A residual correction method for high-resolution PET reconstruction with application to on-the-fly Monte Carlo based model of positron range

Fast 3D kernel computation method for positron range correction in PET

Objective. The positron range is a fundamental, detector-independent physical limitation to spatial resolution in positron emission tomography (PET) as it causes a significant blurring of underlying activity distribution in the reconstructed images. A major challenge for positron range correction methods is to provide accurate range kernels that inherently incorporate the generally inhomogeneous stopping power, especially at tissue boundaries. In this work, we propose a novel approach to generate accurate three-dimensional (3D) blurring kernels both in homogenous and heterogeneous media to improve PET spatial resolution.Approach. In the proposed approach, positron energy deposition was approximately tracked along straight paths, depending on the positron stopping power of the underlying material. The positron stopping power was derived from the attenuation coefficient of 511 keV gamma photons according to the available PET attenuation maps. Thus, the history of energy deposition is taken into account within the range of kernels. Special emphasis was placed on facilitating the very fast computation of the positron annihilation probability in each voxel.Results. Positron path distributions of¹⁸F in low-density polyurethane were in high agreement with Geant4 simulation at an annihilation probability larger than 10^-2∼ 10^-3of the maximum annihilation probability. The Geant4 simulation was further validated with measured¹⁸F depth profiles in these polyurethane phantoms. The tissue boundary of water with cortical bone and lung was correctly modeled. Residual artifacts from the numerical computations were in the range of 1%. The calculated annihilation probability in voxels shows an overall difference of less than 20% compared to the Geant4 simulation.Significance. The proposed method is expected to significantly improve spatial resolution for non-standard isotopes by providing sufficiently accurate range kernels, even in the case of significant tissue inhomogeneities.

Implementation of a Spatially-Variant and Tissue-Dependent Positron Range Correction for PET/CT Imaging

Aim

To develop and evaluate a new approach for spatially variant and tissue-dependent positron range (PR) correction (PRC) during the iterative PET image reconstruction.

Materials and Methods

The PR distributions of three radionuclides (¹⁸F, ⁶⁸Ga, and ¹²⁴I) were simulated using the GATE (GEANT4) framework in different material compositions (lung, water, and bone). For every radionuclide, the uniform PR kernel was created by mapping the simulated 3D PR point cloud to a 3D matrix with its size defined by the maximum PR in lung (¹⁸F) or water (⁶⁸Ga and ¹²⁴I) and the PET voxel size. The spatially variant kernels were composed from the uniform PR kernels by analyzing the material composition of the surrounding medium for each voxel before implementation as tissue-dependent, point-spread functions into the iterative image reconstruction. The proposed PRC method was evaluated using the NEMA image quality phantom (¹⁸F, ⁶⁸Ga, and ¹²⁴I); two unique PR phantoms were scanned and evaluated following OSEM reconstruction with and without PRC using different metrics, such as contrast recovery, contrast-to-noise ratio, image noise and the resolution evaluated in terms of full width at half maximum (FWHM).

Results

The effect of PRC on ¹⁸F-imaging was negligible. In contrast, PRC improved image contrast for the 10-mm sphere of the NEMA image quality phantom filled with ⁶⁸Ga and ¹²⁴I by 33 and 24%, respectively. While the effect of PRC was less noticeable for the larger spheres, contrast recovery still improved by 5%. The spatial resolution was improved by 26% for ¹²⁴I (FWHM of 4.9 vs. 3.7 mm).

Conclusion

For high energy positron-emitting radionuclides, the proposed PRC method helped recover image contrast with reduced noise levels and with improved spatial resolution. As such, the PRC approach proposed here can help improve the quality of PET data in clinical practice and research.

3D/4D Reconstruction and Quantitative Total Body Imaging

Total-body PET image reconstruction follows a similar procedure to the image reconstruction process for standard whole-body PET scanners. One unique aspect of total-body imaging is simultaneous coverage of the entire human body, which makes it convenient to perform total-body dynamic PET scans. Therefore, four-dimensional dynamic PET reconstruction and parametric imaging are of great interest in total-body imaging. This article covers some basics of PET image reconstruction and then focuses on three- and four-dimensional PET reconstruction for total-body imaging. Methods for image formation from raw measurements in total-body PET are described. Challenges and opportunities in total-body PET image reconstruction are discussed.

Deep-Learning Based Positron Range Correction of PET Images

Positron emission tomography (PET) is a molecular imaging technique that provides a 3D image of functional processes in the body in vivo. Some of the radionuclides proposed for PET imaging emit high-energy positrons, which travel some distance before they annihilate (positron range), creating significant blurring in the reconstructed images. Their large positron range compromises the achievable spatial resolution of the system, which is more significant when using high-resolution scanners designed for the imaging of small animals. In this work, we trained a deep neural network named Deep-PRC to correct PET images for positron range effects. Deep-PRC was trained with modeled cases using a realistic Monte Carlo simulation tool that considers the positron energy distribution and the materials and tissues it propagates into. Quantification of the reconstructed PET images corrected with Deep-PRC showed that it was able to restore the images by up to 95% without any significant noise increase. The proposed method, which is accessible via Github, can provide an accurate positron range correction in a few seconds for a typical PET acquisition.

