Optical surface information‐based respiratory phase‐sorting and motion‐incorporated reconstruction for SPECT imaging

Abstract

Background

Respiratory motion during the single photon emission computed tomography (SPECT) acquisition can cause blurring artifacts in the reconstructed images, leading to inaccurate estimates for activity and absorbed doses.

Purpose

To address the impact of respiratory motion, we utilized a new optical surface imaging (OSI) system to extract the respiratory signals for phase sorting and verified its effectiveness through simulation and patient data. Additionally, we implemented GPU‐accelerated motion‐incorporated reconstruction algorithms for the SPECT projections, integrating motion information to produce motion‐free images from all acquired data.

Methods

We used the 4D XCAT Phantom to generate attenuation maps and activity images across different respiratory phases, with activity distributions based on patient images. SPECT projections were simulated using the SIMIND Monte Carlo program with Poisson noise. The OSI system was modeled by introducing Gaussian noise into the point clouds on the body surface within the attenuation map. The body surface images were registered across phases using a Gaussian mixture model combined with principal component analysis. The extracted respiratory signals were compared to the center‐of‐light (COL) approach, with or without filtering and kidney masking. The OSI method was further validated by comparing respiratory signals derived from a real patient using OSI to simultaneous cone‐beam CT (CBCT) projections. Two motion‐incorporated techniques, namely, 4D reconstruction (4D‐Recon) and post‐reconstruction registration and summation (post‐Recon), were compared with non‐motion‐corrected images (non‐MC) and single‐phase gating (Gating). The quantitative evaluation of image quality utilized recovery coefficients (RC), contrast recovery coefficients (CRC), and uncertainty estimation.

Results

In simulation, the correlation between the ground‐truth and OSI‐based signals remained high and stable (0.99 ± 0.004, p‐value $<$ 0.001 vs. COL‐filter with kidney masking). While the kidney mask improved performance (0.87 ± 0.07 without filtering and 0.90 ± 0.06 with filtering, p‐value $<$ 0.001), it was less effective and more uncertain than the OSI method. Validation with patient data showed high consistency in breathing frequencies and phase alignment between CBCT‐based and OSI‐based signals. For reconstruction, both 4D‐Recon and post‐Recon significantly enhanced RC and CRC compared to non‐MC, with less uncertainty than Gating. In addition, 4D‐Recon outperformed post‐Recon in certain aspects.

Conclusions

Our novel respiratory signal extraction approach based on OSI demonstrated superior accuracy and reliability compared to a data‐driven method. Applying motion‐incorporated SPECT reconstruction using these accurate breathing signals has the potential to enhance image quality and improve absorbed dose quantification in radiopharmaceutical therapy. The relevant reconstruction algorithms are also made available for public use in the open‐source library PyTomography.

1. INTRODUCTION

Respiratory motion during the single photon emission computed tomography (SPECT) data acquisition affects image quality by causing signal distortion. ¹ This leads to blurring, reduced contrast in organs and lesions, increased noise, and artifacts, such as ghosting, splitting, and deformation of activity sources, as well as spillover or dispersion of activity. ² , ³ , ⁴ In addition, with the growing use of SPECT for dosimetry in radiopharmaceutical therapies, quantitative SPECT is expected to play a key role in the optimization task of minimizing toxicities to normal organs while maximizing absorbed doses to tumors. ⁵ , ⁶ , ⁷ However, images acquired without accounting for respiratory motion may lead to inaccuracies in the estimated activities. Research indicates that in liver tumor dosimetry using SPECT scans, respiratory motion reduces activity recovery and tumor/non‐tumor ratios by an average of 30$\%$ compared to acquisitions without motion. ⁸ Therefore, efforts are required to reduce or minimize the impact of respiratory motion.

Accurate and robust respiratory signal sensing is a prerequisite for achieving motion correction (MC). ⁹ , ¹⁰ , ¹¹ The signal facilitates the grouping of projection data acquired at different angles, but corresponding to the same respiratory state, into identical bins, which can then be used for motion‐incorporated reconstruction. Some studies have proposed using deep learning methods to extract respiratory signal ¹² ; however, they still require external motion‐tracking devices to train the network. Although 4D CT can directly observe tumor motion, it significantly increases the patient's imaging dose compared to 3D CT. ¹³ Additionally, the respiratory signal obtained from 4D CT may not accurately reflect the conditions during SPECT scanning, as the two are not acquired synchronously.

