Event-by-event respiratory motion correction for PET with 3D internal-1D external
motion correlation
Chung Chan, Xiao Jin, Edward K. Fung, Mika Naganawa, Tim Mulnix, Richard E. Carson, and Chi Liu
Citation: Medical Physics 40, 112507 (2013); doi: 10.1118/1.4826165
View online: http://dx.doi.org/10.1118/1.4826165
View Table of Contents: http://scitation.aip.org/content/aapm/journal/medphys/40/11?ver=pdfcov
Published by the American Association of Physicists in Medicine
Event-by-event respiratory motion correction for PET with 3D internal-1D
external motion correlation
Chung Chana)
Department of Diagnostic Radiology, Yale PET Center, School of Medicine, Yale University,
New Haven, Connecticut 06520
Xiao Jin and Edward K. Fung
Department of Diagnostic Radiology, Yale PET Center, School of Medicine, Yale University,
New Haven, Connecticut 06520 and Department of Biomedical Engineering, Yale University,
New Haven, Connecticut 06520
Mika Naganawa and Tim Mulnix
Department of Diagnostic Radiology, Yale PET Center, School of Medicine, Yale University,
New Haven, Connecticut 06520
Richard E. Carson and Chi Liua)
Department of Diagnostic Radiology, Yale PET Center, School of Medicine, Yale University,
New Haven, Connecticut 06520 and Department of Biomedical Engineering, Yale University,
New Haven, Connecticut 06520
(Received 19 April 2013; revised 14 September 2013; accepted for publication 4 October 2013;
published 29 October 2013)
Purpose: Respiratory motion during PET/CT imaging can cause substantial image blurring and underestimation of tracer concentration for both static and dynamic studies. In this study, the authors developed an event-by-event respiratory motion correction method that used three-dimensional internalone-dimensional external motion correlation (INTEX3D) in listmode reconstruction. The authors aim
to fully correct for organ/tumor-specific rigid motion caused by respiration using all detected events
to eliminate both intraframe and interframe motion, and investigate the quantitative improvement in
static and dynamic imaging.
Methods: The positional translation of an internal organ or tumor during respiration was first determined from the reconstructions of multiple phase-gated images. A level set (active contour) method
was used to segment the targeted internal organs/tumors whose centroids were determined. The mean
displacement of the external respiratory signal acquired by the Anzai system that corresponded to
each phase-gated frame was determined. Three linear correlations between the 1D Anzai mean displacements and the 3D centroids of the internal organ/tumor were established. The 3D internal motion signal with high temporal resolution was then generated by applying each of the three correlation
functions to the entire Anzai trace (40 Hz) to guide event-by-event motion correction in listmode reconstruction. The reference location was determined as the location where CT images were acquired
to facilitate phase-matched attenuation correction and anatomical-based postfiltering. The proposed
method was evaluated with a NEMA phantom driven by a QUASAR respiratory motion platform,
and human studies with two tracers: pancreatic beta cell tracer [18 F]FP(+)DTBZ and tumor hypoxia
tracer [18 F]fluoromisonidazole (FMISO). An anatomical-based postreconstruction filter was applied
to the motion-corrected images to reduce noise while preserving quantitative accuracy and organ
boundaries in the patient studies.
Results: The INTEX3D method yielded an increase of 5%–9% and 32%–40% in contrast recovery
coefficient on the hot spheres in the NEMA phantom, compared to the reconstructions with only 1D
motion correction (INTEX1D) and no motion correction, respectively. The proposed method also
increased the mean activities of the pancreas and kidney by 9.3% and 11.2%, respectively, across
three subjects in the FPDTBZ studies, and the average lesion-to-blood ratio by 20% across three lesions in the FMISO study, compared to the reconstructions without motion correction. In addition,
the proposed method reduced intragate motion as compared to phase-gated images. The application
of the anatomical-based postreconstruction filter further reduced noise in the background by >50%
compared to reconstructions without postfiltering, while preserving quantitative accuracy and organ boundaries. Finally, the measurements of the time-activity curves from a subject with FPDTBZ
showed that INTEX3D yielded 18% and 11% maximum increases in tracer concentration in the pancreas and kidney cortex, respectively.
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Med. Phys. 40 (11), November 2013 0094-2405/2013/40(11)/112507/13/$30.00
© 2013 Am. Assoc. Phys. Med.
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Chan et al.: Event-by-event respiratory motion correction for PET
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Conclusions: These results suggest that the proposed method can effectively compensate
for both intragate and intergate respiratory motion while preserving all the counts, and
is applicable to dynamic studies. © 2013 American Association of Physicists in Medicine.
[http://dx.doi.org/10.1118/1.4826165]
Key words: respiratory motion correction, PET/CT, three-dimensional internal-external motion correlation, INTEX
1. INTRODUCTION
Respiratory motion is one of the major degrading factors in
PET/CT imaging. Typical diaphragm motion amplitude due
to respiration is 11 mm on average in the superior-inferior (SI)
direction.1, 2 The motion is more complicated for organs in the
thorax and lower abdomen because the chest and abdomen
also expand/contract in the anterior-posterior (AP) and leftright (LR) directions during respiration. These motions can
cause substantial image blurring and reduced contrast and accuracy in disease detection and radiotracer quantification for
both static and dynamic studies.
Many methods have been proposed to correct for respiratory motion in the literature.3–6 The most common approach
is respiratory gated PET/CT, which divides PET data into different gates based on either temporal phase or respiratory
displacement information.7, 8 However, this method suffers
from a substantial increase in image noise as only a fraction of the detected coincidence events is used, leading to
potentially reduced signal-to-noise ratios (SNR).9 In order
to use all events to correct for motion, methods were proposed to obtain motion vectors from respiratory gated CT or
PET, and incorporate them into image reconstruction10–12 or
postprocessing.9, 13 However, these methods do not account
for intragate motions due to intercycle and intracycle motion
variations.8 In addition, most of the existing respiratory motion correction methods rely on retrospective binning for the
entire data acquisition, thus can only be applied in static imaging, but not in dynamic imaging, which requires challenging
motion correction for each time point.
