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A method for calculating the system matrix of large animal SPECT with sparse measurement data
Journal of Tsinghua University (Science and Technology) 2026, 66(8): 1726-1736
Published: 31 August 2026
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Objective

Large-animal single-photon emission computed tomography (SPECT) systems are crucial for preclinical cardiovascular research. An accurate system matrix (or system response matrix) is essential for high-quality iterative image reconstruction. However, directly measuring the system matrix on large-animal SPECT systems is often prohibitively time-consuming due to the extensive field of view and high spatial resolution needs. To address the lengthy measurement process for the system matrix in large-animal SPECT, this work proposes and validates a calculation method based on two-dimensional (2D) Gaussian fitting. This method leverages the inherent continuity of the projection probability density function (PPDF) in the image domain. Instead of measuring the system response for each voxel, the proposed approach demonstrates that an accurate system matrix can be built by acquiring only sparse point-source measurement data. Using 2D Gaussian fitting, the method effectively models the system's spatial response and connects sparse data points to synthesize the full matrix.

Methods

The complete dataset of point-source projections for 37 210 voxels was collected on the large-animal SPECT system, with a total acquisition time of 124 h. Down-sampled subsets at ratios of 1/4 and 1/9 were created from the full dataset to simulate accelerated protocols and to thoroughly evaluate the feasibility and robustness of the proposed method. The accuracy of the fitted PPDFs was quantitatively assessed against the fully measured ground truth using two metrics: the relative root mean square error (RRMSE) and the structural similarity index measure (SSIM). Additionally, to evaluate the reconstruction performance of the system matrix derived from the fitted PPDFs both qualitatively and quantitatively, 3.5 and 4 mm hot-rod phantom images were reconstructed. The performance of the proposed method was compared with several traditional approaches, including fully sampled direct measurement, barycentric Lagrange interpolation, and cubic spline interpolation.

Results

Quantitative analyses showed exceptional fidelity in the estimated system matrices. The matrix computed under the 1/4 sparse sampling condition achieved an RRMSE of 0.023 ± 0.068 and an SSIM of 0.997 ± 0.003. Even with the more aggressive 1/9 sparse sampling, the method produced an RRMSE of 0.035 ± 0.095 and an SSIM of 0.996 ± 0.006. The system matrix generated with this method successfully resolved 3.5-mm hot rods. Under the 1/4 sparse sampling, the reconstructed images of 3.5 and 4 mm rods had RRMSE values of 0.795 and 0.654 against the ground truth, and SSIM values of 0.981 and 0.988. For the same sampling, the reconstructed images showed RRMSE values of 1.042 and 0.797, with SSIM values of 0.971 and 0.981. These imaging results were visually and quantitatively superior to those obtained with other methods. Importantly, the computational time remained efficient, with calculations taking only 1.9 hours and 1.8 hours for the 1/4 and 1/9 sparse datasets, respectively.

Conclusions

The proposed 2D Gaussian fitting approach effectively overcomes the traditional limitations in generating system matrices for large-animal SPECT systems. It significantly reduces measurement time and computational costs without sacrificing tomographic image quality. This method presents a practical and efficient solution for acquiring precise system matrices in large-animal SPECT imaging.

Issue
Study on quantification performance evaluation of a domestic SPECT/CT system
Journal of Tsinghua University (Science and Technology) 2024, 64(8): 1509-1515
Published: 15 August 2024
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Objective

Single-photon emission computed tomography (SPECT) is still considered a nonquantitative imaging modality because it cannot perform attenuation correction. To acquire a quantitative SPECT image, Beijing Novel Medical Equipment Co., Ltd. developed a domestic SPECT/CT system, Insight NM/CT Pro. It was equipped with dual digital detectors and enabled various scanning geometries. In addition to better spatial resolution, the system can correct attenuation effects in SPECT and realize quantitative reconstruction using CT. In this study, we evaluated the imaging accuracy of this domestic SPECT/CT system and compared it with advanced abroad systems.

Methods

To obtain quantitatively correct results, physical effects, including collimator blurring, object attenuation, scatter, and radionuclide decay, were modeled and corrected in the reconstruction algorithm. Moreover, a large cylindrical phantom was employed to obtain the calibration factor for the system so that we could convert the reconstruction result to a quantitative image in terms of Bq/mL. Then, the performance of CT-based attenuation correction was tested according to testing method for SPECT imaging based on CT-attenuation correction (YY/T 1546—2017). A cylinder phantom with three cylindrical inserts corresponding to air, nonradioactive water, and bone was filled with a radioactive solution for imaging. The biases inside the air, water, and bone regions of the reconstructed image were calculated to evaluate the performance of CT-based attenuation correction. In addition, the quantitative accuracy of the equipment was tested using the Notional Electrical Manufactures Association (NEMA) torso phantom according to performance measurements of Gamma cameras (NEMA NU 1—2018). Six fillable spheres with different diameters were set as targets for recovery evaluation, and the target-to-background concentration ratio was approximately 8∶1. A large volume of interest (VOI) was placed in the background region to calculate the quantitative bias of the reconstruction. VOIs with the same size of six spheres were drawn based on the registered CT to evaluate recovery coefficients of different sizes. Radionuclide technetium-99m and a low-energy, high-resolution collimator with Insight NM/CT Pro were used for all these tests, and the evaluation results were compared with those of the GE Discovery NM/CT 670.