Data‐driven gating (DDG) methods that utilize emission data have been investigated in positron emission tomography (PET), ¹⁴ , ¹⁵ where count rates are much higher than in SPECT, and all angular views are acquired simultaneously. However, additional challenges arise in conventional rotating SPECT systems, where projection data are available for only two or three angles at a given time, and count rates are lower. These factors lead to significant noise and variations, challenging routine deployment of the DDG method. ¹¹ Furthermore, to the best of our knowledge, most SPECT systems operate in static or frame mode rather than list‐mode, which is necessary for rebinning projections into chronological time frames. ¹⁶ This limitation further hinders the implementation of the DDG method.

Newly developed optical surface imaging (OSI) systems, such as AlignRT (VisionRT, London, Great Britain) and Catalyst (C‐Rad, Uppsala, Sweden), have been introduced in external beam radiation therapy. ¹⁷ These systems enable continuous and touchless scanning of patients' external surfaces, and several studies have shown clear correlations between external surfaces and internal structures. ¹⁸ , ¹⁹ Moreover, implementing this method does not require purchasing expensive equipment, a depth camera alone is sufficient. In addition, the meaning of obtaining accurate respiratory signals is ultimately reflected in the quality of reconstructed images. Unlike rigid‐body motion, which can be corrected using six‐degree‐of‐freedom vectors from an external tracking techniques, respiratory motion involves internal deformations that are more challenging to correct due to its nonrigid nature and its occurrence within the body. ²⁰

As a proof of concept and in preparation for applying the OSI system to SPECT imaging, we developed a novel method for extracting respiratory signals for phase sorting, aiming to validate its feasibility using both simulation and patient data. The results from the OSI system were compared with ground truth data and the DDG method. For motion‐incorporated reconstruction, we integrated the deformation vector field (DVF) into the ordered subset expectation maximization (OSEM) reconstruction of SPECT images and compared the improvement in image quality with MC to that of static or single‐phase reconstructions. To our knowledge, no previous study has applied this method for motion‐compensated reconstruction in SPECT.

2. METHODS

2.1. Digital phantom

The digital 4D XCAT phantom utilized in this study enables the creation of realistic anthropomorphic configurations that are well‐suited for SPECT simulation. ²¹ Activity images at 10 respiratory phases were generated. A tumor with a 20 mm in diameter was positioned in the liver. The ground truth respiratory signal was determined using Equation (1) and input into the XCAT software. The magnitudes were set to +10 and ‐20 mm for the anterior–posterior direction and diaphragm displacement, respectively. Since the tumor's motion curve is not directly set, its motion depends on its position in the body. This setting follows Huang et al.'s method ²²

$$f(t)=A\left\{1-{\left[\cos \left(\frac{\pi }{5}·t\right)\right]}^4\right\}.$$ (1)

The activity settings used in the simulation were derived from the study by Kayal et al., ²³ based on SPECT images acquired 1 h after the injection of 6.85 GBq of ‐labeled DOTATATE, as presented in Table 1. The process began with the generation of over 1 billion counts for the activity map, captured by the virtual detectors. These counts were then normalized to match the activity levels of each organ, resulting in 120 noise‐free SPECT projections for each breathing phase. ²⁴ Each projection had dimensions of 128 × 128 pixels. Poisson noise was then added to simulate projections obtained in clinical scans. It is worth noting that this process transfers the expected mean count to the actual number of counts for each scan. Therefore, adding Poisson noise multiple times to the same noise‐free projection can generate different scans under identical conditions, which is crucial for estimating the uncertainty.

TABLE 1.

Activity setting for simulated images in SIMIND.

