Yiqiang Jian

Assessment of a three-dimensional line-of-response probability density function system matrix for PET

To achieve optimal PET image reconstruction through better system modeling, we developed a system matrix that is based on the probability density function for each line of response (LOR-PDF). The LOR-PDFs are grouped by LOR-to-detector incident angles to form a highly compact system matrix. The system matrix was implemented in the MOLAR list mode reconstruction algorithm for a small animal PET scanner. The impact of LOR-PDF on reconstructed image quality was assessed qualitatively as well as quantitatively in terms of contrast recovery coefficient (CRC) and coefficient of variance (COV), and its performance was compared with a fixed Gaussian (iso-Gaussian) line spread function. The LOR-PDFs of three coincidence signal emitting sources, (1) ideal positron emitter that emits perfect back-to-back γ rays (γγ) in air; (2) fluorine-18 (¹⁸F) nuclide in water; and (3) oxygen-15 (¹⁵O) nuclide in water, were derived, and assessed with simulated and experimental phantom data. The derived LOR-PDFs showed anisotropic and asymmetric characteristics dependent on LOR-detector angle, coincidence emitting source, and the medium, consistent with common PET physical principles. The comparison of the iso-Gaussian function and LOR-PDF showed that: (1) without positron range and acollinearity effects, the LOR-PDF achieved better or similar trade-offs of contrast recovery and noise for objects of 4 mm radius or larger, and this advantage extended to smaller objects (e.g. 2 mm radius sphere, 0.6 mm radius hot-rods) at higher iteration numbers; and (2) with positron range and acollinearity effects, the iso-Gaussian achieved similar or better resolution recovery depending on the significance of positron range effect. We conclude that the 3D LOR-PDF approach is an effective method to generate an accurate and compact system matrix. However, when used directly in expectation-maximization based list-mode iterative reconstruction algorithms such as MOLAR, its superiority is not clear. For this application, using an iso-Gaussian function in MOLAR is a simple but effective technique for PET reconstruction.

Data-driven event-by-event respiratory motion correction using TOF PET list-mode centroid of distribution

Data-driven respiratory gating techniques were developed to correct for respiratory motion in PET studies, without the help of external motion tracking systems. Due to the greatly increased image noise in gated reconstructions, it is desirable to develop a data-driven event-by-event respiratory motion correction method. In this study, using the Centroid-of-distribution (COD) algorithm, we established a data-driven event-by-event respiratory motion correction technique using TOF PET list-mode data, and investigated its performance by comparing with an external system-based correction method. Ten human scans with the pancreatic β-cell tracer 18F-FP-(+)-DTBZ were employed. Data-driven respiratory motions in superior-inferior (SI) and anterior-posterior (AP) directions were first determined by computing the centroid of all radioactive events during each short time frame with further processing. The Anzai belt system was employed to record respiratory motion in all studies. COD traces in both SI and AP directions were first compared with Anzai traces by computing the Pearson correlation coefficients. Then, respiratory gated reconstructions based on either COD or Anzai traces were performed to evaluate their relative performance in capturing respiratory motion. Finally, based on correlations of displacements of organ locations in all directions and COD information, continuous 3D internal organ motion in SI and AP directions was calculated based on COD traces to guide event-by-event respiratory motion correction in the MOLAR reconstruction framework. Continuous respiratory correction results based on COD were compared with that based on Anzai, and without motion correction. Data-driven COD traces showed a good correlation with Anzai in both SI and AP directions for the majority of studies, with correlation coefficients ranging from 63% to 89%. Based on the determined respiratory displacements of pancreas between end-expiration and end-inspiration from gated reconstructions, there was no significant difference between COD-based and Anzai-based methods. Finally, data-driven COD-based event-by-event respiratory motion correction yielded comparable results to that based on Anzai respiratory traces, in terms of contrast recovery and reduced motion-induced blur. Data-driven event-by-event respiratory motion correction using COD showed significant image quality improvement compared with reconstructions with no motion correction, and gave comparable results to the Anzai-based method.

Count-rate dependent resolution degradation from pulse pile-up on the HRRT

Pulse pile-up at high count rates is one factor that degrades spatial resolution of PET images. Most PET scanners with block detector designs suffer misidentification of event position, moving events from the edge to block center at high count rates. For the HRRT with LSO-LYSO phoswich detectors, there is an extra dimension of pile-up, i.e., inter-layer pile-up, which tends to push events to the LYSO layer at high count rates. A study was performed to characterize the resolution variation across the FOV through reconstructing simulated point sources at given levels of pile-up probability (PP). For 20% PP, in-plane FWHM was increased from 1.40 mm to 1.51 mm at the center of the FOV. At a radial distance of 72 mm (axially centered), the radial FWHM was asymmetric and tangential FWHM was 2.18 mm. At an axial distance of 72 mm (transaxially centered), inplane and axial FWHMs were 1.66 mm and 1.54 mm. Thus, higher pile-up probability resulted in greater resolution degradation as well as more inhomogeneous point spread functions. These results were supported by phantom scan results: radial resolution was degraded by 10% at the transaxial periphery, while the degradation of axial counterpart was less evident.

