Can large-area avalanche photodiodes be used for a clinical PET/MRI block detector?

Abstract

We are investigating a high resolution, Angerlogic based PET block detector using large-area avalanche photodiodes (LAAPD). Such block detectors will be used in a simultaneous PET/MRI clinical scanner. Using a Monte-Carlo simulation tool, we systemically optimized the detector design taking into account the following factors: the dimensions of the scintillation crystal and the optical diffuser, the surface finish of crystals, the layout of APD arrays, and the signal-to-noise (SNR) of the system. Based on the simulation results, a block detector prototype was built with an 8×8 LYSO crystal array (crystal pitch size: 2.75 × 3.00 × 20 mm³) coupled to four APDs. The performance of the block detector with regard to the crystal resolving ability and the energy resolution is reported.

Full text

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2008 IEEE Nuclear Science Symposium Conference RecordM10-68
Can large-area avalanche photodiodes be used for a clinical
PETIMRI block detector?
Hao Peng., P. D. Olcott., Virginia Spanoudaki., Craig S. Levin
Fig. 1: (a) Illustration of the proposed PET/MRI system. Each PET block
detector module consists of LSO scintillation crystal, optical diffuser, APD
array and front-end circuits. (b) Diagram ofthe proposed Anger-logic detector
module and 2x2 large-area, high gain APD arrays. A, B, C, D represent the
signals offour APDs within the array.
B. Anger-logicposition scheme
Assuming that each crystal within an array has the same
light spread by neglecting the light compression effect for
comer crystals, the Anger logic positioning ability was
analytically studied using the model proposed by [7].
(1)
(A+(')-(B+D)
(A+B+C+D)
(2)
X(A+B)-(C+D)
(A+B+C+D)
2x2 APD array
¢J ( ) = __ 1_ -«n-J..l)/2CT)2
x na..J2ie
Optical diffuser
(b)
(a)
II.
METHODS
DETECT2000 [5], a light tracking simulation tool, was
used for the study. The refractive index was set to be 1.82 for
LSO and 1.52 for both the optical diffuser and the entry
window of APD [6]. The total attenuation length of LSO was
set to be 138 mm [6]. The simulation consists ofthe following
steps:
A. Lightpoint spreadfunction (LPSF)
The light point spread function (LPSF) was studied with a
single crystal on the top of an optical diffuser, for a given
configuration in terms of crystal size, optical diffuser height,
as well as surface finish. The light spread was analyzed
quantitatively by fitting with the Gaussian distribution on the
top ofa linear background:
LPSF =Ae-(xIB)2 +c
Abstract-We are investigating a high resolution, Anger-
logic based PET block detector using large-area avalanche
photodiodes (LAAPD). Such block detectors will be used in
a simultaneous PET/MRI clinical scanner. Using a Monte-
Carlo simulation tool, we systemically optimized the
detector design taking into account the following factors:
the dimensions of the scintillation crystal and the optical
diffuser, the surface finish of crystals, the layout of APD
arrays, and the signal-to-noise (SNR) of the system. Based
on the simulation results, a block detector prototype was
built with an 8x8 LYSO crystal array (crystal pitch size:
2.75 x 3.00 x 20 mm3) coupled to four APDs. The
performance of the block detector with regard to the
crystal resolving ability and the energy resolution is
reported.
Manuscript received November 18, 2008. This work was supported by GE
healthcare
Hao Peng, P D. Olcott, Virginia Spanoudaki, C. S. Levin are with the
Department of Radiology and Molecular Imaging
University,Stanford,CA. (telephone:
haopeng@2stanford.edu and cslevin@2stanford.edu).
