Monte Carlo Optimization of Crystal Configuration for Pixelated Molecular SPECT Scanners

Author’s Accepted Manuscript Monte Carlo Optimization of Crystal Configuration for Pixelated Molecular SPECT Scanners Hojjat Mahani, Gholamreza Raisali, Alireza Kamali-Asl, Mohammad Reza Ay www.elsevier.com/locate/nima

PII: DOI: Reference:

S0168-9002(16)31162-7 http://dx.doi.org/10.1016/j.nima.2016.11.026 NIMA59445

To appear in: Nuclear Inst. and Methods in Physics Research, A Received date: 18 March 2016 Revised date: 11 November 2016 Accepted date: 12 November 2016 Cite this article as: Hojjat Mahani, Gholamreza Raisali, Alireza Kamali-Asl and Mohammad Reza Ay, Monte Carlo Optimization of Crystal Configuration for Pixelated Molecular SPECT Scanners, Nuclear Inst. and Methods in Physics Research, A, http://dx.doi.org/10.1016/j.nima.2016.11.026 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Monte Carlo Optimization of Crystal Configuration for Pixelated Molecular SPECT Scanners Hojjat Mahani1,2, Gholamreza Raisali1, Alireza Kamali-Asl3 and Mohammad Reza Ay2,4,* 1

Radiation Application Research School, Nuclear Science and Technology Research Institute,

Tehran, Iran 2

Research Center for Molecular and Cellular Imaging, Tehran University of Medical Science,

Tehran, Iran 3

Radiation Medicine Department, Shahid Beheshti University, Tehran, Iran

4

Department of Medical Physics and Biomedical Engineering, Tehran University of Medical

Science, Tehran, Iran *Corresponding author. [email protected]

Abstract Resolution-sensitivity-PDA tradeoff is the most challenging problem in design and optimization of pixelated preclinical SPECT scanners. In this work, we addressed such a challenge from a crystal point-of-view by looking for an optimal pixelated scintillator using GATE Monte Carlo simulation. Various crystal configurations have been investigated and the influence of different pixel sizes, pixel gaps, and three scintillators on tomographic resolution, sensitivity, and PDA of the camera were evaluated. The crystal configuration was then optimized using two objective functions: the weighted-sum and the figure-of-merit methods. The CsI(Na) reveals the highest sensitivity of the order of 43.47 cps/MBq in comparison to the NaI(Tl) and the YAP(Ce), for a 1.5 × 1.5 mm2 pixel size and 0.1 mm gap. The results show that the spatial resolution, in terms of FWHM, improves from 3.38 mm to 2.21 mm while the sensitivity simultaneously deteriorates from 42.39 cps/MBq to 27.81 cps/MBq when pixel size varies from 2 × 2 mm2 to 0.5 × 0.5 mm2 for a 0.2 mm gap, respectively. The PDA worsens from 0.91 to 0.42 when pixel size decreases from 0.5 × 0.5 mm2 to 1 × 1 mm2 for a 0.2 mm gap at 15o incident-angle. The two objective functions agree that the 1.5 × 1.5 mm2 pixel size and 0.1 mm Epoxy gap CsI(Na) configuration

provides the best compromise for small-animal imaging, using the HiReSPECT scanner. Our study highlights that crystal configuration can significantly affect the performance of the camera, and thereby Monte Carlo optimization of pixelated detectors is mandatory in order to achieve an optimal quality tomogram.

