Analytical positron range modelling in heterogeneous media for PET Monte Carlo simulation

M-TAG: A modular teaching-aid for Geant4

Geant4 is a versatile Monte Carlo radiation transport simulation toolkit with a steep learning curve. This work introduces a user-code called M-TAG (Modular Radiation Teaching-Aid for Geant4), built on top of Geant4. M-TAG is designed to help gradually introduce the Geant4 toolkit to new users. The goal of Geant4 is to record quantities from the simulated radiation as it is transported through geometries. M-TAG simplifies the inclusion of new geometric elements and detector components in the simulation by including new classes. M-TAG also provides basic validated examples for some common detector development tasks. Geant4 intercom modules, called messenger classes, manage these classes. To validate M-TAG, simulations were performed to calculate the range of positrons in water. One hundred million decays at the center of a water-filled sphere with a radius of 1 m were allowed for fluorine-18, carbon-11, oxygen-15 and gallium-68. These results were compared to literature values. An inexperienced Geant4 user was tasked with creating a simulation model for a plastic scintillator-based detector and conducting basic tests to assess the effectiveness of M-TAG as a teaching tool. The simulation involved calculating the dose to the detector's sensitive volume using a 2x2 cm planar monoenergetic photon source spanning energies from 20 to 100 keV. One billion particles were simulated twice: once with the actual detector geometry and once with the sensitive volume replaced by water. The validity of M-TAG was also verified by computing dose ratios and comparing them with mass-attenuation ratios obtained from NIST XCOM data sets. The mean positron travel distances were within the distribution of literature values. Simulated positron energy spectra means were within 1.8% of literature means. Simulated dose ratios agreed with literature values within uncertainties. We have developed and verified a modular Geant4 teaching aid called M-TAG. It was used to introduce a new user to Geant4, who used it to perform further validation simulations.

Simulation of a novel, non-invasive radiation detector to measure the arterial input function for dynamic positron emission tomography

BACKGROUND

Dynamic positron emission tomography (dPET) is a nuclear medicine imaging technique providing functional images for organs of interest with applications in oncology, cardiology, and drug discovery. This technique requires the acquisition of the time-course arterial plasma activity concentration, called the arterial input function (AIF), which is conventionally acquired via arterial blood sampling.

PURPOSE

The aim of this study was to (A) optimize the geometry for a novel and cost efficient non-invasive detector called NID designed to measure the AIF for dPET scans through Monte Carlo simulations and (B) develop a clinical data analysis chain to successfully separate the arterial component of a simulated AIF signal from the venous component.

METHODS

The NID was optimized by using an in-house Geant4-based software package. The sensitive volume of the NID consists of a band of 10 cm long and 1 mm in diameter scintillating fibers placed over a wrist phantom. The phantom was simulated as a cylinder, 10 cm long and 6.413 cm in diameter comprised of polyethylene with two holes placed through it to simulate the patient's radial artery and vein. This phantom design was chosen to match the wrist phantom used in our previous proof of concept work. Two geometries were simulated with different arrangements of scintillating fibers. The first design used a single layer of 64 fibers. The second used two layers, an inner layer with 29 fibers and an outer layer with 30 fibers. Four positron emitting radioisotopes were simulated: ¹⁸ F, ¹¹ C, ¹⁵ O, and ⁶⁸ Ga with 100 million simulated decay events per run. The total and intrinsic efficiencies of both designs were calculated as well as the full width half maximum (FWHM) of the signal. In addition, contribution by the annihilation photons versus positrons to the signal was investigated. The results obtained from the two simulated detector models were compared. A clinical data analysis chain using an expectation maximization maximum likelihood algorithm was tested. This analysis chain will be used to separate arterial counts from the total signal.

RESULTS

The second NID design with two layers of scintillating fibers had a higher efficiency for all simulations with a maximum increase of 17% total efficiency for ¹¹ C simulation. All simulations had a significant annihilation photon contribution. The signal for ¹⁸ F and ¹¹ C was almost entirely due to photons. The clinical data analysis chain was within 1% of the true value for 434 out of 440 trials. Further experimental studies to validate these simulations will be required.

CONCLUSIONS

The design of the NID was optimized and its efficiency increased through Monte Carlo simulations. A clinical data analysis chain was successfully developed to separate the arterial component of an AIF signal from the venous component. The simulations show that the NID can be used to accurately measure the AIF non-invasively for dPET scans.

The effect of magnetic field strength on the positron range and projected annihilation artifact in integrated PET/MR systems: A GATE Monte Carlo study

PURPOSE

With improvements in positron emission tomography/magnetic resonance imaging (PET/MRI) over the last decade, there is a need to investigate the projected annihilation (shine-through) artifact and resolution impact for different PET radiopharmaceuticals, magnetic field (MF) strengths, and tissues.

