-angle sorting. 共a兲 A patient 共data set 21兲 with relatively
irreproducible breathing. 共b兲 A patient 共data set 5兲 with reproducible breathing. Variation is taken for data points used in the reconstruction for each of
the 12 3D composite images.
would cause a larger tidal volume variation at EI than that in
Fig. 6. For both patients, the increased variations at EI and
its two neighboring respiratory phases were caused by selecting scans from shallow breaths. The mean variation for the
12 images was smaller with amplitude sorting than with
phase-angle sorting for data set 21, and equal for data set 5.
The mean variation in tidal volume was significantly smaller
共P ⬍ 0.001兲 with amplitude sorting than with phase-angle
sorting for all patients 共Table II兲. There was no significant
difference in the mean variation for amplitude sorting or
phase angle sorting between patients with lung cancer and
patients with upper-abdomen cancers 共both P ⬎ 0.05兲.
4. Entire scan session for 8, 12, 24, and 48
respiratory phases
Figure 8 shows the variation in tidal volume during the
scan session at 8, 12, 24, and 48 respiratory phases for data
set 21 with amplitude sorting and phase-angle sorting, respectively. For amplitude sorting, the variation was reduced
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Lu et al.: Amplitude sorting and phase-angle sorting for 4D CT
2971
with the use of more 共finer兲 phases because the range of tidal
volume within each phase decreased. For phase-angle sorting, the variation was not reduced and the other three variation curves displayed a shape similar to that with 12 phases.
This was because that though using more phases reduced the
within-breath tidal volume variation, it had no effect on the
much larger between-breath variation for each phase. Similar
results were obtained for all 39 patient data sets.
E. Correlating air content with respiratory amplitude
and phase angle
FIG. 8. Variation in tidal volume at 8, 12, 24, and 48 respiratory phases for
amplitude sorting 共Amp兲 and phase-angle sorting 共Pha兲, respectively, from
dataset 21. Variation is taken for all data points in the entire scan session.
Figures 9共a兲 and 9共b兲 show the results of fitting air content
to tidal volume and phase angle for the 25 scans shown in
Fig. 2. The fitting residual is 11.5 ml in air content for amplitude and 29.4 ml for phase angle, out of a total air content
variation of 200 ml. Figures 9共c兲 and 9共d兲 display the fitting
residuals for all couch positions within the lung. For data set
21, the mean residual for respiratory amplitude is smaller
FIG. 9. 共a兲 A linear fit between air content and tidal volume. The fitting residual is 11.5 ml. 共b兲 A quadratic fit between air content and phase angle. The fitting
residual is 29.4 ml. Comparison of fitting residuals throughout all couch positions within the lung for 共c兲 a patient 共data set 21兲 with relatively irreproducible
breathing and 共d兲 a patient 共data set 5兲 with reproducible breathing.
Medical Physics, Vol. 33, No. 8, August 2006
2972
Lu et al.: Amplitude sorting and phase-angle sorting for 4D CT
than that for phase angle. For data set 5, the mean residual
for respiratory amplitude is larger than that for phase angle.
Table II shows that for all 35 patients but two of the four
SBF patients with abdominal compression plate 共patient 3,
data sets 4 and 5; patient 6, data sets 8, 9, and 10; both had
lung cancers兲, the mean fitting residual is smaller for amplitude than for phase angle. The mean fitting residual was
significantly smaller 共P ⬍ 0.001兲 for amplitude than for
phase angle for all patients. This suggests that there is usually a stronger relation between lung motion and respiratory
amplitude than that between lung motion and phase angle.
There was no significant difference in the mean fitting residual for amplitude or phase angle between patients with
lung cancer and patients with upper-abdomen cancers 共both
P ⬎ 0.05兲.
IV. DISCUSSION AND CONCLUSION
The results demonstrate that for all 35 patients, the variation in tidal volume, and by extension that the variation in
respiratory motion, was smaller for amplitude sorting than
for phase-angle sorting with 12 respiratory phases. For all
patients but two SBF patients with abdominal compression
plate, the correlation between lung motion and respiratory
amplitude was stronger than that between lung motion and
phase angle. For all patients, qualitative comparisons demonstrated that images and animations reconstructed by amplitude sorting provided smoother lung-diaphragm boundaries and fewer artifacts than those reconstructed by phaseangle sorting. In summary, for respiration correlated 4D CT
in 35 patients who underwent quiet breathing, amplitude
sorting performed better than phase-angle sorting for 33 patients and equally well for two patients with more reproducible breathing.
