Impact of Collimator Material on Spatial Resolution and Sensitivity in Semiconductor-Based Imaging Systems: A Monte Carlo Evaluation

Abstract

Background:

In gamma cameras, there is significant interest in developing novel devices that employ a semiconductor detector. The most significant quality control parameter for assessing the performance of gamma cameras with parallel-hole collimating is the spatial resolution. Acceptable spatial resolution is due to the high absorption and stopping power of collimator materials, while they may lead to a reduction in sensitivity in the same condition. Thus, a comparison between sensitivity and spatial resolution is crucial in nuclear medicine imaging devices.

Aims and Objectives:

This work aimed to compare spatial resolutions using pixellated parallel-hole collimators with lead and tungsten at equal sensitivity to assess the camera’s performance.

Materials and Methods:

The overall imaging system was simulated using a Geant4 Application for Tomographic Emission simulation tool. Furthermore, source-to-detector distance effects on image performance and spatial resolution were evaluated using a simulated hot-rod phantom. The full width at half maximum (FWHM) and the full width at tenth maximum (FWTM) stand for the spatial resolution.

Results:

The averages of measured FWHM using lead at equivalent sensitivities were 3.28% greater than that of tungsten. Furthermore, the averages of measured FWTM of lead at equivalent sensitivities were 7.99% greater than those obtained with tungsten.

Conclusion:

The results demonstrated that at a specific sensitivity, lead provides better spatial resolution than tungsten.

Introduction

Single-photon emission computed tomography (SPECT) and planar systems employing a sodium iodide (NaI) scintillation detector are commonly utilized in gamma cameras for medical imaging. It can be made of relatively efficient and large scintillation crystals. NaI(Tl) scintillation detectors are available in several different sizes and have a relatively low cost. Consequently, they are commonly employed in nuclear medicine imaging systems. However, they have some obstacles, such as a relatively low-energy resolution. These systems (using NaI[Tl] crystal scintillation and photomultiplier tubes) have inherent spatial resolution issues due to statistical detection fluctuations and mispositioning of gamma photons.[1,2] Many studies have proposed changing the NaI(Tl) scintillator crystals with other types to provide better images and high spatial resolution.[3,4]

Recently, the most developed detectors are semiconductor materials, based on room temperature. These materials enhance both intrinsic spatial resolution, counting efficiency, and sensitivity. For achieving acceptable spatial resolution for the planar or SPECT scintillation camera, semiconductor materials, such as cadmium telluride (CdTe), were usually employed for pinhole collimators.[5,6,7] However, the imaging system based on pinhole collimation and semiconductor materials has a limited use due to its low sensitivity, which is related to its small pinhole size.[8,9,10] Measurement quality control (QC) tests, such as spatial resolution and sensitivity, should use parallel-hole collimators to enhance gamma camera performance. Hence, applications of pixellated semiconductor detectors and parallel-hole collimators are highly recommended to increase these QC tests.[11,12,13] In addition, the collimator should be built of a material with a high-stopping power and atomic number to enhance the spatial resolution of the SPECT imaging systems.[14,15] Collimators made of materials with relatively higher stopping power, such as tungsten and lead (as used in this study), which have atomic numbers of 82 and 74 and densities of 11.53 and 19.3 g/cm³, respectively.[16] However, to achieve better spatial resolution, sensitivity must be sacrificed since fewer gamma photons are detected. Therefore, finding a balance between sensitivity and spatial resolution is crucial for the development of SPECT imaging systems.

The present work aims to compare, at equivalent sensitivities, the spatial resolutions of parallel-hole collimators made from lead and tungsten (with a pixellated semiconductor detector and pixellated collimators for SPECT system). All measurements were conducted employing a Geant4 Application for Tomographic Emission (GATE) simulation. At equivalent sensitivities, spatial resolutions for lead and tungsten collimator materials were measured. Furthermore, hot-rod phantom images were obtained for all source-to-detector distances (SDDs) using the GATE simulation tool.

Materials and Methods

Currently, in the field of nuclear medicine and therapy, Monte Carlo simulations are a crucial and important tool. The medical application of GATE (OpenGATE collaboration institutions laboratories, Lyon, France) simulations has been illustrated in several studies.[17,18,19,20] In this work, GATE 9.1 simulations were carried out using the Geant4 toolkit, a validated physics model, a geometry model tool from the Geant4 (GEometry ANd Tracking) platform, and the ROOT CERN framework. All simulations were measured with GATE 9.1 to estimate the acquired image quality according to the proposed plan.

