Download Asymmetric cone-beam transmission tomography

IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 48, NO. 1, FEBRUARY 2001
I I7
Asymmetric Cone-Beam Transmission Tomography
Gengsheng L. Zeng, Member IEEE, Grant T. Gullberg, Senior Member IEEE, and Paul E. Christian
Department of Radiology, University of Utah
729 Arapeen Drive, Salt Lake City, Utah 84108-1218, USA
Daniel Gagnon and Chi-Hua Tung
Picker International, Inc.
595 Miner Road, Cleveland, Ohio 44143, USA
Abstract
Transmission scans are an important part of the process of
obtaining patient attenuation maps for accurate SPECT (single
photon emission computed tomography) imaging. In order to
avoid truncation of the projection data, asymmetric cone-beam
imaging geometries were investigated. By using the BeaconTM
SPECT system, it was shown that in the acquisition process
transmission and emission imaging geometries can be
different. Utilizing this new system, cone-beam transmission
scans can be performed while the parallel collimators are
attached for emission data acquisition. Patient and phantom
studies were performed and compared with x-ray CT. A
whole-body helical scan to obtain a whole-body attenuation
map is also proposed. For helical asymmetric cone-beam
geometries, at least two detectors are required in order to
provide sufficient cone-beam data. If two detectors are used,
they must have opposite geometries. Computer simulations
were performed to demonstrate the feasibility of the proposed
asymmetric helical cone-beam scanning geometry.
I. INTRODUCTION
In SPECT, an attenuation map is required for accurate
emission attenuation correction. Usually the attenuation map is
formed from transmission data. There are many transmission
data acquisition methods that can be used including a flood
source [I], a scanning line source with parallel-beam geometry
[2], a scanning point source with fan-beam and offset fanbeam geometry [3], or a fixed line source with fan-beam
geometry [4]. In PET, a moving point source has also been
used to obtain transmission information [ 5 ] . The use of a
scanning source is more complicated than the use of a fixed
source because of the additional mechanics and electronics
required for scanning, which can increase cost and potentially
produce an additional factor that may fail during imaging.
Scanning sources are at an advantage when scanning is
combined with an electronic window. With this combination
down scatter fraction from emission to transmission can be
reduced by a factor larger than ten. A point source is preferred
over a line source or a sheet source because the patient will
The research presented in this manuscript was partially
supported by NIH Grant R29 HL51462 and Picker International.
receive less radiation exposure. Additionally, the amount of
activity for a scanning point source can be on an order of
magnitude lower than a scanning line source.
If a fixed transmission point source is used, the necessity of
using a cone-beam imaging geometry is a direct consequence.
However, when using a cone-beam geometry there are two
significant problems that must be addressed. The first problem
is that the projection data of an object will most likely be
truncated due to the converging beam geometry. The second
problem is that a planar scanning orbit does not provide a
complete data set for a stable, artifact-free reconstruction.
The use of offset cone-beam, i.e., asymmetric cone-beam,
collimators has been suggested for combined emission/
transmission brain SPECT [ 6 ] . By using an asymmetric conebeam geometry, as illustrated in Fig. 1, the truncation of
projection data can be avoided if the axis of rotation and one
side of the patient boundary are in view of the detector. In this
paper, we employ the asymmetric cone-beam geometry to
overcome the truncation problem of cone-beam transmission
projections.
If the planar scanning orbit is replaced by a non-planar
orbit, for example a helical orbit, under certain conditions [lo]
a complete cone-beam projection data set can be obtained. In
half fan-angle
Figure 1. Illustration of asymmetric c&e-beam geometry.
The detector is set wide enough to ensure that at least half of
the object from one edge to the center of rotation is in the field
of view.
0018-9499/01$10,00 0 2001 IEEE
118
Patient
w
Parallel Collimator
/
Figure 2. BeaconTM system on Picker's IRX SPECT
scanner.
Figure 3. Illustration of Ba-133 transmission rays penetrating
the parallel collimator.
this paper, a computer simulation is used to illustrate the
application of a helical orbit in asymmetric cone-beam
tomography.
photons penetrated tlie collimator septa, forming an
asymmetric cone-beam imaging geometry (see Fig. 3). The
asymmetric cone of transmission rays from each source
covered slightly more than half of the patient's torso.
In this study the BeaconT" SPECT system is used.
