Reduction method for intrinsic random coincidence eventsfrom 176Lu in low activity PET imaging

Eiji Yoshida • Hideaki Tashima • Fumihiko Nishikido •

Hideo Murayama • Taiga Yamaya

Received: 11 October 2013 / Revised: 17 January 2014 / Accepted: 18 January 2014

� Japanese Society of Radiological Technology and Japan Society of Medical Physics 2014

Abstract For clinical studies, the effects of the intrinsic

radioactivity of lutetium-based scintillators such as LSO

used in PET imaging can be ignored within a narrow

energy window. However, the intrinsic radioactivity

becomes problematic when used in low-count-rate situa-

tions such as gene expression imaging or in-beam PET

imaging. Time-of-flight (TOF) measurement capability

promises not only to improve PET image quality, but also

to reduce intrinsic random coincidences. On the other hand,

we have developed a new reduction method for intrinsic

random coincidence events based on multiple-coincidence

information. Without the energy window, an intrinsic

random coincidence is detected simultaneously with an

intrinsic true coincidence as a multiple coincidence. The

multiple-coincidence events can serve as a guide to iden-

tification of the intrinsic coincidences. After rejection of

multiple-coincidence events detected with a wide energy

window, data obtained included a few intrinsic random and

many intrinsic true coincidence events. We analyzed the

effect of intrinsic radioactivity and used Monte Carlo

simulation to test both the TOF-based method and the

developed multiple-coincidence-based (MC-based) method

for a whole-body LSO-PET scanner. Using the TOF- and

MC-based reduction methods separately, we could reduce

the intrinsic random coincidence rates by 77 and 30 %,

respectively. Also, the intrinsic random coincidence rate

could be reduced by 84 % when the TOF?MC reduction

methods were applied. The developed MC-based method

showed reduced number of the intrinsic random

coincidence events, but the reduction performance was

limited compared to that of the TOF-based reduction

method.

Keywords PET � Simulation

1 Introduction

Lutetium-based scintillators, such as lutetium oxyorthosi-

licate (LSO) [1], are widely used for positron emission

tomography (PET) scanners. These scintillators contain a

small amount of 176Lu intrinsic radioactivity. As shown in

Fig. 1a, 176Lu decays into 176Hf with simultaneous b-par-

ticle emission (average energy 420 keV) and three prompt

c-ray emissions (88, 202, and 307 keV). In a PET detector,

the b particle emitted from the LSO array tends to be

detected in the same LSO array. In contrast, c-rays are

detected not only in the same LSO array, but also in

another LSO array by emission outside the first LSO array.

In this scenario, the b particle and the c-rays can be rec-

ognized as an intrinsic true coincidence, as shown in

Fig. 1b. Intrinsic true coincidence detects two radiations

from one 176Lu nuclide, simultaneously. When two bparticles are detected within the coincidence time window,

these b particles can be recognized as an intrinsic random

coincidence, as shown in Fig. 1b. Intrinsic random coin-

cidence detects two radiations from different 176Lu nuc-

lides, accidentally. In this case, the intrinsic coincidences

are detected as a multiple coincidence, because the intrinsic

random coincidence is detected simultaneously with the

intrinsic true coincidences. A multiple coincidence occurs

when more than two photons are detected in different

detectors within the coincidence time window. Naturally,

both intrinsic true and random coincidences are false

E. Yoshida (&) � H. Tashima � F. Nishikido � H. Murayama �T. Yamaya

Molecular Imaging Center, National Institute of Radiological

Sciences, 4-9-1 Inage-ku, Chiba 263-8555, Japan

e-mail: rush@nirs.go.jp

Radiol Phys Technol

DOI 10.1007/s12194-014-0258-1

coincidences. With a narrow energy window, most intrinsic

coincidences can be prevented. Thus, for clinical studies,

the count rate of the intrinsic radioactivity can be ignored

with a narrow energy window and a narrow coincidence

time window [2–4].

On the other hand, when imaging is done with a low

activity level, a PET scanner detects only a limited number

of true coincidences. In a small-animal PET scanner, for

example, for cell-trafficking studies [5] or gene expression

imaging [6], the injection activity tends to be limited to a

very low level (below 1 kBq for some situations). In these

cases, the intrinsic radioactivity affects the imaging per-

formance with the conventional energy window [7].

