Accelerated time-of-flight (TOF) PET image reconstruction using TOF bin subsetization and TOF weighting matrix pre-computation

Design and proof of concept of a double-panel TOF-PET system

OBJECTIVE

Positron Emission Tomography (PET) is a well-known imaging technology for the diagnosis, treatment, and monitoring of several diseases. Most PET scanners use a Ring-Shaped Detector Configuration (RSDC), which helps obtain homogeneous image quality but are restricted to an invariable Field-of-View (FOV), scarce spatial resolution, and low sensitivity. Alternatively, few PET systems use Open Detector Configurations (ODC) to permit an accessible FOV adaptable to different target sizes, thus optimizing sensitivity. Yet, to compensate the lack of angular coverage in ODC-PET, developing a detector with high-timing performance is mandatory to enable Time-of-Flight (TOF) techniques during reconstruction. The main goal of this work is to provide a proof of concept PET scanner appropriate for constructing the new generation of ODC-PET suitable for biopsy guidance and clinical intervention during acquisition. The designed detector has to be compact and robust, and its requirements in terms of performance are spatial and time resolutions < 2 mm and < 200 ps, respectively.

METHODS

The present work includes a simulation study of an ODC-PET based on 2-panels with variable distance. The image quality (IQ) and Derenzo phantoms have been simulated and evaluated. The phantom simulations have also been performed using a ring-shaped PET for comparison purposes of the ODC approach with conventional systems. Then, an experimental evaluation of a prototype detector that has been designed following the simulation results is presented. This study focused on tuning the ASIC parameters and evaluating the scintillator surface treatment (ESR and TiO2), and configuration that yields the best Coincidence Time Resolution (CTR). Moreover, the scalability of the prototype to a module of 64 × 64mm2 and its preliminary evaluation regarding pixel identification are provided.

RESULTS

The simulation results reported sensitivity (%) values at the center of the FOV of 1.96, 1.63, and 1.18 for panel distances of 200, 250, and 300 mm, respectively. The IQ reconstructed image reported good uniformity (87%) and optimal CRC values, and the Derenzo phantom reconstruction suggests a system resolution of 1.6-2 mm. The experimental results demonstrate that using TiO2 coating yielded better detector performance than ESR. Acquired data was filtered by applying an energy window of ± 30% at the photopeak level. After filtering, best CTR of 230 ± 2 ps was achieved for an 8 × 8 LYSO pixel block with 2 × 2 × 12mm3 each. The detector performance remained constant after scaling-up the prototype to a module of 64 × 64mm2, and the flood map demonstrates the module's capabilities to distinguish the small pixels; thus, a spatial resolution < 2 mm (pixel size) is achieved.

CONCLUSIONS

The simulated results of this biplanar scanner show high performance in terms of image quality and sensitivity. These results are comparable to state-of-the-art PET technology and, demonstrate that including TOF information minimizes the image artifacts due to the lack of angular projections. The experimental results concluded that using TiO2 coating provide the best performance. The results suggest that this scanner may be suitable for organ study, breast, prostate, or cardiac applications, with good uniformity and CRC.

Joint motion estimation and penalized image reconstruction algorithm with anatomical priors for gated TOF-PET/CT

The presence of respiratory motion not only degrades the reconstructed image but also limits the utilization of anatomical priors in emission tomography. In this study, we explore the potential application of a joint motion estimation and penalized image reconstruction algorithm using anatomical priors in gated time-of-flight positron emission tomography/computed tomography (PET/CT). The algorithm is able to warp both the activity image and the attenuation map to align them with the measured data with the facilitation of anatomical information contained in the attenuation map. Five patient datasets, three acquired in single-bed position and two acquired in whole-body continuous-bed-motion mode, are included. For each patient, the attenuation map is derived from a breath-hold CT. The Parallel Levels Sets (PLS) is chosen as a representative anatomical prior. In addition to demonstrating the reliability of the estimated motion and the benefits of incorporating anatomical prior, preliminary results also indicate that the algorithm shows the potential to reconstruct an activity image in the space corresponding to that of the attenuation map, which could be applied to address the potential misalignment issue in applications involving multiple PET acquisitions but a single CT.

A Novel Iterative MLEM Image Reconstruction Algorithm Based on Beltrami Filter: Application to ECT Images

The implementation of emission-computed tomography (ECT), including positron emission tomography and single-photon emission-computed tomography, has been an important research topic in recent years and is of significant and practical importance. However, the slow rate of convergence and the computational complexity have severely impeded the efficient implementation of iterative reconstruction. By combining the maximum-likelihood expectation maximization (MLEM) iteratively along with the Beltrami filter, this paper proposes a new approach to reformulate the MLEM algorithm. Beltrami filtering is applied to an image obtained using the MLEM algorithm for each iteration. The role of Beltrami filtering is to remove mainly out-of-focus slice blurs, which are artifacts present in most existing images. To improve the quality of an image reconstructed using MLEM, the Beltrami filter employs similar structures, which in turn reduce the number of errors in the reconstructed image. Numerical image reconstruction tomography experiments have demonstrated the performance capability of the proposed algorithm in terms of an increase in signal-to-noise ratio (SNR) and the recovery of fine details that can be hidden in the data. The SNR and visual inspections of the reconstructed images are significantly improved compared to those of a standard MLEM. We conclude that the proposed algorithm provides an edge-preserving image reconstruction and substantially suppress noise and edge artifacts.