Organs	Activity concentration (MBq/mL)
Lungs	0.0445
Liver	0.2531
Bones	0.0576
Left kidney	0.5074
Right kidney	0.5155
Spleen	0.5313
Tumor	0.9564
Background	0.0526

To increase the efficiency of Monte Carlo simulations, we utilized a computer with 64 CPUs, with each CPU running the simulation separately to achieve parallel computation. The dual‐head Siemens SPECT, equipped with a parallel medium‐energy general‐purpose (MEGP) collimator, was simulated to match our clinical protocol on a Siemens Symbia SPECT/CT camera. The characteristics of the collimator, such as transparency, spatial resolution, sensitivity, and so forth, are considered in the SIMIND calculations. The specific parameters of the collimator can be found in the “SI‐ME” mode of the SIMIND “collim.col” file. The “scattwin” scoring routine is employed to simulate the triple‐energy window (TEW) scatter correction method. For , the photopeak energy range is 187.2–228.8 keV, with the lower energy window at 169.4–187.2 keV and the higher at 228.8–252.9 keV.

Improving the quality of OSEM‐reconstructed images requires more than just projection data. Additional details about the imaging system are essential. SIMIND can generate a density map aligned with the pixel size and matrix dimensions of the SPECT projections, enabling attenuation correction during reconstruction. Furthermore, an ideal SPECT detector would detect only photons traveling perpendicular to the collimator holes. However, this is not the case in practice. The angle at which photons can enter is influenced by the parameters of the collimator and scintillator. To address this issue, point spread function (PSF) modeling has been developed, with parameters that can be derived based on the distance between the source and the detector. ²⁵ As a result, the system matrix used in OSEM reconstruction incorporates geometry transformation, TEW scatter correction, attenuation correction, and PSF modeling.

2.2. Respiratory signals extraction – OSI simulations

Point clouds within the 64 × 64 body surface region of interest (ROI) on the attenuation map were used to simulate the OSI system. To assess the proposed method's robustness against optical signal noise, the Gaussian noise with a standard deviation of 0.5 mm was added to the surface motion, consistent with the accuracy of existing optical surface monitoring systems. ²⁶ A Gaussian mixture model (GMM) ²⁷ was utilized for image registration of OSI across different phases (Figure 1) to obtain the DVF ($M_{0\to t}$), as described in Equation (2). The core idea of the GMM registration framework is to represent input point clouds as GMMs. The point set registration problem is then reformulated as aligning two Gaussian mixtures by minimizing a statistical discrepancy measure between them. Finally, principal component analysis (PCA) was applied to reduce the dimensionality of $M_{0\to t}$. The weight of the first PCA component ($w_1$) was then utilized as the raw signal for the OSI method.

$$S(t)=M_{0\to t}S(0);M_{0\to t}=\overline{M}+\sum _{i=1}^n{w}_i{\text{PC}}_i$$ (2)

where $S(t)$ and $S(0)$ represent the optical surfaces in the reference and target phases, respectively. $M_{0\to t}$ represents the DVF used for transforming from reference phase to target phase. $\overline{M}$ represents the average DVF; ${\text{PC}}_i$ represents each principal component; $w_i$ represents the corresponding weight.

FIGURE 1.

(a) An optical surface image from XCAT phantom body segmentation, with a red square marking the 64 × 64 pixel ROI for respiratory signal extraction. (b) Registration of surface point clouds to the reference phase using the GMM. GMM, Gaussian mixture model; ROI, region of interest.

2.3. Respiratory signals extraction – Data‐driven simulations

We utilized the center‐of‐light (COL) method, one of the most commonly used DDG techniques, to extract respiratory signals for comparison. This method calculates the axial COL of projection counts in objects with respiratory motion. The continuous motion can then be estimated at a specific frequency and converted into organ displacements in the superior–inferior direction. ¹¹ , ²⁸ To minimize the interference from background noise and organ signals, we compared the COL obtained from various preprocessed projections: filtering (applying a 3D filter with 32 × 32 spatial and 2‐temporal dimension box kernel), ²⁹ kidney masking (obtained from the 3D image and projected to different angles), and threshold sets for counting rates. The kidney mask was selected because the kidney's motion is highly synchronized with respiratory phases, owing to its close proximity to the diaphragm. Furthermore, its high activity concentration enhances noise reduction and allows the COL method to extract an optimal breathing signal.