Deep-Learning Based Positron Range Correction of PET Images

Positron emission tomography (PET) is a molecular imaging technique that provides a 3D image of functional processes in the body in vivo. Some of the radionuclides proposed for PET imaging emit high-energy positrons, which travel some distance before they annihilate (positron range), creating significant blurring in the reconstructed images. Their large positron range compromises the achievable spatial resolution of the system, which is more significant when using high-resolution scanners designed for the imaging of small animals. In this work, we trained a deep neural network named Deep-PRC to correct PET images for positron range effects. Deep-PRC was trained with modeled cases using a realistic Monte Carlo simulation tool that considers the positron energy distribution and the materials and tissues it propagates into. Quantification of the reconstructed PET images corrected with Deep-PRC showed that it was able to restore the images by up to 95% without any significant noise increase. The proposed method, which is accessible via Github, can provide an accurate positron range correction in a few seconds for a typical PET acquisition.

Improving PET Quantification of Small Animal [68Ga]DOTA-Labeled PET/CT Studies by Using a CT-Based Positron Range Correction

PURPOSE

Image quality of positron emission tomography (PET) tracers that emits high-energy positrons, such as Ga-68, Rb-82, or I-124, is significantly affected by positron range (PR) effects. PR effects are especially important in small animal PET studies, since they can limit spatial resolution and quantitative accuracy of the images. Since generators accessibility has made Ga-68 tracers wide available, the aim of this study is to show how the quantitative results of [⁶⁸Ga]DOTA-labeled PET/X-ray computed tomography (CT) imaging of neuroendocrine tumors in mice can be improved using positron range correction (PRC).

PROCEDURES

Eighteen scans in 12 mice were evaluated, with three different models of tumors: PC12, AR42J, and meningiomas. In addition, three different [⁶⁸Ga]DOTA-labeled radiotracers were used to evaluate the PRC with different tracer distributions: [⁶⁸Ga]DOTANOC, [⁶⁸Ga]DOTATOC, and [⁶⁸Ga]DOTATATE. Two PRC methods were evaluated: a tissue-dependent (TD-PRC) and a tissue-dependent spatially-variant correction (TDSV-PRC). Taking a region in the liver as reference, the tissue-to-liver ratio values for tumor tissue (TLR_tumor), lung (TLR_lung), and necrotic areas within the tumors (TLR_necrotic) and their respective relative variations (ΔTLR) were evaluated.

RESULTS

All TLR values in the PRC images were significantly different (p < 0.05) than the ones from non-PRC images. The relative differences of the tumor TLR values, respect to the case with no PRC, were ΔTLR_tumor 87 ± 41 % (TD-PRC) and 85 ± 46 % (TDSV-PRC). TLR_lung decreased when applying PRC, being this effect more remarkable for the TDSV-PRC method, with relative differences respect to no PRC: ΔTLR_lung = - 45 ± 24 (TD-PRC), - 55 ± 18 (TDSV-PRC). TLR_necrotic values also decreased when using PRC, with more noticeable differences for TD-PRC: ΔTLR_necrotic = - 52 ± 6 (TD-PRC), - 48 ± 8 (TDSV-PRC).

CONCLUSION

The PRC methods proposed provide a significant quantitative improvement in [⁶⁸Ga]DOTA-labeled PET/CT imaging of mice with neuroendocrine tumors, hence demonstrating that these techniques could also ameliorate the deleterious effect of the positron range in clinical PET imaging.

Tissue-Dependent and Spatially-Variant Positron Range Correction in 3D PET

Positron range (PR) is a significant factor that limits PET image resolution, especially with some radionuclides currently used in clinical and preclinical studies such as (82)Rb, (124)I and (68)Ga. The use of an accurate model of the PR in the image reconstruction may minimize its impact on the image quality. Nevertheless, PR distributions are difficult to model, as they may be different at each voxel and direction, depending on the materials that the positron flies through. Several approximated methods have been proposed, considering only one or several propagating media without taking into account boundaries effects. In some regions, like lungs or trachea, these methods may not be accurate enough and yield artifacts. In this work, we present an efficient method to accurately incorporate spatially-variant PR corrections. The method is based on pre-computing voxel-dependent PR kernels using a CT or a manually segmented image, and a model of the dependence of the PR on each material derived from Monte Carlo simulations. The images are convoluted with these kernels in the forward-projection step of the iterative reconstruction algorithm. This implementation of the algorithm adds a modest overhead to the overall reconstruction time and it obtains artifact-free PR-corrected images, even when the activity is concentrated at tissue boundaries with extreme changes of density. We verified the method with the preclinical Argus PET/CT scanner, but it can be also applied to other scanners and improve the image quality in clinical PET studies using isotopes with large PR.