Keywords: Monte Carlo, GATE, molecular SPECT, optimization, pixelated crystal 1. INTRODUCTION Small-animal SPECT has undergone rapid development and improvements in performance, particularly spatial resolution, and therefore new detector technologies are expected to lead to further improvements [1]. The need for high spatial resolution and low radiation dose is driving the development of small animal SPECT systems with higher sensitivity [2]. However, all imaging systems exhibit a limited sensitivity that is inversely proportional to the system’s spatial resolution [3]. On the other hand, inter-crystal scattering and penetration (ICS-P) causes mispositioning of scintillation events, which is of particular concern in imaging detectors based on small discrete scintillator elements [4]. Position-detection-accuracy (PDA) is an index of ICSP and plays a crucial role in pixelated molecular SPECT. Therefore, the sensitivity-resolutionPDA tradeoff should be carefully addressed in designing and optimizing pixelated molecular SPECT scanners. So far, several molecular SPECT scanners have been designed and developed with optimal pixelated detectors. Loudos et al. [5] developed a dedicated gamma-camera based on a pixelated CsI(Na) crystal (1 × 1 × 5 mm3 pixel volume), in 2007. Their SPECT camera offers spatial resolution of 1.6 mm and 58.32 cps/MBq sensitivity. A work was conducted, in 2008, by Asma et al. [6] on the impact of resolution-sensitivity tradeoffs on detection performance for SPECT imaging. They concluded that using a multi-pinhole SPECT camera provides a better compromise than a single one. Dey [7], in 2009, addressed the sensitivity-to-resolution tradeoff by designing a curved detector for pinhole SPECT imaging. She showed that using a curved detector provides an improved sensitivity, while maintaining the spatial resolution. Xi and coworkers [8], in 2010, designed a pixelated NaI(Tl)-based SPECT camera benefiting from position-sensitive photomultiplier tubes (PSPMTS). The system has a spatial resolution of 2.2 2

mm and sensitivity of 148.77 cps/MBq. In 2010, effects of pixel size and collimator geometry on performance of a gamma-camera were studied by Rasouli et al. [9]. They showed that a greater pixel size gives rise to a decreased inter-crystal scattering and penetration. The Inveon Smallanimal PET-SPECT-CT scanner was introduced by Magota et al. [10], in 2011. The Inveon system utilized a 2 × 2 × 10 mm3 pixelated NaI(Tl) crystal array. Tomographic resolution and sensitivity of the Inveon camera was 0.84 mm and 35.1 cps/MBq, respectively. One year later, in 2012, Ghazanfari and co-workers [11] assessed effects of crystal material and size on the performance of a dual-head rotating PET scanner. They showed that spatial resolution becomes worse when pixel size increases, while sensitivity of the system improves. Audenhaege et al [12] optimized the pinhole geometry to obtain the best tradeoff for SPECT, in 2012. They concluded that at low activities it is better to use a larger pinhole, while at high activity a smaller pinhole provides a superior image quality. Thus far, to the best of the authors’ knowledge, there is no study on addressing sensitivityresolution-PDA tradeoff from a crystal point-of-view in molecular SPECT systems and also there is no well-documented criterion in selecting crystal topology. For that reason, the primary goal of this study was to introduce an optimized pixelated crystal configuration for our dedicated molecular SPECT scanner, HiReSPECT [13-15], based upon system sensitivity, tomographic resolution, and PDA using GATE Monte Carlo (MC) simulations (i.e., improvement over its predecessor). In other words, we aimed to overcome the existing compromise between spatial resolution, system sensitivity, and PDA in small-animal SPECT systems from a detector perspective.

2. MATERIALS AND METHODS In this section, the accelerated GATE MC simulation, our optimization approaches based upon system sensitivity, tomographic spatial resolution, and PDA and also our validation procedure are extensively described.

2.1. Accelerated Monte Carlo study

3

MC simulations are widely used in nuclear medicine especially in the development of new imaging instrumentation, image acquisition strategies and processing, and reconstruction methods [16]. GATE is a MC simulation package optimized for simulations in emission tomography, and has been well-validated and is currently used by a large number of groups worldwide [17]. We modeled the HiReSPECT, a dual-head high-resolution SPECT camera, equipped with a low-energy, high-resolution (LEHR) parallel-hole collimator (1.2 mm hexagonal holes, 34 mm length, and 0.2 mm septal thickness), a pixelated CsI(Na) detector (1 × 1 mm2 pixel area and 0.2 mm Epoxy gap) as well as two PSPMTs using the GATE in-detail for various crystal configurations and materials. Field-of-view (FOV) of the camera is 5 cm × 10 cm (in other words, a 5 cm × 10 cm effective area of each head). Figure 1 shows a 3D model of the simulated system in the GATE environment in combination with a cylindrical phantom used for assessing system sensitivity. Some key components of the HiReSPECT scanner are shown in Figure 2. Intrinsic spatial and energy resolution (at 140 keV), and dead-time of the candidate crystal materials as well as half-life of the