Compared to the time‐based gating scheme, amplitude‐based gating schemes produced SPECT images with fewer motion artifacts. ³⁰ In addition to the flat amplitude phase (EI), the amplitude on one side is equally divided into three gates. Consequently, the entire breathing cycle was divided into seven amplitude‐based segments (as shown in Figure 2). Since the breathing cycle typically lasts approximately 5 s, the XCAT cycle time was set accordingly. To account for the rapid changes during the middle inhalation (MI) and middle exhalation (ME) phases, both were assigned a duration of 0.4218 s in our original curve setting. Therefore, to simplify the problem, the simulated gating projection scan was set to a duration of 0.5 s for applying the COL algorithm. The difference in sub‐projections used for the COL process between full‐cycle and gating scan durations is illustrated in Figure 3. It is shown that the gating image obtained from the 0.5‐s scan appears to be much noisier than that from the standard 15‐s scan.

FIGURE 2.

The respiratory cycle can be divided into seven distinct phases: II, MI, terminal inhalation (TI), end of inhalation (EI), IE, ME, and EE. EE, end of exhalation; EI, end of inhalation; IE, initial exhalation; II, initial inhalation; ME, middle exhalation; MI, middle inhalation; TI, terminal inhalation.

FIGURE 3.

Simulated SPECT projection for the reference phase (end of expiration), Poisson noise was added. A 15‐s scan (ideal breath‐hold) and a 0.5‐s scan (used for respiratory gating) were shown to compare. SPECT, single photon emission computed tomography.

2.4. Validation of OSI method on patient data

To verify our method using real patient data, we utilized data from a patient who underwent a cone‐beam CT (CBCT) scan before receiving external radiation therapy. The CBCT scan ensured accurate patient positioning and verification. ³¹ During the scan, we positioned a depth camera to record the optical surface information, which was then applied to the OSI method described in Section 2.2. The pronounced difference in x‐ray attenuation between the dense muscle of the diaphragm and the low‐density, air‐filled lungs creates a well‐defined edge in 2D CBCT projections, ensuring the diaphragm's motion is clearly visible. After processing, it can be used as the ground truth for the respiratory signal. ³² The x‐ray voltage is set to 120 kVp, with a current of 20 mA, and the exposure time for each projection is 16 ms.

The depth camera used to capture the patient's surface information is the Azure Kinect (Microsoft Inc., Redmond, WA, USA), an RGB‐D camera popular in research for artificial intelligence applications. It includes a time‐of‐flight depth sensor, which captures depth information by measuring the time difference of amplitude‐modulated continuous wave signals in the near‐infrared spectrum. ³³ Each point in the image is assigned a value corresponding to its depth along the Z‐axis, creating a depth matrix. In addition to depth maps, the camera can also capture color images and infrared images. The infrared image has the same dimensions as the depth map and visually represents the objects captured in the depth map. The depth resolution of the camera is 1 mm. The minimum detectable thoracic motion is determined by 1/$\sin (\theta )$ mm, where $\theta$ is the angle at which the depth camera is positioned relative to the ground. For example, when $\theta$ is 60, the smallest detectable depth change is approximately 1.15 mm.

During the experiment, the depth camera is mounted on a bracket at the foot of the bed, angled downward toward the patient. We begin the depth camera acquisition prior to activating the CBCT scanner. Both the CBCT scanner's 2D projections and the depth camera can record their respective start times and frame intervals. Therefore, in this study, we manually correct the time shift in the camera data to ensure alignment with the projection data during analysis. For full technical integration of the camera into the SPECT system, true time synchronization between the two systems would be required, which involves some engineering adjustments and collaboration with scanner manufacturers. The sampling intervals for CBCT and depth camera are 0.182 and 0.033 s (1/30 s), respectively. The data obtained are shown in Figure 4

FIGURE 4.

(a) Image acquired by the depth camera in real‐time during the CBCT scan; (b) 2D projection obtained from the CBCT scan, with the red box indicating the ROI used to extract respiratory signals; (c) Vertical gradient calculation to enhance the clarity of the diaphragm dome; (d) Summation of pixel values along each row; (e) Combination of ROI line maps from all projections. CBCT, cone‐beam computed tomography; ROI, region of interest.