Assessment of a fully 3D Monte Carlo reconstruction method for preclinical PET with iodine-124

Iodine-124 is a radionuclide well suited to the labeling of intact monoclonal antibodies. Yet, accurate quantification in preclinical imaging with I-124 is challenging due to the large positron range and a complex decay scheme including high-energy gammas. The aim of this work was to assess the quantitative performance of a fully 3D Monte Carlo (MC) reconstruction for preclinical I-124 PET. The high-resolution small animal PET Inveon (Siemens) was simulated using GATE 6.1. Three system matrices (SM) of different complexity were calculated in addition to a Siddon-based ray tracing approach for comparison purpose. Each system matrix accounted for a more or less complete description of the physics processes both in the scanned object and in the PET scanner. One homogeneous water phantom and three heterogeneous phantoms including water, lungs and bones were simulated, where hot and cold regions were used to assess activity recovery as well as the trade-off between contrast recovery and noise in different regions. The benefit of accounting for scatter, attenuation, positron range and spurious coincidences occurring in the object when calculating the system matrix used to reconstruct I-124 PET images was highlighted. We found that the use of an MC SM including a thorough modelling of the detector response and physical effects in a uniform water-equivalent phantom was efficient to get reasonable quantitative accuracy in homogeneous and heterogeneous phantoms. Modelling the phantom heterogeneities in the SM did not necessarily yield the most accurate estimate of the activity distribution, due to the high variance affecting many SM elements in the most sophisticated SM.

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.

Noise propagation in resolution modeled PET imaging and its impact on detectability

Positron emission tomography imaging is affected by a number of resolution degrading phenomena, including positron range, photon non-collinearity and inter-crystal blurring. An approach to this issue is to model some or all of these effects within the image reconstruction task, referred to as resolution modeling (RM). This approach is commonly observed to yield images of higher resolution and subsequently contrast, and can be thought of as improving the modulation transfer function. Nonetheless, RM can substantially alter the noise distribution. In this work, we utilize noise propagation models in order to accurately characterize the noise texture of reconstructed images in the presence of RM. Furthermore we consider the task of lesion or defect detection, which is highly determined by the noise distribution as quantified using the noise power spectrum. Ultimately, we use this framework to demonstrate why conventional trade-off analyses (e.g. contrast versus noise, using simplistic noise metrics) do not provide a complete picture of the impact of RM and that improved performance of RM according to such analyses does not necessarily translate to the superiority of RM in detection task performance.

Positron range estimations with PeneloPET

Technical advances towards high resolution PET imaging try to overcome the inherent physical limitations to spatial resolution. Positrons travel in tissue until they annihilate into the two gamma photons detected. This range is the main detector-independent contribution to PET imaging blurring. To a large extent, it can be remedied during image reconstruction if accurate estimates of positron range are available. However, the existing estimates differ, and the comparison with the scarce experimental data available is not conclusive. In this work we present positron annihilation distributions obtained from Monte Carlo simulations with the PeneloPET simulation toolkit, for several common PET isotopes ((18)F, (11)C, (13)N, (15)O, (68)Ga and (82)Rb) in different biological media (cortical bone, soft bone, skin, muscle striated, brain, water, adipose tissue and lung). We compare PeneloPET simulations against experimental data and other simulation results available in the literature. To this end the different positron range representations employed in the literature are related to each other by means of a new parameterization for positron range profiles. Our results are generally consistent with experiments and with most simulations previously reported with differences of less than 20% in the mean and maximum range values. From these results, we conclude that better experimental measurements are needed, especially to disentangle the effect of positronium formation in positron range. Finally, with the aid of PeneloPET, we confirm that scaling approaches can be used to obtain universal, material and isotope independent, positron range profiles, which would considerably simplify range correction.

Resolution modeling in PET imaging: theory, practice, benefits, and pitfalls

In this paper, the authors review the field of resolution modeling in positron emission tomography (PET) image reconstruction, also referred to as point-spread-function modeling. The review includes theoretical analysis of the resolution modeling framework as well as an overview of various approaches in the literature. It also discusses potential advantages gained via this approach, as discussed with reference to various metrics and tasks, including lesion detection observer studies. Furthermore, attention is paid to issues arising from this approach including the pervasive problem of edge artifacts, as well as explanation and potential remedies for this phenomenon. Furthermore, the authors emphasize limitations encountered in the context of quantitative PET imaging, wherein increased intervoxel correlations due to resolution modeling can lead to significant loss of precision (reproducibility) for small regions of interest, which can be a considerable pitfall depending on the task of interest.

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.