Positron follow-up in liquid water: I. A new Monte Carlo track-structure code

Overlooked potential of positrons in cancer therapy

Positron (β⁺) emitting radionuclides have been used for positron emission tomography (PET) imaging in diagnostic medicine since its development in the 1950s. Development of a fluorinated glucose analog, fluorodeoxyglucose, labelled with a β⁺ emitter fluorine-18 (¹⁸F-FDG), made it possible to image cellular targets with high glycolytic metabolism. These targets include cancer cells based on increased aerobic metabolism due to the Warburg effect, and thus, ¹⁸F-FDG is a staple in nuclear medicine clinics globally. However, due to its attention in the diagnostic setting, the therapeutic potential of β⁺ emitters have been overlooked in cancer medicine. Here we show the first in vitro evidence of β⁺ emitter cytotoxicity on prostate cancer cell line LNCaP C4-2B when treated with 20 Gy of ¹⁸F. Monte Carlo simulation revealed thermalized positrons (sub-keV) traversing DNA can be lethal due to highly localized energy deposition during the thermalization and annihilation processes. The computed single and double strand breakages were ~ 55% and 117% respectively, when compared to electrons at 400 eV. Our in vitro and in silico data imply an unexplored therapeutic potential for β⁺ emitters. These results may also have implications for emerging cancer theranostic strategies, where β⁺ emitting radionuclides could be utilized as a therapeutic as well as a diagnostic agent once the challenges in radiation safety and protection after patient administration of a radioactive compound are overcome.

The Impact of Positron Range on PET Resolution, Evaluated with Phantoms and PHITS Monte Carlo Simulations for Conventional and Non-conventional Radionuclides

PURPOSE

The increasing interest and availability of non-standard positron-emitting radionuclides has heightened the relevance of radionuclide choice in the development and optimization of new positron emission tomography (PET) imaging procedures, both in preclinical research and clinical practice. Differences in achievable resolution arising from positron range can largely influence application suitability of each radionuclide, especially in small-ring preclinical PET where system blurring factors due to annihilation photon acollinearity and detector geometry are less significant. Some resolution degradation can be mitigated with appropriate range corrections implemented during image reconstruction, the quality of which is contingent on an accurate characterization of positron range.

PROCEDURES

To address this need, we have characterized the positron range of several standard and non-standard PET radionuclides (As-72, F-18, Ga-68, Mn-52, Y-86, and Zr-89) through imaging of small-animal quality control phantoms on a benchmark preclinical PET scanner. Further, the Particle and Heavy Ion Transport code System (PHITS v3.02) code was utilized for Monte Carlo modeling of positron range-dependent blurring effects.

RESULTS

Positron range kernels for each radionuclide were derived from simulation of point sources in ICRP reference tissues. PET resolution and quantitative accuracy afforded by various radionuclides in practicable imaging scenarios were characterized using a convolution-based method based on positron annihilation distributions obtained from PHITS. Our imaging and simulation results demonstrate the degradation of small animal PET resolution, and quantitative accuracy correlates with increasing positron energy; however, for a specific "benchmark" preclinical PET scanner and reconstruction workflow, these differences were observed to be minimal given radionuclides with average positron energies below ~ 400 keV.

CONCLUSION

Our measurements and simulations of the influence of positron range on PET resolution compare well with previous efforts documented in the literature and provide new data for several radionuclides in increasing clinical and preclinical use. The results will support current and future improvements in methods for positron range corrections in PET imaging.

Positron annihilation localization by nanoscale magnetization

In positron emission tomography (PET), the finite range over which positrons travel before annihilating with an electron places a fundamental physical limit on the spatial resolution of PET images. After annihilation, the photon pair detected by the PET instrumentation is emitted from a location that is different from the positron-emitting source, resulting in image blurring. Here, we report on the localization of positron range, and hence annihilation quanta, by strong nanoscale magnetization of superparamagnetic iron oxide nanoparticles (SPIONs) in PET-MRI. We found that positron annihilations localize within a region of interest by up to 60% more when SPIONs are present (with [Fe] = 3 mM) compared to when they are not. The resulting full width at half maximum of the PET scans showed the spatial resolution improved by up to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\approx$$\end{document}≈ 30%. We also found evidence suggesting that the radiolabeled SPIONs produced up to a six-fold increase in ortho-positronium. These results may also have implications for emerging cancer theranostic strategies, where charged particles are used as therapeutic as well as diagnostic agents and improved dose localization within a tumor is a determinant of better treatment outcomes.