To correct for intragate motion and to correct motion
for dynamic PET imaging, internal motion information with
high temporal resolution is required, and the most desirable motion correction should be able to correct individual
lines of response (LOR) on an event-by-event basis during
reconstruction.10, 14, 15 However, obtaining internal organ motion information with high temporal resolution is very challenging. Previously, we proposed to convert external respiratory chest/abdomen motion, which was recorded at high
temporal resolution in the AP direction, into internal organ
movement in the SI direction. This was achieved by a linear
correlation established between the mean displacement of the
external motion trace and the center of mass of the internal tumor for each respiratory gate.16 However, the previous study
only corrected motion in the SI direction in sinogram space
with finely rebinned sinograms (1 s per frame). Therefore, the
motion correction may be suboptimal if the patient has large
breathing amplitude in the AP and LR directions. In addition,
the 1-s sinogram rebinning in the previous study reduced
Medical Physics, Vol. 40, No. 11, November 2013
intragate motion by eliminating intercycle variations, but is
still subject to minor intracycle variations.
In this study, we extended the internal-external motion correlation method (INTEX) (Ref. 16) to three-dimensions (3D)
and incorporated the estimated motion parameters in the Motion compensation OSEM List-mode Algorithm for Resolution recovery reconstruction (MOLAR) with time-of-flight
(TOF) capability for event-by-event motion correction.15, 17, 18
The reference location was determined as the location where
CT images were acquired to facilitate phase-matched attenuation correction and anatomical-based postfiltering. We
also investigated its applicability to dynamic studies. A preliminary report of this work was previously presented in
Ref. 19. The proposed method was first evaluated with a
moving NEMA phantom driven by a real patient respiratory motion trace, and four human subjects with two tracers: [18 F]FP(+)DTBZ for studying pancreatic β cells20 and
[18 F]fluoromisonidazole (FMISO) for assessing the hypoxia
level in lung lesions.21 All studies were acquired on a Siemens
Biograph mCT PET/CT scanner with TOF capability. For patient studies, we also applied a 3D anatomical-based median
nonlocal means (AMNLM) filter22, 23 to the motion-corrected
images that incorporate the accurately aligned CT information to suppress noise while preserving quantitative accuracy
and organ boundaries.
2. METHODS
2.A. The Biograph mCT scanner
In this study, all the data were acquired on a Biograph mCT
scanner. The scanner consists of four rings of 48 blocks, each
of which contains 13 × 13 crystals (4.01 × 4.01 × 20 mm).
The TOF information of the detected events is measured with
78 ps time bins, and rebinned into 13 time bins with 312 ps
bin width and 580 ps FWHM.24
2.B. Respiratory signal analysis and processing
Studies have shown that a linear correlation between rigid
internal organ or tumor motion and measured external motion signal that characterizes chest/lower abdomen movement
can be established.16, 25–30 This can be done by measuring the
mean displacement of the external motion trace and the center of mass of the internal organ/tumor for each phase gated
image. In this study, the external respiratory motion in the
AP direction was monitored by the Anzai belt system (Anzai
Medical, Tokyo, Japan), which was attached to the patient’s
lower abdomen, and the respiratory trace was recorded at
Chan et al.: Event-by-event respiratory motion correction for PET
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40 Hz. The trace was first phase-binned into eight gates based
on the triggers registered at each inspiration peak. The mean
displacements of the Anzai trace that corresponded to each
phase gate were determined. Due to the fact that inspiration
peaks were determined prospectively by the Anzai system,
baseline variation may produce some missing triggers at the
inspiration peaks. In such cases, the data acquired without inspiration triggers were discarded in both the trace and the initial gated reconstructions to establish a more accurate linear
correlation that will be introduced in Sec. 2.C. Note that these
missing data were included in the final INTEX reconstructions as the motion field of the internal organ was converted
from the entire respiratory trace.
2.C. 3D internal-1D external motion correlation
To determine the positional translation of an internal structure, i.e., organ or lesion, during respiration, the listmode data
acquired on the mCT scanner were binned into eight phase
gates. Then, a scout reconstruction using OSEM with three
iterations, 21 subsets with point-spread-function (PSF) and
TOF was performed on these rebinned raw data with the manufacturer’s algorithm. A level-set (active contour) segmentation method31 was used to segment the targeted internal
organ/lesion. In order to obtain consistent segmentations
across all the gates for the target structures that may have irregular shapes, such as the pancreas and kidney, we applied
a bounding box around the target organ to limit the segmentation region. This process excluded the high-uptake regions
in the background and accelerated the segmentation process.
As we aimed to correct for rigid motion in this study, we
assumed that the organ volumes do not change during respiration, which has been demonstrated in previous studies
using 4D respiratory-gated CT and MR scans.32, 33 Thus, a
constraint on the segmentation was applied such that the
weighting parameter of the level-set method was adjusted for
each gate to generate segmented volumes with similar number
λn+1
=
j
K
λnj Qj
k=1
T(
j
C
ik ,tk ,j Qj =
1
nT
nτ
nT I of voxels (within 10% difference of the total number of voxels to the reference gate). The centroids of the segmented
structure of interest (i.e., spheres in the phantom study, pancreas/kidney or lesions in the human studies) were then determined. As the centroid was averaged from a large number
of voxels, this measurement is relatively robust to noise and
small segmentation variation across gates.34
Our previous study established a linear correlation between
the external tracking system and the internal organ displacement in one dimension (SI direction).16 However, as the respiratory motion is driven by both the motion of diaphragm
and expansion of chest/lower abdomen, it is natural to extend this correlation to other directions. In this study, three
linear functions in the directions of SI, AP, and LR, were determined to relate the 1D Anzai mean displacements to the
3D centroids of the internal organs/lesions. An internal organ
motion file was then generated by converting the entire Anzai
trace into a 3D transformation matrix to model the internal
structure movement at 40 Hz to guide event-by-event motion
correction in the reconstruction. This transformation matrix
was applied to the entire FOV in the reconstruction.