We utilized the Amsterdam Shroud method ³⁴ , ³⁵ to extract respiratory surrogate signals from 2D CBCT projections, as illustrated in Figure 4. The process involved applying a mean filter with a 3 × 3 averaging kernel to smooth the image, followed by calculating the vertical gradient to enhance the edges of diaphragm dome. The ROI of the diaphragm was then selected, and the projection was summed along the coronal plane, converting the 2D image with dimensions 512 × 512 into a line graph of 512 × 1. This procedure was repeated for each projection, and the resulting ROI line graphs were combined to create a 2D image, where the horizontal axis represents the projection number (i.e., time) and the vertical axis represents the position of structures along the craniocaudal axis of the flat panel detector. ³⁶ Finally, the weighted center of the combined ROI line map was calculated by normalizing column values between 0 and 1, yielding centroids for each column that represent the extracted respiratory signal. ³⁷

2.5. Motion‐incorporated reconstruction

To simulate the patient's SPECT scan with an accurate and reliable breathing signal as the basis for gating, we aimed to achieve a motion‐incorporated reconstruction, demonstrating its crucial role in ensuring dosimetry accuracy. Symmetries in the breathing cycle permit only half the data to be used. Using the XCAT digital phantom software and the SIMIND Monte Carlo program, we obtained 25 time points of breathing with a 0.1‐s interval between each point, as shown in Figure 5, to simulate the list‐mode data of SPECT. The position of organs within 0.1 s can be regarded as static, ³⁸ while a gate consisting of multiple 0.1 s intervals will be blurred due to breathing. Consequently, the data for each gate is the average of the time points within its coverage and scaled by its duration. For instance, our test used a 15‐s projection scan time, and the duration times for the Gates 1–4 are 4.2, 2.4, 5.4, and 3.0 s, respectively. Additionally, to simulate images from noise‐less projections, we increased the scan time by a factor of 10. This mode can be achieved through various methods, such as using isotopes with higher gamma yields and more efficient gamma detection (e.g., ), replacing NaI detectors (as simulated in this study) with more sensitive CZT detectors, extending the scanning time per projection, utilizing equipment with more detectors, or increasing the patient's injection activity. To accommodate these potential improvements, we added this noise‐less mode.

FIGURE 5.

Simulated time points for the motion‐incorporated reconstruction, with black dots indicating the position of each point along the curve. Data from half the cycle is utilized.

The 4D reconstruction algorithm (4D‐Recon) for image reconstruction, proposed by Qiao et al., ³⁹ is defined in Equation (3). We also evaluated the post‐reconstruction registration and summation method for combining independently reconstructed images (post‐Recon, Equation 4). These two motion‐incorporated reconstruction algorithms were compared with images reconstructed without motion correction (non‐MC) and those using single‐phase projections (Gating). The ground truth was established using full‐cycle scans without motion (Static).

$$f^{(n+1)}=\frac{f^{(n)}}{{\sum }_{i=0}^{m-1}{M}_{i\to r}{H}^T\vec{1}}\sum _{i=0}^{m-1}\left[M_{i\to r}{H}^T\left(\frac{g_i}{H{M}_{r\to i}{f}^{(n)}+s_i}\right)\right]$$ (3)

where $f^{(n)}$ is the image estimate of the $n\mathrm{th}$ iteration; $H$ is the system matrix, $g_i$ is the projection data for phase $i$, and $s_i$ is the expected scatter vector for phase $i$ (obtained from the TEW scatter correction). $\vec{1}$ is a vector where all elements are equal to 1, and it is used to construct the normalized back‐projection. $M_{r\to i}$ and $M_{i\to r}$ are the DVF for transforming between the reference phase $r$ to the target phase $i$.

$$f_{\text{sum}}=\sum _{i=0}^{m-1}{M}_{i\to r}{f}_i$$ (4)

where $f_i$ is the reconstructed image of phase $i$; $M_{i\to r}$ represents the DVF for transferring phase $i$ to the reference phase.