Time-of-flight (TOF) implementation for PET reconstruction in practice

The time-of-flight (TOF) feature of PET scanners has been used for a long time in PET reconstruction, but many implementational aspects are still incomplete or ambiguous in the literature. Here we formalize and present theoretical and practical implementation details for the reconstruction of clinical TOF histogram and list-mode data using ML-EM. Relevant aspects include the computation of the TOF component of the system matrix, the processing of TOF bins, the use of estimations of random and scattered coincidences, and differences between histogram and list-mode ML-EM TOF reconstruction. Several approaches and approximations have been implemented in the CASToR platform and compared for OSEM reconstructions of patient data from the GE Signa PET/MR scanner. Differences between implementations are not larger than the typical bias in clinical data reconstruction. The largest difference and contrast loss occur when the processing of histogram TOF bins is simplified, and list-mode reconstruction is most sensitive to the truncation of the Gaussian TOF probability distribution.

Two-crossed-polarizers based optical property modulation method for ionizing radiation detection for positron emission tomography

Recent work shows that Pockels effect and optics pump-probe measurement could be utilized as a novel method for 511 keV ionizing radiation photon detection for positron emission tomography (PET) which could potentially overcome the inherent physical limitation for coincidence time resolution of around 100 ps (Tao et al 2016 Phys. Med. Biol. 61 7600-22). In this paper, we embrace this observation and introduce a two-crossed-polarizers based setup to achieve similar detection concept, which is a simpler and more compact setup with comparable ionizing radiation detection capability as the setup used in the previously proposed work. We evaluated the performance of our experimental setup with Lithium Niobate (LiNbO₃) and Cadmium Telluride (CdTe) detector crystals, and the desired properties of an ideal detector crystal were discussed. The modulation signal induced by 511 keV photons in both LiNbO₃ and CdTe can be detected with repeatable signal amplitude using two-crossed-polarizers based method, while CdTe could provide eight times higher detection sensitivity to 511 keV photons than LiNbO₃ under the same bias voltage, suggesting high effective Z number and high density properties of CdTe, as well as a shorter carrier lifetime and lower carrier mobility of LiNbO₃. In addition, the strength of modulation signal increased linearly with bias voltage before saturation. The modulation signal strength in LiNbO₃ continued to increase after 2000 V due to its high resistivity which could reduce the dark current in the detector, while the modulation signal of CdTe with low resistivity tended to be saturated at a bias voltage higher than 1200 V. Therefore, further increasing the bias voltage for detector crystals (especially for LiNbO₃) may enhance the modulation strength and improve the detection sensitivity for annihilation photons.

Robustness of post-reconstruction and direct kinetic parameter estimates under rigid head motion in dynamic brain PET imaging

OBJECTIVE

Dynamic PET imaging is extensively used in brain imaging to estimate parametric maps. Inter-frame motion can substantially disrupt the voxel-wise time-activity curves (TACs), leading to erroneous maps during kinetic modelling. Therefore, it is important to characterize the robustness of kinetic parameters under various motion and kinetic model related factors.

METHODS

Fully 4D brain simulations ([¹⁵O]H₂O and [¹⁸F]FDG dynamic datasets) were performed using a variety of clinically observed motion patterns. Increasing levels of head motion were investigated as well as varying temporal frames of motion initiation. Kinetic parameter estimation was performed using both post-reconstruction kinetic analysis and direct 4D image reconstruction to assess bias from inter-frame emission blurring and emission/attenuation mismatch.

RESULTS

Kinetic parameter bias heavily depends on the time point of motion initiation. Motion initiated towards the end of the scan results in the most biased parameters. For the [¹⁸F]FDG data, k₄ is the more sensitive parameter to positional changes, while K₁ and blood volume were proven to be relatively robust to motion. Direct 4D image reconstruction appeared more sensitive to changes in TACs due to motion, with parameter bias spatially propagating and depending on the level of motion.

CONCLUSION

Kinetic parameter bias highly depends upon the time frame at which motion occurred, with late frame motion-induced TAC discontinuities resulting in the least accurate parameters. This is of importance during prolonged data acquisition as is often the case in neuro-receptor imaging studies. In the absence of a motion correction, use of TOF information within 4D image reconstruction could limit the error propagation.

Penalized maximum likelihood simultaneous longitudinal PET image reconstruction with difference-image priors

PURPOSE

Many clinical contexts require the acquisition of multiple positron emission tomography (PET) scans of a single subject, for example, to observe and quantitate changes in functional behaviour in tumors after treatment in oncology. Typically, the datasets from each of these scans are reconstructed individually, without exploiting the similarities between them. We have recently shown that sharing information between longitudinal PET datasets by penalizing voxel-wise differences during image reconstruction can improve reconstructed images by reducing background noise and increasing the contrast-to-noise ratio of high-activity lesions. Here, we present two additional novel longitudinal difference-image priors and evaluate their performance using two-dimesional (2D) simulation studies and a three-dimensional (3D) real dataset case study.

