Design and Optimization of Collimator for Preclinical Single-photon Emission Computed Tomography Scanner: A Monte Carlo Study

Abstract

Introduction:

Small animal imaging has an extensive variety of applications, including the design and optimization of novel imaging devices. Monte Carlo (MC) simulations are enhanced due to their high accuracy. The purpose of this investigation was to implement and validate a MC model for a preclinical single-photon emission computed tomography (SPECT) known as high-resolution SPECT II (HiReSPECT II) machine developed in our laboratory and also optimize different collimator materials and geometries for improving the sensitivity and spatial resolution.

Materials and Methods:

The validation of a small animal SPECT scanner equipped with lead hexagonal parallel-hole collimator, CsI (Na) pixelated crystal, and SiPM photodiodes was performed by comparing experimental results with Geant4 application for tomography emission (GATE) simulation data. In the next step, the optimization appraisals for both spatial resolution and sensitivity on the collimator material (W and Pb) and hole diameter were carried out using GATE. The experimental and simulated sensitivities were obtained using a cylindrical phantom at source to the collimator distance (SCD) of 3 cm. Moreover, a line source was applied to assess the spatial resolution in the simulated and experimental environments at different SCDs. Besides, a tungsten collimator with a hole diameter of 0.99 mm is suggested. ^99mTc was used as the radionuclide in all experiments.

Results:

The discrepancy between experimental and simulated sensitivities was <3%. In addition, the differences between simulated and experimental spatial resolutions were about 5%. Furthermore, the optimized hole diameter for tungsten is 0.99 mm according to the curve representing the tradeoff between spatial resolution and sensitivity.

Conclusion:

Lead exhibits a little higher sensitivity compared to tungsten because it has superior penetration and scattering abilities, leading to an increased full width at the tenth maximum that can diminish the spatial resolution. In addition, enlarging the diameter of the holes increases the number of photons that penetrate and scatter, thereby reducing the spatial resolution. The proposed collimator is able to provide adequate sensitivity considering the spatial resolution achieved at the SCD of 3 cm.

INTRODUCTION

Small animal imaging by providing useful information about the physiological and pathological processes in the body of small animals at the cellular and molecular levels is a very valuable tool in cardiovascular, neurological, oncological, and immunological studies because the results of its research can be transferred to clinical imaging.[1]

There is a wide range of imaging methods for small animals, one of which is single-photon emission computed tomography (SPECT).[2] One of the unique features of SPECT imaging is the use of a collimator. A collimator is a thick plate of high-density material, in particular lead or tungsten with hole(s) in it. The collimator’s function is to create a two-dimensional projection image of the distribution of the radiopharmaceutical on the detector, by passing the gamma rays in specific directions of the collimator holes.[3]

To show the details of the organs of small animals, it is necessary that the detector can provide an integrated image of the whole animal with sufficient spatial resolution and sensitivity. Thus, high spatial resolution along with sufficient sensitivity is important in designing the development of small animal imaging systems to have a high-quality image and appropriate quantification accuracy.[4]

Monte Carlo (MC) simulation is a computer-based approach for modeling the stochastic processes also involved in nuclear medicine imaging, for example, photon transport, photon interactions, and radiation detection.[5,6] MC simulation in nuclear medicine imaging for the design and optimization of new systems including SPECT is employed by simulating their performance, spatial resolution, and sensitivity.[7] Furthermore, MC simulation techniques are convenient when experimental measurements are not practical or experiments are too expensive.[8] Therefore, the aim of this study was to validate the MC simulation model for the high-resolution SPECT II (HiReSPECT II) preclinical SPECT scanner and optimize different collimator materials and collimator geometries to achieve the best spatial resolution-sensitivity tradeoff.