Another example is in-beam PET, which is a method for

the in situ monitoring of charged particles therapy [8, 9].

For the usual carbon (12C) beam irradiation, it has been

reported that the activity of positron emitters (e.g., 9C, 10C,11C, 15O, etc.) produced through fragmentation reactions

between the projectiles and the atomic nuclei of the tissue

is generally low. Instead of the 12C beam, therefore, we

aimed at using a 11C radioactive beam as an incident beam

directly. Because the projectiles themselves are positron

emitters, we expected that PET images could be obtained

directly, corresponding to the distribution of the primary

particles. Also, 11C has shown tenfold magnification of the

activity concentration compared to 12C. For in-beam PET

studies, we have developed a small prototype PET scanner

[10, 11] that uses a lutetium gadolinium oxyorthosilicate

scintillator. This small prototype PET scanner had 6.5 %

system sensitivity, 14 % energy resolution (energy window

of 400–600 keV), and 3.0 ns timing resolution (coinci-

dence time window of 20 ns). For 11C irradiation with

70 Gy, the average true coincidence rate was about 2500

cps. This means that the true coincidence rate is expected

to be limited to 35.7 cps at a typical clinical irradiation

dose (1 Gy). Calculated simply from our experiment, the

assumed minimum average activity was about 500 Bq. On

the other hand, the intrinsic coincidence rate of the small

prototype PET scanner has been counted as about 50 cps,

and we expected that the intrinsic coincidence rate of a

human-size PET scanner would be higher, because human-

size PET scanners have about 10 times greater scintillator

volumes than the small prototype PET scanner. It is rec-

ommended that all possible intrinsic coincidences be pre-

vented when a scintillator like LSO is used. The simplest

solution to this is to use scintillators without intrinsic

radioactivity, such as bismuth germinate or gadolinium

oxyorthosilicate; however, LSO offers a better perfor-

mance than do these scintillators, because it has a suffi-

ciently good time-of-flight (TOF) measurement capability

to give improved imaging performance.

Recently, some new TOF-PET scanners have been

developed [12–14]. The time difference between the

detection of two annihilation photons is used so that the

uncertainty of the annihilation positions is reduced. TOF

information decreases the statistical noise values of

reconstructed images. Conti [15] reported that the TOF

measurement capability promised not only to improve the

PET image quality, but also to reduce the number of ran-

dom coincidences. We thought that the LSO-PET scanner

might be able to image low activity levels using TOF

information, although LSO has intrinsic radioactivity.

Thus, we used TOF information to reduce the number of

intrinsic random coincidences.

On the other hand, when coincidence events are not

limited by the energy window, many intrinsic coincidences

are detected as multiple coincidences. At a low activity

level, the multiple-coincidence events are a unique phe-

nomenon for identifying intrinsic coincidences. In this

work, we developed a new reduction method for the

intrinsic random coincidences from 176Lu, based on mul-

tiple-coincidence information. Also, we evaluated the

effects of intrinsic random coincidence reduction by the

narrow energy window and TOF- and multiple coinci-

dence-based (MC-based) reduction methods using Monte

Carlo simulation.

Fig. 1 Illustrations of a the

decay level scheme of 176Lu and

b intrinsic coincidence from176Lu. Intrinsic true coincidence

is caused by b–c coincidence,

and intrinsic random

coincidence is caused by b–bcoincidence

E. Yoshida et al.

2 Materials and methods

2.1 Energy window

In imaging at a low activity level, the energy window must

be set as narrow as possible so that contamination from

intrinsic coincidences is prevented. Especially, in intrinsic

random coincidences, b particles have a broad energy

distribution. Typically, in the newest whole-body LSO-

PET scanners, the lower-level discriminator (LLD) and the

upper-level discriminator (ULD) are set at 425 and

650 keV, respectively. For reducing the number of intrinsic

random coincidences, the LLD should be set at a higher

energy level and the ULD should be set at a lower energy

level.