99m

Tc source were also taken into account during the MC

simulations. Two glass PMTs were also modeled as backscattering media behind the pixelated crystal. Particle interactions that were simulated include photoelectric effect, Compton scattering, electron ionization, multiple-scattering, and bremsstrahlung. To accelerate our GATE MC simulations, a variance reduction technique was implemented by ignoring cumbersome transportation of secondary electrons in both the collimator and the phantom. Fully tracking of the secondary particles within both the collimator and the phantom increases computation expense needed to simulate an SPECT system, while it adds no useful imaging information. It should be highlighted that this variance reduction strategy was not applied to the crystal, and therefore these secondary electrons were fully tracked within the pixelated crystal.

2.2. Monte Carlo optimization In the present study, an optimal crystal configuration was investigated. We repeated all MC simulations for four crystal pixel sizes ranging from 0.5 × 0.5 mm2 to 2 × 2 mm2 (0.5 mm steps), three crystal pixel gaps, 0.1, 0.2, and 0.3 mm Epoxy, and also three common crystal materials,

4

CsI(Na), NaI(Tl), and YAP(Ce), to fully search the solutions space. Crystal thickness was fixed to 5 mm for all designs. System sensitivity, tomographic resolution as well as PDA were evaluated in order to define a single objective function, and consequently, to select the optimal configuration.

2.2.1. System sensitivity In-air system sensitivity was calculated using a cylindrical phantom of 74 MBq

99m

Tc located at

a 30 mm source-to-collimator distance (SCD). The phantom was simply a cylinder of 32 mm in diameter and 5 mm in thickness, and the sensitivity was then calculated for 300 s dataacquisition period. All detected photons within a 20% energy-window centered at the photopeak have been considered for the sensitivity assessment. The system sensitivities were also decaycorrected for the 99mTc tracer (6 h half-life).

2.2.2. Tomographic resolution Tomographic spatial resolution of the scanner, in terms of full-width-at-half-maximum (FWHM), was calculated for an 18.5 MBq

99m

Tc line source, and 30 mm radius-of-rotation

(ROR) at the center of the FOV of the camera using MC simulations. Sixty four equally-angled projection images over 360o were acquired each with adaptive time-per-view (60 s for the first projection and decay-compensated times for the others). Following the GATE MC dataacquisition, the images were iteratively reconstructed using an in-house rotation-based (rotator) projector/backprojector 3D OSEM algorithm, with 4 subsets and 2 full-iterations. The image matrix was 128 × 128 × 256, resulting in a pixel size of 0.39 mm. To derive the FWHMs, the line profile of the reconstructed line-spread-functions (LSFs) was fitted with a Gaussian function using the least squares minimization method, and the FWHM of the fitted curve was reported as tomographic resolution of the system.

2.2.3. Position detection accuracy

5

Apart from spatial resolution and sensitivity of a pixelated SPECT camera, PDA itself reflects pixelated detectors performance. To assess accuracy of the crystal in detection of interactionposition, a pencil-beam of

99m

Tc irradiating the central pixel of the crystal was simulated (the

collimator was removed). The beam-angle was set to 15o degrees to the normal vector of the crystal. The 15o-degree incident-angle was selected based upon two criteria: (1) non-negligible amount of Compton scattering occurred both in the collimator (due to a considerable septum-tohole ratio, 1:6) and in the phantom below this angle, and (2) beyond it, multiple septa crossings are necessary and the photon has a small probability to be transmitted through the collimator. In addition, a 140 keV photon losses only ~1% of its energy after Compton scattering through 15o, and therefore can be directly detected in the photopeak window. PDA, defined as the ratio of detected photons in the irradiated crystal to the total detected events, indicates how accurate the signal positioning is when a Tc-99m photon reaches with an oblique-angle. It should be also highlighted that in an ideal imager, a PDA of unity would be expected.

2.2.4. Objective functions In order to search for an optimum solution (i.e., a crystal configuration), a tri-objective function was considered based upon the three conflicting objectives: system sensitivity, tomographic resolution, and PDA. Then, we scalarized our tri-objective function into a single objective function by using two different well-known approaches: the weighted-sum (WS) as well as the figure-of-merit (FOM) methods. The WS method utilizes an additive objective function and then it is robust to changes in relative importance factor (weight) of each objective. The FOM one benefits from a multiplicative objective function and therefore can potentially differentiate between two close crystal configurations.

