1

Demonstration of in-vivo multi-probe tracker
based on a Si/CdTe semiconductor Compton camera
Shin’ichiro Takeda, Hirokazu Odaka, Shin-nosuke Ishikawa, Shin Watanabe
Hiroyuki Aono, Tadayuki Takahashi, Yousuke Kanayama, Makoto Hiromura and Shuichi Enomoto

Abstract—By using a prototype Compton camera consistingof silicon (Si) and cadmium telluride (CdTe) semiconductor
detectors, originally developed for the ASTRO-H satellite mission,an experiment involving imaging multiple radiopharmaceuticals
injected into a living mouse was conducted to study its feasibility
for medical imaging. The accumulation of both iodinated (131 I)
methylnorcholestenol and 85 Sr into the mouse’s organs was
simultaneously imaged by the prototype. This result implies that
the Compton camera is expected to become a multi-probe tracker
available in nuclear medicine and small animal imaging.
Index Terms—Astrophysics, Si/CdTe Semiconductor Compton
camera, nuclear medicine, small animal imaging

I

I. I NTRODUCTION

N the fields of nuclear medicine and small animal imaging,a next-generation instrument capable of imaging a wide
energy range and fine energy resolution, enabling emission
lines to be precisely distinguished from different radioisotopes, is desirable. In diagnostic imaging, to detect cancer
and recurrence inside the body is a critical issue. However,even with early detections by positron emission tomography(PET), it remains difficult to differentiate between benign andmalignant lesions at various stages. In order to characterize
cancers and their surrounding environment which leads to theimprovement of diagnostic accuracy, and to decide the mostappropriate treatment strategy, diagnosis by means of multiple
probes is required to provide more comprehensive information.
However, such an approach has not been realized by PET since
it only allows tracking of a single positron-emitting probe.
The high energy resolution and sufficient efficiency at a
few hundred keV band are the key to realize the multi-probe
tracker, and there seems to be two prospective approaches.
One is the use of semiconductor SPECT camera against a
backdrop of recent progresses in new semiconductor imagers
represented by cadmium telluride (CdTe) and cadmium zinctelluride (CZT) detectors, which have high stopping power
in comparison with silicon (Si) and germanium (Ge). Fineenergy resolution realized by the detectors (∆E/E ∼1 %)enables gamma-ray lines emitted from various kinds of RIs
to be detected, which was previously impossible when using
traditional NaI scintillation detectors. Some instruments have
S.Takeda, H. Odaka, S. Ishikawa, S. Watanabe and T. Takahashi are
members of the Institute of Space and Astronautical Science, Japan Aerospace
Exploration Agency, 3-1-1 Yoshinodai Sagamihara Kanagawa 229-8510,
Japan, and also the Department of Physics, The University of Tokyo, 7-3-1
Hongo Bunkyo-ku Tokyo 113-0033, Japan (E-mail: takeda@astro.isas.jaxa.jp)
S.Takeda, Y. Kanayama, Makoto Hiromura and S. Enomoto are with the
RIKEN Center for Molecular Imaging Science, 6-7-3 Minatojima Minamimachi, Chuo-ku, Kobe, Hyogo 650-0047, Japanbegun to appear in the market [1], [2]. However, the upper
energy range is limited due to use of mechanical collimator(up to 364 keV from 131 I ), hence the selection of labeled RIs
is also limited to a few varieties such as 99m Tc (140 keV),123
I (159 keV) or 111 In (171 keV). Another approach is asemiconductor Compton camera, which is described in thispaper. The Compton camera detects the Compton scattering
process for image reconstruction, while the SPECT camera
detects the photo absorption process. Because the mechanicalcollimator is not required in Compton imaging, the camera
can image in a wider energy band and covers many kinds of
RIs, including SPECT and PET probes, making it the mostversatile imaging system for use in the multi-probe tracker.
It has been demonstrated that a semiconductor Compton
camera by using germanium detectors has high potential to
make individual images from deferent emission lines. Motomura et al. [3] has shown simultaneous images of multiple
radiopharmaceuticals injected into a living mouse. However,since the system needs to operate at around liquid nitrogen temperature, it would be difficult to make compact andportable system, which would be needed in practical situation.
Therefore, it is desirable to develop a semiconductor Compton
camera which can be operated at around room temperature. In
this paper, we report the first result of experiments involving
imaging radiopharmaceuticals with a new Si/CdTe Compton
camera, consisting of multiple layers of Si and CdTe imaging
detectors. After we describe the set up and analysis procedure,
we present the imaging performance.
II. T HE PROTOTYPE CAMERAISAS/JAXA group, a Japanese space science research institute, has developed a Si/CdTe Compton camera [4], [5] for
the ASTRO-H satellite mission scheduled for launch in 2014[6], [7]. Because details of the detector configuration and dataacquisition for the prototype camera are reported in Takeda etal. [8], we briefly explain the system.
The camera consists of a single layers of double-sided
silicon strip detector (DSSD) and four layers of CdTe pixel
detectors (see Fig. 1). The stacked CdTe module is placed
14.5 mm over the DSSD, in which each CdTe layer contains
four CdTe detectors in a 2×2 arrangement. Table I summarizes
the dimensions and typical performance of each DSSD and
CdTe detector element. The detectors were operated at around-10 ◦ C by circulating cooled liquid ethylene glycol throughaluminum detector box.
In the Si/CdTe Compton camera, the events involving theincident gamma-ray being scattered in the Si detector and fully