2.2 TOF-based reduction method

A fast scintillator like LSO has the advantage of being able

to reduce the number of random coincidences using a

narrow coincidence time window. But, for a clinical PET

scanner, the minimum coincidence time window is limited

by the ring diameter to about 4 ns. On the other hand, by

use of TOF information, the coincidence events detected

outside an object can be identified as random coincidence

events. Therefore, TOF information has random coinci-

dence reduction capability beyond the hardware coinci-

dence timing window [15]. The intrinsic random

coincidences can be reduced in the same way, as shown in

Fig. 2. The reduction performance of intrinsic random

coincidences within the object is defined as follows:

TOF reduction rate ¼ Dring � Dobject

Dring

; ð1Þ

where Dring is the ring diameter and Dobject is the object

diameter. Therefore, the reduction performance of the

TOF-based reduction method depends on the size of the

object. Because the coincidence events detected outside an

object can be identified as random coincidence events. In

particular, we think that the TOF-based reduction method

is suitable for in-beam PET, because the activity distribu-

tion is confined to a localized area in the body.

2.3 MC-based reduction method

An intrinsic true coincidence is a rare event for a narrow

energy window [7], because the maximum energy of the c-

rays is 307 keV. On the other hand, intrinsic random

coincidences cannot be prevented completely by the nar-

row energy window. If the energy window is set wide, both

intrinsic random coincidences and intrinsic true coinci-

dences are detected as multiple coincidences. The multiple-

coincidence events can serve as a guide to the identification

of the intrinsic coincidences at the low activity level.

Figure 3 shows the procedure for the MC-based reduction

method. In the first step, coincidence events within the

wide energy window are measured. After rejection of the

multiple-coincidence events from all coincidence events,

the remaining coincidence events are discriminated within

the narrow energy window again to reduce the number of

intrinsic true coincidences. With the wide energy window,

the number of coincidence events is increased drastically.

Fig. 2 Illustration of TOF

measurement of the random

coincidence event. Events

detected for TOF bins outside

the object can be identified as

random coincidence events. It

should be noted that the random

coincidence rates of each TOF

bin are equal

Reduction method for intrinsic random coincidence events

However, at a low activity level, the PET scanner has

sufficient detectability with the wide energy window.

The MC-based reduction method can be implemented if

the list-mode data include energy information. Acquired

list-mode data reject or allow all multiple coincidences,

depending on the data acquisition system of the PET

scanners. In the data acquisition, the energy window is set

wide. After the data acquisition, acquired list-mode data

reject all multiple coincidences, and the conventional

energy window is applied.

2.4 Simulation setup

We analyzed the coincidence count rate of the 176Lu

intrinsic radioactivity and tested both methods for the

whole-body LSO-PET scanner using the Geant4 Appli-

cation for Tomographic Emission (GATE) [16, 17]

simulation. GATE does not support treatment of the

intrinsic radioactivity. However, the intrinsic radioactiv-

ity in the LSO has been simulated successfully as a176Lu ion source with an activity of 276.75 Bq/cm3 [7].

McIntosh et al. [18] reported that simulation data from

GATE agreed with experimental data for the Siemens

Inveon PET detector modules. We evaluated validation

of the GATE simulation that compared a model of 176Lu

intrinsic radioactivity to measured data for our small

prototype PET scanner [10, 11].

As shown in Fig. 4, a simulated whole-body LSO-PET

scanner was designed with four detector rings of 48

detector blocks. Each detector consisted of a 16 9 16 array

of 2.9 9 2.9 9 20.0 mm3 LSO crystals. Table 1 lists the

basic specifications of the scanner. The intrinsic count rate

was calculated by recording of the number of prompt and

delayed coincidences. However, a subtraction-based ran-

dom correction may not give statistically meaningful

events for a random count rate estimated from the delayed

coincidences, which have a sparse distribution for a limited

measurement time. On the other hand, if emission data do

not depend on intrinsic random coincidences at a very low

activity level, we think that intrinsic random coincidences

can be measured over a long time before the emission data

Fig. 3 Procedure for the MC-

based reduction method. For

conventional PET scanners,

coincidence events are limited

by the narrow energy window.

