⇦Chinese Physics Letters, 2016, Vol. 33, No. 4, Article code 048701 Off-Axis Imaging in Keel-Edge Pinhole Single Photon Emission Computed Tomography System Based on Monte Carlo Simulation Su-Ying Li(李素莹)1**, Zhao-Heng Xie(谢肇恒)1**, Zhi-Yu Huang(黄智宇)1, Kun Yang(杨昆)2, Bai-Xuan Xu(徐白萱)3, Qiu-Shi Ren(任秋实)1 Affiliations 1Department of Biomedical Engineering, College of Engineering, Peking University, Beijing 100871 2Department of Control Technology and Instrumentation, College of Quality and Technical Supervision, Hebei University, Hebei 071002 3General Hospital of Chinese People's Liberation Army, Beijing 100039 Received 24 December 2015 **Corresponding author. Email: renqsh@coe.pku.edu.cn Citation Text: Li S Y, Xie Z H, Huang Z Y, Yang K and Xu B X et al 2016 Chin. Phys. Lett. 33 048701 Abstract Monte Carlo simulation is applied to investigate the off-axis effect in keel-edge pinhole single photon emission computed tomography imaging. Aiming at finding the effective field of view (FOV) for imaging, we simulate point source in off-axis imaging (0, 4, 8 and 12 mm from the central rotation axis) of different collimator designs (channel height with 1.38, 1 and 0.5 mm) with a fixed aperture diameter. Tradeoff curves of rms resolution and sensitivity are plotted to determine the effective FOV for different channel height pinhole collimators. The parameterized model can be further incorporated into image reconstruction algorithms, which compensates for the off-axis effect and is used as a reference for multi-pinhole design. DOI:10.1088/0256-307X/33/4/048701 PACS:87.57.-s, 87.57.uh, 87.57.cp © 2016 Chinese Physics Society Article Text Pinhole single photon emission computed tomography (SPECT) is one of the advanced imaging methods, which is increasingly used for high resolution radionuclide imaging of small animals. With the magnification effect, the pinhole collimator can yield higher resolution, surpassing the limitation of the detector's intrinsic spatial resolution.[1-5] However, the photons' penetration close to the edge of the pinhole broadens the tails of point spread functions (PSF) and degrades resolution, especially for high energy radionuclides.[6] Aiming at minimizing the penetration effect, a pinhole containing a channel called keel-edge pinhole has been investigated and used in SPECT imaging.[7-9] GEANT4 application for emission tomography (GATE), a Monte Carlo simulation platform based on GEANT4, is extensively used in nuclear medicine to address complex problems that are difficult to study by analytical ways. Recently, GATE simulation has been applied to model major geometrical parameters in keel-edge pinhole, including channel height, aperture diameter, source-to-pinhole distance and the angle of incidence. However, there are few studies dedicated to the off-axis effects of keel-edge collimator imaging with $^{99m}$Tc. Increasing the channel height can improve resolution in keel-edge pinhole, meanwhile, steeper decrease in sensitivity is observed during off-axis scanning. The decrease of spatial resolution does not scale linearly with the offset distance of the point source from central axis. Furthermore, the image in the axial direction dramatically blurred after reconstruction due to the incompleteness of projection data at the edge of field of view (FOV). As a result, image resolution and sensitivity varied with off-axis positions, leading to degradation of imaging characteristics at the edge of FOV. The tradeoff relationship between imaging characteristics for off-axis imaging and the size of effective FOV of keel-edge pinhole, however, have not yet been fully investigated by using GATE simulation. Our group has developed a keel-edge pinhole SPECT system based on a cadmium zinc telluride (CZT) semiconductor detector for small animal imaging. The pinhole small animal SPECT system, as shown in Fig. 1, contains the stationary CZT detector, a pinhole collimator and rotary stage. The pinhole collimator is made of tungsten alloy ($\rho=18.5$ g/cm$^{3}$), with 0.8 mm aperture diameter, 1.38 mm channel height, and 60$^{\circ}$ opening angle. It was placed at 200 mm from the detector surface. A standard M1522 CZT Module has an active region of $40\times40$ mm$^{2}$ and 5 mm thick with Au contact ($16\times16$ pixel array, 2.2 mm $\times$ 2.2 mm pixels on a 2.46 mm pitch size, Redlen Technologies Inc., Canada). GATE 6.2 version was used in the keel-edge pinhole SPECT system simulation. GATE incorporates the GEANT4 libraries and combines the GEANT4 strength of precise geometry modeling modules and complicated physic process model for emission tomography simulation. It allows users to model the SPECT system including the system geometry configuration, source selection and physic process. The system geometric parameters are modeled accurately based on the configuration described above, as shown in Fig. 2, including the keel-edge pinhole collimator, CZT crystal, and lead shielding. The crystal was simulated as pixelated CZT with pixel size $2.46\times2.46$ mm$^{2}$ in a $60\times60$ array. Energy threshold is set between 120 keV and 160 keV. The energy resolution of the crystal was modeled with an energy blurring of 8% at 140 keV in simulation, according to the intrinsic energy resolution of CZT crystal. The Compton scatter, the Rayleigh effect and the photon interaction with keel-edge pinhole are also included in the photon transport to simulate the realistic physical process in the detector.