MATERIALS AND METHODS

Illustration of high-resolution single-photon emission computed tomography II gamma camera

In the validation part, the HiReSPECT II scanner, which is a preclinical gamma camera equipped with a low energy all-purpose (LEAP) lead parallel-hole collimator with a 35 mm hole length, 1.5 mm hexagonal hole size, and 0.2 mm septal thickness (nuclear fields Co., Australia) and two 68 × 68 pixelated scintillator array of 1.4 mm × 1.4 mm × 5 mm CsI (Na) crystals with 0.2 mm gap between the crystals coupled to 24 × 24 SiPMs with dimensions of 4.2 mm × 4.2 mm × 20 mm were used. In addition, radionuclide ^99mTc was employed for various experiments and simulations due to its ideal physical and imaging features, including its monoenergetic gamma emission at 140.5 keV, which is well suited for the energy range of the LEAP collimator and the CsI (Na) scintillator. Moreover, it is widely employed in clinical and preclinical SPECT imaging, making it a standard reference for validating imaging systems and optimizing collimator designs.

Monte Carlo model of the high-resolution single-photon emission computed tomography in geant4 application for tomography emission

Several MC codes in the field of nuclear medicine have been proposed, including the Geant4 application for tomography emission (GATE) which is a reliable and versatile software for simulating SPECT scanners. GATE can simulate the geometry of different parts of the scanner, various phantoms, physical interactions, for example, photoelectric effect, Rayleigh scattering and Compton scattering, tracking of optical photons originating from a scintillator, and data collection. The GATE’s striking ability is to simulate time-dependent phenomena such as radioactivity decay, dynamic data gathering, and powerful display of three-dimensional moveable parts of the gamma camera. To simulate the dual-head HiReSPECT II, a hexagonal collimator with dimensions of 10 cm × 10 cm × 3.5 cm, an array of 68 × 68 pixelated crystals with dimensions of 1.4 mm × 1.4 mm × 5 mm, a 24 × 24 SiPMs array with dimensions of 4.2 mm × 4.2 mm × 20 mm, and an aluminum shield were modeled by GATE. In addition, a cylindrical phantom with an outer diameter of 40 mm, an inner diameter of 37 mm, an outer height of 14 mm, and an inner height of 4 mm, and a linear source phantom with an outer diameter of 1.6 mm, an inner diameter of 1.2 mm, and a height of 75 mm was simulated to measure sensitivity and spatial resolution, respectively. Moreover, in the digitizer part, the energy resolution, spatial resolution, dead time, light yield, transfer efficiency, quantum efficiency, thresholds, and upholder modules were added.

Validation of the high-resolution single-photon emission computed tomography II code

The calibration tests for the HiReSPECT II machine, e.g., energy calibration, uniformity, spatial linearity, and center of rotation, were done according to the US National Electrical Manufacturers Association (NEMA) standard.[9] Then, the spatial resolution (full width at half maximum [FWHM]), sensitivity (cpm/µCi), planar uniformity, and energy resolution were experimentally assessed and compared with the corresponding simulation data. Both experimental and simulated data were obtained using a 30% energy window (119–161 keV) centered in the photopeak at 140 keV to diminish the noise effects.

Spatial resolution

The spatial resolution is a value expressing the ability of the imaging system to differentiate two adjacent gamma-ray emitting points. The spatial resolution is generally defined as the FWHM of the point spread function or line spread function (LSF), which is the image of a point source or line source on the detection plane.[10] The system spatial resolution was measured using a polymethyl methacrylate (PMMA) capillary tube with an inner diameter of 1.2 mm, an external diameter of 1.6 mm, and a length of 75 mm, filled with 1.5 mCi of ^99mTc solution. Projections of the capillary tube were obtained in the vertical and horizontal directions at different distances from the collimator face. Then, the spatial resolution was calculated as the FWHM of the LSF according to the NEMA standard.[9] The same procedure was carried out in the GATE environment for calculation of the spatial resolution. The difference between experimental and simulated FWHMs or sensitivities can be calculated using the following formula:

Difference = 100 × (Simulated − Experimental)/mean Eq. 1

Where mean is the average of simulated and experimental spatial resolution or sensitivity values.