Semiconductor materials have been extensively studied for nuclear medicine imaging, especially cadmium zinc telluride and CdTe. Convenient properties of CdTe include its high atomic number and wide bandgap, which can improve detection efficiency performance at room temperature.[21,22] Consequently, CdTe is actually appropriate for gamma-ray detecting applications. A CdTe semiconductor detector was modeled using a PID 350 (AjatOy Ltd., Finland), which consists of a 44.8 × 44.8 mm² detector with a 1 mm thickness and 128 × 128 pixels. The detector thickness strongly affects the detection efficiency. Furthermore, Lee et al. clarified that the CdTe semiconductor detector produces a better detection efficiency at 140 keV of gamma photon energy.

The linear attenuation coefficient exhibits the effectiveness of a particular material at generating gamma-ray interactions per unit thickness. To describe attenuation, the mass attenuation coefficient is frequently used. CdTe material has a higher attenuation coefficient than the commonly used NaI(Tl) material in scintillation detectors. In addition, a pixellated semiconductor detector from CdTe provides better detection efficiency than NaI material with similar thickness (for 140 keV gamma photons).[12]

The collimator is an important part of the SPECT and imaging systems. Gamma photons travel through one or more collimator septa without interacting, whereas the photons that interact with collimator septal material deflect the scattered photons onto the detector. The imaging system detects both scattered and nonscattered photons. The collimator septal would prevent more scattered photons from being counted and detected. These scattered photons are generally inappropriate due to their false positional information. Both primary and scattered photons play a crucial role in image formation; however, scattered photons could significantly degrade image quality, resulting in inaccuracies. Thus, the collimator design has a strong effect on the image quality and some quality assurance parameters such as contrast, uniformity, spatial resolution, and sensitivity.[23,24]

There are different types of collimators: converging, diverging, pinhole, and parallel-hole. Parallel-hole collimators are widely employed for planar and SPECT acquisitions. These collimators are designed to allow the system to be uniform, which gives better results in spatial resolution and sensitivity according to its geometry.[25,26] A parallel-hole collimator’s resolution R, and its efficiency ε, can be determined as follows:[27]

where, h_effective=h–2μ^-1,      (2)

where d stands for the hole’s diameter, h_effective stands for the effective septal height, and h stands for the septal height. The effective length of the collimator is less than the geometric length because gamma rays penetrate the edges of the collimator material.[28] L stands for the SDD, µ stands for the collimator material’s linear attenuation coefficient, t stands for the septal thickness, and F stands for a factor that relies on the pattern alongside the collimator hole’s shape (F = 0.28 for square patterns, 0.24 for round patterns, and 0.26 for hexagonal patterns).[29]

A parallel-hole collimator with a square hole was designed for a semiconductor detector. The collimator hole was equal to the pixel size. Excellent spatial resolution results were provided using this collimator because each pixel could individually collect gamma photon signals. The collimator’s hole dimensions were 0.3 × 0.3 mm² with a 0.05 mm thickness of the septum from lead and tungsten materials. These materials have high densities, so they have greater linear attenuation coefficients for gamma photons. Therefore, these collimator materials were used in this work.

Several methods have been introduced for determining the thickness of the septum using the shortest path length, as a gamma photon must penetrate through collimator material.[30]

The values of the minimal septal thickness for hole diameters d and h_effective can be calculated from Equation (4) which provides the relation between h_effective, d, and t.

where ω is the smallest distance (a gamma photon can travel between one hole and an adjacent one). Gamma photons have a 5% penetration limit along the smallest path length. Therefore, Equation (4) can be modified to provide the transmission according to the collimator materials (linear attenuation coefficient, µ).

The linear attenuation coefficients, µ, of lead and tungsten materials are 27.51 cm⁻¹ and 36.21 cm⁻¹, respectively, for ^99mTc photon energy (140 keV). As mentioned above, a septal thickness was verified that 0.05 mm was appropriate (at a photon energy peak of 140 keV of ^99mTc).