2

Detector
DSSD (Si)
CdTe pixel

Active Area [mm]25.6 × 25.6
13.2 × 13.2

Thickness [mm]0.50.5Strip pitch (Pixel size) [mm]
0.4
1.35

Bias [V]250
600

Energy resolution
1.6 keV (FWHM) at 59.5 keV
2.0 keV (FWHM) at 81 keV∆E/E ∼1 % (FWHM) at 511 keV

TABLE ID IMENSIONS , OPERATING BIAS VOLTAGES , ENERGY RESOLUTIONS FOR DSSD AND C D T E DETECTORS .

In addition, both the scattering position and the direction of" are required for the back-projection
the scattered gamma-ray S(see Section III-B). The steps for the event selection are shownin Fig. 2.

14.5 mm

CdTe~15 mm

45 mm

DSSD

Stage

heatingpadFig. 1. Setup of mouse imaging as described in section IV. The camera
consists of a single layer of the DSSD and four layers of CdTe pixel detectors.
The distance between the mouse and camera is about 30 mm.

absorbed in the CdTe detectors are used for Compton imaging.
Since the effect of the Doppler broadening is smaller in the Si
devices than other semiconductor devices [9], the camera allows the difference between the measured and actual scattering
angles to be constrained, meaning higher position resolution
is expected. Therefore, the coincidence trigger measurement
between DSSD and CdTe pixel detectors is performed for
effective data acquisition. The trigger thresholds are set toaround 30 and 20 keV for DSSD and CdTe pixel detectors,
respectively.
III. DATA ANALYSIS
We study near-field Compton imaging by using the dataof two point sources, 133 Ba (356 keV, 2.8 MBq) and 22 Na(511 keV, 1.3 MBq), located at a 30 mm plane from thedetector surface (see the upper panel of Fig.9).
A. Event selection
To image using the Compton camera, we first have to search
the list mode data to find candidates of the Compton event,in which gamma-rays are scattered in the Si part and fully
absorbed in the CdTe part. The goal of this event selection isto determine the energy transported to an electron Ee$ and theenergy of the scattered gamma-ray Eγ$ in order to solve thescattering angle θ with the Compton kinematics;! 1"
1
cos θ = 1 − me c2
− $
.
(1)
$
$
Eγ
Ee + Eγ

Fig. 2.

Event selection flow

After reading an event which comprises the pulse heights ofall detector channels, the first step involves determining the hit
in the DSSD to obtain the scattering position and its energy
deposit. Here, we search the strips recording peak energy ineach Pside and Nside, and if the peak energies on each side
exceed the threshold of 10 keV, we decide the hit in the DSSD.
The x-y position of the hit is determined from the configurationof the P and N strips, and the z position is assigned to thecenter of depth of the DSSD. The energy deposit is determinedby the Pside pulse height because the Pside has better energy
resolution than the Nside. This energy deposit is the energy
transported to an electron Ee$ .

Silicon energy deposit [keV]3

Fig. 4. The multiplicity of the CdTe part for the event inside the energy
windows of 350–360 and 500–520 keV drawn in Fig.3

Sum of CdTe energy deposits [keV]
Fig. 3. A two-dimensional scatter plot of Si and CdTe energy deposits. Theenergy deposits in the CdTe part are added.