System sensitivity

The sensitivity of a gamma camera is the quantity of how well it can detect gamma rays emitted by a radioactive source. It is usually expressed as the number of recorded counts per minute (cpm) per unit of source activity (µCurie) at a specified distance from the camera.[11] To acquire system sensitivity, a PMMA cylindrical phantom with an inner diameter of 36.5 mm and height of 4 mm was filled with 3 mCi of ^99mTc, located at the center of the field of view (FOV), at 3 cm away from the collimator face. A planar acquisition of this source was performed over 720 s and the total number of counts in the photopeak window (119–161 keV) was recorded. After image acquisition, the number of recorded photons was divided by the acquisition time and the source activity. Finally, the system sensitivity was calculated based on cpm/µCi. The same was implemented in the GATE environment and the sensitivity was computed in a similar way.

Energy resolution

The energy resolution was carried out using a PMMA flood phantom with dimensions 120 mm × 90 mm × 23 mm filled with 3 mCi ^99mTc. The phantom was placed on the collimator face so that it covers the entire useful FOV (UFOV). In the simulation environment, all parameters, for example, the energy window, the number of recorded photons etc., were set exactly like the experimental situation. The imaging ends after collecting 20 million photons. After plotting the detected photon energy spectrum for the experimental and simulated photons, a Gaussian curve was fitted to the spectrum to calculate the energy resolution. The energy resolution was expressed as the ratio of photopeak FWHM to photopeak energy (Eq. 2).[12]

Energy resolution(%)=      Eq. 2

Planar uniformity

Planar uniformity was tested using the same flood phantom and acquisition parameters for energy resolution. Then, the integral (IU) and differential (DU) uniformities for planar images were calculated according to the NEMA standard using the following formula:[9]

IU(%)=100×(Max-Min)/(Max+Min)      Eq. 3

DU(%)=100×(Max-Min)/(Max+Min)      Eq. 4

Maximum and minimum are defined as the maximum and minimum counts per pixel in the determined region. For IU, it is defined as the largest variation (maximum–minimum) in counts over the UFOV. This provides a general measure of uniformity across the entire imaging area. However, the DU is a more localized measure, evaluating the uniformity over small regions, typically using 5 × 5 pixels in both x and y directions, within the UFOV.

Optimization studies

The system spatial resolution is determined by two factors: (1) collimator spatial resolution which relies on collimator geometry, collimator material, source to the collimator distance (SCD), and radionuclide energy. (2) The detector spatial resolution: the accuracy of the scintillation events can be characterized, which is limited by the statistical fluctuations in the number of photons of light produced by the crystal and the output pulse from the SiPMs.[13] Therefore, it is very crucial to choose the appropriate materials and geometry for both the collimator and detector. To have the best collimator material and shape, parameters affecting the performance of imaging systems should be optimized by MC simulation. After that, the optimized setup is experimentally evaluated. In this part of the research, different collimator geometries and collimator materials were simulated using GATE to determine the optimal options for each of them.

Different configurations for the parallel-hole collimator

A parallel-hole collimator consists of a thick sheet of high-density and high atomic number metal with many tiny holes drilled through it. The holes are parallel to each other and perpendicular to the detection plane.[14] The parallel-hole collimator is the most ordinary kind of collimator employed in clinical SPECT imaging due to its simplicity, robustness, and versatility. Several factors affect the sensitivity and spatial resolution of a parallel-hole collimator, such as hole size and septa material.[15] Different hole diameters, namely, 0.6, 0.9, 1.2, and 1.5 mm, were studied. The septum was constant and equal to 0.2 mm. The collimator’s materials were tungsten and lead [Table 1]. The collimator thickness was constant and set to 35 mm.

Table 1.