Program,Stanford
e-mail 650-736-7093,
I. INTRODUCTION
The integration of PET and MRI has caused intensive
research interest until recently, which is able to correlate the
physiological information from PET with the anatomical
information from MRI [1-2]. We are developing a high
resolution, Anger-logic based PET block detector using large
area, high gain avalanche photodetectors (APDs) (RMD, Inc.,
USA), which exhibit a number of the advantages over the
PMT-based detector, such as such as compact size, high
quantum efficiency and magnetic immunity. In addition, ifthe
Anger logic positioning scheme can be successfully applied to
APD block detectors, the total number of electronic channels
for the proposed PET system will be reduced by a factor of
four [3]. The detectors will be used inside a GE 1.5T MRI
scanner for brain imaging but are able to be scaled up towards
the whole-body applications. The detector module is designed
to operate outside RF coils but inside gradient coils, with an
inner radius of approximately 36 cm (Fig.1). The electro-
optical coupling scheme through VCSELs (Vertical-cavity
surface-emitting laser) [4], was deployed aiming to minimize
the interactions between PET and MRI components. The
crystal resolving ability ofthe block detector is ofour primary
concern in this work. First, the Monte-Carlo simulation was
used to optimize the detector design with respect to several
factors: the size of crystal and optical diffuser, the surface
finish, the dead area of APDs and the SNR of the system.
Based on the simulation, a block detector prototype was built
and its preliminary performance was evaluated.
978-1-4244-2715-4/08/$25.00 ©2008 IEEE
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noisesplial =Var(S) =E(M)2 (iy 2 +(iM 2E(Y)F
The total noise of the detector is then represented by the
addition ofspatial noise and shot noise:
where M is the gain of APD, Y is the number of e-h pairs
directly generated by the incident visible photons and S is the
overall signal to be detected. Assuming that the variation of
photons follows the Poisson statistics, the expected mean and
the variance ofthe signal are:
where
(J'=,JNPq ,
p = N+x / N,
q = 1- P
<Px represents the normal approximation of the binomial
distribution along one dimension, as shown in Fig.2. The
LPSF kernel obtained above was convolved with each crystal
pitch within the array to obtain p and q (the light sharing ratio
fortwo APDs). The N
photoelectrons)waschosen
retrospectively estimated from the energy resolution of LSO-
APD detectors (-10-12%). N+xrepresents the number of the
photoelectron being detected by one ofthe two detectors.
(the
to
effective
be
number
which
of
600,was
E(8)=E(M)E(Y)
(4)
noiSetolal2 = noise!)palial2+ishol2
(5)
where ishol is resulted from both the surface leakage current
and bulk leakage current. Y was obtained from the simulation
output. The quantum efficiency of APD was set to be 600/0.
Based on our previous characterization of the individual APD
device [9], the APD's gain M was set to be 1000 and the
excess noise factor F was set to be 2.5. B is the frequency
bandwidth of the APDs and front-end electronics obtained
from SPICE simulation. The voltage signal resulted from ishot
was 0.0391 Vnos' The Anger logic position information
without and with noise was studied. In addition, for a corner
crystal, the SNR ofthe detector is defined as the ratio between
the highest signal among four APDs and the total noise. The
performance of Anger logic
investigated.
with different SNRs was
E. Preliminary experimental results:
A prototype LYSO-APD block detector was built (Fig.3).
The outputs of four APDs were connected to charge sensitive
preamplifier (Cremat) and Gaussian shaping amplifiers. The
sum of four signals was used as the trigger. The National
Instrument data acquisition system was used to detect the peak
signals of four channels, which were subsequently used in the
Anger logic positioning algorithm.
~
01I
!
. ~ !
";ft
Di:j
't::
'·f·
• -I -.
I:;:
6._
1i
D3 = (PVR1+PVR2)/2
!
;>t
.t'
.j.
..
:s
.-
.a
~
a..
i
.tI
Ci
~
••QZ15
"
!
:t
!
:!
t'
"
.'
"
::.. '
~ l'
Oclll
I
t!