Having obtained the scattering position and Ee$ , the direction" and Eγ$ ) provide comand energy of scattered gamma-ray (Splete information for the back-projection. The Eγ$ is obtainedby adding the energy deposits in the CdTe part. Before the" we apply the energy window selection to
calculation of S,
image the distribution of multiple radioisotopes individually.
Figure 3 shows a two-dimensional scatter plot of Si and
CdTe energy deposits by locating two point sources of 133 Ba(356 keV) and 22 Na (511 keV) in front of the camera. Theenergy deposits in the CdTe part are added. A structure inwhich the energy sum of Si and CdTe are equal to the input
energies of 356 and 511 keV contains fully energy depositedCompton events, hence we use the events within the energy
window drawn with cyan lines, which correspond to 350–360
and 500–520 keV, in the following analysis.
In addition to the energy window selection, we also apply
the selection derived from Compton kinematics. Because theright-hand side of Eq.(1) must be between −1 and 1, we
otherwise skip the following analysis and read the next event.
Here, we have already obtained the energy transported toan electron Ee$ , the scattering position in the DSSD, and theenergy of the scattered gamma-ray Eγ$ . The final step involves" If
calculating the direction of the scattered gamma-ray S.
the number of hits in the CdTe part is one, the direction is
simply calculated by connecting the scattering position in the
DSSD and the hit’s position in the CdTe. Figure 4 shows
the multiplicity of the CdTe part for the event inside theenergy window of 350–360 and 500–520 keV. Although 70–
75% of all events are distributed as a single hit in the CdTe
part, extended analysis of multiple hits, which originate frommultiple Compton scattering in the CdTe part, could increase
the detection efficiency by about one and a half times. One
difficulty is that the inability to time-of-flight measurement
due to the short distance of the detectors means we cannot
directly determine the interaction sequence in the CdTe part.
We attempted the following figure of merit (FOM) analysis.

N! of sequences are possible for N hits in the CdTe part.
The FOM analysis uses the fact that the scattering angle
φ in the diagram of Fig. 5 is also calculated by energetic
information. Here, we define [φ|t] and [φ|e] for the topologicaland energetic scattering angle, respectively. The [φ|t] corresponds to the φ in the diagram, while the [φ|e] is calculatedby the energy deposit at the reference point and the sumof the following energy deposits in sequence with Compton
kinematics as described in Eq. (1). Since N-hits provides a
total of (N − 1) calculations of [φ|t] and [φ|e], the FOM fora certain sequence could be defined as;
F OM =

N−1#i([φ|t]i − [φ|e]i )2(∆[φ|t]i )2 + (∆[φ|e]i )2(2)

The most probable sequence is expected to minimize the FOM"
value. Once the most probable sequence is determined, the S
is derived from the scattering position in the DSSD and thefirst interaction position in the CdTe part. In practical terms,
since the multi-hit event with N > 5 is negligible, we skip theanalysis in that case. The scope of this paper does not include
the φ-dependance of ∆[φ|t] and ∆[φ|e].

Sequence 1

Sequence 2
DSSD[φl t]
2
1
2

CdTe[φl t]
1

Fig. 5. Possible sequences for N=2. Here, N is the number of the hits in
the CdTe part.

In the multi-hit analysis, the calculation of Eγ$ by adding
the energy deposits in the CdTe part should be reconsidered.

4

By applying error propagation to Eq.(1)
$
%2
me c2
1
2
(∆θ) =(∆Ee$ )2sin θ (Ee$ + Eγ$ )2$%2
me c2 !
1
1 "
+
− $2
(∆Eγ$ )2 (3)sin θ (Ee$ + Eγ$ )2Eγ

we limited the back-projection region to 3×∆θ and applied the
Source Space Tree Algorithm (SSTA) [10] to our cone spreadprojection. Briefly, the SSTA provides an effective voxel
search by dividing the back-projection space into successively
smaller subdivisions, testing for cone-surface interception ateach subdivision branch level, until the subdivision regions
are identical with the voxels.

is given. Therefore, in the case of known energy Eγ , the subtraction by Eγ$ = Eγ − Ee$ provides better angular resolution
than the addition because the increase of ∆Eγ$ is constrained.
B. Near-field back-projection

Uniformly enlarged
projection

Sampling equivalentprojectionz = 30 mm

z = 30 mm

z = 60 mm

z = 60 mm

S

Unlike astrophysical observation, the targets are located in
the near-field in medical imaging, meaning the direction of theincident gamma-ray, as calculated by the parameters derived in
section III-A, should be projected in three-dimensional space.
We describe our back-projection method and experimental
verification in this section.

