1 Introduction

211At is an alpha-emitter nuclide that has been used in targeted alpha-particle therapy for cancers such as ovarian cancer [1–3]. Figure 1 shows the decay scheme of this nuclide. Alpha particles possess large emission energies (5–9 MeV) and extremely short path lengths (40–100 μm) compared to beta particles; therefore, linear energy transfer is significantly large [4–8]. The advantage of alpha particles lies in their ability to concentrate energy on an extremely small tumor without affecting normal tissue. Astatine belongs to the halogen family, and its chemical properties resemble those of iodine; therefore, it may be a promising nuclide for the radiotherapy of thyroid cancer instead of the beta-emitter 131I [3].

Fig. 1
figure 1

Decay scheme of 211At

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Owing to the increasing expectations for the clinical application of 211At, its direct imaging for the in vivo evaluation of alpha-particle dosimetry has gained importance. Because the path length of alpha particles is extremely short, the distribution of the administered radioactive drug corresponds to the distribution of the absorption of alpha particles. After alpha decay, 211At emits X-rays between 70 and 90 keV and a few gamma rays that are available for the evaluation of alpha-particle dosimetry. 211At imaging has recently been attempted using Compton cameras [9, 10]. However, the intensity of high-energy gamma rays (570 keV), which was targeted in the Compton camera study, has been shown to be considerably low for imaging [10]. Therefore, currently, conventional gamma camera equipment will be promising.

Several researchers have already reported single-photon emission tomography (SPECT) of 211At [11–14]. In these studies, X-rays of approximately 80 keV were detected using a medium-energy collimator. The deterioration of the image quality owing to scattering photons and characteristic X-rays from the lead collimator is a drawback. In the case of radium-223 (223Ra), when X-rays of 84 keV are used for imaging with a low-energy collimator, many characteristic X-rays pass through the energy window and disturb the image. This problem can be partially resolved using a medium-energy collimator with a thicker septum [15–17]. Thus, the choice of collimator is an important factor in obtaining a suitable image [18, 19]. In addition, attenuation and scatter corrections affect the image quality and feasibility of SPECT imaging. Few studies have been conducted on SPECT imaging of 211At [11–14]. Turkington et al. conducted the first study on SPECT imaging of 211At and concluded that a medium-energy collimator is optimal [11]. Subsequent studies used medium-energy collimators with reference to their conclusion [12–14]. However, investigations for the optimum collimator appear insufficient because they focus only on the energy spectrum. Furthermore, the effect of correction on the image quality has not yet been quantified.

In this study, we investigated the optimal conditions for producing 211At SPECT images and the feasibility of using Monte Carlo simulations. Simulation studies are advantageous because they allow the testing of various conditions and settings and provide information that is unavailable in experiments. In this study, we focused on the impact of the collimator, attenuation correction (AC), and scatter correction (SC) on the image quality.

2 Materials and methods

The Monte Carlo simulation used in this study was the MCEP-SPECT model [20], which is based on the gamma camera simulation codes HEXAGON and NAI developed by Tanaka et al. [21]. The simulation setup is shown in Fig. 2. A National Electrical Manufacturers Association (NEMA) body phantom containing six spheres of different diameters (37, 28, 22, 17, 13, and 10 mm) was used. Two gamma cameras were placed 26 cm from the center of the phantom. The phantom was filled with water with a radioactivity concentration of 1 kBq/mL, and six spheres were filled with radioactivity concentrations of 5, 10, and 20 kBq/mL. The projection number was 60 (separation angle: 6°), and the acquisition time was 60 s per direction (total acquisition time: 30 min).

Fig. 2
figure 2

Setup of a gamma camera for the simulation and cross-sectional view of the phantom

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Table 1 presents the radiation used in the simulation model. The main radiation is of 79.29 keV, and thus, the energy window was set to 71–88 keV (± 10%). Two radiations at 569.6 keV and 897.8 keV are attributed to polonium-211 (211Po), the daughter nuclide of 211At. Table 2 lists the dimensions of the collimators used in the simulation. Three collimators were used for low-energy and one for medium-energy.

Table 1 List of radiations
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Table 2 Dimensions of collimators
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The projection data were preprocessed using the Butterworth filter (order: 8 and cutoff frequency: 0.5 cycle/cm) and reconstructed using the ordered subset-expectation maximization (OSEM) method with subsets 6 and 10. Attenuation and scattering corrections were applied to improve the image quality. The Chang method with an attenuation coefficient of 0.182 cm−1 was used for attenuation correction [11]. The triple-energy-window (TEW) method, in which the upper and lower energy windows are 88–96 keV and 63–71 keV, respectively, was used for scatter correction. These processes were performed using Prominence Processor Version 3.1, a software package for research and education in nuclear medicine [22].