Recently, Picker Inc. introduced the BeaconTMSPECT system
(see Fig. 2) which can acquire transmission and emission data
simultaneously.The transmission source has enough energy to
penetrate the collimator, which makes it possible to use
different imaging geometries for transmission, and emission
data acquisition. In clinical application Beacon' is designed
to perform fan-beam transmission scans with scanning point
sources a i d scanning electronic data acquisition windows. I n
this paper, we use a cone-beam transmission data acquisition
with fixed point sources. In practice this does not prevent us
from using a cone-beam geometry for transmission imaging
while using a parallel-beam geometry for emission imaging at
the same time.
"
11. METHODS
A. Bra conTMConP -Bea r n St it dies
A picture of tlie BeaconT" system (Picker's IRIX) is
shown in Fig. 2. The configuration shown includes a Barium133 point source of 10 mCi (370 M B q ) mounted on the edge of
detectors #1 and #2.Detector #3 was iiot used for transmission
data acquisition. Ba-133 has a half-life of approximately 10.5
years aid has a main energy peak at 356 keV and two small
energy peaks at 383 keV a i d 302 keV. respectively. Lowenergy (140 keV) high-resolution 1LEHR) parallel collimators
were mounted for the emission scan. The LEHR collimators
had a hole size of 1.22 mm, a hole length of 27 mm, and a
septum thickness of 2.03 mm. The high energy transmission
This BeaconT" system c a i also be used in an alternative
uansmission/emission SPECT study, in which asymmetric
cone-beam transmission data and parallel-beam emission data
are acquired non-simultaneously. At each projection stop,
transmission aid emission data are acquired sequentially.
When the emission data are acquired, the transmission source
shutter is closed. Assuming that the emission photon energy
range is between 70 and 140 keV, which is much lower than
the transmission photon energy (356 keV), the transmission
data are not affected by the emission photons.
We have applied the B e a c o ~ i " cone-beam
~
transmission
data acyuisitioii metliod to other parallel collimators, including
medium-energy general all-purpose (MEGAP) and 5 1 1 keV
axial collimators. The 5 1 1 keV collimator is made of parallel
lead slits. Reconstructioiis using projection data from only one
detector has also been performed.
hi these reconstructions, a planar scanning orbit is used. It
is well known that this orbit does not provide a complete data
set that enables artifact-free reconstruction, especially in the
regions far away from the orbit plane. Fortunately, we have a
relatively long fcxal length, and the artifacts due to cone-beam
data-incomplete scampling are small and do not &tract from
the quality of the reconstruction. Another fact one needs to
keep in mind is that the cone-beam data-incomplete artifacts
are much less pronounced when using an iterative
reconstruction than when using a filtered backprojection
reconstruction [9].
119
Point Source Orbit
I
Detector #1
Figure 5. In a helical scan, the table that the patient lies
on translates as the detectors rotate. The equivalent
point source trajectory is a helix.
Detector #2
Figure 6. When two detectors are used, one should have a focal
point off-centered to the left and the other to the right. Detector
#1 has a ‘‘left’’ half cone, and Detector #2 has a “right” half
cone.
Same Point-SourcePosition
Point
Source
v
Data from Detector #I
Figure 7. Untruncated projection data can be formed by using truncated data collected from both detectors, provided both
detectors have the same point source position.
A. 1. A patient BeaconTMstudy
In a patient study, the detectors rotated 360” with 120 stops.
The data acquisition time was 1 second per view. Data were
acquired in 128 x 128 arrays, of which only 40 rows were
illuminated by the point source due to the small point-source
collimator angle. The detector pixel size was 4.669 mm. The
cone-beam focal length was 82 cm, and the focal point was
shifted by 14.94 cm towards the edge of the collimator. The
angle between the two detectors that acquired projection data
was 78”. The detectors rotated in a noncircular, planar orbit
around the patient. After the patient was removed from the
scanner, a one minute reference scan was acquired, and was
used to convert the transmission data into line-integrals.
After the patient transmission projections were converted
into line-integrals, a cone-beam iterative (emission) ML-EM
(maximum likelihood expectation maximization) algorithm [8]
was used to reconstruct the image (100 iterations). Our
previous study shows that the emission ML-EM algorithm
results in better images than the transmission ML-EM
algorithm in attenuation map reconstruction. The instability of
the transmission ML-EM algorithm is partially caused by the
approximation used during the derivation of the algorithm.
The patient scanned was a 134 pound male. Larger patients
would require a longer scanning time.