2.D. Reference frame and matched
attenuation correction
In this study, the reference frame was chosen at the endexpiration period, at which CT images were acquired for attenuation correction to minimize any attenuation correction
mismatch. By monitoring the subject respiratory traces on the
Anzai system, the subject was directed to hold their breath at
end-expiration when CT data were acquired.
2.E. Motion compensation and postprocessing
The transformation matrix was incorporated into TOFMOLAR reconstruction in listmode notation as described in
Eq. (1)
Cik ,tk ,j Lik ,tk Aik ,tk Nik ζik ,tk ,τk ,j
,
Lik ,tk Aik ,tk Nik ζik ,tk ,τk ,j λnj + Rik ,tk ,τk + Sik ,tk ,τk )
where
Ci ,t,j Li,t Ai ,t Ni ζi ,t,j,τ ,
t=1 i=1 τ =1
ik = k (ik ),
(2)
where λnj is the average activity in voxel j at iteration n, k
represents the index of each detected event, ik , tk , and τ k represent the LOR index, the time stamp, and the TOF bin for
event k, respectively. Since every event k occurs at time t, the
subscript tk was dropped in the following discussion. Cik ,j is
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(1)
the system matrix that represents the contribution of voxel j to
LOR ik , accounting for geometry, resolution, and solid angle
effects. Lik is the decay factor, Aik is the attenuation factor,
Nik is the sensitivity (normalization) term, Rik ,τk is the randoms rate estimate, and Sik ,τk is the scatter rate estimate. Each
time frame of duration T (s) is divided into nT sub-bins of duration t in seconds. nτ represents the total number of TOF bins
(nτ = 13 for the mCT). ζik ,τk ,j is the TOF kernel indicating
the contribution of image voxel j to time bin τ k on LOR ik .
To perform event-by-event motion correction, as illustrated
in Fig. 1, the position of each LOR was first corrected by a
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gan boundaries. This filter has been demonstrated to suppress
noise effectively while preserving signal and boundaries for
whole body PET/CT images, thus leading to improved SNR.
In this study, the dimension of the 3D search window N and
the 2D patch M were set to 11 × 11 × 3 and 3 × 3, respectively, as previously√proposed.22 The smoothing parameter h
was determined as 2σ , where σ was the standard deviation
in a region-of-interest (ROI) that was expected to have uniform uptake, such as in the liver region for the FPDTBZ and
lung region for the FMISO studies, respectively.
F IG . 1. An illustration of event-by-event motion correction during reconstruction. LOR ik generated at (x,y,z) during inspiration, is transformed to a
reference location, i.e., end-expiration (x1 ,y1 ,z1 ) where the attenuation CT
was acquired, as LOR ik .
transformation matrix that transforms the endpoint coordinates of LOR ik , to ik , the comparable LOR in the reference
position, such as at the end-expiration phase where the attenuation CT was acquired. In this application, the transformation matrix consisted of time-dependent translations in x, y,
and z, but no rotations. A motion-dependent sensitivity image
Q was computed from a subset of randomly selected LORs.
The details of TOF-MOLAR implementation can be found in
Refs. 17 and 18. The workflow of the proposed motion correction is summarized in Fig. 2.
In this study, the images were reconstructed with MOLAR
at three iterations and 21 subsets using 2 × 2 × 2 mm voxels. A spatially invariant Gaussian kernel with 4-mm FWHM
was used to model the point-spread function. As PET and CT
were aligned accurately at end-expiration location after respiration motion correction, an anatomically guided median
nonlocal means filter (AMNLM) was also applied to the reconstructed human studies with motion correction.22, 23 While
details can be found in Refs. 22 and 23, a brief description
of AMNLM filter is given here. To suppress noise, this filter
computes the weighted average of voxels based on a similarity measurement between 2D patches of voxels within a
3D search window in the image. Anatomical knowledge obtained from the accurately aligned attenuation CT was incorporated through a segmentation-free approach to preserve or-
3. EXPERIMENTS AND EVALUATIONS
3.A. Phantom experiment
A phantom experiment was performed to evaluate the
proposed INTEX3D for respiratory motion correction. The
NEMA IEC Body phantom filled with 74 MBq of [18 F]FDG
was placed on the QUASAR programmable respiratory
motion platform (Modus Medical Devices, Inc., London,
Canada). Four hot spheres (10, 13, 17, 22 mm in diameter)
had a contrast of 4:1 to the background, and two cold spheres
(28, 37 mm in diameter) were filled with water. A static PET
scan without motion was first acquired to serve as the ground
truth. To create motion in the AP and LR directions, we raised
the platform by ∼2.5 cm and tilted it by ∼7◦ as shown in
Fig. 3(a). The movement of the platform was driven by a typical patient’s respiratory trace as shown in Fig. 3(b). This trace
was rescaled in mm, thus the displacement of the motion platform in the SI direction matches with the magnitude of the
rescaled motion trace. Data were acquired on the Siemens Biograph mCT PET/CT scanner for 10 min. The attenuation CT
was acquired at the end-expiration position where the motion of the platform was suspended. To assess the effectiveness of 3D motion correction, these data were reconstructed
with no motion correction (NMC), motion correction in onedimensional superior-inferior direction only (INTEX1D), and
3D motion correction (INTEX3D). For quantitative evaluation, contrast recovery coefficient (CRC) was computed as
CRC =
Mhot /Mbkg − 1
,
Ctrue − 1
(3)
where Mhot and Mbkg are the mean values in the hot spheres
and in the background regions, respectively. The volumes
of interest (VOI) of the hot spheres were defined from the
CT images, i.e., they encompassed the entire sphere, and the
background VOIs were defined as four spheres with diameter
30 mm in the background. Ctrue = 4 is the true contrast value
between the hot spheres and the background, measured by
samples counted in a gamma counter.
3.B. Human studies: [18 F]FP(+)DTBZ
F IG . 2. The work flow of INTEX3D and MOLAR reconstruction.