On the other hand, for the MC-

based reduction method, in the

first step, coincidence events

within the wide energy window

are measured. After rejection of

the multiple-coincidence events

from all coincidence events, the

remaining coincidence events

are discriminated within the

narrow energy window again to

reduce the number of intrinsic

true coincidences

Fig. 4 Schematic geometry of the whole-body LSO-PET scanner

E. Yoshida et al.

measurement. However, the calculation time is just not

realistic for obtaining statistically meaningful events.

Therefore, in this study, we used only prompt coincidences.

The intrinsic true and random coincidences were cal-

culated with several energy windows. Also, for evaluation

of the TOF- and MC-based reduction methods, the imaging

target was a set of cylindrical polyethylene phantoms,

without activity, with diameters of 10 and 20 cm (both

were 20 cm long). In this case, the lines of response

(LORs) outside the imaging target were rejected before the

reduction process because these LORs cannot contribute to

the imaging quality. For the MC-based reduction method,

the energy window was set at 100–1000 keV. Also, we

evaluated the reduction performance of the TOF- and MC-

based reduction methods for several scanner configurations

(varying timing resolution, axial field of view (FOV), and

crystal thickness). The reduction performance was calcu-

lated as follows:

Reduction rate ¼ Ro � Rp

Ro

; ð2Þ

where Ro and Rp are the random count rate without the

reduction method and the random count rate of the devel-

oped method, respectively. Each measurement time was

10 s. (The calculation time was about 10 h with a 2.8 GHz

Xeon Processor.)

To evaluate the effective count rate for practical use, we

calculated the noise equivalent count rate (NECR) of this

PET scanner as follows:

NECR ¼ T2

T þ Sþ k � R ; ð3Þ

where T, S, and R are the true, scatter, and random count

rates, respectively. The factor k is the fraction of the pro-

jection occupied by the cylindrical phantom. Because the

random count rate was determined directly from the sim-

ulation data, there was no factor of 2 in front of R, as would

be the case from error propagation considerations when a

delayed coincidence window is used. The NECR test uti-

lized a solid polyethylene cylinder phantom (70 cm long

and 20 cm in diameter) with a 70-cm line source at 4 cm

off-axis. The phantom was based on the NEMA NU-2 2001

standard [19]. The phantom was placed in the center of the

FOV, and the acquisition time was 10 s.

2.5 Imaging simulation

Images of intrinsic random coincidence events were gen-

erated for several FOVs by use of random coincidence

reduction methods. The measurement time was 600 s. (The

calculation time was about 20 days with the 2.8 GHz Xeon

Processor.) The 2D ML-EM algorithm with a matrix size of

200 9 200 9 48 was applied to the data rebinned by the

single-slice rebinning method [20]. The voxel size was

4 9 4 9 4 mm3. An imaging quality test was calculated

by uses of four spherical sources with 3-cm diameter.

Source activities were 100, 250, 500, and 1000 Bq. The

FOV was limited to 20 cm in diameter. Normalization was

applied, but a scatter correction and attenuation correction

were not applied to the data because we used the ideal

phantom without the scatter and attenuation defined only

for activity. Also, no random correction was applied to the

data because the sinogram of delayed coincidences had too

few counts. The contrast-to-noise ratio (CNR) was calcu-

lated for each source as follows:

CNR ¼ SROI � Sbackgroundffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

r2ROI þ r2

background

� �

=2

r ð4Þ

where SROI and rROI are the mean signal and standard

deviation of each weak source, and Sbackground and

rbackground are the mean signal and standard deviation of

the background data, respectively.

3 Results

3.1 Evaluation of intrinsic coincidence events

For validation of the GATE simulation, Fig. 5 shows

simulated and measured energy spectra from 176Lu intrin-

sic radioactivity for the small prototype PET scanner. The

simulated energy spectrum was obtained with the

0–1000 keV energy window. There was a good agreement

between the results with the simulated model and the

measurements. This energy spectrum showed photopeaks

of 88, 202, and 307 keV. Most of the 88-keV c-rays

seemed to be detected by the detector that detected the bparticles. The peak at 650 keV was the sum of the peaks

for the three c-rays and the b particles.