These algorithms require motion transforms between phases ($M_{i\to r}$ and $M_{r\to i}$, hereafter referred to as DVF), whose accuracy significantly impacts the effectiveness of MC. ⁴⁰ The DVF can be obtained by: (i) reconstructing the SPECT projections for each phase independently (Gating SPECT), and (ii) registering the reconstructed Gating SPECT via the target DVF. Additionally, we tested these algorithms by applying the ground truth DVF produced by XCAT using its “vectors” mode (by setting “mode = 4” in the parameter file). This mode outputs the motion vectors for each voxel of the reference phase image to each target phase, providing the ground truth motion vectors. The time point of each phase was set at the middle of each breathing gate to simulate the ideal DVF that can be obtained from 4D CT. To ensure accurate deformable registration for the Gating SPECT, this study utilized the pTV‐reg algorithm as proposed by Vishnevskiy et al., ⁴¹ along with their publicly available Matlab package. Gate 3 (TI+IE in Figure 2), with its central position and longer coverage time, serves as the reference gate for both 4D‐Recon and post‐Recon.

The attenuation correction and the TEW scatter correction were applied in all of the reconstructions. All reconstructions in this study were performed using PyTomography, an open‐source Python library initiated by our lab for fast, GPU‐accelerated medical image reconstruction. ²⁵ As the computation time of 4D‐Recon and post‐Recon scales with the number of gates, GPU acceleration is essential for the practical application of this function. To encourage community use, we have released nine tutorials demonstrating how to use the toolbox and integrate the models in PyTomography. The PyTomography project can be accessed at https://github.com/PyTomography. The source codes for this MC study are also made publicly available.

Quantitative evaluation of image quality utilized the recovery coefficient (RC) and contrast recovery coefficient (CRC, Equation 5). To assess the uncertainty of RC and CRC, each algorithm was evaluated using 10 noise realizations with varying random seeds, and the uncertainty range was represented as the mean ± standard deviation. The tumor ROI was determined by the ground truth in the XCAT file. To calculate the tumor's CRC, an ROI in the liver was used, consisting of two 30‐mm diameter spheres positioned within a uniform area.

$$CRC=\frac{M_{\text{tumor}}/M_{\text{liver}}-1}{C_{\text{true}}-1}$$ (5)

where $M_{\text{tumor}}$ and $M_{\text{liver}}$ represent the mean values within the tumor and liver regions, respectively, while $C_{\text{true}}$ is the true contrast value between them.

3. RESULTS

3.1. Simulated respiratory signals

The Pearson correlation results for comparing different respiratory signals are presented in Table 2. We applied 20 different noise realizations for the OSI method. In the COL method based on Dual‐head SPECT simulation, two 0.5‐s projections at supplementary angles were combined after flipping one side to reduce the impact of noise. Therefore, we tested 60 different noise realizations for the 120 projections.

TABLE 2.

Pearson correlation between respiratory curves from various methods and ground truth.

	Algorithm
Scenario	COL	COL‐filter	OSI
Baseline	0.62 ± 0.20	0.71 ± 0.19	0.99 ± 0.004
40% Threshold	0.64 ± 0.18	0.57 ± 0.28	—
Kidney's masking	0.87 ± 0.07	0.90 ± 0.06	—

Note: Values are mean ± standard deviation.

Abbreviations: COL, center‐of‐light method; OSI, optical surface imaging.

The correlation between the ground‐truth signal and the OSI‐based signal remains highly consistent and stable (0.99 ± 0.004, p‐$\mathrm{value}<$0.001 when comparing OSI and COL‐filter with Kidney's masking). The correlations for COL and COL‐filter exhibit unsatisfactory outcomes, with means and standard deviations of 0.62 ± 0.20 and 0.71 ± 0.19, respectively). A noticeable enhancement was observed when using the kidney region mask, achieving 0.87 ± 0.07 and 0.90 ± 0.06 using the filter, both with p‐$\mathrm{value}<$0.001). However, these still performed less effectively than the OSI method, as further illustrated by the comparison signals depicted in Figure 6, the grey shaded area indicates the uncertainty of respiratory curves when using the COL method with different post‐processing techniques, while the red shaded area represents the OSI method for comparison.

FIGURE 6.

Comparing the respiratory curves from various methods. Different colors represent the error range of each method. The six subplots represent different post‐processing methods of COL. COL, center‐of‐light.

3.2. Validation of OSI method on patient data

Based on the patient data, Figure 7a shows the respiratory signals extracted from CBCT 2D projections and the OSI method. A Gaussian filter with a standard deviation of 2 was applied to the OSI signal to reduce high‐frequency noise. Given that the sampling interval of the OSI (0.033 s) is substantially shorter than that of CBCT (0.182 s), the filtered OSI signal was resampled to align with the lower sampling frequency of the CBCT projection data. This adjustment facilitates a more intuitive comparison of their respective spectral distributions.