2.2.4.1. The weighted-sum method In this method, each objective is multiplied by a user supplied weight, using the widely used, WS approach as [18]: [

(

) 6

(

)]

(1)

where K is a constant and can be set arbitrarily to 1000; α, , and < 1 and

are weighting factors (0 <

) tuning relative importance of the three objectives, FWHM is the

normalized tomographic resolution calculated for a 30 mm ROR (a typical ROR in small-animal SPECT imaging), S is the normalized system sensitivity at the same ROR, and PDA is the position-detection-accuracy for an 15-degree incident photon. PDA15degree is a reasonable measure of crystal identification (CI) in order to compare performance of different configurations. The rationale behind introducing the PDA into the objective function is that the PDA affects more the full-width-at-tenth-maximum (FWTM) of the projection images rather than the FWHM. In other words, defining a combination of the FWHM and the FWTM of the images reflects spatial uncertainty of position estimation better. All resolutions and sensitivities were normalized to the resolution and the sensitivity of the current configuration (1 × 1 mm2 pixel area, 0.2 mm Epoxy gap, and CsI(Na) crystal), respectively. A crystal configuration with a specific pixel size and pixel gap was called a possible solution, and the objective function was then calculated for all solution candidates. A solution with the lowest cost, was considered as the optimum configuration. Mathematically, the resultant configuration is optimistically a global minimum of the objective function in the search-space domain. It is obvious from the Equation (1), that there is a strong tradeoff between the three objectives. For calculation of the costs, the parameters α,

, and

were fixed to 0.5, 0.25, and 0.25,

respectively. Such a weighting is, on one hand, reasonable in molecular SPECT where spatial resolution is of great consideration. On the other hand, since the sensitivity and the PDA approximately behave in the same way, an identical importance factor was assigned to each. Therefore, this weighting can balance the three objectives for whole-body 99mTc SPECT imaging tasks.

2.2.4.2. The figure-of-merit method Alternatively, we sought the optimal topology using a metric by calculating a FOM associated to each configuration using: [

]

7

(2)

where all terms are as in the previous method. K is a constant (can be set arbitrarily to 1000). The powers a, b, and c tune relative importance of the each objective based upon the imaging task (a, b, c > 0). By definition, the optimal configuration would hold the largest FOM. As for the WS method, setting the powers a, b, and c in Equation (2) to 1, 1, and 2, respectively, ensures a balance between the three objectives.

2.3. Experimental study and validation The MC simulations were validated against the experiments for the current configuration. The experiments were conducted with imaging and data-acquisition parameters and phantoms as for the GATE simulations. A line source of 99mTc located at 30 mm ROR and a cylindrical phantom at various distances (zero, 40 mm, 80 mm, and 120 mm) were used for measuring tomographic resolution and sensitivity, respectively.

3. RESULTS 3.1. System sensitivity MC simulated system sensitivity for the three investigated crystal materials, CsI(Na), NaI(Tl), and YAP(Ce) as a function of distance from the collimator (all for the current configuration) is shown in Figure 3.

8

Figure 4, illustrates the influence of crystal pixel size on system sensitivity, and also includes the values for the three Epoxy gaps. By increasing the pixel size, sensitivity of the system linearly improves.

3.2. Tomographic spatial resolution Tomographic resolution of the scanner (in terms of FWHM) as a function of pixel size for three pixel gaps is depicted in Figure 5. The images becomes poorer in tomographic resolution when pixel size increases.

3.3. Position detection accuracy Figure 6 reports dependency of PDA (at 15o incident-angle) on crystal material as a function of pixel size. Variation of PDA (at 15o incident-angle) against pixel size for three pixel gaps is reported in Figure 7. The crystal is CsI(Na).

3.4. Optimal pixelated crystal configuration Table 1 compares various crystal configurations (solution candidates) based upon their corresponding scores obtained by both the WS and the FOM methods. For calculation of the scores, all MC simulated spatial resolutions and sensitivities are normalized to resultant spatial resolution and sensitivity of the current configuration, respectively. In Table 1, the crystal configurations are ranked from the lowest cost (the optimal configuration) to the highest one based upon the WS method. It should be highlighted that the parameters α, , and

(in Equation

(1)) are set to 0.5, 0.25, and 0.25, respectively; indicating relative importance of the three objectives. Similarly, the powers a, b, and c in Equation (2) were set to 1, 1, and 2, respectively.

