Optimization of image reconstruction method of cerebral blood flow perfusion imaging with digital CZT SPECT

Purpose The purpose of this study is to evaluate the effects of filtered back projection (FBP), ordered subset expectation maximisation (OSEM), and different filters on cadmium zinc telluride single-photon emission computed tomography [CZT single-photon emission computed tomography (SPECT)] cerebral blood perfusion image quality to optimise the image reconstruction method. Methods Under routine clinical conditions, tomographic imaging was performed on the phantom and patients. Image processing included image reconstruction using FBP and OSEM, and the filtering method used Butterworth (Bw) and Gaussian (Gs) filters. Visual and semi-quantitative parameters [integral uniformity, root mean square (RMS) noise and contrast and contrast-to-noise ratio (CNR)] were used to evaluate image quality to optimise image reconstruction parameters. One-way and two-way analysis of variance were used to process phantom and clinical data. Results In the tomographic images of the phantom, the semi-quantitative analysis showed that the integral uniformity of FBP+Bw was better than that of OSEM+Bw and OSEM+Gs (P < 0.05), and that the RMS noise of FBP+Bw was lower than that of OSEM+Bw and OSEM+Gs (P < 0.001). The contrast of FBP+Bw and OSEM+Bw in the cold area diameter ≥2 cm group was higher than that of OSEM+Gs (P < 0.001), whereas the CNR of FBP+Bw was higher than that of OSEM+Bw and OSEM+Gs (P < 0.001); the contrast of OSEM+Bw cold area diameter <2 cm was higher than that of FBP+Bw (P < 0.01). The semi-quantitative analysis results of the clinical images were consistent with the phantom’s. Conclusion In CZT SPECT cerebral blood flow perfusion imaging, it is suggested that the image postprocessing method of FBP+Bw (fc = 0.40; n = 10) should be used routinely in clinical application, and if there are uncertain small lesions in the processed image, it is suggested to use the reconstruction method of OSEM+Bw (EM-equivalent iterations = 60; fc = 0.45; n = 10) instead.


Introduction
As a common clinical neurologic disease, the ischemic cerebrovascular disease has high disability and mortality rates worldwide. Cerebral blood perfusion imaging can be used to assess the local cerebral blood flow and cerebrovascular reserve at rest, and it has unique advantages in lesion guidance; prognostic evaluation of many diseases such as cerebral infarction, transient ischemic attack (TIA), epilepsy and other ischemic lesions [1][2][3].
With the development of imaging technology, especially functional imaging, single-photon emission computed tomography (SPECT) has played an increasingly important role in the localisation and diagnosis of ischemic cerebrovascular diseases. In recent years, the development of digital universal cadmium zinc telluride (CZT) cameras has promoted new advances in SPECT imaging technology. When compared to SPECT equipped with a traditional sodium iodide detector (NaI SPECT), cadmium zinc telluride single photon emission computed tomography (CZT SPECT) provides better image quality, and and was equipped with wide-energy high-resolution collimators aligned with the pixel array. The image was processed using a Xeleris 4.0 workstation (GE Healthcare, USA).
The phantom used was the Jaszczak phantom (Deluxe ECT Phantom, Model ECT/DLX/P, Data Spectrum Corporation, USA), which was divided into a uniform area (background area) and a cold area (defect area). There were no plug-ins in the uniform zone, and there were six solid ball plug-ins in the cold zone (their diameters were 31. 8, 25.4, 19.1, 15.9, 12.7 and 9.5 mm).
The background area of the phantom was filled with water and injected with 99m TCO 4 solution 480 MBq (specific activity: 0.069 MBq/mL). After the phantom was full oscillation, it was placed for 2 h, so that the solution in the phantom was fully mixed.

Phantom imaging
The phantom was placed within the detector's field of view (FOV), where the axis was parallel to the long axis of the scanning bed. The image acquisition scheme simulated the clinical acquisition method. The SPECT parameters used were automatic human body contour technology, the acquisition matrix was 128 × 128, the pixel size was 3.32 mm, the zoom was 1.33, the acquisition speed was 20 s/frame, with a total of 120 frames, with the photopeak of 99m Tc as the centre, and the energy window was 140 keV ± 7.5%. The CT scanning parameters were as follows: tube voltage was 120 keV; tube current, 150 mA; slice thickness, 2.5 mm and pitch, 0.875:1. The phantom imaging experiments were repeated five times, and all the data were studied by taking the average of the five experiments.