The atomic number, density, and linear attenuation coefficient of collimator materials

Properties	Collimator material
	Pb	W
Atomic number	82	74
Density (g/cm3)	11.53	19.30
Linear attenuation coefficient (cm−1)	27.51	36.21

Spatial resolution in optimization evaluations

In the GATE environment, a capillary tube with an inner diameter of 1.2 mm, an external diameter of 1.6 mm, and a length of 75 mm, filled with 1.5 mCi of ^99mTc solution was placed at 0, 2, 4, 6, and 10 cm away from the collimator face with hole diameters of 0.6, 0.9, 1.2, and 1.5 mm. Then, the FWHM and full width at the tenth maximum (FWTM) of the LSFs were calculated. FWTM is a parameter that helps illustrate the effects of penetration and scattering on the image profile. Penetration and scattering are two important physical processes that degrade the quality and accuracy of SPECT images.

Sensitivity in optimization evaluations

A disc phantom with an inner diameter of 36.5 mm and a height of 4 mm was filled with 3 mCi of ^99mTc and acquisition time of 720 s, at 3 cm away from the collimator face. Then, the sensitivity (cpm/µCi) was expressed as the number of recorded photons over the acquisition time and the source activity. The collimator detector response function has three parts for the collimator, including the geometric, penetrating, and scattering. These three sections were analyzed for different collimator materials and hole diameters.

The spatial resolution-sensitivity tradeoff curve for tungsten

The sensitivity adjustment was made to range from the lowest to the highest planar FWHM for the SCD of 3 cm as this is the normal SCD for mouse imaging. Then, a trade-off curve for tungsten was drawn to improve the design of the collimating system, which shows the relationship between sensitivity and spatial resolution.

RESULTS

Validation of the Monte Carlo code

In the validation part, the results of the simulation against experimental data were compared and reported as follows:

Spatial resolution

The FWHMs of the experimental and simulated data as a function of SCD in the vertical and horizontal directions were computed [Figure 1]. The maximum difference between experimental and simulated FWHMs based on Eq. 1 was about 5% in the vertical and horizontal directions at the collimator surface.

Figure 1.

The system spatial resolution (mm) expressed as full width at half maximum for experimental and simulated data at different distances along Y (a) and X (b) axes

Sensitivity

The simulated and experimental planar sensitivities were 87.71 and 90.2 cpm/µCi at 3 cm away from the collimator face, respectively. The difference between them was <3% based on Eq. 1.

Energy resolution

The simulated and experimental energy resolutions were 27.0% and 26.6%, respectively. Hence, the difference between simulated and experimental is about 1%.

Uniformity

The IU and DU in UFOV and central FOV for simulated and experimental data were <3% and 2.5%, respectively [Table 2].

Table 2.

The integral and differential uniformity in useful field of view and central field of view for simulated and experimental data

	UFOV		CFOV
	Integral (%)	Differential (%)	Integral (%)	Differential (%)
Simulated	2.42	2.08	2.30	2.08
Experimental	2.91	2.35	2.82	2.35

UFOV: Useful field of view, CFOV: Central field of view

Collimator optimization

Spatial resolution

The planar spatial resolution based on FWHM (mm) for a variety of collimator materials, i.e., Pb and W, and hole diameters of 0.6, 0.9, 1.2, and 1.5 mm at different SCDs along X and Y axes is shown in Figure 2. Furthermore, FWTM (mm) for each material and hole diameter at different SCDs along X and Y axes is demonstrated in Figure 3.

Figure 2.

The planar spatial resolution for W and Pb with different hole diameters at source-to-collimator distances of 0, 2, 4, 6, 8, and 10 mm, along Y (a) and X (b) axes

Figure 3.

Full width at tenth maximum as a function of source-to-collimator distances for different collimator materials with hole diameters of 0.6, 0.9, 1.2, and 1.5 mm along Y (a) and X (b) axes. FWTM: Full width at tenth maximum

Sensitivity, geometric, penetrated, and scattering sections

The number of detected photons per minute per µCurie for various collimator materials and hole diameters at different SCDs is presented in Figure 4. The scattering, penetration, and geometric percentages as a function of collimator materials, for example, W and Pb with various hole diameters are also shown in Figure 5.