Data in the literature, though limited, all reached the same
conclusion.9–11 Phase-angle sorting, however, is still more
widely used than amplitude sorting for 4D CT. This choice
might be due to the ease of access to hardware and software
for phase-angle-based electrocardiogram-gated heart imaging. While heart motion is highly reproducible with respect
to the cardiac phase angle,25 respiratory motion is far less
reproducible with respect to the respiratory phase angle. As
shown in both this study and other studies,10,11 phase angles
do not 共sufficiently兲 represent respiratory motion for irreproducible breathing, which is the case for most patients who
undergo free/quiet breathing.
One may argue that an advantage of phase-angle sorting is
that a complete phase angle range 共0 ° – 360° 兲 is completely
covered with each respiratory cycle; therefore, the time for
data acquisition is shortened by requiring data acquisition for
only one respiratory cycle at each couch position.6 With this
approach, the image reconstruction quality relies greatly on
the reproducibility of breathing. It has been reported10,11 that
when the respiratory pattern 共period, amplitude, and respiratory trace shape兲 was not sufficiently reproducible, phaseangle sorting resulted in missing images and significant residual motion artifacts. Amplitude sorting clearly reduced the
residual motion artifacts in those studies and in the present
Medical Physics, Vol. 33, No. 8, August 2006
2972
study. The current ciné protocol acquires images at each
couch position while the patient breathes two to six cycles
during the 18 s acquisition time. The probability that no image falls into a specific respiratory phase with amplitude
sorting is thus reduced, and the error it creates is reduced as
well.
By using the amplitude sorting and the percentile scheme,
the extreme breaths 共very deep inhalation or exhalation兲 are
excluded from the 4D CT reconstruction. This improves the
consistency in the reconstructed images. Because phase
angle does not contain sufficient amplitude information, amplitude monitoring is necessary to detect and ignore imaged
data acquired during such extreme breaths. In a study for five
patients, breathing coaching using audio instruction resulted
in reproducible breathing period, but with increased variability and magnitude of amplitude.26 In the same study, obtaining more controllable breathing amplitudes was attempted
using visual feedback.26 In another study for 24 lung cancer
patients, however, free breathing was reported to have
smaller variations in amplitude and period than audio instruction and audio-visual biofeedback.27 Breathing coaching
is usually considered an important component for 4D CT
techniques when phase-angle sorting is used.2,3,5,28 Although
breathing coaching was not used in our 4D CT technique, the
images reconstructed using amplitude sorting showed good
quality with minimal reconstruction artifacts even for irregular breathers. Breathing coaching may benefit both amplitude
sorting and phase-angle sorting, but several questions on its
efficacy and practicability would need further investigation:
共1兲 Does breathing coaching significantly improve the reproducibility of the comprehensive breathing pattern, including
the reproducibility of amplitude and period? 共2兲 Does breathing coaching significantly improve the consistency of the
relationship between the target motion and the 共external兲 respiratory measurements? 共3兲 What is the percentage of patients who can be trained successfully? 共4兲 Which respiratory
feedback measurement should be used for coaching?
The results of the amplitude sorting and phase-angle sorting comparisons do not depend on the external respiratory
measurement used for the sorting process, provided that it is
functionally related to the breathing depth. Some external
respiratory measurement systems, such as spirometry, cannot
be used independently because their signal drifts with
time.12,13,15 Drift corrections are necessary when using such a
system for amplitude sorting.7,13,15 The baseline drift usually
is not sufficiently large to affect neither phase angle definition nor phase-angle sorting. Other measurements, such as
the “bellows,” reflective surface markers 共as used in the
Real-Time Position Management, RPM, Varian Medical Systems, Palo Alto, CA兲, or position-sensitive semiconductor
detectors, are considered drift-free.16,17,29 A drift-free measurement or a combination of a drift-free measurement and
spirometry12,16 is recommended for amplitude-based sorting.