Image reconstruction Phantom images reconstruction
In CZT SPECT cerebral blood flow perfusion imaging, the main methods for image reconstruction are filtered back projection (FBP) [5] and ordered subset expectation maximization (OSEM) [6]. The most commonly used filters for cerebral blood flow perfusion imaging are the Butterworth (Bw) filter and Gaussian (Gs) filter [7][8][9]. Therefore, three image reconstruction methods commonly used in clinics were used to process phantom images:

Combination 1: FBP reconstruction + Butterworth postfiltering (later replaced by FBP+Bw)
The phantom image was reconstructed using the FBP with Chang's attenuation correction (FBP ChangAC ), and the Chang's AC assumed a broad-beam attenuation coefficient μ was 0.12 cm -1 . Then, the FBP ChangAC image was postfiltered using a Bw filter with different filter parameters. First, different cutoff frequency (fc) values were selected (0.30, 0.35, 0.40, 0.45, 0.50 and 0.55) under the condition that the order(n) = 10 (manufacturer's recommended reference value) remained unchanged. Then, according to the results of semi-quantitative analysis, the optimal value of fc was determined to remain unchanged, and different n values (5, 10, 15, 20, 25 and 30) were selected, and different filter parameters were used for postprocessing of FBP ChangAC images.

Combination 2: OSEM reconstruction + Butterworth postfiltering (later replaced by OSEM+Bw)
Subset and iteration times had the same effects on image improvement; therefore, we could define a number of expectation maximisation-equivalent iterations (EM-equivalent iterations), which represented the product of the subset and the number of iterations [7,10].
The phantom image was reconstructed using the OSEM with CT-based ttenuation correction (CTAC), scatter correction (SC) and resolution recovery (RR) (OSEM CTAC-SC-RR ). The Bw filter was used to postfilter the OSEM CTAC-SC-RR image. First, the filter parameters were fixed (referred to combination 1: fc = 0.40-0.45; n = 10); then, the subset of OSEM CTAC-SC-RR was fixed at 10 and the number of iterations were 2, 4, 6, 8, 10 and 12 to determine the optimal number of EM-equivalent iterations. The optimal parameters of the filter were verified; the selection of filter parameters referred to the method of combination 1. Furthermore, n = 10 was fixed, different fc values were selected (0.30, 0.35, 0.40, 0.45, 0.50 and 0.55), and then the optimal value of fc was determined, different n values were chosen (5, 10, 15, 20, 25 and 30), and the best filtering parameters in the OSEM+Bw were determined.

Combination 3: OSEM reconstruction + Gaussian postfiltering (later replaced by OSEM+Gs)
The OSEM CTAC-SC-RR was used to reconstruct the image, the EM-equivalent iteration was fixed at 60 (referred to the result of combination 2), and a Gs filter was used [full width at half maximum (FWHM) = 2.50, 2.75, 3.00, 3.25, 3.50and 3.75 mm) to smooth the OSEM CTAC-SC-RR image, to determine the best parameters of the Gs filter. Then, the filter parameters were fixed to verify the best EM-equivalent iteration number of OSEM reconstruction in combination 3. With reference to the method of combination 2, the subset of OSEM CTAC-SC-RR was fixed at 10, and the numbers of iterations were 2, 4, 6, 8, 10 and 12 to determine the optimal number of EM-equivalent iteration.

Semi-quantitative analysis
To more accurately compare the phantom image quality after different processing, the phantom image quality was quantitatively evaluated by calculating integral uniformity, root mean square (RMS) noise, contrast and contrastto-noise ratio (CNR) [11].

Uniformity and noise
Five 15 × 15-pixel square regions of interest (ROIs) were drawn at different positions on the transverse of the uniform part of the phantom to record the average, maximum, minimum and SD of the radioactivity count in each ROI, and the formula calculation was carried out after taking the average of each value, such as formulas (1) and (2).
Integral uniformity % count count count co RMS noise % SD mean count % 100 100

Contrast
The most obvious transverse of the cold areas was selected, the minimum value of the radioactivity count in each cold area of the selected layer was determined, and five 15 × 15-pixel square ROIs were drawn to record the average radioactivity count value in different positions of the uniform background of the phantom, such as formula (3).