~
: ~
~ ;
,,'
l:
!:
:~
f ~
: \
" ;:l:
"
'j
"
'i'
'"
0
z
Fig.2: The calculated position distribution for a Ix8 crystal array. The crystal
width is 2.75 mm and the height is 20 mm. The gap between crystals is 0.1
mm. The height of the optical diffuser is 8 mm. 01 and 02 represent the
distances indicated.
03 is the average peak-to-valley ratio (PVR) for two
crystals at the edge. Minimum 0 I but maximum 02 and 03 are desired.
c. The effects ofAPD's dead area andlight compression
A fullLSO array (8x8) was chosen based on the
optimization from two previous steps (the crystal size of
2.75x2.75x20 mm3and the inter-crystal gap of 0.1 mm). We
iterated the simulation searching for the optimum conditions
with respect to the optical diffuser's size and the dead area in-
between APDs. Within each iteration, 15,000 photons were
generated at a fixed position inside the crystal pitch (6.0 mm
from the entry face, which is the mean height based on
exponential attenuation of 51 IkeV photons). The optimization
criterion is that the configuration should result in the
maximum separation (X2-XI) (X is the spatial position derived
from Anger logic) between two crystals (the corner crystal and
the adjacent crystal along the diagonal line). As to be seen in
the Results section, even the optimized design from all the
iterations could not provide satisfactory crystal separation. A
concept of dual layer optical diffuser design was developed to
address the light compression problem.
0.2
X position from Anger
D. Noise model
Two sources of noise were incorporated into our model:
spatial noise due to statistics of light photon generation and
APD's shot noise due to leakage current, which both degrade
the performance ofAnger logic scheme. The noise model used
in our simulation was described below [8-9]:
M
S = L ~
;=1
(3)
Fig. 3: (Left) the block detector prototype comprising LYSO, light diffuser,
2x2 array of I cm2area, large area, high gain APOs, and highly compact
custom readout electronics. (Right) the APO-block detector prototype test
board. In the test board, four APO detectors (RMO, Inc) are coupled to
commercially available eremat charge sensitive preamplifiers. The dead areas
ofthe APOs are located in the central region rather than the edge ofthe array.
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III.
RESULTS
A. Crystal size
Based on the simulation results, an 8x8 LYSO array with
the crystal size of2.75 x 3.00 x 20.0 mm3was selected, which
provides the maximum D3based on the methods described in
Fig. 2. It should be noted that the crystal's width (2.75 mm)
can be slightly adjusted while not significantly affecting the
rest of simulation, as the light spread is mainly caused by the
optical diffuser in our design. The crystal height of 20 mm
was chosen in order to assure high detector's intrinsic
sensitivity for 511 keV photons.
B. Suiface treatment
The dependency of crystal separation (characterized by D3,
shown in Fig.2) on surface finish conditions and the height of
optical diffuser is shown in Fig.4. The METAL surface finish
provides the best crystal separation when the optical diffuser
of 6-9 mm height is used. This can be attributed to its LPSF
having higher light collection efficiency and smaller light
spread, compared to other surface conditions.
(a)
Light
diffuser
(b)
35.0
30.0
25.0
-.-PAINT
-"'-METAL
____ POLISH
~GROUND
Diffusor height (mm)
10
(X_offset =1.4 mm V_offset =1.8 mm)
(c)
-4- 24 5 mm -4- 240 mm -6-23 5 mm
-y-23.0 mm -+--22.5 mm-+- 220 mm
~ ~ ~ / ~ ; ~
J
0.01
~ /\ .
B.
0.02
.y
~ i
N
,..
1\;
W J
,j
't
Iteration number
(d)
Fig. 4: D3 (average peak-to-valley ratio) as a function of surface treatment
and optical diffuser height. The surface finishes used in the simulation were
GROUND (rough surface), PAINT (polish surface and diffusive reflective
coating, reflective coefficient (RC): 98%), POLISH (mechanically polished
and only air gap), METAL (mechanically polished and specular reflective
materials, RC: 96%).