A point source of ^99mTc with 1 MBq activity was simulated to evaluate the detector’s counting performance. The acquisition time was 15 min; over 360°, 90 projection views were obtained through 4° steps. Events were taken using an energy window range of ^99mTc (133 − 153 keV), which is used in imaging. The acquisition period was 10 s/view. The ordered subset expectation maximization method with four subsets and five iterations was used for image reconstruction. At a specific sensitivity, the full width at half maximum (FWHM) and the full width at tenth maximum (FWTM) of the point spread function were used to calculate and evaluate the spatial resolution. Both FWTM and FWHM values were calculated, estimating the radius where the total distribution achieved one tenth or one half, respectively, of its peak (greatest value).

These calculations were carried out for various collimator materials to determine the sensitivity equivalence. The septal height of collimator materials (lead and tungsten) varied with 1 mm increments from 15 up to 30 mm. Calculations for sensitivities were performed at 7.2, 3.98, 2.89, and 2.20 k counts per second per kBq (kcps/kBq). According to these results, the septal heights were calculated for various collimator materials at equivalent sensitivities [Table 1]. In this work, eight simulations were carried out for each SDD with uncertainties provided by the standard deviation from the mean.

Table 1.

Height of the septum in mm for equivalent sensitivities normalized to tungsten

Sensitivity (kcps/kBq)	Septal heights (mm)
	Tungsten	Lead
7.20	15	15.24
3.98	20	20.47
2.89	25	25.32
2.20	30	31.49

Finally, to assess the system’s overall image quality, a hot-rod phantom was designed using the GATE tool. The phantom contained a ^99mTc water solution and six rods (six hot areas with different diameters and different activities). The rods were placed in the water solution with diameters of 2.1, 1.8, 1.5, 1.2, 0.85, and 0.5 mm and different activities of 90, 60, 45, 30, 15.5, and 9 kBq, respectively [Figure 1]. Large diameters are to simulate the large organs (imaging is 2–3 mm in size, e.g., in thyroid nodules), and small diameters are to simulate the smaller organs (spatial resolution is below 1 mm, e.g., in brain imaging). As the organs within the body have different responses to radioactive substances, rod activities were chosen to evaluate the system sensitivity.[17]

Figure 1.

The phantom containing six hot-rod areas with different diameters and activities[17]

Results and Discussion

A pixellated CdTe semiconductor detector with a pixellated parallel-hole collimator was employed to improve both resolution and sensitivity. Based on the study by Lee et al.[6] in 2013, our system exhibited a similar behavior; at a 2 cm SDD, the spatial resolution was approximately 0.70 mm. The enhanced sensitivity was attributed to the detection of gamma photons by each of the pixels. The investigation focused on lead and tungsten, which are the most commonly used collimator materials. As high-absorption collimator materials have the potential to enhance the spatial resolution, they simultaneously reduce the sensitivity. On the other hand, increasing the sensitivity using low-absorption materials may reduce the spatial resolution. Consequently, developers have to investigate this trade-off to achieve better sensitivity and acceptable spatial resolution. The improvement of these quantities is the main goal for any imaging system.

In this work, at equal sensitivity, the spatial resolutions for lead and tungsten were evaluated. The sensitivities for both materials were calculated to estimate the septal heights at equal sensitivities. This calculation was conducted for septal heights ranging from 15 to 30 mm, in 1 mm increments. Subsequently, spatial resolutions were measured at 7.20, 3.98, 2.89, and 2.20 kcps/kBq.

Figure 2a illustrates that at SDD = 1 cm, there is a gradual increase in the FWTM with increasing detector sensitivity for tungsten and lead collimator materials (e.g., from 1.01 to 1.17 mm for tungsten material, with uncertainty ranging from 4.8 × 10⁻³ mm to 12 × 10⁻³ mm, respectively, and from 0.961 to 1.116 mm for lead material, with uncertainty ranging from 5.7 × 10⁻³ mm to 12.9 × 10⁻³ mm, respectively). The same graph exhibits that at SDD = 1 cm, there is a slight increase in FWHM with increasing the system sensitivity for tungsten and lead collimator materials (e.g., from 0.546 to 0.649 mm for tungsten material, with uncertainty ranging from 3.7 × 10⁻³ mm to 9.8 × 10⁻³ mm, respectively, and from 0.494 to 0.584 mm for lead material, with uncertainty ranging from 5.3 × 10⁻³to 9.1 × 10⁻³ mm, respectively). Moreover, the graph demonstrates the increase of the values of FWTM and FWHM at equal sensitivities and equal SDD for different collimator materials (for example, at a sensitivity of 7.20 kcps/kBq and SDD = 1, there are clear increases in FWTM from 1.116 for lead to 1.17 for tungsten and increases in FWHM from 0.584 for lead to 0.649 for tungsten).