Contrast-to-noise ratio
To objectively compare the effects of different processing combinations on image quality, the CNR of different spheres was calculated, using formula (4). CNR was not a standard parameter but could be expressed by the quotient of contrast and noise. When further increasing the number of EM-equivalent iteration caused the CNR of the visible minimum sphere to increase by less than 5% [12], it was defined as the best equivalent number of iterations of the OSEM reconstruction algorithm. (1) all cases were composed of patients with cerebral blood perfusion defect or relative decrease diagnosed by doctors and (2) the lesion size of 20 patients was less than 2 cm, and the lesion size of the other 20 patients was ≥2 cm. The best parameters of the three reconstruction methods (FBP+Bw, OSEM+Bw and OSEM+Gs) were used to postprocess the CZT SPECT images of all patients.
According to the semi-quantitative analysis method of the phantom study, the integral uniformity, RMS noise, contrast and CNR of lesions and background were calculated to evaluate the image quality. Two ROIs of the same size (the same size as the focus) were drawn on the clinical image: one on the focus (cold area) and one on the healthy tissue near the lesion (background area).
In addition, all clinical images were visually evaluated by two experienced nuclear medicine physicians and one clinical technologist (nuclear medicine technician) who were blinded to the origin of images and were graded on a scale of 1-5 (1, very poor; 2, poor; 3, moderate; 4, good and 5, excellent) according to the visibility of the lesions, uniformity of the background and explicitness for the diagnosis. The visual score was obtained by averaging the results of these observers' scores.

Statistical analysis
Data were presented as the mean ± SD (x±s). The data were analysed using SPSS 26.0 software, one-way analysis of variance (ANOVA) and two-way ANOVA were used for phantom data, one-way ANOVA were used for clinical data, and pairwise comparison were used least significant difference method. Each experiment was performed in quintuplicate unless otherwise stated. A P value <0.05 indicated that the difference was statistically significant.

Phantom study Combination 1: FBP+Bw
When fc = 0.30-0.35, the image was too smooth and the contrast was poor. When the fc ≥ 0.5, the image uniformity was poor and the noise level increased significantly. When fc = 0.40-0.45, the cold area contrast was better and the image quality was relatively good. When n < 10, the uniformity of the image was poor, and the noise was obvious, as shown in Figs. 1and 2.
With an increase in the fc value, the contrast of the cold areas increased (Fig. 4a), the CNR decreased (Fig. 5a), the uniformity and noise of the uniform areas increased (Fig. 3a), and the contrast and CNR decreased with decreasing diameter of the cold spheres. With an increase in the n value, the contrast (Fig. 4b,c) and CNR (Figs. 5b and 4c) of the cold areas increased, whereas the uniformity and noise decreased and converged uniformly when n > 10 (Fig. 3b).

Combination 2: OSEM+Bw
When EM-equivalent iterations <60, the image was too smooth, and the small diameter of the cold areas was unclear; when EM-equivalent iterations ≥60, the contrast of the cold areas was better, but the noise level increased, as shown in Figs. 1 and 2.
With the increase in EM-equivalent iterations, the contrast of the cold areas increased (Fig. 4d,e), the CNR decreased (Fig. 5d,e), the noise of the image also increased (Fig. 3c), and the uniformity of the image became worse (Fig. 3c). When EM-equivalent iterations = 60, the CNR of the smallest cold area that could be recognised increased by less than 5%.
The verification of the best parameters of the Bw filter showed that when EM-equivalent iterations = 60 was the same as the result of combination 1, the overall quality of the image was the best when the filtering parameters were 'fc = 0.40-0.45, n = 10'.
In addition, for different Bw parameters ('fc = 0.40; n = 10' and 'fc = 0.45; n = 10') under OSEM (EM-equivalent iterations = 60) reconstruction, it could be concluded that the CNR value of fc = 0.45 was larger than that of fc = 0.40, especially for cold areas with small diameters.