Figure 6 shows the simulated energy spectrum with the

intrinsic coincidence events from the 176Lu intrinsic radio-

activity and 511 keV annihilation photons (back-to-back

Table 1 Basic specifications of the whole-body LSO-PET scanner

Crystal material LSO

Crystal size 2.9 9 2.9 9 20 mm3

Number of crystals 16 9 16 (per detector)

Number of rings 64

Ring diameter 80 cm

Axial FOV 19.2 cm

Time resolution 500 ps

Energy resolution 15 %

Coincidence time window 4.5 ns

Energy window 425–650 keV

Reduction method for intrinsic random coincidence events

annihilation photons) for the whole-body LSO-PET scanner.

The sum peak at 650 keV as shown in Fig. 5 was rejected by

coincidence measurement. The b particles had a very broad

distribution. Also, this energy spectrum showed three peaks

that corresponded to the photopeaks of 88, 202, and 307 keV.

For coincidence measurement, most events of the summed

peak at 650 keV were rejected. Also, the 425 keV LLD was

suitable, but the 650 keV ULD was too large for the 15 %

energy resolution.

Figure 7a and b show the intrinsic true and random

count rates for the LLD and the ULD, respectively. The

ULD of Fig. 7a and the LLD of Fig. 7b were 600 and

425 keV, respectively. The intrinsic true coincidence rate

tended to depend on only the LLD, but the intrinsic random

coincidence rate depended on both LLD and ULD. The

intrinsic true coincidence could be ignored with the

375 keV LLD. Our prototype system’s energy window of

400–600 keV completely included the photopeak.

However, it is recommended that all possible intrinsic

coincidences be prevented when LSO is used. Therefore,

the energy window was selected as 425–575 keV by cut-

ting of 25 keV from both the LLD and ULD. The count

rate of the photopeak with the energy window of

425–575 keV decreased by only 3 % against that with the

energy window of 400–600 keV. In this energy window,

the 511 keV annihilation photons could be detected ade-

quately, and the intrinsic random coincidence rate was 226

cps.

3.2 Evaluation of TOF- and MC-based reduction

methods

Figure 8 shows the intrinsic random count rates for the

TOF- and MC-based reduction methods for the 10- and

20-cm-diameter cylinder phantoms without activity. The

coincidence timing window was 4.5 ns. The intrinsic ran-

dom coincidences were counted only as LORs through the

phantom. After selection of the narrow energy window for

the 15 % energy resolution, the intrinsic random count rate

with the energy window of 425–575 keV was 56 cps for

the 20-cm-diameter cylinder phantom. By using the TOF-

and MC-based reduction methods separately, we could

reduce the intrinsic random count rate by 77 and 30 %,

respectively. Also, the intrinsic random count rate could be

reduced by 84 % when the TOF?MC reduction method

was applied. Figure 9 shows reduction rates of the TOF-

and MC-based reduction methods, separately and com-

bined, as a function of the diameter of the cylinder phan-

tom for several timing resolutions. Figure 10 shows

reduction rates of TOF- and MC-based reduction methods,

separately and combined, for the 20-cm-diameter cylinder

phantom as a function of the number of detector rings for

several crystal thicknesses. The random coincidence

reduction performance of the TOF-based reduction method

Fig. 5 Simulated and measured energy spectra from 176Lu intrinsic

radioactivity for the small prototype PET scanner. Measured energy

spectrum was obtained by our small prototype PET scanner with 16

detectors consisting of a 14 9 14 9 4 array of 2.9 9 2.9 9 5.0 mm3

LGSO crystals. Measurement time was 1 h

Fig. 6 Simulated energy spectra with intrinsic coincidence events from a 176Lu intrinsic radioactivity and b 511-keV annihilation photons for

the whole-body LSO-PET scanner

E. Yoshida et al.

depends only on the diameter of the cylinder phantom. On

the other hand, the random coincidence reduction perfor-

mance of the MC-based reduction method depends on the

number of the LSO scintillator crystals.

Figure 11 shows the random fraction with use of the

TOF- and MC-based reduction methods, separately and

combined, for the NEMA cylinder phantom. At 50 kBq,

the true coincidence rate was about 60 cps, and the random

fraction was 10 % with the TOF?MC reduction methods.