Medical Physics, Vol. 40, No. 11, November 2013
The proposed method was applied to scans from
three healthy control human subjects with approval of
our institutional review board (IRB) and injected with
[18 F]FP(+)DTBZ.20 This tracer binds to the VMAT2 site,
which is expressed in beta cells in the pancreas and can be
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IRB and injected with FMISO, a PET tracer used to measure
tumor hypoxia. Due to the low contrast of this tracer, it is critical to correct for respiratory motion to achieve higher lesionto-blood contrast and quantitative results.21 The patient was
injected with 180 MBq FMISO and a 30-min scan was acquired 2.5 h after the injection. Similarly, the Anzai system
was attached to the patient’s lower abdomen, and the images
were reconstructed with NMC, the end-expiration phase of
eight-bin phase gating, INTEX1D, and INTEX3D.
3.D. Quantitative evaluations in human studies
F IG . 3. (a) Illustration of the NEMA phantom setup placed on the QUASAR
motion platform. The bold arrows indicate the displacement in each direction.
(b) The respiratory trace used to drive the QUASAR motion platform. The
first 180 s data are shown here.
used to study patients with diabetes. An average of 248 MBq
was injected and the first 10 min of the 2-h scan was analyzed. The Anzai system was attached to the subject’s lower
abdomen to record the respiratory motion. Since kidney cortex has been used as the reference region in kinetic modeling, it is crucial to correct respiratory motion of both pancreas
and kidney. As will be shown in Sec. 4.B, the motion amplitude and internal-external correlations of pancreas and kidney
were consistent for all the subjects, therefore the transformation matrices were generated from the pancreas and applied
to the entire FOV. INTEX3D was applied to a 10-min acquisition and compared to the images reconstructed with NMC,
the end-expiration phase of eight-bin phase gating, and INTEX1D that only corrected SI motion. In addition, in order to
demonstrate the effectiveness of event-by-event motion correction for intragate motion, we also compared the gated images without intragate motion correction and with INTEX3D,
which corrects intragate motion, at both end-expiration and
inspiration phases for these subjects.
To investigate the applicability of the proposed event-byevent INTEX3D for dynamic applications, we measured the
time-activity-curves (TAC) for subject 1. The dynamic frame
durations for the first 10-min acquisition were 0.5 min × 6,
1 min × 3, 2 min × 2. Pancreas and kidney VOIs were obtained using the level set segmentation applied on both NMC
and INTEX3D reconstructions of the 10-min scan and then
applied to the dynamic frames. The weighting parameters of
the segmentation were adjusted to yield similar segmentation
volume on both reconstructions.
3.C. Human studies: FMISO
We further evaluated the proposed method on a nonsmall
cell lung cancer (NSCLC) patient study with approval of our
Medical Physics, Vol. 40, No. 11, November 2013
The quantitative evaluations were assessed by measuring
mean activity concentrations (Bq/ml) in pancreas and kidney
for the FPDTBZ studies, and lesion-to-blood ratio (L/B) was
computed to assess the level of hypoxia of the lesions for the
FMISO study. The organ/lesion VOIs were defined by applying the level set segmentation on the reconstructed images
with INTEX3D motion correction. The same VOI was also
applied to the gated images at end-expiration phase. For NMC
and INTEX1D images, the VOIs were shifted according to the
average organ displacement. To evaluate image noise levels,
we also computed the standard deviations in the background
VOIs (i.e., liver/soft tissue) using a sphere with 20 mm diameter. For the FMISO study, since the normoxic tissues have
tissue-to-blood ratio of almost 1, the activity in blood was
measured as the mean value from a large VOI (a sphere with
30 mm diameter) in the heart that consists of both blood pool
and myocardium where the radiotracer uptake was uniform.
4. RESULTS
4.A. NEMA phantom study
The reconstructions of the NEMA phantoms are shown in
Fig. 4. The central slices that cut through the 10-mm sphere in
the transaxial and coronal views, and the 13-mm sphere in the
sagittal view are displayed in each column. The images shown
in Fig. 4(a) were reconstructed from the static acquisition. The
images reconstructed with NMC, the end-expiration gate of
eight-bin phase gating, INTEX1D, and INTEX3D from the
acquisition with simulated respiratory motion are shown in
Figs. 4(b)–4(e), respectively. The motion platform yielded an
average motion of ∼18 mm in the SI direction, and ∼3 mm
motion in the AP and LR directions, as measured
from the mean displacements of the centroid of the
22 mm hot sphere. The correlation coefficients in the LR, AP,
and SI directions were 0.77, 0.72, and 0.92, respectively. It
can be observed that the moving phantom acquisition without motion correction caused substantial blurring of the hot
spheres. The 10- and 13-mm spheres were smeared into the
background, as seen in the coronal and sagittal views, respectively. The cold sphere (28 mm) was also blurred in the SI
direction as seen in the sagittal view. The phase gating compensated for motion and restored all the hot spheres at the
expense of substantial increase in image noise, which led to
reduced image quality visually. INTEX1D corrected the motion in the SI direction, and restored the shape of the cold
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Gate
Kidney
Pancreas
F IG . 5. The maximum intensity projection in coronal view of the segmentations of the left kidney (top) and pancreas (bottom) across eight respiratory gates from a sample subject with [18 F]FP(+)DTBZ. The horizontal
lines above and under each organ reveal the magnitude of organ displacement across eight gates.
reduced the bias in CRC to 4%–5% for the smaller spheres
and 2% for the larger spheres as compared to the static scan.
4.B. Human studies: [18 F]FP(+)DTBZ
F IG . 4. Reconstructed images of the NEMA phantom in transaxial, coronal, and sagittal views. Images in each row are the central slices that cut
through the smallest sphere in that view. The axis in the first row indicates
the directions of the respiration motion in that view. (a) The static acquisition.
The acquisition with motion and reconstructed with (b) NMC, (c) The endexpiration gate of eight-bin phase gating, (d) INTEX1D, and (e) INTEX3D.
sphere. However, the hot spheres were slightly blurred in the
horizontal direction when compared to the static acquisition
visually. INTEX3D corrected the motion in all directions and
yielded similar image quality to the static scan visually.