A.2. A phantom BeaconTM study with LEHR collimators
A torso phantom was used in a cone-beam BeaconTMstudy
with LEHR (low energy high resolution) parallel collimators.
The data acquisition parameters were the same as in the patient
study, except that the transmission data were acquired for 3
seconds per view, and the reference scan was 2 minutes long.
The images were reconstructed with 100 iterations of emission
using the ML-EM algorithm.
A.3. A phantom BeaconTM study with 511 keV axial
collimators
The same torso phantom used in A.2 was used in another
cone-beam BeaconTM study with 51 1 keV parallel axial
collimators, which were designed for positron coincident
detection (PCD) data acquisition. The data acquisition setup
was the same as in A.2 except that the transmission data were
acquired in 60 stops over 360”, with 8 seconds per view. A
one-minute reference scan was also acquired. Image
f
f
Figure 8. The side-view shows that the focal point can be shifted axially.
reconstruction was performed using 100 iterations of the MLEM algorithm.
A.4. X-ray CT study
A Picker PQ-6000 CT scatiner was used to scan a tcirso
phantom. The x-ray CT study was used as the gold standard
against which other nuclear medicine studies were to be
compared. The transaxial resolution was 1 mm and the slice
thickness was 1 cm in the x-ray CT study. The scan was
perfcmned with 200 mA and 100 kV. The acquisition time was
1 second per slice. The CT images were reconstructed in 5 12 x
512 arrays, which were subsequently collapsed to 128 x 128.
B. Asymnietric Cone-Brcim Hrliccil Sccins
In this section, we outline the admitages of using a helical
scanning orbit (see Fig. 5 ) to obtain a whole-body attenuation
map. An orbit is referred to as the point source trajectory in a
scm. In a helical scan the orbit pitch requirement is crucial
[IO]. In a previous study, the pitch requirement was
dctermined by Palamcxiov's data sufficiency condition [9].
[SIDE VIEW]
Figure 9. Helical cone-beam Defrise phantom study. The
helical focal-point trajectory has two turns. Results shown are
of ML-EM reconstruction ( 3 central cuts) after 30 itcrations.
Palamdov's condition can be stated as ever?. plane flzcif
pcisses throiigh un object tilitst contciiti N line t k i t is riiecisirred
in cif lecist one projection. Using this condition, it can be seen
that a single asymmetric, cone-beam geometry does not have
the capacity to provide sufficient data with a helical scanning
In this applicationt if the focal-point of one detector is offcentered to the IeJi, then the focal-point of the otlier detector
must be off-centered to the right (see Fig. 6 ) . Figure 7
illustrates that untruncated projection data can be formed by
combining data from detectors #1 and #2 when they have the
same point source position. Therefore. the design of tlie
whole-body helical asymmetric cone-beam system requires at
least two detectors. The third detector, when used. cm be
dedicated to emission data acquisition.
orbit. Thus for our application, two asymmetric cone-heam
detectors were used.
The detectors can be arranged in an L-shape (90' apart) as
depicted in Fig. 7. The angle between the two detectors can
121
Slices #53 to #76
Slice #56
Slice #64
Slice #72
Figure 12. Patient cone-beam transmission data reconstruction.Projections were acquired with a BeaconT“ system with LEHR
parallel collimatcxs attached.
vary. It is important that the two detectors must have opposire
geonletries. One detector gives a “left” half-cone-kam, and
the other a “right” half-cone-beam geometry. The fc>calpoint
of both detectors must follow the Same orbit. If the two
detectors must be in the same plane. their focal points should
be shifted differently in the axial direction (see Fig. 8). For
example. one can be shifted towards the patient’s head and the
other can be shifted towards the feet.
A computer generated Defrisr phantom, shown in Fig. 9,
was used in this simulation. The phantom consisted of 19
identical, flat, uniform ellipsoids with semi-axes of 24, 24, and
4, respectively (units in detector pixel-size). The center-tocenter distances between neighboring ellipsoids were 14.
Noise-less projection data were calculated analytically.
utilizing a detector radius of R = 0. The two detectors were 90
apart in an L-shape. The detector size was M x 64,and the
image array size was 64 x 64 x 320. The cone-beam focallength was 75. The detector pixel-size and the image voxelsize were the same. The helical focal-point orbit consisted of
two tunis and the pitch of die orbit was 100. In the simulation
there were 240 projections simulated aloirg each tun).