Figure 12 shows the NECR and the NECR gain for the

TOF- and MC-based reduction methods, separately and

combined, for the NEMA cylinder phantom. At lower

activity, the NECR gain was increased with the TOF-based

and TOF?MC reduction methods.

3.3 Imaging study

Figure 13a shows reconstructed images of intrinsic random

coincidences for the 20-cm FOV with use of the random

coincidence reduction methods. These images were sum-

med for two centered slices. In background images, the

intrinsic random count had the same tendency as in Fig. 8.

The TOF?MC methods could provide the cleanest image.

The TOF- and MC-based reduction methods were not

observed to have any characteristic distribution.

Figure 13b shows reconstructed images of the phantom

with four weak sources for the random coincidence

reduction methods. The image obtained identified each

sphere for all situations. However, for the results of

425–650 keV, background from the intrinsic random

coincidences reduced the visual contrast. Table 2 lists

CNRs for weak-source phantom images. There was an

improvement in CNR for all sources for all three methods.

The TOF?MC method provided the highest CNR.

4 Discussion and conclusion

The intrinsic random coincidences depended on the energy

window. The intrinsic random coincidences had a broad

energy distribution and could not be prevented completely.

To prevent intrinsic random coincidences, using the narrow

Fig. 7 Intrinsic true and random count rates as a function of a LLD (ULD was 600 keV) and b ULD (LLD was 425 keV)

Fig. 8 Intrinsic random count rates with use of TOF- and MC-based reduction methods for cylinder phantoms with diameters of a 10 and

b 20 cm. The coincidence timing window was 4.5 ns for all cases

Reduction method for intrinsic random coincidence events

energy window that does not reduce the sensitivity is the

simplest method. After selection of the narrow energy

window (425–575 keV), the intrinsic random coincidence

rate could be reduced by about 70 % compared to the

energy window of 425–650 keV.

Using the MC-based reduction method, we could

reduce the intrinsic random coincidence rate by 30 %

compared to the energy window of 425–575 keV. The

intrinsic random coincidence rate with the energy window

of 100–1000 keV was 165 times larger than that with the

energy window of 425–575 keV. This is not a problem,

because the newest PET scanners have sufficient detect-

ability for the energy window of 100–1000 keV. How-

ever, NECR improvement of the MC-based reduction

method was limited. The MC-based reduction method can

be used for a conventional non-TOF-PET scanner. Also,

the performance of the MC-based reduction method

depended on the number of LSO scintillator crystals, as

shown in Fig. 10. As the axial FOV was extended and the

crystal thickness was large, the performance of the MC-

based reduction method was high. When the axial FOV is

extended for an entire whole-body PET scanner [21, 22],

for clinical studies it may not be possible to ignore the

intrinsic random coincidence for these LSO-PET scanners.

By using the TOF-based reduction method, we could

reduce the intrinsic random coincidence rate by 77 %

compared to the energy window of 425–575 keV. Also, the

NECR of the TOF-based reduction method was clearly

improved. The TOF-based reduction method had a higher

reduction capability than did the MC-based reduction

method. As shown in Fig. 9, the random coincidence

reduction performance did not depend on the timing reso-

lution. This was because the intrinsic random coincidences

had no true annihilation position on the LOR, and they

were spread out uniformly across the FOV. When the PET

scanner had a sufficient number of TOF bins, this reduction

performance depended on the occupancy of the imaging

target in the ring diameter. For the 10-cm-diameter cylin-

der phantom, the intrinsic random coincidence rate could

be ignored. However, the reduction performance of the

TOF-based reduction method depended on the size of the

object because the coincidence events detected outside an

object can be identified as random coincidence events. As

the diameter of the phantom was large, the reduction per-

formance was degraded. On the other hand, TOF infor-

mation can improve the imaging quality for well-known

enhancement of true coincidence. This enhancement per-

formance depends on the timing resolution. Crespo et al.

Fig. 9 Reduction rates of TOF- and MC-based reduction methods as a function of the diameter of the cylinder phantom for several timing

resolutions. The ideal line was defined by Eq. (1)

E. Yoshida et al.

[9] reported the feasibility of in-beam TOF-PET for

obtaining highly precise images.