METHODS

The GATE Monte Carlo (MC) simulation was used to simulate the annihilation distribution of positrons in different tissues and MFs. The positron distribution was studied in magnetic field (MF) intensities up to 15 T for ¹¹ C, ¹³ N, ¹⁵ O, ¹⁸ F, ⁶⁸ Ga, and ⁸² Rb. Moreover, the image quality in terms of the occurrence of projected annihilation artifacts was investigated using the 4D anthropomorphic digital extended cardiac-torso (XCAT) phantom.

RESULTS

Positron ranges were restricted across the directions perpendicular to the MF, but no change along the direction of the MF was detected. The projected annihilation artifacts were observed with the presence of MF in the sagittal and coronal view of PET images prepared from the XCAT phantom. The intensity of artifact was constant in MFs higher than 3 T. The significant effect of the MF on resolution improvement was observed in soft tissue for ⁶⁸ Ga in 7 T and ⁸² Rb in 3 and 7 T, while higher MFs have no impact on resolution. The improvement of resolution in the lung tissue was observed for the medium- and high-energy radionuclides in 7 T MF.

CONCLUSION

The MF can create the projected annihilation artifact in the boundary of air cavities and other tissues for medium- and high-energy radionuclides especially for ⁶⁸ Ga in clinical studies. In addition, the strength of the MFs more than 3 T was ineffective on the intensity of the projected annihilation artifact. In a clinical PET/MR scanner, MF has remarkable spatial resolution improvement in lung tissue, especially for medium- and high-energy radionuclides, and negligible effect in bone and soft tissue for most radionuclides.

Comparison of scandium-44 g with other PET radionuclides in pre-clinical PET phantom imaging

PURPOSE

The decay characteristics of radionuclides in PET studies can impact image reconstruction. ^44gSc has been the topic of recent research due to potential theranostic applications and is a promising radiometal for PET imaging. In this study, the reconstructed images from phantom measurements with scandium in a small-animal PET scanner are compared with ¹⁸F and two prominent radiometals: ⁶⁴Cu and ⁶⁸Ga METHODS: Three phantoms filled with ¹⁸F, ⁶⁴C, ⁶⁸Ga, and ^44gSc were imaged in the Siemens Inveon PET scanner. The NEMA image quality phantom was used to determine the recovery coefficients (RCs), spill-over ratios (SORs), and noise (%SD) under typical pre-clinical imaging conditions. Image contrast was determined using a Derenzo phantom, while the coincidence characteristics were investigated using an NEC phantom. Three reconstruction algorithms were used, namely filtered back projection (FBP), ordered subset expectation maximization (OSEM), and maximum a-posteriori (MAP).

RESULTS

Image quality parameters were measured for ¹⁸F, ⁶⁴Cu, ⁶⁸Ga, and ^44gSc respectively; using FBP, the %SD are 5.65, 5.88, 7.28, and 7.70; the RCs for the 5-mm rod are 0.849, 1.01, 0.615, and 0.825; the SORs in water are 0.0473, 0.0595, 0.141, 0.0923; and the SORs in air are 0.0589, 0.0484, 0.0525, and 0.0509. The contrast measured in the 2.5-mm rods are 0.674, 0.637, 0.196, and 0.347. The NEC rate with ^44gSc increased at a slower rate than ¹⁸F and ⁶⁸Ga as a function of activity in the field of view.

CONCLUSION

^44gSc demonstrates intermediate behavior relative to ¹⁸F and ⁶⁸Ga with regard to RC and contrast measurements. It is a promising radionuclide for preclinical imaging.

Positron range effects of 66Ga in small-animal PET imaging

PURPOSE

Gallium-66 is a non-conventional positron emitter that stands out not only for its high potential to label peptides, proteins and antibodies, but also because it can provide spatio-temporal information of relatively slow physiological processes in the body due to its conveniently long half-life of 9.5 h. However, ⁶⁶Ga emits the most energetic positrons for PET imaging. The lack of information of the positron range effect on spatial resolution for this positron emitter is an issue, particularly in preclinical imaging.

METHODS

The line spread function (LSF) in tissue-equivalent materials with densities between 0.2 and 1.93 g/cm³ was obtained with ⁶⁶Ga and ¹⁸F. A complementary study with the NEMA NU 4-2008 image quality phantom is also included.