Combination 3: OSEM+Gs
With an increase in the FWHM value, the image tended to be smooth. Additionally, the contrast of the image also decreased, and some details of the image were lost, as shown in Figs. 1 and 2.
Under the condition of constant EM-equivalent iterations = 60, when the FWHM <3.00, the image uniformity was worse and the noise was greater; with an increase in the FWHM value, the image uniformity was better, and the noise was reduced (Fig. 3d). However, when the FWHM >3.25, the image was too smooth, the cold area contrast decreased (Fig. 4f) and the CNR value was also reduced (Fig. 5f). Therefore, when FWHM = 3.0-3.25, the overall quality of the image was better. The The cross-sectional images of the cold areas obtained by the reconstruction methods of FBP+Bw, OSEM+Bw and OSEM+Gs. EM, expectation maximization; FBP+Bw, filtered back projection+Butterworth filter; FWHM, full width at half maximum; OSEM+Bw, ordered subset expectation maximisation+ Butterworth filter; OSEM+Gs, ordered subset expectation maximisation+Gaussian filter.
optimal EM-equivalent iteration number was verified in the OSEM+Gs: when EM = 80, further increased the EM-equivalent iterations, the CNR value of the minimum cold area that could be identified increased by less than 5%.
Among the three processing combinations, from the point of view of uniformity, noiseand CNR, the image quality of FBP+Bw was significantly better than that of OSEM+Bw and OSEM+Gs. From the point of view of contrast, the image contrast of OSEM+Bw was significantly better than that of FBP+Bw and OSEM+Gs. Therefore, the semi-quantitative parameters obtained from the visual analysis and semi-quantitative analysis were as follows: FBP+Bw (fc = 0.40-0.45; n = 10), OSEM+Bw (EM-equivalent iterations = 60; fc = 0.40-0.45, n = 10) and OSEM+Gs (EM-equivalent iterations = 80; FWHM = 3.00-3.25) for further optimization.

Comparison of semi-quantitative analysis results of cold areas of different sizes in the phantom
From the phantom images, there were differences in the display of cold areas of different sizes using different methods. Therefore, the five identifiable cold areas were divided into two groups (diameter ≥2 cm group: 31.8 and 25.4 mm cold areas, diameter <2 cm group: 19.1, 15.4 and 12.7 mm cold areas), and the differences were analysed using three reconstruction methods: FBP+Bw (fc = 0.40; n = 10), OSEM+Bw (EM-equivalent iterations = 60; The cross-sectional images of the uniform areas obtained by the reconstruction methods of FBP+Bw, OSEM+Bw and OSEM+Gs. EM, expectation maximization; FBP+Bw, filtered back projection+Butterworth filter; FWHM, full width at half maximum; OSEM+Bw, ordered subset expectation maximisation+ Butterworth filter; OSEM+Gs, ordered subset expectation maximisation+Gaussian filter. fc = 0.45; n = 10) and OSEM+Gs (EM-equivalent iterations = 80; FWHM = 3.25) (Fig. 6a,b).
For the 31.8 mm cold area (Fig. 6a), the contrast of FBP+Bw and OSEM+Bw were significantly higher than that of OSEM+Gs (P < 0.001). In addition, the CNR value of FBP+Bw was higher than that of OSEM+Bw and OSEM+Gs (P < 0.001).
Furthermore, the difference in the 25.4 mm cold area under the three reconstruction methods was also analysed, and it was found that the contrast of FBP+Bw was lower than that of OSEM+Bw (P < 0.05). The other results were the same as those of the 31.8 mm cold area.
For the 12.7 mm cold area (Fig. 6b), the contrast of OSEM+Bw was significantly higher than that of FBP+Bw (P < 0.01). Similarly, the differences in cold areas with 15.9 and 19.1 mm under the three reconstruction methods were statistically analysed, and the results were similar to those of the 12.7 mm cold area.
Clinical case images Figure 7 shows that the image quality of cerebral perfusion tomography in patients with lesion size ≥2 cm was the best under FBP+Bw. Excessive compensation of OSEM+Bw images might have lead to false-negative results, whereas OSEM+Gs images were too smooth, which was not conducive to clinical diagnosis. In the   patients with lesion size <2 cm, the focus was shown most clearly on OSEM+Bw, followed by FBP+Bw, and the worst on OSEM+Gs.