Table I presents the CRC of each sphere from all reconstructions; the % bias between each reconstruction and
the static scan are shown in parentheses. Respiratory motion
caused −54.0%, −49.5%, −43.3%, and −36.1% bias in CRC
on the 10, 13, 17, and 22 mm hot spheres, respectively. Phase
gating yielded 8.7% overestimation in CRC on the 10 mm
hot sphere due to the increased noise, and reduced the bias
to −8%, −4.9%, and −6.5% on the 13, 17, and 22 mm hot
spheres, respectively. Although INTEX1D recovered the CRC
to some extent, there were still −14.6% and −13.9% biases in
CRC on the smaller hot spheres (10 and 13 mm), and −10.2%
and −7.4% biases on the larger hot spheres (17 and 22 mm).
By correcting the motion in all directions, INTEX3D further
TABLE I. CRC of the NEMA phantom study. The percentage changes compared to the static acquisition are shown in the parentheses.
Sphere
(mm) Static
10
13
17
22
0.65
0.88
0.91
0.96
NMC
End-expiration
gate
INTEX1D
INTEX3D
0.30 (−54.0%)
0.45 (−49.5%)
0.53 (−43.3%)
0.61 (−36.1%)
0.71 (8.7%)
0.81 (−8.0%)
0.87 (−4.9%)
0.90 (−6.5%)
0.56 (−14.6%)
0.76 (−13.9%)
0.82 (−10.2%)
0.89 (−7.4%)
0.62 (−4.9%)
0.85 (−3.8%)
0.89 (−2.0%)
0.94 (−2.0%)
Medical Physics, Vol. 40, No. 11, November 2013
The segmentation results of the pancreas and kidney across
eight gates from a sample subject are shown in Fig. 5. The
horizontal lines above and under each organ indicate the highest and lowest positions of the objects across eight respiratory gates to illustrate the magnitude of organ displacements,
where gate 4 and 8 correspond to the end-expiration and inspiration gates, respectively.
The motion amplitudes measured from the centroids of the
segmented pancreas in SI, AP, and LR axis, between the peak
inspiration gate and end-expiration gate, for all three subjects
are shown in Table II. It can be seen that the organ displacement in the LR direction was negligible compared to the intrinsic resolution of the PET scanner (∼4 mm) and voxel dimension (2 mm) for all subjects. However, the motion in the
AP direction was relatively large for subject 1. Table II also
showed that the variation of motion amplitudes across subjects can be substantial, thus motion correction may significantly reduce intersubject variation in quantitative outcome
measures.
The correlations between the centroids of the pancreas and
kidney with the Anzai trace of a sample subject in the LR,
AP, and SI directions are shown in Fig. 6. The means and
standard deviations of the correlation coefficient for the pancreas of all the subjects were 0.43 ± 0.35, 0.85 ± 0.15, and
0.93 ± 0.05 for LR, AP, and SI, respectively. This shows high
correlation was obtained in the SI and AP directions, but not
in the LR direction. As the motion in the LR direction was
negligible (Table II) and its correlation with the external trace
was poor, we therefore applied INTEX3D in the AP and SI
directions only for these subjects. The summary of the slopes
of the regression lines for both pancreas and kidneys in the
TABLE II. Motion amplitudes of three subjects for [18 F]FP(+)DTBZ measured from the centroids of the pancreas.
Subjects
1
2
3
Mean
LR (mm)
AP (mm)
SI (mm)
1.1
1.3
0.8
0.9
9.1
3.8
3.7
5.5
17.4
8.3
7.4
11.0
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F IG . 6. The linear correlations between the center of mass (COM) of the (a) pancreas and (b) kidney with Anzai mean displacement derived from eight
respiratory gates of a sample human study. The correlation in the LR direction was small since the motion in that direction was negligible and its correlation
with the external trace was poor. The numbers denote the corresponding gating phase where gates 5 and 8 were the end-expiration and inspiration gates,
respectively.
AP and SI directions is shown in Table III. The consistency of
the slopes reveals that pancreas and kidney moved together,
so the same regression line and thus the same transformation
matrix were applied to both organs in the reconstruction.
The sample reconstructed slices of pancreas and kidney
of all the subjects are shown in Figs. 7 and 8, respectively.
As can be seen in the NMC images, the pancreas and the
fine structures on the kidney cortex (denoted by arrows) were
blurred due to respiratory motion. Although the single gated
reconstruction at end-expiration phase compensated for respiratory motion, it yielded substantially increased image noise
due to the fact that only a portion of the counts was used
in the reconstruction. INTEX1D recovered the fine structures
to some extent; however, it can be observed that some blurring still remained in the image, as compared to INTEX3D,
that was caused by the motion in the AP direction. As the
INTEX methods preserved all the events in the reconstruction, both images with 1D and 3D motion correction showed
TABLE III. The slopes of the regression lines obtained from INTEX for three
[18 F]FP(+)DTBZ subjects in AP and SI directions. The LR is not shown as
the correlation in that direction was small.
Pancreas
Subjects
1
2
3
Kidney
AP
SI
AP
SI
−0.0789
−0.1278
−0.0682
−0.1937
−0.2388
−0.1482
−0.0799
−0.1229
−0.0688
−0.2013
−0.2359
−0.1532
Medical Physics, Vol. 40, No. 11, November 2013
similar noise level to the NMC images. Finally, the application of the AMNLM to the INTEX3D reconstructions suppressed noise effectively, preserved sharp organ boundaries,
and yielded lower noise images than other methods.
Figure 9 presents the images reconstructed using eightbin phase gating with and without incorporating INTEX3D at
both end-expiration and inspiration phases. This comparison
demonstrates the effectiveness of correction for intragate motion achieved by the event-by-event approach at high temporal
resolution. It can be seen that, at end-expiration, the visual differences between gated reconstruction without intragate motion correction and gated INTEX3D reconstruction are subtle.
This is because the end-expiration phase is generally motion
free, consistent with our previous observations.35 In contrast,
the gated images at inspiration phase show more pronounced
differences in the pancreas, fine structures of kidney cortex,
and the liver domes, as denoted by the arrows. These objects are more blurred than in the images at end-expiration
phase. This was due to larger intragate motion during inspiration phase. Indeed, the standard deviations of the displacement measured from the Anzai trace for three subjects were
11.1 ± 3.4 and 6.2 ± 1.8 at inspiration and end-expiration
phases, respectively. The bigger variation of the displacement
value (unitless) also reveals the larger intragate motion during
inspiration phase. In contrast, these objects appear with similar resolution in both inspiration and end-expiration phases of
the images reconstructed with INTEX3D due to the intragate
motion correction.