Figure 4.

The planar sensitivity as a function of hole diameter for different collimator materials

Figure 5.

The scattering and penetrated sections (a) and geometric portion (b) as a function of collimator materials with various hole diameters

The spatial resolution-sensitivity tradeoff for tungsten

The sensitivity adjustment was made to range from the lowest to the highest planar FWHM. A graph depicting the altered sensitivity and spatial resolution across various tungsten hole sizes was created, revealing an intersection at a hole diameter of 0.99 mm for the declared activity and acquisition time, indicating the point of tradeoff [Figure 6].

Figure 6.

The spatial resolution-sensitivity tradeoff as a function of hole diameter in tungsten. FWHM: Full width at half maximum

DISCUSSION

The purpose of this research was to validate an MC code for the HiReSPECT II scanner with a LEAP collimator and to discover the most optimal collimator material and hole diameter for this scanner using GATE. To validate the MC code, the simulated spatial resolution, sensitivity, energy resolution, and uniformity were compared with the experimental measurements. In the optimization part, two high-density collimator materials, namely, lead and tungsten with hole sizes of 0.6, 0.9, 1.2, and 1.5 mm, were used to evaluate the planar spatial resolution and sensitivity. Then, a tungsten collimator with a hole diameter of 0.99 mm was proposed according to the curve representing the tradeoff between spatial resolution and sensitivity.

In our study, the maximum difference (Eq. 1) between experimental and simulated results for spatial resolution along the horizontal and vertical directions was about 5% [Figure 1]. In addition, the spatial resolution along the horizontal (long) axis of the hexagonal collimator was worse than that along the vertical (short) axis. The holes are elongated along the horizontal axis, resulting in more blurring and reduced resolution. The longer holes allow more photons to pass through at varying angles, spreading the detected signals and hence diminishing the resolution. Conversely, the narrower holes along the vertical axis restrict the angles at which photons can pass through, leading to a more focused and sharper image. The difference in hole length and shape between the axes generates the anisotropic resolution, altering the spatial resolution depending on the collimator direction. Furthermore, the mean discrepancy between experimental and simulated sensitivities was <3%. The differences in energy resolution and uniformity were negligible.

Our findings are consistent with previous studies. For example, Telikani and Sadremomtaz[16] reported the experimental and simulated planar sensitivities of 1.31 and 1.38 cps/mCi on the collimator surface, respectively. The simulated and experimental spatial resolutions at 2.5 cm from the collimator surface were approximately 2.35 and 2.5 mm along the vertical direction, respectively. Furthermore, the simulated and experimental spatial resolutions were approximately 3.01 and 3.14 mm along the horizontal direction. Taheri et al.[17] found that sensitivities simulated by SIMIND, GATE, and MCNP were about 35.14, 35.25, and 36.85 cps/MBq, respectively. Furthermore, the spatial resolutions simulated by SIMIND, GATE, and MCNP were 2, 2, and 1.8 mm, respectively. Abbaspour et al.[18] validated HiReSPECT I using SIMIND, reporting the experimental and simulated energy resolutions for a ^99mTc point source at 5 cm distance from the collimator surface as 20.14% and 20.00%, respectively. Furthermore, the experimental and simulated planar sensitivities at 4 cm from the collimator surface were 33.585 and 34.259 cps/MBq, respectively. In addition, the experimental and simulated spatial resolution at 10 cm from the collimator surface was 5.8 and 5.7 mm, respectively. Pells et al.[19] modeled the Mediso AnyScan SCP SPECT system using GATE. The experimental and simulated planar sensitivities were 37.39 and 36.33 cps/MBq, respectively. The experimental and simulated spatial resolutions were 10.14 and 11.15 mm, respectively. These discrepancies between experimental and simulation results, which might be due to the imperfect modeling of the SiPMs response, differences between the simulated and actual back components of the detection plane, and the probabilistic nature of the physical processes involved in the simulation. The simulated model may not have all the complexities and details of the real imaging system. In other words, it may not have the exact, composition, component sizes, and/or parameters provided by the manufacturer. The model may also have some assumptions and simplifications that cause errors and fluctuations in the simulation results.