As shown in Table 2, the images obtained had better

CNRs for all three reduction methods. As the activity of the

source was low, the CNR improvement was high for all

three reduction methods. Especially, the TOF?MC

reduction method had the highest CNR for all activities. On

the other hand, the difference between the TOF-based

reduction method and the MC reduction method was small.

This was because the background of the MC reduction

method that remained was about three times that of the

TOF-based reduction method for the whole FOV, but the

difference for the background in the region of the source

was limited.

Random and scatter corrections were not applied to the

data in this work. Simple subtraction-based random and

scatter corrections may not give statistically meaningful

events in a sparse distribution for a limited measurement

time. As a result, subtraction-based random and scatter

corrections may increase the statistical error.

For our 11C beam irradiation study, the average true

coincidence rate was assumed to be about 36 cps [10]. On

the other hand, the intrinsic random coincidence rate has

been calculated as 9 cps for the 20-cm-diameter cylinder

phantom with use of the TOF?MC reduction method. We

think that the intrinsic random coincidence can be ignored

for in-beam PET when the TOF?MC reduction method is

used because the activity distribution of in-beam PET is

confined to a localized area in the body.

In summary, we developed a reduction method for the

intrinsic random coincidence rate based on multiple-coin-

cidence information. We evaluated the reduction perfor-

mance using the developed MC-based reduction method

and the TOF-based reduction method, separately and in

Fig. 10 Reduction rates of TOF- and MC-based reduction methods as a function of the number of detector rings. There were three crystal

thicknesses, and the 20-cm-diameter cylinder phantom was used

Fig. 11 Random fraction with use of TOF- and MC-based reduction

methods for the NEMA cylinder phantom

Reduction method for intrinsic random coincidence events

combination. The developed method provided a 30 %

reduction in the intrinsic random coincidence rate, but the

contribution of the NECR was limited. On the other hand,

the TOF-based reduction method showed good promise for

reducing the intrinsic random coincidence rate, but the

level of the reduction for the TOF-based reduction method

depended on the size of the object. When the developed

method and the TOF-based reduction method were com-

bined, the reduction performance of the intrinsic random

coincidence rate was higher than that with use of only the

TOF-based reduction method.

Acknowledgments This work was supported by Grants-in-Aid for

Scientists Research of Kakenhi (22240065, 25242052, 24601019).

Conflict of interest The authors declare that they have no conflict

of interest.

Fig. 12 Results obtained with the TOF- and MC-based reduction methods for the NEMA cylinder phantom: a NECR and b NECR gain

Fig. 13 Reconstructed images of a the intrinsic random coincidence

events and b the phantom with four weak sources for the 20-cm FOV.

Background images are scaled for maximum intensity of the

425–575 keV energy window. Phantom images are scaled for

maximum intensity of the 250-Bq source

Table 2 CNRs for weak-source phantom images

ROI

activity

(Bq)

CNR

425–650 keV 425–575 keV MC TOF TOF?MC

100 1.45 1.64 1.76 1.89 1.95

250 2.01 2.62 3.07 3.19 3.22

500 3.78 4.36 4.40 4.52 4.55

1000 4.71 4.94 5.34 5.38 5.50

E. Yoshida et al.

References

1. Melcher CL, Schweitzer JS. Cerium-doped lutetium oxyorthosi-

licate: a fast, efficient new scintillator. IEEE Trans Nucl Sci.

1992;39:502–5.

2. Watson CC, Casey ME, Eriksson L, Mulnix T, Adams D,

Bendriem B. NEMA NU 2 performance tests for scanners with

intrinsic radioactivity. J Nucl Med. 2004;45:822–6.

3. Eriksson L, Watson CC, Wienhard K, Eriksson M, Casey ME,

Knoess C, et al. The ECAT HRRT: an example of NEMA scatter

estimation issues for LSO-based PET systems. IEEE Trans Nucl

Sci. 2005;52:90–4.

4. Yamamoto S, Horii H, Hurutani M, Matsumoto K, Senda M.

Investigation of single, random, and true counts from natural

radioactivity in LSO-based clinical PET. Ann Nucl Med.

2005;19:109–14.