The SPECT images were evaluated based on two quantitative indices: contrast-to-noise ratio (CNR) and contrast recovery coefficient (CRC). The CNR is expressed as.

$${\text{CNR}} = \frac{{C_{{\text{H}}} - C_{{\text{B}}} }}{{SD_{{\text{B}}} }},$$
(1)

where CH and CB denote the mean counts inside the region of interest (ROI) of the hot area and ten ROIs of the background areas, respectively, and SDB denotes the standard deviation of the counts inside the background ROIs. CNR, which is the ratio of the net magnitude of the signal in the hot area to the fluctuation of the background, indicates the detectability of the hot area. This area was detectable when the CNR value exceeded 5.

The CRC is expressed as.

$${\text{CRC}} = \frac{{{\raise0.7ex\hbox{${C_{{\text{H}}} }$} \!\mathord{\left/ {\vphantom {{C_{{\text{H}}} } {C_{{\text{B}}} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${C_{{\text{B}}} }$}} - 1}}{{R_{{{\text{HB}}}} - 1}} \times 100 \left( \% \right),$$
(2)
$$R_{{{\text{HB}}}} = \frac{{A_{H} }}{{A_{B} }},$$

where AH and AB denote the activity concentrations of the hot sphere, and background, respectively, and RHB denotes the ratio of the hot concentration to the background. CRC indicates the measurement and quantitative accuracies of the activity. The distribution of the ten background ROIs is shown in Fig. 3.

Fig. 3
figure 3

Regions of interest used in the calculation of the CNR and CRC. The solid and dashed circles represent the hot and background areas, respectively

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3 Results

Figure 4 shows SPECT images (RHB = 20) with both attenuation and scatter corrections. The image with the low-energy high-resolution (LEHR) collimator is the clearest, and the outline of the hot sphere is clearly visible.

Fig. 4
figure 4

Simulated SPECT images for RHB = 20, 10, 5

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Figure 5 shows the CNR values for each sphere and each ratio of hot to background concentrations. The low-energy high-sensitivity (LEHS) collimator exhibited the highest detectability among the four types of collimators, with a maximum CNR value of 43. However, the CNR value decreased rapidly with decreasing sphere size. The LEHR collimator generally demonstrated better detectability and was detectable (CNR > 5) in a 13-mm sphere.

Fig. 5
figure 5

CNR values for a each sphere size and b each ratio of hot to background concentration. The dashed line represents the threshold of detection (CNR = 5)

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Figure 6 shows the CRC values. The LEHR collimator exhibited excellent quantitativity, and the maximum CRC value was approximately 100%. The performance of the LEHS collimator was inferior in terms of quantitativity. The low-energy general-purpose (LEGP) collimator performed better than LEHS.

Fig. 6
figure 6

CRC values for a each sphere size and b each ratio of hot to background concentration

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The aforementioned results were obtained using both attenuation and scatter corrections. To assess the impact of scatter correction, Fig. 7 shows the results with only attenuation correction and those with both attenuation and scatter correction. Both the CNR and CRC values improved for all collimators when both corrections were used. In particular, the CRC values doubled when the scatter correction was used. The scatter correction was more effective in improving the CRC value (quantitativity) than the CNR value (detectability).

Fig. 7
figure 7

Impact of attenuation correction (AC) and scatter correction (SC) on a CNR and b CRC values

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To consider these characteristics, Fig. 8 shows the partial sensitivity of projection data. The partial sensitivity indicates the counts per source radioactivity (counts/MBq) in each photon detection process denoted as “dir0,” “dir1,” “indir,” and “Pb-X.” In Fig. 8, “dir0” denotes the detection process of photons passing through the collimator hole without interacting with the phantom. The detection of photons that interact with the phantom but pass through the collimator hole without interacting with the collimator wall is indicated as “dir1.” The process that collide with, penetrate, or interact with the collimator wall irrespective of whether they interact with the phantom are shown as “indir,” and “Pb-X” denotes characteristic X-rays from lead [21]. Such “partial sensitivity” cannot be measured experimentally.