FIGURE 7.

(a) Respiratory signals extracted based on the patient data. (b) Spectrum analysis of the respiratory signals.

We used the discrete Fourier transform (DFT) to compare the two respiratory motion signals in the frequency domain, as shown in Figure 7b. The frequency of the respiratory motion was determined by the maximum amplitude on the spectrogram, indicating the largest component proportion. Both the OSI signal and the projection signal showed the same breathing frequency (0.2839 Hz), corresponding to a breathing cycle of approximately 3.5 s.

3.3. Motion‐incorporated reconstruction

For clinical observation, Figure 8a shows the central cross‐section of the tumor area, reconstructed using different algorithms described in Section 2.5. The voxel values are converted from counts to mega Becquerels per milliliter using the scanning time of each projection and a calibration factor derived from a point source simulation in SIMIND. For quantitative analysis, the RC and CRC results for the tumor from noisy (15‐s scan per projection) and noiseless (150‐s scan per projection) are presented in Figure 8b. This figure also displays the uncertainty range (mean ± standard deviation) resulting from 10 noise realizations. They also demonstrate the impacts of applying DVF from Gating images or the ground‐truth data. With GPU acceleration achieved using an NVIDIA Tesla V100, each iteration with six subsets requires approximately 7.5 s of computation. For instance, completing 10 iterations with six subsets would take only about 75 s, meeting the clinical requirements for efficiency.

FIGURE 8.

(a) Cross‐sections of reconstructed images: OSEM with 10 iterations and 6 subsets. (b)RC and CRC using six subsets for OSEM across various iterations. To avoid overlap, the Static and Gating results are shown as the area between two dashed lines. “Noisy” refers to a 15‐s scan per projection in simulations, while “Noiseless” refers to a 150‐s scan per projection. CRC, Contrast recovery coefficient; OSEM, ordered subset expectation maximization; RC, recovery coefficient.

4. DISCUSSION

The respiratory signals extracted by the OSI system show a high correlation with the ground truth, as verified by both simulation results and patient data, as illustrated in Sections 3.1 and 3.2. Furthermore, because this experiment directly observes the patient's diaphragm movement through CBCT, ⁴² the reference curves are closer to the patient's actual breathing movements. ³⁶ The results shown in Table 2 indicate that OSI offers advantages in terms of accuracy and stability compared to the existing data‐driven methods (p‐value $<$ 0.001). It is even significantly better than the COL‐filter with Kidney's masking, which requires an accurate mask to cover the entire breathing cycle of the kidney. Achieving this would lead to additional workload and may need the 4D‐CT. As shown in Figure 6, using kidney masking for COL can significantly reduce uncertainty and make the curves closer to the ground truth. However, it still remains less accurate than OSI due to noisy projection images from the gating SPECT. Thus, if this method is used for guiding motion‐incorporated reconstruction, the EE phase, for example, could be misclassified as the IE phase or other phases, leading to different phases being mixed together. Consequently, the reconstructed images would be similar to non‐MC images. In this study, we simulated ‐DOTATATE, as it is widely used in radiopharmaceutical therapy for neuroendocrine tumors. Further studies could explore various types of radiolabeled agents targeting specific therapeutic applications. For simulations, only the activity settings for each organ, as outlined in Table 1, need to be adjusted.

The higher sampling rate of the depth camera enables it to capture high‐frequency movements, such as sudden patient movements. Additionally, its relatively low cost (approximately $400) increases its potential for wider adoption. The device is also compact and portable, requiring only a standard mounting bracket to ensure compatibility with various systems. Furthermore, the OSI method is a touchless approach that does not require markers to be securely attached to the patient's body, ³⁸ , ⁴³ thereby improving clinical efficiency. Markers may introduce artifacts or affect the accuracy of attenuation correction during reconstruction if they fall within the SPECT signal acquisition area. Additional types of devices have been evaluated for respiratory gating in emission tomography, such as spirometers ⁴⁴ and the pressure belt‐based systems. ⁴⁵ However, these devices must be worn by patients and may increase errors and workload. To implement the COL method and motion‐incorporated reconstruction, normal scanning projections must be divided into shorter time‐period sub‐projections. This step is crucial because, without it, organs cannot be assumed to remain nearly stationary within the respiratory gating images. Using the list‐mode data format is essential for capturing this detailed motion data. However, due to significant data storage requirements, clinical SPECT systems typically bin the data. Given the limitations of our current results, we were unable to experimentally verify 4D reconstruction for SPECT images, which will be a focus of our future research.