Applications of the line-of-response probability density function resolution model in PET list mode reconstruction.

Resolution degradation in PET image reconstruction can be caused by inaccurate modeling of the physical factors in the acquisition process. Resolution modeling (RM) is a common technique that takes into account the resolution degrading factors in the system matrix. Our previous work has introduced a probability density function (PDF) method of deriving the resolution kernels from Monte Carlo simulation and parameterizing the LORs to reduce the number of kernels needed for image reconstruction. In addition, LOR-PDF allows different PDFs to be applied to LORs from different crystal layer pairs of the HRRT. In this study, a thorough test was performed with this new model (LOR-PDF) applied to two PET scanners-the HRRT and Focus-220. A more uniform resolution distribution was observed in point source reconstructions by replacing the spatially-invariant kernels with the spatially-variant LOR-PDF. Specifically, from the center to the edge of radial field of view (FOV) of the HRRT, the measured in-plane FWHMs of point sources in a warm background varied slightly from 1.7 mm to 1.9 mm in LOR-PDF reconstructions. In Minihot and contrast phantom reconstructions, LOR-PDF resulted in up to 9% higher contrast at any given noise level than image-space resolution model. LOR-PDF also has the advantage in performing crystal-layer-dependent resolution modeling. The contrast improvement by using LOR-PDF was verified statistically by replicate reconstructions. In addition, [(11)C]AFM rats imaged on the HRRT and [(11)C]PHNO rats imaged on the Focus-220 were utilized to demonstrated the advantage of the new model. Higher contrast between high-uptake regions of only a few millimeter diameter and the background was observed in LOR-PDF reconstruction than in other methods.

Effect of subsets on bias and variance in low-count iterative PET reconstruction

Statistical reconstruction produces bias in images reconstructed with low counts, such as short-duration frames in dynamic PET studies. While the bias is usually considered to be the consequence of the positivity constraint in MLEM reconstruction, there is no evidence of comparable bias observed with list-mode OSEM reconstruction (MOLAR). Simulation studies were performed of a human brain scan for the HRRT. Without scatter effects, there was only 0.5-4% negative bias in brain image reconstructed from as little as 0.2M events. With scatter included in the simulation and corrected in the reconstruction, additional bias was introduced, i.e., bias values were between -7% and -15% reconstructed from 0.2M prompt events (0.07M NEC). On the other hand, in both simulation and real phantom experiments, larger bias was found in low-count reconstructions if the events are divided into larger numbers of subsets. Compared to the case with only one subset, the bias and variability increased by 1-2% and 1-3% respectively when 30 subsets are employed in HRRT reconstruction from 0.2M simulated events. A similar tendency of increased bias was also observed when comparing 3 to 21 subsets in low-count reconstructions of a phantom scanned on the mCT. The negative bias in low-count OSEM reconstructions is presumably produced by too few counts being backprojected into the image at each subset, producing “holes”. This phenomenon is worsened by higher numbers of subset, i.e., fewer events in each subset. The results of this study indicated that image bias and noise in ultra low-count reconstructions with MOLAR can be potentially reduced by employing less subsets and more iterations.

Validation of the spatially variant probability density functions for the HRRT

The probability density function (PDF) is a new concept of modeling the spatial dependence of the system response. In iterative reconstruction algorithms, the PDF plays the same important role as the point spread function in recovering images of high resolution. For the HRRT with a large number of lines of response, Monte Carlo simulation, along with an effective parameterization strategy, provides a practical solution to generating the PDFs that can be used in our listmode reconstruction algorithm (MOLAR). However, the PDFs accuracy, which depends on the accuracy of the simulated HRRT scanner, is still unverified. This study aims to validate the PDFs derived from simulation for the HRRT, by comparison to binned point source data. It is shown that the shape and width of the PDFs vary as a function of the incident angles to the detectors, and depth along each LOR, consistent with simulation results. However, the variability by detector layer for the HRRT phoswich is found to be significant in the experimental results, with roughly 20–40% degradations in FWHM and FWTM between the front-layer and back-layer PDFs, as compare to simulated results. On the other hand, all experimentally derived PDFs have larger spread than the simulated PDFs. The differences in FWHM, which are layer-dependent, range from 0.5mm to 1.5mm. We conclude that corrections of simulated PDF are required in order to achieve accurate resolution modeling.