C. APD's layout anddiffuser design
The dependence of crystal separation (characterized by X2-
Xl, referred to Method section B) on APD's layout and the
height of optical diffuser are shown in Fig.5. Diffuser width
varies from 22.0 mm to 24.5 mm (step size: 0.5 mm). Within
11 iterations for a given diffuser width, the increase of the
iteration index corresponds to the diffuser height increasing
from 5 to
10 mm. The optimization provides the best
configuration for both APD's layout and the size ofdiffuser.
By merely optimizing the configuration of APD's layout
and the size ofthe optical diffuser, no good crystal separation
could be achieved. As a result, a slotted light guide was
deployed by providing an optical barrier for the corner and
edge crystals.
- o _ ~ 8
..078
-07fii
. . ( ) 7 ~
-072-07 -OBI·051 -ou
·OU-05
Xfrom Anger logic
Fig. 5: (8) Illustration of the optimization parameters, w, h, and X_offset
(Y_offset is not shown). The width of the light diffuser is chosen to be larger
than that of the individual crystal pitch to investigate degree of light
compression near the edge. (b) (X2-Xl) (see Fig. 2) as a function of the
separation between APDs along two dimensions. (c) For a given diffuser
height and width, the maximum value of(X2-Xl) obtained from simulations of
the configuration shown in Fig. 5a was plotted versus iteration number. For a
given diffuser width, the diffuser's height is adjusted from 5 to 10 mm at a
step size of 0.5 mm and this corresponds to ]1 iterations. (d) Even under the
condition that provides the maximum separation (width: 24.0 mm and height:
8-9 mm), the two edge diagonal crystals are stil1 not resolved, due to a light
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spread "compression" effect occurring at the comer and edges of the light
diffuser.
D. Noise model
With all 64 crystals in existence (8x8) array, the flood maps
without and with noise model were studied and shown in Fig.6.
Only a quadrant of the map was shown due to the symmetry.
The noise degrades both the dynamic range and the distances
in-between crystals. Alternatively, the impact of different
SNRs on the crystal separation was shown. The resolving
ability significantly degrades as the SNR decreases. The
results show that a SNR around 30 is required to resolve all 64
crystals.
Fig. 8, a comer crystal was chosen for the SNR calculation.
The energy spectrums oftwo APDs were studied to obtain the
signal and noise respectively. The SNR of 30.9 is in a good
agreement with the simulation result shown in Fig. 6.
For each crystal after the segmentation, the crystal gated
energy spectrum was derived to evaluate the uniformity ofthe
block detector as shown in Fig. 9(a)-(c). It is noticed that the
edge and comer crystals have lower sensitivity, lower gain and
poorer energy resolution, compared to the crystals in the
central region. The reduction ofthe sensitivity is mainly due to
the fact that the incoming 511 keV photons are more likely to
escape from the edge crystals without being stopped by the
adjacent crystals, compared to the central crystals. The
O ~
OJ112
1,4
1.81.8
22224
Fig. 8: The crystal map was segmented and the SNR analysis was made for a
comer crystal. The energy spectrum gated corresponding to the comer crystal
for two APDs are shown. The 511 keY peak for APD A and the full-width-
half-maximum (FWHM) of the noise peak in the APD C were used to
characterize the SNR as dermed in the section II.D.
eo
x
SNR= 30.9
(b)
(a)
11
»••••
I'
a••
X
II•
X
Fig. 6: The simulated flood map for the optimized detector design. Surface
treatment (METAL). Each crystal has 600 events (511 keY) simulated and
each event generates 12,500 photons based on the true light yield of LYSO
crystal. The degradation ofthe flood histogram as scintillation detector pulse
SNR decreases is observed. (a) No noise. (b) SNR=50. (c) SNR=30. (d)
SNR=15. Refer to the section II.D for the definition ofSNR.