5. Adonai N, Nguyen KN, Walsh J, Iyer M, Toyokuni T, et al. Ex

vivo cell labeling with 64Cu-pyruvaldehyde-bis(N4-methylthi-

osemicarbazone) for imaging cell trafficking in mice with posi-

tron-emission tomography. Proc Natl Acad Sci USA.

2002;99:3030–5.

6. Sundaresan G, Yazaki PJ, Shively JE, Finn RD, Larson SM,

Raubitschek AA, et al. 124I-labeled engineered anti-CEA mini-

bodies and diabodies allow high-contrast, antigen-specific small-

animal PET imaging of xenografts in athymic mice. J Nucl Med.

2003;44:1962–9.

7. Goertzen AL, Suk JY, Thompson CJ. Imaging of weak-source

distributions in LSO-based small-animal PET scanners. J Nucl

Med. 2007;48:1692–8.

8. Enghardt W. Charged hadron tumor therapy monitoring by means

of PET. Nuclear Inst Methods Phys Res A. 2004;525:284–8.

9. Crespo P, Shakirin G, Fiedler F, Enghardt W, Wagner A. Direct

time-of-flight for quantitative, real-time in-beam PET: a concept

and feasibility study. Phys Med Biol. 2007;52:6795–811.

10. Yamaya T, Yoshida E, Inaniwa T, Sato S, Nakajima Y, Wakizaka

H, et al. Development of a small prototype for a proof-of-concept

of OpenPET imaging. Phys Med Biol. 2011;56:1123–37.

11. Yoshida E, Kinouchi S, Tashima H, Nishikido F, Inadama N,

Murayama H, et al. System design of a small OpenPET prototype

with 4-layer DOI detectors. Radiol Phys Technol. 2012;5:92–7.

12. Surti S, Kuhn A, Werner ME, Perkins AE, Kolthammer J, Karp

JS. Performance of Philips Gemini TF PET/CT scanner with

special consideration for its time-of-flight imaging capabilities.

J Nucl Med. 2007;48:471–80.

13. Daube-Witherspoon ME, Surti S, Perkins A, Kyba CCM, Wiener

R, Werner ME, et al. The imaging performance of a LaBr 3-based

PET scanner. Phys Med Biol. 2009;55:45–64.

14. Jakoby BW, Bercier Y, Conti M, Casey ME, Bendriem B,

Townsend DW. Physical and clinical performance of the mCT

time-of-flight PET/CT scanner. Phys Med Biol.

2011;56:2375–89.

15. Conti M. Effect of randoms on signal-to-noise ratio in TOF PET.

IEEE Trans Nucl Sci. 2006;53:1188–93.

16. Jan S, Santin G, Strul D, Staelens S, Assie K, Autret D, et al.

GATE: a simulation toolkit for PET and SPECT. Phys Med Biol.

2004;49:4543–61.

17. Jan S, Benoit D, Becheva E, Carlier T, Cassol F, Descourt P, et al.

GATE V6: a major enhancement of the GATE simulation plat-

form enabling modeling of CT and radiotherapy. Phys Med Biol.

2011;56:881–901.

18. McIntosh B, Stout DB, Goertzen AL. Validation of a GATE

Model of 176Lu intrinsic radioactivity in LSO PET systems. IEEE

Trans Nucl Sci. 2011;58:682–6.

19. Performance measurements of positron emission tomographs.

Nat. Elect. Manufact. Assoc., Rosslyn, VA, NEMA Standards

Pub. NU 2-2001, 2001.

20. Daube-Witherspoon ME, Muehllehner G. Treatment of axial data

in three dimensional PET. J Nucl Med. 1987;28:1717–24.

21. Couceiro M, Blanco A, Ferreira F, Ferreira Marques R, Fonte P,

Lopes L. RPC-PET: status and perspectives. Nuclear Inst Meth-

ods Phys Res A. 2007;580:915–8.

22. Eriksson L, Conti M, Melcher CL, Townsend DW, Eriksson M,

Rothfuss H, et al. Towards sub-minute PET examination times.

IEEE Trans Nucl Sci. 2011;58:76–81.

Reduction method for intrinsic random coincidence events