RESULTS

High-energy positrons moving in lower density materials produce far-reaching activity distributions. The LSFs were characterized with Lorentzian-Gaussian fits, with spatial resolution (FWHM) in the 2.14-3.2 mm range, and long tails extending a few tens of mm depending on the material type and density. A narrowing of the LSF was observed for lung-equivalent materials, indicating the lack of enough material for the positron annihilation to take place. The NEMA NU 4-2008 image quality phantom produced blurred images, notoriously observed in the hot and cold cylinders used for evaluation of recovery coefficients (RC) and spill-over ratios (SOR), producing very low RC and very large SOR.

CONCLUSIONS

Quantitative PET imaging with the non-conventional ⁶⁶Ga is hampered due to the large range of its high-energy positrons affecting both spatial resolution and activity concentration quantification.

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.

Singular value decomposition analysis of back projection operator of maximum likelihood expectation maximization PET image reconstruction

Background

In emission tomography maximum likelihood expectation maximization reconstruction technique has replaced the analytical approaches in several applications. The most important drawback of this iterative method is its linear rate of convergence and the corresponding computational burden. Therefore, simplifications are usually required in the Monte Carlo simulation of the back projection step. In order to overcome these problems, a reconstruction code has been developed with graphical processing unit based Monte Carlo engine which enabled full physical modelling in the back projection.

Materials and methods

Code performance was evaluated with simulations on two geometries. One is a sophisticated scanner geometry which consists of a dodecagon with inscribed circle radius of 8.7 cm, packed on each side with an array of 39 × 81 LYSO detector pixels of 1.17 mm sided squares, similar to a Mediso nanoScan PET/CT scanner. The other, simplified geometry contains a 38,4mm long interval as a voxel space, detector pixels are assigned in two parallel sections each containing 81 crystals of a size 1.17×1.17 mm.

Results

We have demonstrated that full Monte Carlo modelling in the back projection step leads to material dependent inhomogeneities in the reconstructed image. The reasons behind this apparently anomalous behaviour was analysed in the simplified system by means of singular value decomposition and explained by different speed of convergence.

Conclusions

To still take advantage of the higher noise stability of the full physical modelling, a new filtering technique is proposed for convergence acceleration. Some theoretical considerations for the practical implementation and for further development are also presented.

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.

Absolute Differential Positronium-Formation Cross Sections

The first absolute experimental determinations of the differential cross sections for the formation of ground-state positronium are presented for He, Ar, H2, and CO2 near 0°. Results are compared with available theories. The ratio of the differential and integrated cross sections for the targets exposes the higher propensity for forward emission of positronium formed from He and H2.

4D PET iterative deconvolution with spatiotemporal regularization for quantitative dynamic PET imaging

Quantitative measurements in dynamic PET imaging are usually limited by the poor counting statistics particularly in short dynamic frames and by the low spatial resolution of the detection system, resulting in partial volume effects (PVEs). In this work, we present a fast and easy to implement method for the restoration of dynamic PET images that have suffered from both PVE and noise degradation. It is based on a weighted least squares iterative deconvolution approach of the dynamic PET image with spatial and temporal regularization. Using simulated dynamic [(11)C] Raclopride PET data with controlled biological variations in the striata between scans, we showed that the restoration method provides images which exhibit less noise and better contrast between emitting structures than the original images. In addition, the method is able to recover the true time activity curve in the striata region with an error below 3% while it was underestimated by more than 20% without correction. As a result, the method improves the accuracy and reduces the variability of the kinetic parameter estimates calculated from the corrected images. More importantly it increases the accuracy (from less than 66% to more than 95%) of measured biological variations as well as their statistical detectivity.

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.

Simulation-based optimisation of the PET data processing for partial saturation approach protocols

Positron emission tomography (PET) with [(11)C]Raclopride is an important tool for studying dopamine D2 receptor expression in vivo. [(11)C]Raclopride PET binding experiments conducted using the Partial Saturation Approach (PSA) allow the estimation of receptor density (B(avail)) and the in vivo affinity appK(D). The PSA is a simple, single injection, single scan experimental protocol that does not require blood sampling, making it ideal for use in longitudinal studies. In this work, we generated a complete Monte Carlo simulated PET study involving two groups of scans, in between which a biological phenomenon was inferred (a 30% decrease of B(avail)), and used it in order to design an optimal data processing chain for the parameter estimation from PSA data. The impact of spatial smoothing, noise removal and image resolution recovery technique on the statistical detection was investigated in depth. We found that image resolution recovery using iterative deconvolution of the image with the system point spread function associated with temporal data denoising greatly improves the accuracy and the statistical reliability of detecting the imposed phenomenon. Before optimisation, the inferred B(avail) variation between the two groups was underestimated by 42% and detected in 66% of cases, while a false decrease of appK(D) by 13% was detected in more than 11% of cases. After optimisation, the calculated B(avail) variation was underestimated by only 3.7% and detected in 89% of cases, while a false slight increase of appK(D) by 3.7% was detected in only 2% of cases. We found during this investigation that it was essential to adjust a factor that accounts for difference in magnitude between the non-displaceable ligand concentrations measured in the target and in the reference regions, for different data processing pathways as this ratio was affected by different image resolutions.