3.5. Validation

9

For validation, tomographic resolution (at a 30 mm ROR) and system sensitivity at various distances from the collimator are compared with experimental data. MC simulations yields a tomographic resolution of 2.65 mm and a value of 2.77 mm is obtained through the experiment. Figure 8, provides a comparison between the decay-corrected simulated and the experimental system sensitivity.

4. DISCUSSION According to the Figure 3, CsI(Na) is more efficient compared to NaI(Tl) and YAP(Ce) over all distances. At 140 keV, the CsI(Na) has the largest linear attenuation coefficient (3.61 cm-1 versus 2.64 cm-1 and 1.43 cm-1 for NaI(Tl) and YAP(Ce), respectively) [19], and therefore, the

99m

Tc

photons have a higher likelihood to be detected by the CsI(Na) crystal. On the other hand, intercrystal scatter and penetration (ICS-P), in the CsI(Na) are considerably lower than both for the NaI(Tl) and the YAP(Ce) crystals due to its higher cross-section at 99mTc energy [20], leading to a subtle improvement in spatial resolution as well. The CsI(Na) is therefore the crystal of choice considering both the highest-sensitivity as well as the highest-PDA criteria. The CsI(Na) introduces a constant sensitivity of 35.64 cps/MBq over all distances from the collimator’s face, as would be expected for parallel-hole collimated SPECT scanners. The GATE-provided sensitivities cab be compared to analytical calculations. Intrinsic detection efficiency of a crystal, in the simplest terms, is proportional to

, where

is photoelectric linear attenuation coefficient of the crystal and t is its thickness [21]. A sensitivity ratio of 1.35 and 2.62 was obtained for CsI(Na)-to-Na(Tl) and CsI(Na)-to-YAP(Ce), respectively. Comparing these ratios with the sensitivities presented in Figure 3, one can conclude a reasonable agreement. It should be mentioned that the CsI(Na) benefited also from a relatively lower cost rather NaI(Tl) and YAP(Ce). In addition, the CsI(Na) crystal has the highest absolute light-yield compared to its alternatives, the NaI(Tl) and the YAP(Ce) scintillators (i.e., 39 versus 38, and 18 photons/keV, respectively) [21] leading to a superior energy resolution. Comparison of the intrinsic collimator performance (perfect detector) to the simulated detector performances allows to evaluate the impact of the detector. Geometric efficiency of a 10

parallel-hole collimated SPECT camera can be calculated using

[22] where A is the

area of a single hole, h is the collimator height, and g is the ratio of the total area of holes in the collimator face to the area of the collimator face. Thus, geometric sensitivity of the current HiReSPECT’s collimator (here, A is about 1.25 mm2, g is approximately 0.8, and h is 34 mm) is in the order of ~0.005% (49.95 cps/MBq). Also, the collimator (geometric) resolution is given by [22] where d is the hole diameter, h is the collimator height, and ROR is the radius-of-rotation. Therefore, the collimator, itself, results in a ~2.25 mm spatial resolution (for an 1.2 mm hole size, a 34 mm h, and an ROR of 30 mm). A perfect pixelated detector would also offer a PDA of unity. From Figure 4, it can be seen that as the crystal pixel size increases, the system sensitivity improves due to an increase in effective area of the crystal. Similarly, a lower crystal pixel gap leads to a higher system sensitivity, because the effective area of the crystal increases. There is an inverse relationship between system sensitivity and crystal pixel gap. A sensitivity of 45.63 cps/MBq would be obtained for a 2 × 2 mm2 pixel size and 0.1 mm Epoxy gap configuration. On the contrary, when the crystal pixel size increases, the spatial resolution becomes poorer due to an increase in sampling-pitch of the acquired data. Likewise, as for system sensitivity, an approximately increasing behavior exists for spatial resolution (in terms of FWHM) when pixel size increases. Referring to Figure 5, a 57.3% deterioration in spatial resolution is observed when pixel size varies from 0.5 × 0.5 mm2 to 2 × 2 mm2 (for a 0.2 mm Epoxy gap). In the same way, smaller Epoxy gaps, result in a finer object sampling interval (pixel pitch), and consequently offer a higher resolution image, for a given pixel size. When a photon arrives at a specific pixel with an oblique angle, it may penetrate to adjacent pixels without any interaction and can be detected by a pixel different from the irradiated one. This probability is a function of both crystal size and material. A crystal with a higher linear attenuation coefficient offers a higher PDA (Figure 6). According to Figure 7, a smaller pixel size provides more ICS-P and consequently leads to a more noticeable parallax artifact. Given a pixel size, a smaller Epoxy gap results in more inter-crystal penetrations and thus inaccurate incident crystal assignment. Quantitatively, for a 0.2 mm Epoxy gap, the PDA increases from 0.42 to 0.91 when pixel size varies from 0.5 mm to 2 mm, respectively. 11