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.

Low energy electron and positron impact differential cross sections for the ionization of water molecules in the coplanar and perpendicular kinematics

We report here triply differential cross sections (TDCSs) for 81 eV electron and positron-impact ionization of the combined (1b₁ + 3a₁) orbitals of the water molecule by using the second-order distorted wave Born approximation (DWBA2) for ejection electron and positron energies of 5 eV and 10 eV and different momentum transfer conditions. The electron-impact TDCS will be compared with the experimental data measured by Ren et al. [Phys. Rev. A 95, 022701 (2017)] and with the molecular 3-body distorted wave (M3DW) approximation results in the scattering plane as well as the perpendicular plane. The DWBA2 results are in better agreement with the experiment than the M3DW results for the scattering plane, and the M3DW results are somewhat better for the perpendicular plane. This observation is explained in terms of collision interactions. The electron and positron TDCSs are indistinguishable in the scattering plane. In the perpendicular plane, the positron results are similar in shape, but smaller in magnitude. However, the difference reduces with increasing projectile scattering angle and increasing ejected electron energy.

Positron kinetics in an idealized PET environment

The kinetic theory of non-relativistic positrons in an idealized positron emission tomography PET environment is developed by solving the Boltzmann equation, allowing for coherent and incoherent elastic, inelastic, ionizing and annihilating collisions through positronium formation. An analytic expression is obtained for the positronium formation rate, as a function of distance from a spherical source, in terms of the solutions of the general kinetic eigenvalue problem. Numerical estimates of the positron range - a fundamental limitation on the accuracy of PET, are given for positrons in a model of liquid water, a surrogate for human tissue. Comparisons are made with the ‘gas-phase’ assumption used in current models in which coherent scattering is suppressed. Our results show that this assumption leads to an error of the order of a factor of approximately 2, emphasizing the need to accurately account for the structure of the medium in PET simulations.

Monte Carlo study of coherent scattering effects of low-energy charged particle transport in Percus-Yevick liquids

We generalize a simple Monte Carlo (MC) model for dilute gases to consider the transport behavior of positrons and electrons in Percus-Yevick model liquids under highly nonequilibrium conditions, accounting rigorously for coherent scattering processes. The procedure extends an existing technique [Wojcik and Tachiya, Chem. Phys. Lett. 363, 381 (2002)], using the static structure factor to account for the altered anisotropy of coherent scattering in structured material. We identify the effects of the approximation used in the original method, and we develop a modified method that does not require that approximation. We also present an enhanced MC technique that has been designed to improve the accuracy and flexibility of simulations in spatially varying electric fields. All of the results are found to be in excellent agreement with an independent multiterm Boltzmann equation solution, providing benchmarks for future transport models in liquids and structured systems.

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.

Dose point kernels in liquid water: an intra-comparison between GEANT4-DNA and a variety of Monte Carlo codes

Modeling the radio-induced effects in biological medium still requires accurate physics models to describe the interactions induced by all the charged particles present in the irradiated medium in detail. These interactions include inelastic as well as elastic processes. To check the accuracy of the very low energy models recently implemented into the GEANT4 toolkit for modeling the electron slowing-down in liquid water, the simulation of electron dose point kernels remains the preferential test. In this context, we here report normalized radial dose profiles, for mono-energetic point sources, computed in liquid water by using the very low energy "GEANT4-DNA" physics processes available in the GEANT4 toolkit. In the present study, we report an extensive intra-comparison of profiles obtained by a large selection of existing and well-documented Monte-Carlo codes, namely, EGSnrc, PENELOPE, CPA100, FLUKA and MCNPX.

Transport coefficients and cross sections for electrons in water vapour: comparison of cross section sets using an improved Boltzmann equation solution

This paper revisits the issues surrounding computation of electron transport properties in water vapour as a function of E/n(0) (the ratio of the applied electric field to the water vapour number density) up to 1200 Td. We solve the Boltzmann equation using an improved version of the code of Ness and Robson [Phys. Rev. A 38, 1446 (1988)], facilitating the calculation of transport coefficients to a considerably higher degree of accuracy. This allows a correspondingly more discriminating test of the various electron-water vapour cross section sets proposed by a number of authors, which has become an important issue as such sets are now being applied to study electron driven processes in atmospheric phenomena [P. Thorn, L. Campbell, and M. Brunger, PMC Physics B 2, 1 (2009)] and in modeling charged particle tracks in matter [A. Munoz, F. Blanco, G. Garcia, P. A. Thorn, M. J. Brunger, J. P. Sullivan, and S. J. Buckman, Int. J. Mass Spectrom. 277, 175 (2008)].