Accurate and efficient modeling of the detector response in small animal multi-head PET systems

In fully three-dimensional PET imaging, iterative image reconstruction techniques usually outperform analytical algorithms in terms of image quality provided that an appropriate system model is used. In this study we concentrate on the calculation of an accurate system model for the YAP-(S)PET II small animal scanner, with the aim to obtain fully resolution- and contrast-recovered images at low levels of image roughness. For this purpose we calculate the system model by decomposing it into a product of five matrices: (1) a detector response component obtained via Monte Carlo simulations, (2) a geometric component which describes the scanner geometry and which is calculated via a multi-ray method, (3) a detector normalization component derived from the acquisition of a planar source, (4) a photon attenuation component calculated from x-ray computed tomography data, and finally, (5) a positron range component is formally included. This system model factorization allows the optimization of each component in terms of computation time, storage requirements and accuracy. The main contribution of this work is a new, efficient way to calculate the detector response component for rotating, planar detectors, that consists of a GEANT4 based simulation of a subset of lines of flight (LOFs) for a single detector head whereas the missing LOFs are obtained by using intrinsic detector symmetries. Additionally, we introduce and analyze a probability threshold for matrix elements of the detector component to optimize the trade-off between the matrix size in terms of non-zero elements and the resulting quality of the reconstructed images. In order to evaluate our proposed system model we reconstructed various images of objects, acquired according to the NEMA NU 4-2008 standard, and we compared them to the images reconstructed with two other system models: a model that does not include any detector response component and a model that approximates analytically the depth of interaction as detector response component. The comparisons confirm previous research results, showing that the usage of an accurate system model with a realistic detector response leads to reconstructed images with better resolution and contrast recovery at low levels of image roughness.

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.

Characterisation of partial volume effect and region-based correction in small animal positron emission tomography (PET) of the rat brain

Accurate quantification of PET imaging data is required for a useful interpretation of the measured radioactive tracer concentrations. The partial volume effect (PVE) describes signal dilution and mixing due to spatial resolution and sampling limitations, which introduces bias in quantitative results. In the present study we investigated the magnitude of PVE for volumes of interest (VOIs) in the rat brain and the effect of positron range. In simulated (11)C-raclopride studies we examined the influence of PVE on time activity curves in striatal and cerebellar VOIs and binding potential estimation. The performance of partial volume correction (PVC) was studied using the region-based geometric transfer matrix (GTM) method including the question of whether a spatially variant point spread function (PSF) is necessary for PVC of a rat brain close to the centre of the field of view. Furthermore, we determined the effect of spillover from activity outside the brain. The results confirmed that PVE is significant in rat brain PET and showed that positron range is an important factor that needs to be included in the PSF. There was considerable bias in time activity curves for the simulated (11)C-raclopride studies and significant underestimation of binding potential even for very small centred VOIs. Good activity recovery was achieved with the GTM PVC using a spatially invariant simulated PSF when no activity was present outside the brain. PVC using a simple Gaussian fit point spread function was not sufficiently accurate. Spillover from regions outside the brain had a significant impact on measured activity concentrations and reduced the accuracy of PVC with the GTM method using rat brain regions alone, except for the smallest VOI size but at the cost of increased noise. Voxel-based partial volume correction methods which inherently compensate for spillover from outside the brain might be a more suitable choice.

The importance of correction for tissue fraction effects in lung PET: preliminary findings

PURPOSE

It has recently been recognized that PET/CT may play a role in diffuse parenchymal lung disease. However, interpretation can be confounded due to the variability in lung density both within and between individuals. To address this issue a novel correction method is proposed.

METHODS

A CT scan acquired during shallow breathing is registered to a PET study and smoothed so as to match the PET resolution. This is used to derive voxel-based tissue fraction correction factors for the individual. The method was evaluated in a lung phantom study in which the lung was simulated by a Styrofoam/water mixture. The method was further evaluated using (18)F-FDG in 12 subjects free from pulmonary disease where ranges before and after correction were considered.

RESULTS

Correction resulted in similar activity concentrations for the lung and background regions, consistent with the experimental phantom set-up. Correction resulted in reduced inter- and intrasubject variability in the estimated SUV. The possible application of the method was further demonstrated in five subjects with interstitial lung changes where increased SUV was demonstrated. Single study pre- and post-treatment studies were also analysed to further illustrate the utility of the method.

CONCLUSION

The proposed tissue fraction correction method is a promising technique to account for variability of density in interpreting lung PET studies.