The spatial resolution of a parallel-hole collimator generally has a linear relationship with the SCD. However, in our study, this relationship was not consistently linear at certain distances [Figure 1]. When capillary tubes are employed for quantification in the pixelated detector, the spatial resolution particularly relies on the relative position of the capillary source to the detector’s elements. If the capillary tube is situated above the center of a physical pixel, the optical signal is shared between fewer pixels, resulting in a narrower FWHM. Nonetheless, when the source location is between the pixels, the emission signal is divided between a larger number of pixels, so FWHM becomes wider and the spatial resolution worse.

In general, the sensitivity of a gamma camera depends on the collimator configuration, collimator material, energy resolution, energy window, and intrinsic crystal efficiency.[20] In other words, larger hole diameter, increasing the number of holes, thinner septa, and shorter hole length, using collimator materials with low density and low atomic number will boost the sensitivity of the collimator.[21] According to the results of our study, lead has more sensitivity than tungsten, which is related to the lower density and linear attenuation coefficient of Pb compared to W [Table 1 and Figure 4]. Consequently, there is an increase in penetrated and scattered photons, resulting in a broader FWTM and a decline in spatial resolution [Figures 3 and 5]. Given that spatial resolution takes precedence over sensitivity in imaging small animals, tungsten is favored over lead due to its superior properties in this regard.

Furthermore, increasing the hole diameter from 0.6 to 1.5 mm degrades the planar and augments the sensitivity. A smaller hole diameter results in better spatial resolution as it allows for a tighter focus of the incoming gamma rays, generating a sharper image. As the hole’s diameter increases, the gamma rays pass through each hole through a wide range of angles, allowing more photons to penetrate and scatter. This blurs the image and thus degrades the spatial resolution [Figures 2, 3 and 5]. A larger hole diameter improves sensitivity since more gamma rays can pass through the collimator and reach the detector [Figure 4]. This results in a higher count rate, which is particularly beneficial when the radiotracer’s activity is low or when rapid scanning is required. Besides, the optimized hole diameter for tungsten is 0.99 mm as indicated by the curve representing the tradeoff between spatial resolution and sensitivity [Figure 6].

CONCLUSION

The collimator is an essential component in SPECT because it determines the spatial resolution and sensitivity, which affects image quality and quantitative accuracy. In particular, the collimator geometry and material have a significant impact on image quality. The results of our research suggest that enlarging the hole diameter enhances sensitivity while diminishing spatial resolution. The observed effects are not solely due to the increased hole size but also to the amplified penetration and scattering that occur as the hole diameter grows.

Furthermore, a hexagonal-hole collimator made of Pb showed better sensitivity than W collimator due to lower density and linear attenuation coefficient. Moreover, the maximum difference between planar spatial resolutions in Pb and W for hole diameters of 0.6, 0.9, and 1.2 mm is 0.9 mm in conventional SCDs, i.e., below 60 mm. To sum up, the spatial resolution of lead is slightly lower than that of tungsten because lead allows for greater penetration and scattering. Furthermore, expanding the hole size further enhances these penetration and scattering effects. Furthermore, the curve for the trade-off between spatial resolution and sensitivity shows a hole diameter of 0.99 mm. Therefore, a tungsten collimator with a hole diameter of 0.99 mm is suggested.

Conflicts of interest

There are no conflicts of interest.

Funding Statement

This project was supported by Tehran University of Medical Sciences under grant number [67946].