Spatially Variant Positron Range Modeling Derived from CT for PET Image Reconstruction

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.

Effect of positron range on PET quantification in diseased and normal lungs

The impact of positron range on PET image reconstruction has often been investigated as a blurring effect that can be partly corrected by adding an element to the PET system matrix in the reconstruction, usually based on a Gaussian kernel constructed from the attenuation values. However, the physics involved in PET is more complex. In regions where density does not vary, positron range indeed involves mainly blurring. However, in more heterogeneous media it can cause other effects. This work focuses on positron range in the lungs and its impact on quantification, especially in the case of pathologies such as cancer or pulmonary fibrosis, for which the lungs have localised varying density. Using Monte Carlo simulations, we evaluate the effects of positron range for multiple radionuclides (¹⁸F, ¹⁵O, ⁶⁸Ga, ⁸⁹Zr, ⁸²Rb, ⁶⁴Cu and ¹²⁴I) as, for novel radiotracers, the choice of the labelling radionuclide is important. The results demonstrate quantification biases in highly heterogeneous media, where the measured uptake of high-density regions can be increased by the neighbouring radioactivity from regions of lower density, with the effect more noticeable for radionuclides with high-energy positron emission. When the low-density regions are considered to have less radioactive uptake (e.g. due to the presence of air), the effect is less severe.

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.

Feasibility of in situ, high-resolution correlation of tracer uptake with histopathology by quantitative autoradiography of biopsy specimens obtained under 18F-FDG PET/CT guidance

Core biopsies obtained using PET/CT guidance contain bound radiotracer and therefore provide information about tracer uptake in situ. Our goal was to develop a method for quantitative autoradiography of biopsy specimens (QABS), to use this method to correlate (18)F-FDG tracer uptake in situ with histopathology findings, and to briefly discuss its potential application.

METHODS

Twenty-seven patients referred for a PET/CT-guided biopsy of (18)F-FDG-avid primary or metastatic lesions in different locations consented to participate in this institutional review board-approved study, which complied with the Health Insurance Portability and Accountability Act. Autoradiography of biopsy specimens obtained using 5 types of needles was performed immediately after extraction. The response of autoradiography imaging plates was calibrated using dummy specimens with known activity obtained using 2 core-biopsy needle sizes. The calibration curves were used to quantify the activity along biopsy specimens obtained with these 2 needles and to calculate the standardized uptake value, SUVARG. Autoradiography images were correlated with histopathologic findings and fused with PET/CT images demonstrating the position of the biopsy needle within the lesion. Logistic regression analysis was performed to search for an SUVARG threshold distinguishing benign from malignant tissue in liver biopsy specimens. Pearson correlation between SUVARG of the whole biopsy specimen and average SUVPET over the voxels intersected by the needle in the fused PET/CT image was calculated.

RESULTS

Activity concentrations were obtained using autoradiography for 20 specimens extracted with 18- and 20-gauge needles. The probability of finding malignancy in a specimen is greater than 50% (95% confidence) if SUVARG is greater than 7.3. For core specimens with preserved shape and orientation and in the absence of motion, one can achieve autoradiography, CT, and PET image registration with spatial accuracy better than 2 mm. The correlation coefficient between the mean specimen SUVARG and SUVPET was 0.66.

CONCLUSION

Performing QABS on core-biopsy specimens obtained using PET/CT guidance enables in situ correlation of (18)F-FDG tracer uptake and histopathology on a millimeter scale. QABS promises to provide useful information for guiding interventional radiology procedures and localized therapies and for in situ high-spatial-resolution validation of radiopharmaceutical uptake.

Positron range in PET imaging: non-conventional isotopes

In addition to conventional short-lived radionuclides, longer-lived isotopes are becoming increasingly important to positron emission tomography (PET). The longer half-life both allows for circumvention of the in-house production of radionuclides, and expands the spectrum of physiological processes amenable to PET imaging, including processes with prohibitively slow kinetics for investigation with short-lived radiotracers. However, many of these radionuclides emit 'high-energy' positrons and gamma rays which affect the spatial resolution and quantitative accuracy of PET images. The objective of the present work is to investigate the positron range distribution for some of these long-lived isotopes. Based on existing Monte Carlo simulations of positron interactions in water, the probability distribution of the line of response displacement have been empirically described by means of analytic displacement functions. Relevant distributions have been derived for the isotopes (22)Na, (52)Mn, (89)Zr, (45)Ti, (51)Mn, (94 m)Tc, (52 m)Mn, (38)K, (64)Cu, (86)Y, (124)I, and (120)I. It was found that the distribution functions previously found for a series of conventional isotopes (Jødal et al 2012 Phys. Med. Bio. 57 3931-43), were also applicable to these non-conventional isotopes, except that for (120)I, (124)I, (89)Zr, (52)Mn, and (64)Cu, parameters in the formulae were less well predicted by mean positron energy alone. Both conventional and non-conventional range distributions can be described by relatively simple analytic expressions. The results will be applicable to image-reconstruction software to improve the resolution.