Tables IV and V summarize the percentage changes of the
activity in pancreas and kidney, respectively, as compared to
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Chan et al.: Event-by-event respiratory motion correction for PET
NMC
End-expiration gate
INTEX1D
112507-8
INTEX3D
INTEX3DAMNLM
Subject 1
Subject 2
Subject 3
F IG . 7. Reconstructed images in the coronal view of the pancreas study with [18 F]FP(+)DTBZ from three healthy subjects with NMC, gated image at endexpiration phase, INTEX1D, INTEX3D, and INTEX3D with AMNLM postfiltering. The arrows indicate that the blurring caused by respiratory motion in
pancreas has been recovered by INTEX3D without increasing noise. The further application of AMNLM on the INTEX3D images suppressed noise effectively
while preserving boundaries and fine structures. Images in each row are displayed in the same intensity scale.
the images without motion correction. It can be seen that the
gated reconstruction led to an average of 9.9% and 11.8% increase of radioactivity concentration in pancreas and kidney,
respectively. INTEX1D improved the concentration by 6.8%
and 6.4% in pancreas and kidney, respectively. INTEX3D further improved these increments to 9.3% and 11.2%, which is
similar to the percentage improvements achieved by the gating method. These tables also show that the correction of motion in the AP direction can be critical for the subjects with
large breathing magnitudes in three dimensions, such as subject 1, who had ∼9 mm AP motion. INTEX1D only improved
the uptake concentration by 10.6% in the kidney cortex while
INTEX3D achieved 17.1% increase. The INTEX3D reconstruction with AMNLM postfiltering yielded similar improvement to the mean radiotracer concentration as INTEX3D.
NMC
End-expiration gate
Table VI presents the standard deviation of a VOI within
the liver, where the uptake was relatively uniform, to reveal
the noise level. As expected, the standard deviations in gated
images are about twofold that of NMC and reconstructions
with INTEX due to the fact that only a fraction of the events
were used to reconstruct a single gated image. In contrast, the
INTEX approach used all the counts and thus yielded similar
noise level as NMC images. The application of the AMNLM
filter on INTEX3D images suppressed the image noise effectively and led to an average of 64% reduction in standard deviation as compared to INTEX3D while preserving the mean
activity (as shown in Tables IV and V), and thus led to improved SNR.
The pancreas and kidney TACs of subject 1 from the
first 10 min are shown in Fig. 10. Compared to the NMC
INTEX1D
INTEX3D
INTEX3DAMNLM
Subject 1
Subject 2
Subject 3
F IG . 8. Reconstructed images in the coronal view at the level of the kidneys for the same subjects as shown in Fig. 7. The arrows indicate the blurring on the
kidney cortex caused by respiratory motion that was effectively corrected by INTEX3D. Images in each row are displayed in the same intensity scale.
Medical Physics, Vol. 40, No. 11, November 2013
112507-9
Chan et al.: Event-by-event respiratory motion correction for PET
End-expiration gate
No intra-gate MC
112507-9
Inspiration gate
INTEX3D
No intra-gate MC
INTEX3D
Subject 1
Subject 2
Subject 3
F IG . 9. Comparisons of gated images in the coronal view (same locations at the pancreas and kidney as the images shown in Figs. 7 and 8) without intragate
motion correction, and with event-by-event intragate motion correction (INTEX3D) at end-expiration and inspiration phases. All the images were postsmoothed
with a 3D Gaussian filter with 4 mm FWHM. It can be seen that the differences between NMC and INTEX3D are subtle at end-expiration gate but are substantial
at inspiration phase (as denoted by the arrows) due to the larger amount of intragate motion during inspiration.
reconstruction, INTEX3D yielded 18% and 11% maximum
increases in the radioactivity in pancreas and kidney cortex,
respectively. The shape of TAC also changed slightly due to
motion correction. These corrections may lead to more accurate parameter estimation and need further investigation. Note
the activity increase in the organs was not uniform across
time. The maximum activity increase was obtained at 10-min
in the pancreas and 2-min in the kidney, due to the dynamic
changes of tracer concentration in these organs.
Figure 11 presents the results of the FMISO study. Three
lung lesions (L1–L3) can be identified in the PET images as
denoted by the arrows. The largest lesion L1 measured from
CT images was ∼37 (vertical direction) × 32 mm (horizontal direction). This lesion was used to generate the INTEX
correlation and transformation matrix. The correlation coefficients r between the Anzai mean displacement and mean displacement of L1 were 0.001, 0.38, and 0.94 in LR, AP, and
SI directions, respectively. The motion amplitude measured
from the centroid of the lesion in the LR, AP, and SI directions were 1.6, 2.9, and 6 mm, respectively. Similar to the
FPDTBZ studies, INTEX1D was applied to correct motion in
the SI direction, and INTEX3D was used to correct for motion
in the AP and SI directions only, as the motion in the LR direction was negligible compared to the intrinsic spatial resolution
(∼4 mm) and the correlation was poor. It can be seen that in
the NMC images, the lesion boundaries appear blurred visually in both transaxial and coronal views. The smaller lesions
L2 and L3 appear to be stretched in the SI direction compared
to other images. Although the gated reconstruction yielded
sharper lesion boundaries, the substantial increase in image
noise led to degradation of lesion detection visually, particularly for smaller lesions L2 and L3. INTEX1D corrected motion in SI direction and yielded sharper lesion boundaries such
that lesion L3 appeared to be more compact. In contrast to the
FPDTBZ studies, INTEX3D yielded slightly blurrier boundaries on lesions L2 and L3 than INTEX1D. This may be due to
the small correlation in the AP direction for this case, which
may have yielded worse performance on motion correction.
Thus, the AMNLM was applied to the INTEX1D image to
reduce image noise while preserving the lesions and organ
boundaries.