cpl-33-4-048701-fig1.png
Fig. 1. (A) Schematic diagram of the pinhole SPECT system design, consisting of rotary stage, a collimator and a CZT detector. (B) Close-up of the pinhole SPECT system.
cpl-33-4-048701-fig2.png
Fig. 2. Geometry architecture of the pinhole SPECT simulation model.
In GATE simulation, spatial resolution was measured by using a point source (inner diameter 1.0 mm, $^{99}$mTc total activity of 10 MBq) placed 60 mm from the pinhole collimator. We measured the image resolution and sensitivity, at the same position of FOV in the GATE simulation platform, to validate the simulation model. Experimental and simulation points-spread function (PSF) profiles are shown in Fig. 3, where the experimental and simulated results were normalized to the maximum counts. There is a reasonable agreement between PSF profiles. Further investigation on off-axis imaging of this SPECT was simulated on the GATE platform. In this work, we mainly focus on studying the imaging characteristics in off-axis locations while changing the channel height of keel-edge pinhole. Several figures of merit were calculated to study the imaging properties, mainly focusing on image resolution and sensitivity. For pinhole collimators, the collimator geometric efficiency $g$ can be calculated as $$\begin{align} g=\frac{d_{\rm e} ^2\cos ^3\theta }{16b^2},~~ \tag {1} \end{align} $$ where $\theta$ is the angle between the source and central axis of the pinhole collimator, $b$ is the perpendicular distance between source and the focal point (pinhole center), and $d_{\rm e}$, the effective diameter of pinhole sensitivity, is given by $$\begin{align} d_{\rm e} =\sqrt {d\Big(d+\frac{2}{\mu }\cdot \tan \alpha +\frac{2}{\mu ^2}\cdot \tan ^2\alpha\Big)},~~ \tag {2} \end{align} $$ where $d$ is the physical diameter of pinhole, $\mu$ is the linear attenuation coefficient, and $\alpha$ is half the pinhole opening angle. A diagram of a keel-edge pinhole collimator is shown in Fig. 4.
cpl-33-4-048701-fig3.png
Fig. 3. Point spread function (PSF) of simulation and experimental data.