For the reconstructed images shown in Figure 8a from the 4D digital phantom simulation, as expected, non‐MC reconstruction results in a more blurred image. This situation could happen when performing MC based on nonideal respiratory signals (such as the aforementioned COL method). For quantitative analysis, as shown in Figure 8b, increasing the number of iterations results in a decrease in bias but an increase in variability. This is reflected in the fact that the shaded areas become closer to the true value but expands as more iterations are used. For both noisy and noiseless images, the reconstructed images with MC, in contrast to the non‐MC results, notably enhance RC and CRC. Moreover, a longer scanning time or higher injection dose (noiseless mode) will increase this difference. In addition, as shown in Figure 8b, the 4D‐Recon shows greater accuracy (RC and CRC for “XCAT DVF”) or lower uncertainty (RC for “Gating DVF”) compared to the post‐Recon method. Similar conclusions have been confirmed in several PET studies. ¹⁰ , ⁴⁶ The Gating method achieves bias levels comparable to MC methods; however, due to utilizing only partially acquired data, it incurs higher uncertainty.

Comparing the results of the “Gating DVF” and “XCAT DVF”, the changes in RC and CRC are not significant. This similarity may be due to the localized high‐dose characteristics of the tumor region, which enhance image registration accuracy for the Gating images, making the DVFs from two methods consistent. However, the more accurate DVF appears to provide a greater benefit for the 4D‐Recon compared to the post‐Recon. This is evident in the “XCAT DVF” plots in Figure 8b, where 4D‐Recon outperforms post‐Recon, a trend not seen in the “Gating DVF” plots. Therefore, if this distinction is not critical, we recommend using the Gating DVF for 4D‐Recon, as it is more accessible. However, the post‐Recon and 4D‐Recon methods represent one class of motion compensation approaches, where respiratory motion is first estimated from individually reconstructed respiratory bins and then corrected in the reconstructed images. Other approaches, such as applying MC directly to the 2D projection data before image reconstruction, ⁴⁷ require further comparative analysis to determine their optimal application scenarios.

Regarding the limitations of this study, the current SPECT scan results are based on Monte Carlo simulations. Therefore, the actual improvement of the OSI method requires further validation through real scans. This involves conducting experiments with an anthropomorphic phantom injected with , specifically designed to simulate patient breathing. The phantom's thoracic cavity surface should be made from an elastic material that mimics the rise and fall of breathing movements, enabling the depth camera to acquire the signals. Consequently, the method proposed in this paper remains in the proof‐of‐concept stage. Additionally, the study assessed the effectiveness of the OSI method exclusively on data from normal‐sized adult patients. Further validation is necessary to establish its applicability to other patient groups, such as pediatric, obese, and elderly populations.

5. CONCLUSIONS

We evaluated a respiratory phase sorting approach using the optical surface signals and compared it with a data‐driven method, utilizing both simulated and patient data. Overall, our approach combines several advantages, including high accuracy and stability, having non‐contact operation, no need to observe the ROI mask in projections, and better compatibility with various imaging systems. Furthermore, we achieved 4D reconstruction of SPECT by integrating DVF into the OSEM algorithm and confirmed that it produces significantly higher‐quality images compared to those without MC, thereby improving the accuracy of radiopharmaceutical therapy. Additionally, with our GPU‐accelerated PyTomography library, the 4D reconstruction, which we release publicly can be completed in significantly shorter time, enabling extensive studies and applications.

CONFLICT OF INTEREST STATEMENT

The authors have no relevant conflicts of interest to disclose.

Li C, Polson LA, Wu X, Zhang Y, Uribe C, Rahmim A. Optical surface information‐based respiratory phase‐sorting and motion‐incorporated reconstruction for SPECT imaging. Med Phys. 2025;52:4330–4340. 10.1002/mp.17769