The image array was five times larger than the detector size
in the axial direction. The ML-EM algorithm was used to
reconstruct the image; the number of iterations was 100.
111. RESULTS
A. BeaconTMCone-Beam Studies
The transmission projections were acquired using
asymmetric cone-beam geometry. Due to the point-source
coIIimation, the cone-angle in the axial direction was smaller
ttian the cone-angle in the transaxial direction. In a typical
scan, approximately 40 rows of pixels (about 18 cm) on Ihe
detector were illuminated.Figures 10 and 11 show a projection
view in a tcxso phantom study with a LEHR collimator and a
PCD collimator, respectively. The brightest spot in the
projection image was caused by the photons that passed
directly thrc~~gh
the collimator holes, indicating the location of
the point source. This bright spot also appears in the blank
scans, which were taken &er the subject (patient or phantom)
was removed. The irormalizeci projections, which are the ratio
122
TOP-SLICE
BOTTOM-SLICE
MID-SLICE
CT
,101 I
I
1161
I
. 1 LU
,101
.076
.OS0
,025
WJ
'JU
3U
I WJ
Figure 13. Torso phantom traismissio~ix-ray CT study and conc-beam BeaconTMstuditfs in which LEHR aid PCD collimators
are used. Profiles are drawn along the horizontal line shown in the corresponding image'S.
123
Sagittal Slice #32
Sagittal Slice #1S
Transaxial Slice #268
Transaxial Slice #160
Figure 14.Three central cuts of an ML-EM reconstructionofa long Defrise phantom after 100 iterations. Detector size = 64x64.
Image m a y size = 64x63~320.In the profiles. die solid lines are for the reconstructed image and tlie dotted lines are the ideal.
f tlie blank scan and the patiendphantom scan, do not have the
bright spot.
Figure 12 shows the patient cone-beam transmission data
reconstruction as desaibed in Section 1I.A.1. Slices #53 to #76
are displayed in 128 x 128 images, and the cardiac region is
within the range of these slices. Larger views of the top, mid,
and bottom images are also shown in Figure 12 with tiit same
pixel size. If more slices in an attenuation map are reyuired,
one can use a different source-collimator that has a larger
cone-angle in the axial direction.
Figure 13 shows the reconstructionsof the attenuation map
for the torso phantom studies. An x-ray CT study (i.e., the gold
standard) and three asymmetric cone-beam studies are
presented. The first asymmetric cone-beam study was
performed with the two-detector, LEHR-collimator, at 3
seconds per view, arid 120 views per detector. The second
study was the same as the first, except that only projection data
from detector #1 were used in the reconstruction and
projection data from detector #2 were not used. The third study
was performed using the two-detector, PCD-collimator, at 8
seconds per view. and 60 views per detector. The study with
PCD-collimatorsbad more photon counts tlian the studies with
LEHR-collimators. thus the images obtained from the PCD
study are not as noisy as diey are in the LEHR studies. Three
slices (top. mid, arid bottom) from each study were selected fix
display. A horizontal profile was drawn across the image array
(i.e., 128 pixels) on each selected slice. In order to show the
same relative phantom size. a sub-repion of the 128 x 128
image m a y is displayed. Due to tlie poor resolution ot SPECT
cameras and the partial volume effect. the detail structure
within the lungs cannot be see11 in nuclear medicine studies,
however they can be clearly observed in the x-ray CT study.
B. Asjmrnrtric Cone-Bemi Helicai Sciins
Figure 14 shows an ML-EM reconstruction of computer
simulated data. Two sagittal cuts and two traiisaxial cuts are
displayed. Severe artifacts can be seen at the top and bottom ol
the phantom, where the projection data are unavailable.
However. the ceiitral region, where the projection data are
I24
complete, is accurately reconstructed as indicated by the
profiles.
ACKNOWLEDGMENTS
IV. DISCUSSION
We thank Roger Roberts for acquiring x-ray C T data in this
study. Also, we thank Sean Webb for editing the manuscript.
When using Picker’s BeaconTM SPECT system, the
emission data acquisition geometry can be different from the
transmission data. With parallel collimators attached, a fixed
Ba-133 point source can be used to acquire asymmetric conebeam transmission data. Fixed point sources reduce
complications in transmission imaging. The truncation
problem is avoided by using an asymmetric cone-beam
geometry requires no moving parts are required.
REFERENCES
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Therefore, approximately 24% of the Ba-133 gamma rays that
travel through the patient (in the 35% 356 keV energy
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