Results

For attenuation accuracy testing, the biases inside the air, water, and bone regions of Insight NM/CT Pro were 7.84%, 8.38%, and 4.66%, respectively, whereas the corresponding biases in GE Discovery NM/CT 670 were 16.64%, 18.01%, and 11.02%, respectively. For quantitative accuracy testing, in GE discovery NM/CT 670, the quantitative recovery coefficients of the hot spheres with diameters of 13, 17, 22, and 28 mm were 31.04%, 51.36%, 59.91%, and 66.39%, respectively, and the background concentration bias was 10.84%. Insight NM/CT Pro achieved higher recovery coefficients and lower bias. The recovery coefficients were 38.22%, 50.98%, 66.55%, and 71.32% for 13, 17, 22, and 28 mm hot rods, respectively, and the bias in the background region was 7.95%.

Conclusions

Phantom studies have demonstrated that the domestic Insight NM/CT Pro imaging system can obtain smaller biases after CT attenuation correction and achieve quantitative images with high accuracy. The reliability of the Insight NM/CT Pro system for quantitative imaging is validated in this study, and its performance is comparable to that of the advanced GE Discovery NM/CT 670 imaging system.

Issue
Design of dedicated collimator for whole-body bone scanning on single photon emission computed tomography based on Monte Carlo simulation
Journal of Tsinghua University (Science and Technology) 2023, 63(5): 811-817
Published: 15 May 2023
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Objective

Single photon emission computed tomography (SPECT) is an important imaging method of radionuclide bone imaging. It can obtain noninvasive three-dimensional functional images for early diagnosis and staged prognostic evaluation of disease by detecting γ photons emitted by radioactive drugs in the human body. According to the results of the national nuclear medicine census in 2020, more than 60% of SPECT clinical examinations in China are bone system examinations, indicating a great demand for bone imaging. Bone system examination generally refers to bone scanning, which is a nuclear medical imaging examination for systemic bones and can effectively diagnose various primary or secondary bone tumors. However, the low-energy general-purpose parallel-hole collimator, which is clinically used for SPECT bone scanning, has a low detection sensitivity, which leads to low patient comfort and scanning efficiency. Thus, this study aimes to optimize the detection sensitivity of SPECT system for bone imaging in clinical practice, which can not only reduce bone scanning time but also improve bone scanning efficiency and increase clinical-conomic benefits.

Methods

Based on the clinical dual-head SPECT system, this paper designed a specific collimator for bone imaging with high detection sensitivity. This study focuses on simulation experiments, including the construction of an overall simulation system, design of collimator parameters, and performance evaluation. The overall simulation system refers to the parameters of the SPECT system developed by this paper's cooperative company. In collimator parameter design, based on the formula derived in theory, which guides this paper in identifying the factors related to the detection sensitivity and resolution of SPECT system, different collimator parameters are tested by changing the collimator thickness, hole spacing, and hole diameter. Then, a Monte Carlo simulation, which is supported by center of high performance computing, Tsinghua University, is conducted with a point source for performance evaluation, including the detection sensitivity and image spatial resolution.

Results

The results indicates that the relationship between the geometric parameters and performance of the collimator matched well with the theoretical formula: as the increase of hole septal increases, the effective area of photon penetration on the collimator decreases, which reduces the detection sensitivity, while there is no obvious change in the image resolution. As the aperture increases, the collimation effect of the collimator is weakened, resulting in a serious decline in resolution. However, more scintillation photons will reach the scintillation crystal, there by hugely improving the detection sensitivity. When the aperture becomes larger, the improvement in detection sensitivity cannot make up for the loss brought by the reduction in resolution. When the collimator thickens, the collimation effect is enhanced, and the number of oblique incident photons that can be detected is reduced, so the detection sensitivity shows a downward trend. However, the image resolution can be improved.

Conclusions

Thinning the collimator and hole diameter is feasible in designing the SPECT collimator for bone scanning. According to the results of the performance evaluation, a collimator design (collimator thickness, 25.5 mm; hole septal, 0.15 mm; hole diameter, 0.5 mm) is empirically selected. It has a detection sensitivity of 183 cpm/μCi and a spatial resolution of 13.6 mm, which can significantly reduce the bone scanning acquisition time while ensuring image quality. The imaging effect of the collimator is evaluated using a hot-rod phantom experiment. The results show that hot rods with a 5.5-mm diameter could be distinguished, demonstrating the imaging performance of our proposed dedicated collimator design for bone scanning.

Issue
Design and numerical simulations of a large animal SPECT system
Journal of Tsinghua University (Science and Technology) 2022, 62(12): 1875-1883
Published: 15 December 2022
Abstract PDF (3.2 MB) Collect
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This study analyzed the collimator parameters of a large animal single photon emission computed tomography (SPECT) detector. Six collimator design schemes were chosen by thoretical calculation of the spatial resolution, the sensitivity at the field of view (FOV) center and the projection overlap ratio with specified constraints. A performance evaluation method was used to evaluate the six collimator design schemes by calculating the contrast recovery coefficient (CRC) and the variance of the local impulse response of selected pixels to find the best design scheme. The imaging effect of the design scheme was verified by numerical simulations of imaging experiments of a hotrod phantom. The theoretical calculations and the numerical simulations demonstrate that the design scheme gives a spatial resolution of the hotrod phantom that is better than 3.0 mm with better than 0.03% sensitivity at the FOV center, which meets the technical requirements.

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