Equations of geometric efficiency indicate that for pinhole collimators, sensitivity associated with efficiency decreasing with the off-axis angle becomes larger. In addition to the geometry configuration, scatter and penetration are the other two major factors which severely affect pinhole collimator performance. Especially for larger off-axis angle incident, the expanded passing distance $L$, as shown in Fig. 4(B), will lead to blurring artifacts. Here we choose to investigate three channel height values of 1.38, 1, and 0.5 mm. With the high resolution ($ < $2.0 mm) designed for the pinhole-SPECT system and relatively large pixel size (2.46 mm) of the CZT detector, we choose rms resolution to represent image resolution instead of FWHM. The photons emitted from the point source reach corresponding detector pixel, as shown in Fig. 4(B). The rms resolution is calculated according to Eq. (3) and it is one-dimensional calculation along the center line of the image, $$\begin{align} {\rm rms}=\sqrt {\frac{\sum\limits_{i=i_{\rm start}}^{i_{\rm end}} {pi(z_i -\overline z )}}{\sum\limits_{i=i_{\rm start}}^{i_{\rm end}} {pi} }},~~ \tag {3} \end{align} $$ where ${\overline z}$ is the centroid position of PSF, $i_{\rm start}$ and $i_{\rm end}$ are the start and ending pixel index of PSF in the axial direction, respectively, and $pi$ is the number of photons detected by the $i$th pixel. In this study, ${\overline z}$ is calculated as $$\begin{align} \overline z =\frac{\sum\limits_{i_{\rm start}}^{i_{\rm end}} {pi\cdot z_i }}{\sum\limits_{i_{\rm start}}^{i_{\rm end}} {pi} }.~~ \tag {4} \end{align} $$ With the limited size of mouse, the FOV for small animal imaging is usually within a radius of 14 mm, a series of off-axis planar scans were acquired in a plane 60 mm from the pinhole, at distances of 0, 4, 8 and 12 mm from the rotation axis center. These gave rays passing through the pinhole at an angle with values of 0$^{\circ}$, 3.81$^{\circ}$, 7.59$^{\circ}$ and 11.3$^{\circ}$, respectively, with the respect to the pinhole axis. Each scan is conducted in 100 s frames by using $^{99m}$Tc (10 MBq). The changes of rms resolution and sensitivity in various off-axis locations are recorded with different channel height setups (Table 1).
cpl-33-4-048701-fig4.png
Fig. 4. (A) The geometry of keel-edge pinhole aperture and off-axis simulation. (B) Three major effects in the keel-edge pinhole, including absorption, penetration and scatter between photon and attenuating material interaction.
Table 1. Simulation result of sensitivity and rms resolution for off-axis imaging of different channel heights.
Axial position (equivalent off-axis angle) Performance Channel height (mm)
1.38 1 0.5
0 mm (0$^{\circ}$) Sensitivity (cps/MBq) 9.622 9.912 10.816
rms 0.572 0.623 0.861
4mm(3.8$^{\circ}$) Sensitivity (cps/MBq) 5.858 5.881 6.367
rms 0.584 0.653 0.885
8mm(7.6$^{\circ}$) Sensitivity (cps/MBq) 0.821 1.509 1.71
rms 0.686 0.813 1.243
12mm(11.3$^{\circ}$) Sensitivity (cps/MBq) 0.378 0.386 0.544
rms 1.422 1.927 2.138
cpl-33-4-048701-fig5.png
Fig. 5. Tradeoff curves of rms resolution and sensitivity with different-channel-height pinhole in off-axis imaging.
As the channel height becomes lower, the sensitivity increases at the expense of rms resolution, and this trend is especially obvious at the position of 0 mm off-axis. With lower channel heights of 1.0 mm and 0.5 mm (0 mm off-axis), the sensitivity increases by 3% and 12%, while the rms resolution degrades 8.9% and 50%. It is due to the penetration of gamma rays through the pinhole insert near the channel. The sensitivity and rms resolution of simulation are plotted in Fig. 5. From Fig. 5, we can find that the sensitivity and rms resolution become worse when the point source is placed off axis. The point source was placed farther, the decrease rate of sensitivity with lower channel height was similar, however, the degradation of rms resolution changes greatly, as the solid line shown in Fig. 5. In this study, we set the acceptable sensitivity baseline as 1.08 cps/MBq, 10% of the sensitivity value of 0.5 mm channel height pinhole at the center of rotation axis. When the point source is placed at 12 mm from the axis center, the rms resolution of 1.38 mm channel height increases to 