Sz = 30 mm
z = 60 mm

Z

Fig. 7. The cross-sectional view of the back-projection cone for the uniformly
enlarged projection (UEP) and sampling equivalent projection (SEP).

θ

X

Δθ

L

S

Uniformly enlarged
projection

Sampling equivalentprojectionσxFig. 6.

Diagram of the three-dimensional back-projection

Figure 6 shows the diagram of the three-dimensional backprojection. The back-projection cone is drawn from the starting" where the angle of the conepoint of the direction vector S,
θ is calculated by Compton kinematics of Eq.(1). Due to theuncertainty originating from the incomplete position, energy
measurement with a real detector and the Doppler broadening
effect, the θ contains uncertainty. Therefore, with increasing
distance, the cone profile shows a wider spread. To consider" at the reference
the spread, we define the voxel value V (X)"point vector X (voxel center) as follows;&! "2 '" = |L|" −w exp − 1 x
V (X)
(4)
2 σ
here,
" − L|"
x = |X" tan(∆θ).
σ = |L|(5)(6)

where, ∆θ is the parameter for angular uncertainty and w is
" Typically, thethe weighting parameter for the distance |L|.
value of ∆θ in our camera is around 1 degree. We adopt a
Gaussian distribution to express the cone spread in this study.
Practically, to avoid loss of time in the back-projection process,Fig. 8.

Same as Fig.7, but a diagonal cross-section.

Among any weighting parameter, w = 0 and 2 are characteristic cases. Here, we name the case of w = 0 uniformly
enlarged projection (UEP) and that of w = 2 sampling
equivalent projection (SEP), respectively. A comparison of theprobability density profile between these methods is shown in
Fig. 7, in which two cross-sectional views parallel to a base atdiffering distances from the apex are presented. For simplicity,
the probability at z = 30 is normalized. In the UEP, the voxel
values are identical anywhere on the cone surface, meaning
the profile looks to be uniformly enlarged. Conversely, in the
SEP, the same is true for the integral of voxel values within asolid angle as viewed from the apex. For example, the whole
integration at a z = 30 plane becomes equal to that at z = 60
plane. This method corresponds to the projection whereby
random sampling of a certain direction is repeated from the
spread cone with the Gaussian distribution characterized by∆θ. In Fig. 8, we also show the diagonal cross-section forreference.
In our previous study, we tried LM-ML-EM method [11] forthe sensitivity (sj ) correction after the SEP, where sj is the

5

Z

45

mm

25 mm
22 Na

133 Ba

30 mm

X

56 º

DSSD

CdTe

Uniformly enlarged projection

Sampling equivalent projection

133Ba(356 keV)

133Ba(356 keV)

22Na(511 keV)

22Na(511 keV)

Fig. 9. The UEP and SEP images of 133 Ba (356 keV, 2.8 MBq) and 22 Na(511 keV, 1.3 MBq) point sources at the z=30 mm plane. The sources arelocated at about 45 mm apart from the center of the camera to verify two
back-projection methods.

probability that an event emitted from voxel j is measured, andthe event responses derived from the SEP were used during theiteration process. The image quantitativity of phantoms with
2D internal structure was successfully improved [8]. However,for a 3D target such as a mouse, the present data set shows
the lack of information as viewed from multi-angle such as
SPECTs and PETs, since the prototype camera can not rotate
around a target. Therefore, the combination of the SEP and
LM-ML-EM method for 3D imaging still needs more careful
verification. Conversely, the UEP could be regarded as an
approximate way including the sensitivity correction. Because
the dominant factor to the position dependance of sj is thesolid angle of the camera looking from the voxel j, sj canbe approximately represented as a function of L−2 . The UEP(w = 0) attempts to cancel out the L−2 dependance in backprojection process, which is obvious when compared with theSEP (w = 2).
Figure 9 shows the resulting UEP and SEP images of133
Ba (356 keV, 2.8 MBq) and 22 Na (511 keV, 1.3 MBq)
point sources located at the z=30 mm plane. The sources areplaced 45 mm apart from the center of the camera to verify
two back-projection methods. After the back-projection to thethree-dimensional space, we picked out the slice where thesources were located. As shown in the right-hand panels, the
SEP image is contaminated by “ghost” structure around thecamera’s center of (0,0). This is because many cones pile up at
the very near-field in front of the camera, which unfortunately
leads to misunderstanding of the source distribution unless thesensitivity is corrected. Conversely, the UEP relatively evades
contamination due to its differences in the probability density
profile, aiming the sensitivity correction in back-projection
process. Besides, we obtained a reasonable result in thepretest of mouse imaging using the UEP method (see SectionIV-A), hence the UEP method was selected for the mouse
imaging described in the next section. As noted previously,
the application of LM-ML-EM method for 3D imaging needs
further experimental studies using 3D phantoms. The dataacquisition from multiple angle to reconstruct the 3D source
distribution seems to be important, which is planed in futuresystem development.