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

Monte Carlo simulation codes that model positron interactions along their tortuous path are expected to be accurate but are usually slow. A simpler and potentially faster approach is to model positron range from analytical annihilation density distributions. The aims of this paper were to efficiently implement and validate such a method, with the addition of medium heterogeneity representing a further challenge. The analytical positron range model was evaluated by comparing annihilation density distributions with those produced by the Monte Carlo simulator GATE and by quantitatively analysing the final reconstructed images of Monte Carlo simulated data. In addition, the influence of positronium formation on positron range and hence on the performance of Monte Carlo simulation was investigated. The results demonstrate that 1D annihilation density distributions for different isotope-media combinations can be fitted with Gaussian functions and hence be described by simple look-up-tables of fitting coefficients. Together with the method developed for simulating positron range in heterogeneous media, this allows for efficient modelling of positron range in Monte Carlo simulation. The level of agreement of the analytical model with GATE depends somewhat on the simulated scanner and the particular research task, but appears to be suitable for lower energy positron emitters, such as (18)F or (11)C. No reliable conclusion about the influence of positronium formation on positron range and simulation accuracy could be drawn.

Resonant scattering of positronium in collision with CO2

The total cross sections of positronium (Ps) scattering from a carbon-dioxide molecule have been measured over the range (7-400) eV incident-Ps energy. For the first time in Ps collisions, a resonantlike structure is observed. For the present target, it occurs around 9.5 eV followed by a broader peak at ∼60 eV. Following Brawley et al. [Science 330, 789 (2010)] who have observed similarities between the total cross sections of positronium and of electrons incident upon a given target at the same velocity, a corresponding comparison is made for CO2. The comparison suggests that the former peak corresponds to the well-known 2Π(u) shape resonance which occurs for electrons at an incident velocity of 0.5 a.u. Further features are discussed and theoretical input is sought.

Triply differential single ionization of argon: charge effects for positron and electron impact

Triply differential single ionization of Ar by 200 eV positron and electron impact is measured and calculated. For an unequivocal test of kinematic differences, fully differential ejected electron angular distributions are measured using the same experimental apparatus and conditions for both positron and electron impact. The binary/recoil intensity ratios are shown to significantly differ for the two projectiles. These data are used to test theoretical calculations.

Optical observation of energy loss distribution and practical range of positrons from a 18F water solution in a water-equivalent phantom

The energy loss distribution of beta+ particles is closely related to their maximum penetration depth distribution and annihilation point distribution. The latter is of practical importance for positron emission tomography. Experimental data related to the energy loss distribution are important for comprehensive validation of physics and simulation models of beta+ interactions. In this paper the authors present a new experimental approach that allows them to visually observe the beta+ energy loss distribution of a solution of nuclear medicine radioisotopes in a plastic scintillator using an optical camera. The authors also report a set of the first experimental results. A water solution of 18F was localized in a small hole in a plastic scintillator (BC430). Optical imaging of the scintillator yielded visual images of the energy loss distribution with a submillimeter resolution. The radial dependence in the energy distribution was quantitatively measured by analysis of the images, and exponential fitting parameters were obtained. The authors observed that the results of Monte Carlo simulation with EGS5 (version 1.0.2) and GEANT4 (version 4.9.01.p01) were consistent with those obtained experimentally. The results of the Monte Carlo simulation indicated that for a linear scale, the energy loss distribution in the scintillator was approximately the same as that in water, and the relative shape of the energy loss distribution was close to those of the maximum penetration depth distribution and annihilation point distribution. This paper also presents discussions about the further possibilities of this optical imaging approach. Thus, optical observation of the beta+ energy loss distribution in a scintillator is a promising technique for visual and quantitative experimental studies of beta+ emission from a solution of radioisotopes that are used in nuclear medicine.

Excited-state positronium formation from helium, argon, and xenon

The cross sections for the formation of positronium in the 2P state in collisions of positrons with He, Ar, and Xe atoms have been determined by measuring coincidences between the remnant ion and the Lyman-alpha photon from positronium. The maximum fractional contributions of these to the total Ps formation cross sections increase from approximately 0.06+/-0.01 in He to 0.12+/-0.04 in Ar and 0.26+/-0.09 in Xe. In the case of He, good agreement is found with a coupled-state calculation; for Ar and Xe, measurements are compared with a distorted-wave Born approximation.