Data-driven respiratory motion estimation and correction using TOF PET list-mode centroid of distribution

Respiratory motion degrades PET image quality and is unavoidable. Respiratory gating and/or motion correction are usually performed to reduce the effect of respiratory motion. However, these methods generally require motion information from external devices. Several groups have proposed data-driven motion extraction methods by analyzing variation of counts, or center-of-mass in reconstructed dynamic images or in sinogram space. Now, with time-of-flight (TOF) PET, better localization of each annihilation point in three dimensions can be obtained. Here we propose a data-driven respiratory estimation method. Motion estimation is performed by computing centroids-of-distribution (COD) of all radioactive events in the field-of-view using list-mode PET data with TOF information, with time resolution of 100ms. We applied COD motion estimation in dynamic studies with 3 tracers targeted for the pancreas, lung fibrosis, and lung tumors, respectively. Firstly, COD traces were compared with measured motion from the Anzai system for all three studies. COD traces showed very good correlation with the Anzai data in pancreas studies. When comparing the trigger information extracted from COD and Anzai traces, about 90% of respiratory peak times could be identified to within 200ms. COD traces for the lung fibrosis study also visually showed a good correlation with Anzai traces. In the lung tumor study, COD did not provide reliable motion traces because of low contrast between moving organs and the background. Next, COD was used to gate a pancreas study, and the resulting respiratory-gated images were comparable to those based on Anzai data. Finally, using the same data, we performed the first completely data-driven continuous motion correction based on COD traces combined with 3D internal-external correlation. Initial qualitative results showed that COD-based continuous motion correction is visually comparable to Anzai-based motion correction, both showing substantial improvements in image quality.

Uniform Spatial resolution list mode reconstruction for the HRRT

In expectation-maximization (EM) reconstruction, uniform spatial resolution in the field of view (FOV) is difficult to achieve as the iterations are typically stopped prematurely. Maximum-a-posterior (MAP) reconstruction is known to accelerate convergence by applying desirable constraints on the estimated parameters. However, object-dependent spatial resolution is still present using traditional penalty functions, even when the algorithm fully converges. The goal of this study is to test a uniform-resolution MAP (UR-MAP) algorithm for static PET reconstruction, as an extension of the work of Fessler et at and our list-mode OSEM algorithm (MOLAR), for the HRRT. The local spatial resolution, characterized by local impulse response (LIR) function is adjusted by applying spatially varying smoothing to the image based on local counts. A simulation study shows that standard MAP reconstruction with a global smoothing parameter over-smoothed high-activity regions and reduced the contrast between hot regions and the background. With the global smoothing parameter P=O.Ol, the contrast recovery coefficient (CRC) reaches 87% in low-background areas and 77% in high background areas. UR-MAP reduced the effective smoothing in high-background areas, and thus produced a uniform CRC of 87%, independent of background activity and local contrast. Preliminary results in human brain reconstructions show that UR-MAP yields images with reduced smoothing in high-activity regions than the standard MAP method.

Feasible uniform-resolution penalized likelihood reconstruction for static- and multi-frame 3D PET

Penalized likelihood reconstruction provides the possibility to produce images with desirable features. However, in some dynamic applications where system sensitivity and emission distribution are spatially and temporally variant, simple quadratic regularization does not produce uniform resolution over space and time for multi-frame reconstructions. In this study, we extended the spatially-invariant resolution regularization method of Fessler et al. to accommodate static- and multi-frame reconstruction in 3D PET systems. The proposed regularizations, denoted as UR3D/M-UR3D, were compared with the original method (UR2D) in HRRT simulations and real phantom experiments, and showed superior performance. Specifically, in single-frame reconstructions, UR3D regularization reduced the axial-position-dependent resolution degradation seen in UR2D regularization. In multi-frame reconstructions, M-UR3D also achieved more consistent resolution recovery across frames for reconstructed point sources/line sources than the original method.

List-mode reconstruction for the FOCUS-220 with motion correction and spatially-variant probability density functions: Application to awake monkey imaging

Motion correction for PET brain imaging of awake non-human primates (NHP) is critical if head fixation is not used. We have previously implemented a multi-acquisition frame (MAF) method, in which the Iist-mode data were divided into sub-frames for reconstruction, based on thresholds for intra-frame motion and minimum frame duration. In this method, residual intra-frame motion is present and scan data are discarded when large motion occurs within short time intervals. In this study, we implemented a list-mode reconstruction algorithm for the FOCUS-220 with motion correction, based on MOLAR (Motion-compensation OSEM Listmode Algorithm for Resolution-recovery Reconstruction). Also, we incorporated spatially-variant resolution kernels in the algorithm to account for varying spatial resolution throughout the field-of-view (FOV). The combination of event-by-event motion correction and spatially varying kernels is important for this application since the NHP moves its head throughout the FOV. Point sources reconstructed using MOLAR with spatially-variant resolution kernels gave 1~mm tangential resolution, better than the maximum a posteriori (MAP) method for the entire FOV. Radial resolution was below 2mm at 7cm radial offset, better than the 2.7mm FWHM for MAP. Fine structures (1.6mm diameter) of a mini-hot phantom were more clearly recovered by MOLAR than MAP at the edge of the FOV. When applied to awake NHP imaging, MOLAR with event-by-event motion correction produced better image delineation of small brain regions than the MAF -based motion correction method, and yielded images of comparable quality to anesthetized scans. We conclude that list-mode reconstruction using MOLAR with motion correction and spatially-variant resolution kernels generates high quality images for awake NHP brain PET studies.