METHODS

We have previously proposed a simultaneous difference-image-based penalized maximum likelihood (PML) longitudinal image reconstruction method that encourages sparse difference images (DS-PML), and in this work we propose two further novel prior terms. The priors are designed to encourage longitudinal images with corresponding differences which have (a) low entropy (DE-PML), and (b) high sparsity in their spatial gradients (DTV-PML). These two new priors and the originally proposed longitudinal prior were applied to 2D-simulated treatment response [¹⁸ F]fluorodeoxyglucose (FDG) brain tumor datasets and compared to standard maximum likelihood expectation-maximization (MLEM) reconstructions. These 2D simulation studies explored the effects of penalty strengths, tumor behaviour, and interscan coupling on reconstructed images. Finally, a real two-scan longitudinal data series acquired from a head and neck cancer patient was reconstructed with the proposed methods and the results compared to standard reconstruction methods.

RESULTS

Using any of the three priors with an appropriate penalty strength produced images with noise levels equivalent to those seen when using standard reconstructions with increased counts levels. In tumor regions, each method produces subtly different results in terms of preservation of tumor quantitation and reconstruction root mean-squared error (RMSE). In particular, in the two-scan simulations, the DE-PML method produced tumor means in close agreement with MLEM reconstructions, while the DTV-PML method produced the lowest errors due to noise reduction within the tumor. Across a range of tumor responses and different numbers of scans, similar results were observed, with DTV-PML producing the lowest errors of the three priors and DE-PML producing the lowest bias. Similar improvements were observed in the reconstructions of the real longitudinal datasets, although imperfect alignment of the two PET images resulted in additional changes in the difference image that affected the performance of the proposed methods.

CONCLUSION

Reconstruction of longitudinal datasets by penalizing difference images between pairs of scans from a data series allows for noise reduction in all reconstructed images. An appropriate choice of penalty term and penalty strength allows for this noise reduction to be achieved while maintaining reconstruction performance in regions of change, either in terms of quantitation of mean intensity via DE-PML, or in terms of tumor RMSE via DTV-PML. Overall, improving the image quality of longitudinal datasets via simultaneous reconstruction has the potential to improve upon currently used methods, allow dose reduction, or reduce scan time while maintaining image quality at current levels.

Numerical algorithms for scatter-to-attenuation reconstruction in PET: empirical comparison of convergence, acceleration, and the effect of subsets

The use of scattered coincidences for attenuation correction of positron emission tomography (PET) data has recently been proposed. For practical applications, convergence speeds require further improvement, yet there exists a trade-off between convergence speed and the risk of non-convergence. In this respect, a maximum-likelihood gradient-ascent (MLGA) algorithm and a two-branch back-projection (2BP), which was previously proposed, were evaluated.

METHODS

MLGA was combined with the Armijo step size rule; and accelerated using conjugate gradients, Nesterov's momentum method, and data subsets of different sizes. In 2BP, we varied the subset size, an important determinant of convergence speed and computational burden. We used three sets of simulation data to evaluate the impact of a spatial scale factor.

RESULTS AND DISCUSSION

The Armijo step size allowed 10-fold increased step sizes compared to native MLGA. Conjugate gradients and Nesterov momentum lead to slightly faster, yet non-uniform convergence; improvements were mostly confined to later iterations, possibly due to the non-linearity of the problem. MLGA with data subsets achieved faster, uniform, and predictable convergence, with a speed-up factor equivalent to the number of subsets and no increase in computational burden. By contrast, 2BP computational burden increased linearly with the number of subsets due to repeated evaluation of the objective function, and convergence was limited to the case of many (and therefore small) subsets, which resulted in high computational burden.

CONCLUSION

Possibilities of improving 2BP appear limited. While general-purpose acceleration methods appear insufficient for MLGA, results suggest that data subsets are a promising way of improving MLGA performance.

A promising new mechanism of ionizing radiation detection for positron emission tomography: modulation of optical properties

Using conventional scintillation detection, the fundamental limit in positron emission tomography (PET) time resolution is strongly dependent on the inherent temporal variances generated during the scintillation process, yielding an intrinsic physical limit for the coincidence time resolution of around 100 ps. On the other hand, modulation mechanisms of the optical properties of a material exploited in the optical telecommunications industry can be orders of magnitude faster. In this paper we borrow from the concept of optics pump-probe measurement to for the first time study whether ionizing radiation can produce modulations of optical properties, which can be utilized as a novel method for radiation detection. We show that a refractive index modulation of approximately [Formula: see text] is induced by interactions in a cadmium telluride (CdTe) crystal from a 511 keV photon source. Furthermore, using additional radionuclide sources, we show that the amplitude of the optical modulation signal varies linearly with both the detected event rate and average photon energy of the radiation source.