1.4, regarded as the rms reference. Hence, the effective FOV ($r$, short for radius) for various-channel-height pinholes can be concluded as $r=7.8$ mm (angle=7.4$^{\circ}$) for 1.38 mm channel height, $r=9.1$ mm (angle=8.6$^{\circ}$) for 1.0 mm channel height, $r=8.7$ mm (angle=8.25$^{\circ}$) for 0.5 mm channel height. Moreover, for relatively low channel height (0.5 mm) pinhole, when the point source is placed 8 mm off the center, the rms resolution degrades in a steeper slope than the change of sensitivity, thus the advantage of sensitivity is not dominant compared with the other two higher channel height setups in 8 mm off-axis location. One reason is that the lower channel height has relatively higher penetration, which decreases the resolution, especially in the far off-axis imaging situation. Thus for the channel height lower than 0.5 mm, the sensitivity advantage cannot compensate for its resolution loss. From the tradeoff curves, it is noticed that when the off-axis angle is less than 5$^{\circ}$, pinholes with 1 mm and 1.38 mm channel heights have similar resolution, however, the sensitivities decline linearly with increasing the off-central-axis distance. The reduction of sensitivity is a consequence of the scatter photon in the keel-edge pinhole configuration. The results also show that both different channel height collimators have the similar increasing rate of rms and this trend speeds up when the off-axis angle goes beyond 5$^{\circ}$. When the off-axis angle is larger than 11$^{\circ}$, there is no distinction in sensitivity between different-channel-height keel-edge collimators. In conclusion, GATE simulation of the pinhole SPECT system has been modeled to investigate the off-axis imaging characteristics. Comparison between experimental and simulation results suggests that the GATE model can obtain precise results that follow the experimental results. Then the off-axis imaging characteristics are investigated based on this GATE model, mainly in terms of sensitivity and rms resolution, and their relationship with the channel height of pinhole. When the channel height becomes lower, the sensitivity becomes better at cost of image resolution, and the loss of image resolution becomes greater in off-axis locations, which degrade the image quality. Thus there is a compromising relationship among sensitivity, spatial resolution and the size of effective FOV. A series of tradeoff curves are plotted, helping us to conclude the effective FOV of keel-edge pinhole imaging in a quantitative way. Meanwhile, this tradeoff relationship is also essential in the multi-pinhole design, assisting in fabricating optimal pinhole patterns. Experimental phantom validations for the off-axis effect with different channel heights and pinhole apertures will be conducted in our future research. References Performance evaluation of A-SPECT: a high resolution desktop pinhole SPECT system for imaging small animalsSmall animal imaging with pinhole single-photon emission computed tomographyPinhole SPECT of mice using the LumaGEM gamma cameraTowards in vivo nuclear microscopy: iodine-125 imaging in mice using micro-pinholesPinhole aperture design for /sup 131/I tumor imagingOptimization of pinhole collimator for small animal SPECT using Monte Carlo simulation
[1] McElroy D P, MacDonald L R, Beekman F J, Wang Y, Patt B E, Iwanczyk J S, Tsui B M and Hoffman E J 2002 IEEE Trans. Nucl. Sci. 49 2139
[2] Strand S E, Ivanovic M, Erlandsson K, Franceschi D, Button T, Sjogren K and Weber D 1994 Cancer 73 981
[3]Weber D A, Ivanovic M, Franceschi D, Strand S, Erlandsson K, Franceschi M, Atkins H L, Coderre J, Susskind H and Button T 1994 J. Nucl. Med. 35 342
[4] MacDonald L R, Patt B E, Iwanczyk J S, Tsui B M, Wang Y, Frey E C, Wessell D E, Acton P D and Kung H F 2001 IEEE Trans. Nucl. Sci. 48 830
[5]Dai Q S and Qi Y J 2010 Acta Phys. Sin. 59 1357 (in Chinese)
[6] Have F and Beekman F J 2006 IEEE Trans. Nucl. Sci. 53 2635
[7] Beekman F J, McElroy D P, Berger F, Gambhir S S, Hoffman E J and Cherry S R 2002 Eur. J. Nucl. Med. Mol. Imaging 29 933
[8] Smith M, Jaszczak R and Wang H 1997 IEEE Trans. Nucl. Sci. 44 1154
[9] Song T Y, Choi Y, Chung Y H, Jung J H, Choe Y S, Lee K H, Kim S E and Kim B T 2003 IEEE Trans. Nucl. Sci. 50 327