Results of semi-quantitative analysis and visual analysis of clinical images.
The results of the semi-quantitative analysis were shown in Table 2. By visual assessment, the quality of the SPECT images reconstructed by OSEM+Bw (4.27 ± 0.52) was superior to that by FBP+Bw (3.29 ± 0.85) and OSEM+Gs (2.80 ± 0.81) in the cases with lesion diameter <2 cm (P < 0.001), while in the cases with lesion diameter ≥2 cm, the quality of SPECT images reconstructed by FBP+Bw (4.32 ± 0.77) was better than that by OSEM+Bw (3.73 ± 0.52) and OSEM+Gs (2.93 ± 0.78) (P < 0.001).

Discussion
Different reconstruction algorithms and filters can be used in CZT SPECT imaging to achieve different purposes, such as reducing star artefacts, suppressing noise and restoring or enhancing signals. The OSEM used RR method has been shown to improve the spatial resolution, contrast and quantitative accuracy of cerebral perfusion SPECT [13,14]. CTAC has been considered to be the most accurate AC method for measuring radioactivity in real areas [15].
Clinically, different reconstruction algorithms and filters are often selected for different diseases to achieve the best quality of tomographic images. The SPECT images of patients with brain defects such as cerebral infarction and epilepsy [16] usually used the reconstruction Table 1 The results of integral uniformity, root mean square noise, contrast and contrast-to-noise ratio of the phantom image after processing the best parameters of the three reconstruction combinations All data are expressed as x ± s. The values of contrast and CNR are derived from the average of all cold spheres. CNR, contrast-to-noise ratio; FBP+Bw, filtered back projection+Butterworth filter; OSEM+Bw, ordered subset expectation maximisation+ Butterworth filter; OSEM+Gs, ordered subset expectation maximisation+Gaussian filter; RMS, root mean square.