The quantification of the FMISO patient is shown in
Table VII. The L/B ratio was used to assess the level of hypoxia of the lesions relative to the normoxic tissues.36 It can
be seen that, although the gated images yielded an average
of 16% increase in L/B ratio, the noise in the background
measured as the standard deviation in the blood pool also
TABLE IV. Percentage change of the mean activity in the pancreas compared
to NMC.
TABLE V. Percentage change of the mean activity in the kidneys compared
to NMC.
4.C. FMISO patient results
Subjects
1
2
3
Mean
End-expiration
gate (%)
INTEX1D
(%)
INTEX3D
(%)
INTEX3DAMNLM (%)
17.4
5.8
6.6
9.9
15.5
2.5
2.2
6.8
16.8
5.3
5.7
9.3
16.3
5.1
4.7
8.7
Medical Physics, Vol. 40, No. 11, November 2013
Subjects
1
2
3
Mean
End-expiration
gate (%)
INTEX1D
(%)
INTEX3D
(%)
INTEX3DAMNLM (%)
14.8
11.1
9.5
11.8
10.6
4.4
4.2
6.4
17.1
9.6
6.8
11.2
16.0
9.2
5.2
10.1
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Chan et al.: Event-by-event respiratory motion correction for PET
TABLE VI. Percentage change of the noise level (standard deviation) in the
liver VOI compared to NMC.
Subjects
1
2
3
Mean
End-expiration
gate (%)
INTEX1D
(%)
INTEX3D
(%)
INTEX3DAMNLM (%)
102.2
85.1
143.4
110.2
− 3.8
− 2.8
8.7
− 0.7
− 3.7
− 1.1
− 1.3
− 2.0
− 56.3
− 56.5
− 78.6
− 63.8
increased substantially by 149%. INTEX1D and INTEX1D
+ AMNLM yielded nearly equivalent improvement in L/B
contrast over NMC by 20% on average for three lesions, with
the larger increases for the smaller lesions. INTEX3D yielded
the same amount of improvement for L1, however, the increase was smaller for L2 and L3 due to the less effective motion correction as described above. INTEX1D and INTEX3D
yielded similar standard deviation in the blood pool as the
NMC images, while AMNLM reduced the standard deviation
in the blood pool by 55%.
5. DISCUSSION
This study extended the previously developed INTEX
method to correct for respiratory motion in three-dimensions.
In contrast to the original INTEX, motion correction was carried out in an event-by-event manner with high temporal resolution (40 Hz). Thus, the proposed method can uniquely correct for intragate respiratory motion and facilitate respiratory
motion correction for dynamic studies that, to the best of our
knowledge, has not yet been realized for internal organs in
whole-body PET.
The effectiveness of 3D and intragate motion corrections
was assessed using the NEMA phantom driven by a real patient respiratory trace, and four patient studies with targeted
tracers of FPDTBZ and FMISO. Both NEMA and FPDTBZ
results demonstrate that, although the respiratory motion was
the largest in the superior-inferior direction, motion in other
directions can still lead to considerable blurring and under-
TAC of pancreas
112507-10
estimation in quantification of small objects. In the NEMA
study, INTEX1D corrected motion in the SI direction effectively. However, there was still an average of ∼14% and ∼9%
underestimation in the smaller spheres (10 and 13 mm) and
bigger spheres (17 and 22 mm), respectively, compared to
the static acquisition, mainly due to the remaining motions
in LR and AP directions. By correcting motion in all directions, INTEX3D further reduced the relative bias to ∼4% in
the smaller spheres, and nearly recovered the contrast for the
bigger spheres to the level of the static acquisition (2% relative bias). Note, we consistently observed higher CRC on
the bigger spheres than the smaller spheres for all the methods due to the partial volume effect of PET image.37 Similarly, the FPDTBZ human studies also showed that INTEX1D
achieved comparable quantifications to INTEX3D for large
organs, such as the pancreas (the difference of the mean
percentage improvement was 2.5% as shown in Table IV),
but the difference can be substantial in the fine structures,
such as in the kidney (the difference was 4.8% as shown in
Table V). In those cases, INTEX3D yielded superior performance over INTEX1D both visually and quantitatively.
Therefore, as state-of-the-art PET/CT scanners can achieve
high spatial resolution (typically ∼4 mm FWHM) and the
variation of motion in different directions between subjects
can be substantial, it is essential to correct motion in all directions to achieve optimal image quality and to minimize intersubject variation in quantitative outcome measures.
On the other hand, the incorporation of poor correlation
into event-by-event motion correction can lead to reduced
quality in motion correction. One example is the FMISO
study, INTEX3D was applied to correct the motion in both
the AP and SI directions, where the correlation coefficient
between the AP direction and the external trace was relatively poor at 0.38. INTEX3D yielded lower lesion-to-blood
ratio than INTEX1D on the smaller lesions L2 and L3 in the
FMISO study. The poor correlation may be caused by several
factors. First, the internal landmarks that are not substantially
influenced by respiratory motion and thus exhibiting small
motion amplitude, e.g., apex and sternum, are more likely to
have poor internal-external correlation as demonstrated in the
TAC of kidney
F IG . 10. Time-activity-curves measured in the pancreas and kidney of subject 1 from the first 10 min scan with NMC and INTEX3D. It can be seen that
the tracer concentration increased by 18% in the pancreas and 11% in the kidney at the maximum of the curves after correcting for respiratory motion using
INTEX3D.
Medical Physics, Vol. 40, No. 11, November 2013
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Chan et al.: Event-by-event respiratory motion correction for PET
NMC
L1
L2
End-expiration
gate
INTEX1D
112507-11
INTEX3D
INTEX1D +
AMNLM
L3
F IG . 11. Sample slices of the FMISO study in transaxial (top) and coronal (bottom) views. The arrows indicate three lesions (L1–L3) in the lung. All images
are displayed in the same intensity scale.
previous studies.25, 28, 30 Second, the positioning of the respiratory monitoring devices can also have substantial impact on
the correlation, such that a worse correlation was observed
when the external tracking devices were placed between the
chest and the abdominal region,30 which had little motion externally. Third, the determination of the centroids from inaccurate segmentations may also lead to worse correlation due
to the noise in the gated PET images. The worse performance
of INTEX3D compared to INTEX1D may be caused by a
combination of all these factors. Therefore, we suggest applying INTEX only in the directions with high correlation
coefficient, e.g., r > 0.6, and with motion magnitude that is
discernible with the intrinsic spatial resolution and voxel dimension, e.g., >2 mm, for more effective motion correction.