Finally, one should be cautious when using an external respiratory measurement to infer internal tumor or tissue
motion.12,30,31
With current scanner rotation speeds 共0.3– 0.5 s rotation
time兲, 8 to 12 respiratory phases are reconstructed in 4D CT.
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Lu et al.: Amplitude sorting and phase-angle sorting for 4D CT
If the scanner rotation time is shortened and the temporal
resolution is improved, it may be feasible to reconstruct images at more 共finer兲 respiratory phases. We have shown that
the use of finer respiratory phases may improve the consistency in tidal volume for amplitude sorting, but not for
phase-angle sorting. This suggests that amplitude sorting will
take advantage of the increased scanner speed relative to
phase-angle sorting.
For all 35 patients but the two SBF patients with abdominal compression plate 共patients 3 and 6兲, there was a stronger
relation between internal air content 共or equivalently lung
motion兲 with respiratory amplitude than with phase angle.
The compression plate provided more restricted immobilization and limited the respiration amplitude. As a result, a more
reproducible breathing pattern was observed for the two patients, such as relatively more consistent tidal volume as a
function of phase angle for patient 3 关Fig. 5共b兲兴. On the other
hand, patient 3 共data sets 4 and 5兲 had small variations in
both the mean breathing period and amplitude 共Table I兲; patient 6 共data sets 8, 9, and 10兲 had medium variations in both
共Table I兲. Small variations in the mean period and amplitude,
however, did not necessarily suggest a stronger relation between air content and phase angle. Also note that in this
correlation analysis, we introduced a quadratic relationship
between phase angle and air content. In the variation analysis, however, phase angle was used directly to infer the tidal
amplitude or target position. This might explain why phase
angle performed better in the correlation analysis than in the
variation analysis 共Table II兲. Nevertheless, phase angle did
not correlate as strongly as amplitude to air content for most
patients.
Data in this paper indicated that there was no significant
difference 共all P ⬎ 0.05兲, in the patient breathing characteristics 共mean or s.d. of amplitude, mean or s.d. of period兲, or in
the calculated variables 共mean fitting residual, mean variation in tidal volume, for either amplitude or phase angle兲,
between patients with lung cancer and patients with upperabdomen cancers. When we examined the respiratory waveforms, we observed arbitrary variations for each patient
rather than systematic differences between these two groups
of patients. This suggested that for our data the respiration
motion was not affected by the type of cancer a patient had.
Among patients with lung cancers, the fitting residuals with
phase angle 共resP兲 were significantly smaller 共P = 0.04兲 for
the four SBRT patients. This implies that using the SBF with
the optional compression plate may improve the correlation
between internal motion and phase angle. There was no significant difference 共all P ⬎ 0.05兲 in the other variables.
A limitation of this work is that true, real-time target 共tumor兲 motion is not available and surrogates 共tidal volume
and air content兲 are being used. Reliably tracking tumor motion in 3-D is an ongoing research. Fluoroscopically tracking
implanted markers4,14,31–35 may yield the most reliable 3-D
tumor position, however, this technique is invasive and has
other limitations.14,34 A recent study showed that tumors in
the lung can be tracked with a biplane digital radiography
unit, while implanted markers were still needed for tumors in
Medical Physics, Vol. 33, No. 8, August 2006
2973
the liver and esophagus.35 Fluoroscopically tracking the
superior-inferior diaphragm motion has been conducted but
is limited by the fact that only 1-D diaphragm motion was
measured.9,17,36,37 Our institution is investigating the use of
non-ionizing implanted AC electromagnetic transponders
共4D Localization System, Calypso Medical, Seattle, WA兲 for
tracking organ motions.38,39 When reliable target motion data
are available, we would be able to compare the two sorting
approaches in terms of the variation in target motion and
correlation with target motion.
ACKNOWLEDGMENTS
This work was supported in part by National Institute of
Health Grant No. R01 CA 096679. The authors thank Joe
Repp and Roy Wood for help in collecting some data.
a兲
Author to whom correspondence should be addressed. Electronic mail:
dlow@radonc.wustl.edu
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