As summarized in Table 1, the 1.5 × 1.5 mm2 pixel size and 0.1 mm Epoxy configuration keeps the smallest cost (using the WS method) and simultaneously the highest merit (using the FOM method), and consequently, is considered as the optimum configuration (dashed box). It is evident from Table 1 that the two objective functions are approximately in line. Hence, the two procedures offer the same optimal configuration (1.5 × 1.5 mm2 pixel size and 0.1 mm Epoxy). An advantage of the additive method (the WS) over the multiplicative one (the FOM) is that it is more robust to the weights. Because of the multiplicative nature of the FOM method, an increase/decrease in the powers would result in a higher change in the objective function compared with the additive form (the WS one). In other words, the FOM method requires an expert decision maker to choose appropriate weights/powers. In contrast, the FOM method can better distinguish between two candidates. In comparison to the FOM method, the WS approach, although is more robust, cannot clearly distinguish between those two candidates that are very close (in pixel size, pixel gap, linear attenuation coefficient (crystal material) and so on). To sum up, if the decision maker cannot exactly determine relative importance of the three objectives, it is recommended following the WS method. Also, when the user searches among very close candidates for an optimal configuration, the FOM can be the method of choice. Some manufactures provide pixelated crystals with a fixed crystal gap, for example 0.2 mm. It is obvious from Table 1 that neglecting those configurations with 0.1 mm gap, the 1.5 × 1.5 mm2 pixel size and 0.2 mm Epoxy configuration (solid box) is the optimal pixelated crystal and will be the basis for the current design successor. Such an optimal configuration yields to only 14% deterioration in spatial resolution but gives rise to a 12% increase in system sensitivity as well as a 64% more accurate PDA. Another possible application of objective functions such as discussed here is in the case of pinhole collimators. In pinhole (or multipinhole) collimation systems, spatial resolution is usually specified and reported at central axis of the collimator, the axis perpendicular to the crystal’s face. At the edges of the FOV, spatial resolution considerably degrades due to a high ICS-P for oblique projections, commonly referred to as the parallax artefact. In other words, photons originating from a source at the edge of FOV of the camera can introduce a high value of ICS-P. Therefore, non-uniformity of the spatial resolution on the detector can be taken into account by introducing the PDA into these objective functions. 12

A good agreement (i.e., 4.3% difference) between the simulated and the measured FWHM at 30 mm SCD was observed. Moreover, there is a maximum 9.1% difference, at 120 mm SCD, between our MC calculations and the measurements for system sensitivity (Figure 8). As would be expected, system sensitivity remains approximately constant across all distances from the collimator for both MC simulated data and the experimental ones.

5. CONCLUSION In this paper, an optimal crystal configuration (a 1.5 × 1.5 mm2 pixel size and 0.1 mm Epoxy gap CsI(Na) scintillator array) was introduced based upon a tri-objective MC optimization, using the GATE simulator. Based upon our findings, one can conclude that different pixelated crystal configurations result in different tradeoffs between spatial resolution, system sensitivity, and PDA. Accordingly, a balance among the three contradictory objectives is required. Pixelated crystals potentially offer a higher-resolution SPECT image, but always at the expense of both a significant drop in sensitivity and simultaneously producing parallax artifact resulting from ICS-P. A high-sensitivity molecular SPECT system allows to dynamically study the animal being imaged due to an improvement in time resolution afforded by a shorter acquisition time. In addition, a high-sensitivity scanner is also preferred for tracer kinetics analysis and parametric image reconstruction. However, different weighting factors (using either the WS or the FOM methods) may lead to a different geometrical setting, and it is up to the decision maker to choose appropriate weights (or powers) based on the imaging task. In high-energy SPECT (e.g.