Figure 2.

Variation of full width at half maximum and full width at tenth maximum was evaluated at equivalent sensitivities (7.20, 3.98, 2.89, and 2.20 kcps/kBq) for lead and tungsten collimator materials with SDD ranging from 1 to 5 cm. (a-e) correspond to SDD = 1, 2, 3, 4, and 5 cm, respectively. The error bars on the figures stand for the standard deviation from the mean (most of the error bars do not appear on the graph because they are too small). FWHM: Full width at half maximum, FWTM: Full width at tenth maximum, SSD: Source-to-detector distance

Based on these results, as depicted in Figure 2a-e, the spatial resolutions at equivalent sensitivities change when transitioning from lead to tungsten. The average spatial resolutions for lead and tungsten were evaluated and compared from the FWHM at 7.20 kcps/kBq; lead was 3.28% greater than that of tungsten. In the instance of FWTM, the values obtained with lead were 7.99% greater than those obtained with tungsten. Furthermore, results at 3.98, 2.89, and 2.20 kcps/kBq behaved a similar behavior. Based on these findings and regardless of the SDD, the spatial resolution of lead had a better value at a constant sensitivity.

Figure 3 reveals the reconstructed hot areas (rods) images of the simulated phantom at SDDs of 1 and 5 cm. At a distance of 1 cm from the detector, the rods of 0.85 mm and 0.5 mm were distinguishable for every value of sensitivity. Highly resolved SPECT devices are valuable in preclinical research and tracer development. Lee et al.,[6] 2013, have revealed a technique on a small-animal imaging system and the pinhole collimator SPECT that can provide images with spatial resolutions of around 0.4 mm (2.4 magnification factor with a 0.25 mm hole diameter). The spatial resolutions of pixellated systems (have parallel-hole collimators and semiconductor SPECT detectors) are comparable to those of pinhole collimators (nonpixellated). While pixellated detectors using pinhole SPECT detectors have less sensitivity than parallel-hole SPECT systems. Moreover, at the SDD of 5 cm, all rods in the acquired images with diameters of 1.5, 1.8, and 2.1 mm were resolved for every equivalent sensitivity.

Figure 3.

The images of the hot-rod phantom were taken using different collimator materials (lead and tungsten) at certain sensitivities and a source-to-detector distances (SDDs) of 1 and 5 cm (SDDs of 2, 3, and 4 cm not shown). SSD: Source-to-detector distance

While lead possesses impressive attenuation properties suitable for gamma-ray collimation, tungsten exhibits superior attenuation capabilities. Nevertheless, lead is generally favored over tungsten because of its lower cost. However, the higher cost and weight of tungsten collimators make them more beneficial for smaller applications, like pinhole collimators, where the actual aperture can be constructed from tungsten while the surrounding collimator housing is made of lead.[31,32] Furthermore, a limitation of tungsten is its high melting point, which prevents it from being cast like lead-based collimators. In addition, tungsten is difficult to machine, making tungsten collimators more expensive compared to lead collimators. All collimator materials used in commercial collimating for nuclear medicine imaging must have acceptable attenuation characteristics, be easily available, be low-cost, and be easily machinable.

Conclusion

The spatial resolution for a pixellated semiconductor detector at equivalent sensitivities using GATE simulations was studied. Pixellated parallel-hole collimators made from tungsten and lead materials were applied. The results demonstrated that at a specific sensitivity, lead provides better spatial resolution than tungsten. Moreover, when comparing the obtained phantom images using each collimator material at equivalent sensitivities, it was challenging to make accurate distinctions. Finally, the results showed that materials with lower absorption and stopping power, such as lead, performed nearly as effectively in imaging systems as tungsten at an equivalent sensitivity.

Conflicts of interest

There are no conflicts of interest.

Funding Statement

Nil.