Fig. 8
figure 8

a Partial sensitivities (cps/MBq) in the window of 77–88 keV and b ratio of the partial sensitivity to the total sensitivity

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The ratios of the “dir0,” “dir1,” “indir,” and “Pb-X” components to the total sensitivity were 40–50%, 30–40%, 10–20%, and 3–10%, respectively. The total sensitivity was the highest for the LEHS collimator. The ratios of “indir” and “Pb-X” of the LEHR and LEGP collimators were larger than those of the other collimators.

4 Discussion

The results in Figs. 5 and 6 show that the collimators in this study performed well when the hot-to-background ratio (RHG) was high and the sphere size was large. However, even the detection of the 37-mm-sphere became difficult when the RHG decreased to 5. The performance of the LEHS and medium-energy general-purpose (MEGP) collimators deteriorated more rapidly as the size of the spheres decreased.

The collimator performance depends on the dimensions, particularly the aspect ratio, which is the ratio of the length to the hole diameter [23]. A collimator with a large aspect ratio effectively blocks photons that do not enter perpendicular to the detection surface. This results in less sensitivity, less blurring of the image, and higher resolution. The aspect ratio of the LEHR and LEGP collimators was 20 or more, whereas those of the LEHS and MEGP collimators were approximately 10. Therefore, the CRC values for the LEHR and LEGP collimators were higher than those for the LEHS and MEGP collimators. The images generated by a collimator with a large aspect ratio have less spread owing to blurring and less leakage of counts from the ROI, resulting in a larger CRC value. A low aspect ratio yields a low spatial resolution. The CNR values for the LEHS and MEGP collimators were high for large spheres; however, the CNR value decreased rapidly with decreasing sphere size owing to the low resolution.

Our study revealed that the effect of scatter correction was particularly significant. The scattered photons blur the image and increase the background count (CB in Eq. 2), resulting in a reduced CRC value. Because X-rays of 80 keV are used for 211At SPECT, the scattered photons have a significant impact. As shown in Fig. 8, the components of the scattered (“dir1”) and direct photons (“dir0”) were approximately equal. The count leaks from the ROI were effectively removed, and the CRC value was significantly improved by removing these large numbers of scattered photons. On the other hand, scatter correction reduced CB and increased SDB, resulting in increased background noise. However, the contrast of the hot area (CH–CB) improved, and the CNR value consequently increased for the setting in this study. To improve quantification, scatter correction is important and necessary.

Another problem with 211At SPECT is the effect of characteristic X-rays emitted from the lead collimators and scattered photons in the collimators. The energy of the characteristic X-rays was approximately 77 keV; this was within the main energy window. The “Pb-X” component cannot be removed by scatter correction; therefore, the image quality is not improved. In 223Ra imaging using a low-energy collimator, a large number of characteristic X-rays disturb the image. This difficulty can be partially resolved using a medium-energy collimator with a thicker septum. MEGP and high-energy general-purpose (HEGP) collimators have been reported to be suitable for imaging 223Ra [16, 17]. In contrast, low-energy collimators performed well for 211At imaging because 211At emits fewer high-energy gamma rays that generate characteristic X-rays. The emission intensities of high-energy gamma rays presented in Table 2 are two to six orders of magnitude lower than those of X-rays (in the case of 223Ra, the difference is within one order of magnitude). The component of the characteristic X-ray (“Pb-X”) shown in Fig. 8 is approximately 10% or less; this is considerably less than the 30–40% of 223Ra [16]. For the same reason, the effect of the scattered radiation from the collimator is small. The “indir” component for low-energy collimators is 10–20%; this is half that of 223Ra [16] and one third that of 123I [21]. Finally, the “Pb-X” and “indir” components within the main energy window depend on the intensity of high-energy γ-rays. 211At produces less high-energy gamma rays than 223Ra and 123I, and the use of low-energy collimators is possible for 211At.

The first SPECT imaging study on 211At concluded that the optimal collimator is a medium-energy collimator because it has a small high-energy tail above the photopeak of 90 keV [11]. This matches with the smallest “indir” for the MEGP collimator, as shown in Fig. 8. However, our study suggested that low-energy collimators were more suitable than medium-energy collimators. As shown in Fig. 6, low-energy collimators (LEHR and LEGP) were superior to MEGP in terms of quantification.

5 Conclusion

Low-energy collimators with high aspect ratios were noted to be suitable for SPECT imaging of 211At. Scatter correction was extremely effective in improving the image quality. The feasibility of 211At was demonstrated for lesions larger than 20 mm.