Isotope specific resolution recovery image reconstruction in high resolution PET imaging

PURPOSE

Measuring and incorporating a scanner-specific point spread function (PSF) within image reconstruction has been shown to improve spatial resolution in PET. However, due to the short half-life of clinically used isotopes, other long-lived isotopes not used in clinical practice are used to perform the PSF measurements. As such, non-optimal PSF models that do not correspond to those needed for the data to be reconstructed are used within resolution modeling (RM) image reconstruction, usually underestimating the true PSF owing to the difference in positron range. In high resolution brain and preclinical imaging, this effect is of particular importance since the PSFs become more positron range limited and isotope-specific PSFs can help maximize the performance benefit from using resolution recovery image reconstruction algorithms.

METHODS

In this work, the authors used a printing technique to simultaneously measure multiple point sources on the High Resolution Research Tomograph (HRRT), and the authors demonstrated the feasibility of deriving isotope-dependent system matrices from fluorine-18 and carbon-11 point sources. Furthermore, the authors evaluated the impact of incorporating them within RM image reconstruction, using carbon-11 phantom and clinical datasets on the HRRT.

RESULTS

The results obtained using these two isotopes illustrate that even small differences in positron range can result in different PSF maps, leading to further improvements in contrast recovery when used in image reconstruction. The difference is more pronounced in the centre of the field-of-view where the full width at half maximum (FWHM) from the positron range has a larger contribution to the overall FWHM compared to the edge where the parallax error dominates the overall FWHM.

CONCLUSIONS

Based on the proposed methodology, measured isotope-specific and spatially variant PSFs can be reliably derived and used for improved spatial resolution and variance performance in resolution recovery image reconstruction. The benefits are expected to be more substantial for more energetic positron emitting isotopes such as Oxygen-15 and Rubidium-82.

Effects of magnetic fields of up to 9.4 T on resolution and contrast of PET images as measured with an MR-BrainPET

Simultaneous, hybrid MR-PET is expected to improve PET image resolution in the plane perpendicular to the static magnetic field of the scanner. Previous papers have reported this either by simulation or experiment with simple sources and detector arrangements. Here, we extend those studies using a realistic brain phantom in a recently installed MR-PET system comprising a 9.4 T MRI-scanner and an APD-based BrainPET insert in the magnet bore. Point and line sources and a 3D brain phantom were filled with 18F (low-energy positron emitter), 68Ga (medium energy positron emitter) or 120I, a non-standard positron emitter (high positron energies of up to 4.6 MeV). Using the BrainPET insert, emission scans of the phantoms were recorded at different positions inside and outside the magnet bore such that the magnetic field was 0 T, 3 T, 7 T or 9.4 T. Brain phantom images, with the 'grey matter' compartment filled with 18F, showed no obvious resolution improvement with increasing field. This is confirmed by practically unchanged transaxial FWHM and 'grey/white matter' ratio values between at 0T and 9.4T. Field-dependent improvements in the resolution and contrast of transaxial PET images were clearly evident when the brain phantom was filled with 68Ga or 120I. The grey/white matter ratio increased by 7.3% and 16.3%, respectively. The greater reduction of the FWTM compared to FWHM in 68Ga or 120I line-spread images was in agreement with the improved contrast of 68Ga or 120I images. Notwithstanding elongations seen in the z-direction of 68Ga or 120I point source images acquired in foam, brain phantom images show no comparable extension. Our experimental study confirms that integrated MR-PET delivers improved PET image resolution and contrast for medium- and high-energy positron emitters even though the positron range is reduced only in directions perpendicular to the magnetic field.

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.

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.