An eight-bin phase gating was used in this study to correlate the 3D internal organ motion and the 1D external respiratory trace. With these settings, we observed consistent high
correlation (i.e., r > 0.9) in the SI direction in both phantom
and patient studies. Increasing the number of phase bins may
lead to improved correlations, especially in the AP and LR
directions. This is because the intragate motion may affect
the segmentation outcomes and hence the estimation of the
centroids. However, the number of events within each gate
will decrease correspondingly and may impact the accuracy
of segmentation, and hence the estimation of the centroids.
The optimal number of gates depends on numerous factors
that affect the segmentation outcomes on the gated images
including the scanner, injection dose, acquisition duration, reconstruction parameters, the organ size/shape, etc. Therefore,
the number of gates needs to be determined to optimize the
tradeoff between the effect of intragate motion and number of
counts per gate, which requires future investigation.
In this study, the measurement of the centroid of the organ/
tumor was based on an assumption that the target organ
does not deform across the respiratory gates and that motion
mainly involves rigid transformation as the diaphragm moves
and chest/abdomen expands during inspiration.32, 33 Thus, a
constraint was applied to preserve the volume of the segmented organ across all the gates to obtain a reliable measurement of the internal organ displacement. Although this can be
applied to most of the lesions and small organs such as pancreas and kidney, studies have shown that the motion of other
larger organs, such as the heart, due to respiration also includes rotational and deformable motions in some patients.38
Future development is needed for these types of organs to include nonrigid motion estimation in the voxel-by-voxel correlation model and to perform event-by-event nonrigid motion correction, and some “weights” need to be determined for
regions/organs with poor correlations.
In addition, the FPDTBZ studies revealed that the pancreas
and kidneys displacements were consistent in all the patients,
such that the slopes of the regression lines of pancreas and
kidney had less than 5% difference in both AP and SI directions (Table III). As the internal-external correlation was similar for both organs, one motion correction file applied to the
entire FOV could effectively correct the motions for both organs. Although this approach did not show any artifact here,
for whole-body imaging that involves multiple bed positions
and multiple organs/lesions with different motion profiles,
multiple sets of INTEX correlations and reconstructions may
be required for each individual bed position or specific organ.
In this study, the attenuation correction mismatch was minimized by using the end-expiration phase as the reference
frame where the CT images were acquired. In addition, the
TABLE VII. The L/B ratio and standard deviation in the blood pool comparing to NMC of the FMISO study.
The percentage changes comparing to NMC are shown in the parentheses.
L1/B ratio
L2/B ratio
L3/B ratio
Mean
Std dev in blood pool
NMC
End-expiration
gate (%)
INTEX1D
(%)
INTEX3D
(%)
INTEX1D + AMNLM
(%)
2.2
2.4
2.7
2.4
795.0
2.3 (4%)
2.9 (21%)
3.3 (22%)
2.8 (16%)
1982.9 (149%)
2.4 (9%)
2.8 (17%)
3.6 (33%)
2.9 (20%)
771.2 (−3%)
2.4 (9%)
2.6 (8%)
3.3 (20%)
2.7 (12%)
751.8 (−5%)
2.4 (9%)
2.8 (17%)
3.6 (33%)
2.9 (20%)
355.0 (−55%)
Medical Physics, Vol. 40, No. 11, November 2013
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Chan et al.: Event-by-event respiratory motion correction for PET
accurately aligned PET and CT images also facilitate the use
of anatomical knowledge to suppress noise while preserving organ boundaries. As demonstrated in both FPDTBZ and
FMISO studies, the application of AMNLM to the motion
corrected images reduced the background noise by >50%
while preserving the quantitative accuracy (as shown in
Tables IV–VI) in the targeted organs, and organ boundaries.
Without accurately aligned PET and CT images, the use of the
anatomical based filter may cause artifacts due to mismatched
boundaries, and preserve artifacts caused by respiratory
motion.
One of the goals of this study was to correct for intragate motion. The standard deviation of the Anzai respiratory
displacements obtained from the FPDTBZ studies revealed
that the intragate motion at inspiration phase can be substantially larger than the end-expiration phase for some subjects. By comparing the gated reconstructions with and without INTEX3D at both end-expiration and inspiration phases,
the results demonstrated that the use of the external motion
trace with high temporal resolution in the event-by-event motion correction effectively eliminated intragate motion in both
phases, and thus led to reduced image blurring in the final
reconstructed images.
Finally, to demonstrate the feasibility of respiratory motion correction for dynamic studies, we compared the TACs
for both pancreas and kidney before and after motion correction. As expected, the proposed method increased the values
of the TACs for both organs. However, without knowing the
ground truth, it remains unclear what the impact of event-byevent motion correction is on kinetic modeling. Therefore, the
application of INTEX motion correction on tracer kinetic parameter estimation warrants comprehensive investigation in
the future using simulations similar to the previous study.39
6. CONCLUSIONS
This study showed that the proposed INTEX3D method
with matched attenuation correction can effectively compensate for respiratory motion while preserving all the counts,
leading to improved image quality and contrast recovery of
the target organs. The proposed framework of event-by-event
motion correction can uniquely correct intragate motion and
can be applied to dynamic imaging that may lead to improved tracer kinetic modeling. With aligned PET and CT,
this method also facilitates the use of anatomical knowledge to suppress noise while preserving organ boundaries and
quantitative accuracy.
ACKNOWLEDGMENTS
The authors thank the staff at the Yale PET Center and Radiation Oncology for the studies that formed the basis of this
work, a research contract from Siemens Medical Solutions,
a research contract from Pfizer, and support from the Yale
Cancer Center.
a) Electronic
addresses: [email protected] and [email protected];
Telephone: +12037375481.
Medical Physics, Vol. 40, No. 11, November 2013
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