Fig. 6
The contrast and CNR of a cold area with a diameter of 31.8 mm (a) and a cold area with a diameter of 12.7 mm (b) after processing the best parameters of the three reconstruction combinations. CNR, contrast-to-noise ratio; EM, expectation maximization; FBP+Bw, filtered back projec-tion+Butterworth filter; FWHM, full width at half maximum; OSEM+Bw, ordered subset expectation maximisation+ Butterworth filter; OSEM+Gs, ordered subset expectation maximisation+Gaussian filter.
methods of FBP+Bw and OSEM+Bw, while for the SPECT images of patients with Parkinson's disease, the reconstruction method of OSEM+Gs was often used [17,18]. Similarly, different processing parameters could also meet the needs of image reconstruction in different situations. Winz et al. [19] reported that the relatively low filter cutoff frequency in OSEM reconstruction reduced the image quality to some extent, but the resulting lownoise image was beneficial to the definition of the reference area in dopamine transporter imaging and avoided uptake asymmetry in the posterior putamen, which could avoid misdiagnosis as neurodegeneration. In this study, using the reconstruction method of OSEM+Bw and choosing a slightly higher fc value could improve the contrast of small lesions in patients with brain defects and avoid missed diagnoses.
First, in the phantom tomographic images, the integral uniformity, RMS noise and contrast of FBP+Bw increased with increasing fc value, but CNR decreased with an increase in fc value. This difference was caused by the enhancement of the high-frequency noise. The higher the fc value was, the more high-frequency components were enhanced, which increased the detection of the image and focus edge and increased the high-frequency noise. Therefore, the smaller the size of the focus to be resolved, the higher the fc value to meet the diagnostic requirements of the image, but not an excessively high fc value because it would lead to excessive amplification of noise and increase of artefacts, affecting image quality. Therefore, we determined that the best reconstruction parameter of conventional brain imaging was 'fc = 0.40-0.45, n = 10'. Khorshidi et al. [20] reported that in conventional NaI SPECT studies, the ideal image quality of brain defects could be obtained when the order of Bw was 7-10 and the cutoff frequency was 0.45-0.50. This conclusion was similar to the results of this study.
Second, the integral uniformity, RMS noise and contrast in OSEM+Bw increased with the increase in EM-equivalent iterations but CNR decreased with the increase in EM-equivalent iterations. It might be that with the increase in EM-equivalent iterations, the effect on image noise exceeded the influence of contrast but when EM-equivalent iterations ≥60, the contrast and CNR converged uniformly. Compared with FBP+Bw, the best reconstruction parameter of OSEM+Bw was that 'EM-equivalent iterations = 60; fc = 0.45 and n = 10' was more accurate in the diagnosis of small lesions. Van Laere et al. [21] reported that in traditional NaI SPECT studies, the best processing parameter for normal brain imaging was OSEM (4 iterations, 6 subsets) + Bw (fc = 0.40; n = 8).
The integral uniformity and RMS noise in OSEM+Gs decreased with the increase in FWHM, whereas the contrast increased with the increase in FWHM, and the overall quality of the image was not as good as that of the combination of the other two processes. For example, of the three, OSEM+Gs has the worst contrast and CNR, and OSEM+Gs has worse integral uniformity and RMS noise than FBP+Bw (Table 1). Lingfeng et al. [22] showed that the pure noise reduction of 3D Gs filters in postfiltering would lead to a decrease in image contrast with the Images of patients with lesion size <2 cm or ≥2 cm reconstructed using three methods: FBP+Bw (fc = 0.40, n = 10) (a,d); OSEM+Bw (EM-equivalent iterations = 60, fc = 0.45, n = 10) (b, e); and OSEM+Gs (EM-equivalent iterations = 80, FWHM = 3.25) (c,f). EM, expectation maximization; FBP+Bw, filtered back projection+Butterworth filter; FWHM, full width at half maximum; OSEM+Bw, ordered subset expectation maximisation+ Butterworth filter; OSEM+Gs, ordered subset expectation maximisation+Gaussian filter. reduction of noise. However, in a study by Matsutomo et al. [17] of conventional NaI SPECT, the reconstruction method of OSEM+Gs could improve the performance and image quality of 123 I-Nomega-fluoropropyl-2betacarbomethoxy-3beta-(4-iodophenyl) nortropane ( 123 I-FP-CIT) SPECT dopamine transporter imaging during the 'EM-equivalent iterations = 90 and FWHM = 6.6 mm'. Therefore, it was speculated that the reconstruction method of OSEM+Gs in CZT SPECT imaging might be more suitable for 123 I-FP-CIT SPECT imaging. This imaging method has been widely used in the diagnosis of Parkinson's disease and Lewy body dementia [18].
For patients with large lesions, more attention should be paid to the quality of image uniformity and noise in image postprocessing, so the postprocessing method of FBP+Bw should be adopted. In the phantom study, the recognisability of FBP+Bw was lower than that of OSEM+Bw with the cold area diameter <2 cm. Therefore, when small ischemic lesions are suspected, the OSEM reconstruction algorithm and a slightly higher fc value could increase the contrast between lesions and normal tissue and improve the sensitivity of finding lesions and avoid a missed diagnosis.
In the phantom image, the size of these cold areas was smaller than the actual size of these cold areas, especially in the smaller structure, which was partly due to the influence of the partial volume effect (PVE). Matsuda et al. [23] reported that SPECT images could reflect not only the loss of brain volume, but also the changes in brain function, and the regional cerebral blood flow could be measured more accurately by using PVE correction in cerebral perfusion SPECT. In addition, in OSEM reconstruction, the visual distortion of circular cold areas might be caused using the RR algorithm [24].
The limitations of this study are as follows. First, to simulate the current clinical acquisition methods, the matrix size was 128 × 128. If a matrix size of 256 × 256 was used, a better image spatial resolution could be obtained, which may improve the image quality. Second, we did not evaluate the impact on image quality and quantisation by the number of subsets, although image quality was generally not affected by the number of subsets [25]. In addition, different machines, different image processing workstations and different operators may produce different results so if possible, we will conduct a multicenter study to rule out such errors. At present, there are few studies on CZT SPECT cerebral blood flow perfusion imaging, which need more in-depth study. Further research is underway, and we will increase clinical studies to prove the feasibility of different reconstruction methods for different lesion sizes.

Conclusion
In conclusion, it is suggested that the image postprocessing method of FBP+Bw (fc = 0.40; n = 10) should be used routinely in clinical application of CZT SPECT cerebral blood flow perfusion, and if there are uncertain small lesions in the processed image, it is suggested to use the reconstruction method of OSEM+Bw (EM-equivalent iterations = 60; fc = 0.45; n = 10) instead.