Microfluidic reactor geometries for radiolysis reduction in radiopharmaceuticals

Autoradiolysis describes the degradation of radioactively labeled compounds due to the activity of the labeled compounds themselves. It scales with activity concentration and is of importance for high activity and microfluidic PET tracer synthesis. This study shows that microfluidic devices can be shaped to reduce autoradiolysis by geometric exclusion of positron interaction. A model is developed and confirmed by demonstrating in-capillary storage of non-stabilized [(18)F]FDG (2-[(18)F]Fluoro-2-deoxy-d-glucose) at max. 23 GBq/ml while maintaining >90% radiochemical purity over 14 h.

Effect of the positron range of 18F, 68Ga and 124I on PET/CT in lung-equivalent materials

PURPOSE

The aim of this study was to investigate the effect of positron range on visualization and quantification in (18)F, (68)Ga and (124)I positron emission tomography (PET)/CT of lung-like tissue.

METHODS

Different sources were measured in air, in lung-equivalent foams and in water, using a clinical PET/CT and a microPET system. Intensity profiles and curves with the cumulative number of annihilations were derived and numerically characterized.

RESULTS

(68)Ga and (124)I gave similar results. Their intensity profiles in lung-like foam had a peak similar to that for (18)F, and tails of very low intensity, but extending over distances of centimetres and containing a large fraction of all annihilations. For 90% recovery, volumes of interest with diameters up to 50 mm were required, and recovery within the 10% intensity isocontour was as low as 30%. In contrast, tailing was minor for (18)F.

CONCLUSION

Lung lesions containing (18)F, (68)Ga or (124)I will be visualized similarly, and at least as sharp as in soft tissue. Nevertheless, for quantification of (68)Ga and (124)I large volumes of interest are needed for complete activity recovery. For clinical studies containing noise and background, new quantification approaches may have to be developed.

Characterization of the ringing artifacts in rotator-based reconstruction with Monte Carlo-based resolution compensation for PET

PURPOSE

Studies have shown that Monte Carlo-based reconstruction could effectively improve the image quality of positron emission tomography. The authors have previously used a Gaussian rotator-based algorithm to efficiently reduce the computational cost for system matrix (SM) calculation and to meet the large memory requirements for SM storage. However, pronounced ringing artifacts were observed in the reconstructed image. In this article, the authors investigated and characterized these artifacts.

METHODS

The authors proposed an "ideal" rotator and used it as a baseline in the artifacts evaluation. This ideal rotator produces perfectly rotated images. The Gaussian rotator method was evaluated by a full system model and a partial system model without positron range and acolinearity, which could be compensated for by the blurring of the Gaussian rotator for 18F studies. Noiseless data, Monte Carlo simulation data, as well as acquired experimental data were used to quantitatively characterize the behavior of the artifacts.

RESULTS

The study of the noiseless data indicated that the artifacts were mainly attributed to the rotator, which further blurred the simulated system responses. The simulation study suggested that the artifacts become less pronounced and not quantitatively significant in practice. This result is consistent with the experimental data study. Better contrast recovery was achieved with an over-compensated system model. Traditionally, an undercompensated system model was preferred to avoid artifacts. The authors' studies suggest that the Gaussian rotator with the full system model yields the best image quality among the evaluated methods with considerably reduced quantitative error and quantitatively insignificant artifacts in practice.

CONCLUSIONS

The authors' investigation indicated that a moderately overcompensated system model (about 2 mm FWHM in this study) yielded better contrast recovery and quantitatively insignificant artifacts in practice.

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

PURPOSE

The quality of tomographic images is directly affected by the system model being used in image reconstruction. An accurate system matrix is desirable for high-resolution image reconstruction, but it often leads to high computation cost. In this work the authors present a maximum a posteriori reconstruction algorithm with residual correction to alleviate the tradeoff between the model accuracy and the computation efficiency in image reconstruction.

METHODS

Unlike conventional iterative methods that assume that the system matrix is accurate, the proposed method reconstructs an image with a simplified system matrix and then removes the reconstruction artifacts through residual correction. Since the time-consuming forward and back projection operations using the accurate system matrix are not required in every iteration, image reconstruction time can be greatly reduced.

RESULTS

The authors apply the new algorithm to high-resolution positron emission tomography reconstruction with an on-the-fly Monte Carlo (MC) based positron range model. Computer simulations show that the new method is an order of magnitude faster than the traditional MC-based method, whereas the visual quality and quantitative accuracy of the reconstructed images are much better than that obtained by using the simplified system matrix alone.

CONCLUSIONS

The residual correction method can reconstruct high-resolution images and is computationally efficient.