131

I imaging) the PDA

becomes increasingly important and the designer may put more focuses on it by leveling-up its weight. Searching for an optimal parallel-hole collimator geometry for the optimized crystal configuration is an avenue of further study.

13

ACKNOWLEDGMENTS This work was supported by Research Center for Molecular and Cellular Imaging (RCMCI), Tehran University of Medical Science under grant No. 29885.

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Table 1. Comparison of different CsI(Na)-based configurations based on their ranks obtained by Equation (1) for α = 2β = 2γ = 0.5. FOM associated to each candidate is also calculated using Equation (2) for a = b =

Spatial resolutions and sensitivities are normalized to those of

the current configuration. The optimal configuration is indicated by a dashed box. The solid box represents the best configuration with 0.2 mm Epoxy gap. Pixel size

Pixel gap

Normalized

Normalized

(mm2)

(mm)

FWHM

sensitivity

PDA

Cost†

FOM††

1.5 × 1.5

0.1

1.11

1.30

0.78

1067

822

2×2

0.1

1.25

1.42

0.85

1095

772

1.5 × 1.5

0.2

1.14

1.12

0.82

1098

707

1×1

0.1

0.99

1.13

0.61

1126

703

2×2

0.2

1.3

1.19

0.91

1134

641

1.5 × 1.5

0.3

1.17

0.99

0.84

1136

607

1×1

0.2

1

1

0.64

1140

640

2×2

0.3

1.32

1.09

0.94

1155

588

1×1

0.3

1.02

0.86

0.68

1168

562

0.5 × 0.5

0.1

0.77

0.89

0.38

1323

570

0.5 × 0.5

0.2

0.83

0.78

0.42

1330

476

0.5 × 0.5

0.3

0.87

0.59

0.48

1379

374

†

The costs are sorted from the smallest to the largest, using Equation (1)

††

The FOMs are calculated using Equation (2)

16

Figure 1. Three-dimensional model of the HiReSPECT system in the GATE along with a cylindrical phantom used for sensitivity calculation.

Figure 2. A close-up view of the HiReSPECT scanner. The HiReSPECT is a dual-headed gamma camera designed for molecular SPECT.

Figure 3. Comparison of system sensitivity for CsI(Na), NaI(Tl), and YAP(Ce), all for the current HiReSPECT’s crystal configuration.

Figure 4. Variation of system sensitivity in a CsI(Na)-based scanner across pixel size for three pixel gaps, 0.1 mm, 0.2 mm, and 0.3 mm Epoxy.

Figure 5. Variation of tomographic spatial resolution (in terms of FWHM) in a CsI(Na)-based scanner as a function pixel size for three pixel gaps: 0.1 mm, 0.2 mm, and 0.3 mm Epoxy.

Figure 6. Comparison of PDA15degree for three crystal materials across pixel size, all for a 0.2 mm Epoxy gap.

Figure 7. Dependency of PDA15degree on pixel size for different pixel gaps. The crystal is CsI(Na).

Figure 8. Comparison of the MC simulated with the measured system sensitivity across distance from the collimator, for the current HiReSPECT’s crystal configuration. 17

.

Figure 1

18

Figure 2

19

Figure 3

20

Figure 4

21

Figure 5

22

Figure 6

23

Figure 7

24

Figure 8

25

Highlights     

We optimized pixelated crystal configuration for the purpose of molecular SPECT imaging. The weighted-sum and the figure-of-merit approaches were utilized in order to search for an optimal crystal configuration. The higher the pixel size, the poorer the tomographic resolution and simultaneously the higher the sensitivity and the PDA. The higher the pixel gap, the poorer the tomographic resolution and simultaneously the lower the sensitivity in contrast to the greater PDA. Based upon relative importance of tomographic resolution, system sensitivity, and PDA, the optimal configuration was investigated.

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