6

IV. MOUSE IMAGING
Having established the Compton camera system and confirmed the near-field back-projection, we tried imaging ofmultiple radiopharmaceuticals injected into a living mouse
to demonstrate the concept of the multi-probe tracker. The
location between the mouse and camera is shown in Fig.1. This
experiment was conducted at RIKEN, Japan, in collaboration
with the Multiple Molecular Imaging Research Laboratory.

ROI size

A. Pretest
To determine the accumulation of radiopharmaceuticals ina mouse, it is important to understand the image response.
We conducted a pretest by using a point source of 133 Ba(356 keV, 2.8 MBq) in advance of the mouse imaging. In
this test, the point source with a diameter of 1.0 mm wasplaced at a 30 mm plane from the camera and moved witha pitch of 20 mm along the Y-axis as shown in Fig.10 toinvestigate the imaging response around the mouse’s setting
position. The observation time at each position is set to take thesame livetime of 650 seconds in order to simulate the imaging
result of arranged point sources with equivalent intensities.
Z[mm]

Fig. 11.
Resulting UEP image of the preset. The angular uncertainty
parameter ∆θ is set to 1 degree (see Fig. 6).

Y

20

m
m

pi

tc
h

133 Ba30 mm

X

4.7 mm

12 mm

DSSD

CdTe

[mm]

Fig. 12. The line profile through the center of the points, in which the image
responses at each position are shown with different colors.

Fig. 10. Setup for the pretest. A 133 Ba (356 keV, 2.8 MBq) point source
was moved along the Y-axis with a pitch of 20 mm. The observation time ateach position is set to take the same livetime of 650 seconds.

The resulting UEP image picked out at the source’s moving
plane is shown in Fig.11. First, we indicate that all sources
located at (0,-40) (0,-20) (0,0) (0,20) and (0,40) successfully
imaged at their correct positions. This is an impressive result
because the camera can shoot the whole body of the mouse by
fixed point observation. Figure 12 shows a line profile throughthe center of the points, in which the image responses at eachposition are shown with different colors. The FWHM of thepoint spread function (PSF) at the center position is 4.7 mm.
As the source shifts away from the center of the camera,
the PSF gradually expands and becomes 12 mm at (0,-40)

and (0,40). We also confirmed sensitivity correction by the
UEP. The ratios of counts to livetime within 350–360 keV
window were 1.8 (0,-40), 3.3 (0,-20), 4.5 (0,0), 3.3 (0,20) and1.8 (0,40) counts/sec at each position, meaning a 44 % dropfrom the center to the edge. Conversely, the intensities within
the region-of-interest (ROI), setting a circle with a radius of
10 mm (see Fig. 11) at each PSF, were 0.89 (0,-40), 0.94 (0,20), 1 (0,0), 0.94 (0,20) and 0.86 (0,40), where that at (0,0)
was normalized to unity, meaning that the sensitivity is wellcorrected. The absolute detection efficiency, that defined as theprobability that a single gamma-ray emitted from the source is
detected within the energy window, was 2.6 ×10−6 @ 30 mm,(0,0).