E. Experimental results
The slotted light guide diagram and the flood map of the
block detector are shown in Fig. 7.
!Optical barrier
reduction of the gain for the comer and edge crystals can be
attributed to reasons. First, as the slotted light guide was used,
the existing optical barrier prevents the output light from
getting across and hitting the detectors on the opposite side.
Therefore, the effective area seen by these crystals is smaller
than that seen by central crystals. Second, as the edge of the
light diffuser has a tapered shape, for those lights interacting
with the tapered edge, some of them will experience a light
loss through the total inertial reflection. The extent of such
light loss is proportional to the tapered angle. The global
energy spectrum for the block detector with the gain
normalization has an energy resolution of 16.5+/-0.4% for the
511 keY photopeak.
Fig. 7: (Left) The slotted, tapered light diffuser, which not only reduces the
light sharing for the edge crystal, but also avoids the light loss due to the
APD's dead area. (Right): The flood image of the 8x8 array. All 64 crystals
are clearly resolved.
The flood map was segmented and the region-of-interest
(ROJ) information for each crystal was stored. As shown in
(a)
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(b)
(c)
Xindex
Xindex
PVR: 2.61+/-0.50
~
(b)
Fig. 9: (a)-(c) The unifonnity ofthe sensitivity, gain and energy resolution for
64 crystals. (d) The global energy spectnun for the block detector with the
fitted results for both 511 keY and 1 275 MeV. The gain variation among
crystals has been nonnalized.
For the quantitative analysis ofthe crystal resolving ability,
the peak-to-valley ratio (PVR) results are shown in Fig. 10.
For the selected central row and column, the 1-0 profile was
obtained and fitted by the summation of multiple Gaussian
functions. The average PVR was 2.61+/-0.50 and 2.05+/-0.40,
respectively, which we expect might be further improved with
a more controlled process for the slotted light diffuser
assembly.
V. CONCLUSIONS
Using
optimized the detector design for the proposed PET block
detector, including the optical diffuser thickness, the surface
finish of crystals, the separation between APO arrays, and the
SNR of the system. The framework built in the model will
enable us to design the detectors for other applications as well.
For instance, the current design can be easily scaled down to a
preclinical PET system with even smaller crystal pitch, or be
scaled up to a whole-body clinical scanner. In addition, other
noveldetectorswithbetter
photomultiplier (SSPM), could also be used to replace APOs
for our project and to improve the detector performance.
An 8x8 array of 2.75x3.00x20 mm3LYSO crystals was
built and tested with a slotted light diffuser. The detector is
able to resolve all 64 crystals with satisfactory uniformity and
peak-to-valley ratio. The global energy resolution ofthe block
is 16.5+/-0.4% FWHM for the 511 keY photopeak.
Light output from scintillation crystals, Anger-logic light
sharing and the SNR of the photodetector are three critical
factors impacting the flood histogram crystal separation for a
block detector. The light output is mainly determined by the
properties of the scintillation material itself though it is also
affected by the aspect ratio ofcrystal and the surface treatment
to a certain extent. The optimum light sharing condition can be
realized through the use ofa slotted light diffuser at the cost of
system complexity. Once the light sharing is optimized, there
is also a threshold of SNR that the photodetector needs to
exceed for resolving crystals.
With the block detector prototype built, we are currently
working towards the evaluation of the coincidence time
resolution, coincidence point
incorporation ofdepth-of-interaction.
a Monte-Carlosimulation, wesystematically
SNRsuch as solid state
spread functionandthe
Fig. 10: (a) The flood map with two regions selected for PVR analysis. The
1D profile and the PVR results for the profiles corresponding to the horizontal
(b) and vertical regions (c) that were circled in (a).
1.275 MeV photopeak
Energy resolution:
8.8 +/- 0.2%
511 keV photopeak
Energy resolution:
16.5 +/- 0.4%
/
If"
(c)
(d)
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IV.
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