7

B. Setting
We use a male 8 week-old ICR mouse in the mouse imaging,
into which iodinated (131 I) methylnorcholestenol producedby FUJIFILM RI Pharma Co., Ltd. and 85 SrCl2 solution
by PerkinElmer Japan Co., Ltd were injected. In order toobtain appropriate accumulation, 18.7 MBq of iodinated (131 I)
methylnorcholestenol was injected three, four and five days
before the imaging, respectively, and 2.0 MBq of 85 SrCl2
solution injected one day before the imaging. The 131 I and85
Sr emit 364 and 514 keV gamma-rays, respectively.
Iodinated (131 I) methylnorcholestenol is a widely-used radiopharmaceutical for adrenal scintigraphy. Also, marked accumulation in the thyroid has been identified in rats according
to the product sheet [12]. Conversely, since the strontium wastaken up in new bone growth as well as calcium, 85 Sr wasused for many years in medicine to scan for bone lesions, ortumors [13].
The mouse was set on a heating pad, which was placed
at 45 mm underneath the camera, and the observation was
conducted for 6 hours. During the imaging, the mouse was
kept anesthetized by inhalation of 1.5 % isoflurane and its
body temperature was kept at a 37 ◦ C. The energy windows
were set to 355–370 and 500–524 keV for 131 I and 85 Sr,
respectively. During the back-projection process, the angular
uncertainty parameter ∆θ was set to 1 degree for both 131 I and85
Sr. The animal experiments were carried out in compliancewith the guidelines for the care and use of laboratory animals
and approved by the Committee on Animal Experimentationof RIKEN.
C. Results[counts/bin=0.4 keV]

After observation for 6 hours, we obtained 2.93 × 104
and 8.64 × 103 counts of Compton event candidates for 131 I
and 85 Sr, respectively. The candidates were derived from theenergy windows presented in Fig. 13 via the scheme describedin section III-A.

[keV]

Fig. 13. Energy spectrum obtained by mouse imaging with two energy
windows for 131 I (364 keV) and 85 Sr (514 keV)

The accumulation of iodinated (131 I) methylnorcholestenol(left) and 85 Sr (right) is shown in Fig. 14 with the picture of
the subject mouse. The slice image picked out at the plane
40 mm underneath the camera is presented, approximately at

the center of the mouse’s body. In the case of iodinated (131 I)
methylnorcholestenol, we can see three areas of accumulation
around the neck, abdomen and genitals. The accumulations
around neck and abdomen are thought to originate fromthe thyroid and adrenal regions. Intense accumulation wasdetermined around the genitals, which might be from thetesticle or prostate. Conversely, accumulations of 85 Sr in newbone growth, such as the skull, spine, lumbar and femur, wereclearly identified. The similar accumulations were observedin imaging of another mouse with the some amount of dose
injections.
V. C ONCLUSION AND FUTURE PROSPECTS
Although the use of a Compton camera in medical imaging was proposed in the early 1970s and thought to haveconsiderable potential [14], no adequate spatial resolution
for medical use has yet been achieved by traditional sensor
technologies. Utilizing the prototype Si/CdTe semiconductor
Compton camera, we achieved a few mm-level spatial resolution, and successfully imaged distinguishable accumulationsof iodinated (131 I) methylnorcholestenol and 85 Sr injected intoa living mouse. The development of a new Si and CdTe strip
detector with a pitch of 250 µm is on going, aiming for
improvement of the position resolution up to 1 mm @ 30 mm
in the next system.
From these experiments, we also determined two problems
to be solved in future developments. One is poor detection efficiency. The efficiency obtained by the prototype is 0.23×10−6(356 keV) @ 10 cm, while that of the existing clinical SPECT
system is around 100×10−6 . Although the efficiency is improved up to 3.4×10−6 in the latest Compton camera [15],thirty times’ better efficiency is required to arrive at the clinical
SPECT system, which could be realized by SGD-base detector
configuration [16]. The soft gamma-ray detector (SGD) isa astrophysical Compton camera developing for ASTRO-H
satellite mission, and one hundred times’ better efficiency
than the latest camera is realized by a single detector module(around 400×10−6 ). Arranging several camera modules is also
effective because the Compton camera has a very large field ofview. Another is to realize three-dimensional imaging. Usingmouse imaging, we found that three dimensional information was required to precisely determine the distribution into
the mouse’s organ around the abdomen and genitals. Multiangle imaging with a ring-like camera configuration would be
required to overcome this problem, according to simulation
studies [16].
ACKNOWLEDGMENTS
The authors thank all the staff at RIKEN Multiple Molecular
Imaging Research Laboratory for supporting this work.
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