Coincidence Correction Research Articles

Time-of-flight PET/CT suppresses CT based attenuation correction and scatter coincidence correction errors due to misalignment of the gastrointestinal tract.

This study aimed to examine the influence of changes in CT values on PET images, specifically focusing on errors in CT-based attenuation correction and scatter coincidence correction (CTAC/SC) caused by gastrointestinal gas. Furthermore, it aimed to demonstrate the effectiveness of time-of-flight (TOF) PET in reducing CTAC/SC errors. PET images were reconstructed using multiple CT images with varying CT values. The study then compared the fluctuations in pixel values of the PET images corresponding to the different CT values utilized for CTAC/SC between non-TOF and TOF acquisitions. PET pixel values fluctuated with changes in CT values. In the phantom study, TOF showed a significantly smaller change in PET pixel value of 1.00±0.27 kBq/mL compared to 3.72±1.33 kBq/mL in the non-TOF at sites with a CT change of +1000 HU. In the patient study, a linear regression analysis was performed to determine the effect of changes in CT values due to gastrointestinal gas migration on standard uptake value (SUV).The results showed that the TOF group had a lower ratio of change in SUV to change in CT values compared to the non-TOF group. These findings revealed that PET pixel values exhibited fluctuations in response to changes in CT values, and TOF-PET effectively mitigated CTAC/SC errors arising from gastrointestinal gas. TOF-PET has the potential to reduce the occurrence of suspicious accumulation.

True coincidence summing corrections in HPGe detectors

The true coincidence effect is studied in two High Purity Germanium (HPGe) detectors for a variety of isotopes, source geometries and source to detector configurations, via computational tools based on Monte–Carlo simulations. Τhe upgraded patch of MCNP code MCNP–CP and the 2018 version of PENELOPE, which take into account the decay scheme of each cascade emitter, are used to calculate the Full Energy Peak Efficiency (FEPE) for the corresponding gamma-ray energies. The true coincidence correction (TCC) factor is calculated as the ratio of the FEPE derived for each nuclide taking into consideration the true coincidence effect, to the FEPE estimated without considering the phenomenon. In all cases, a satisfactory agreement is observed between the TCC factors calculated using MCNP–CP and PENELOPE 2018. Moreover, the results of the calculations are compared against experimentally derived efficiency values. The correction factors obtained using the TrueCoinc software are applied on experimentally determined FEPE curves, based on measurements performed using reference sources, and consequently the corrected data are compared against the simulations for the "non-coincidence" case. The results of this work contribute to the validation of the computational tools and codes used to study the true coincidence effect and determine the corresponding correction factors, providing useful data for gamma–spectrometry studies of cascade emitters.

Artificial neural network based coincidence correction for optical aerosol spectrometers

Many applications such as filter testing, healthcare, quality monitoring, and environmental measurements require precise aerosol quantification by optical aerosol spectrometers. This type of measurement equipment is capable of in-situ measurements and provides easy access to the size distribution of the particles. Due to the coincidence error, optical aerosol spectrometers are limited to applications with relatively low concentrations. At high concentrations, the counting efficiency is reduced, while the size distribution is shifted towards larger particles. In 1984 Raasch and Umhauer proposed an analytical correction method for the size distribution. Although the approach is easy to implement, it has some disadvantages. In this work, an alternative correction method for the size distribution is presented, which is based on neural networks. The performance of both correction methods is evaluated on the cumulative distribution of raw detector voltages. The relative error of the median, as well as an error integral over the whole distribution is used as a measure. The neural network-based method gives a correction result that shows approximately half the relative median error, and a third of the error integral compared to the method of Raasch and Umhauer, for high concentrations.

Coincidence summing corrections using PENELOPE/PENNUC Monte Carlo code for volume sources of different densities

This work aims at providing a Monte-Carlo based methodology for calculating true coincidence correction (TCC) factors for volume sources of varying density. All simulations were carried out using the most recent version of Monte Carlo code PENELOPE. The main program PENMAIN was used for the calculation of full energy peak efficiencies. The subroutine PENNUC was utilized for the same calculation while taking summation effects into account. It was applied to Eu-152 and Cs-134 volume sources of 9 different densities, whilst the effect of the source's density on the TCC factor was investigated. There are differences between current results and the ones calculated by the TrueCoinc software. A relative bias up to 15% was observed, while the mean relative bias was 4.5%. The different approaches between the two codes could explain these deviations.

Determination of Appropriate Source-to-Detector Distance Dependence of Gamma Spectrometry System to Achieve Higher Resolution

Operation of gamma spectrometry requires intensive monitoring of gamma ray fluxes. When a radioactive intense source is placed close to a crystal detector, it becomes saturated as a result of detector dead time. On the contrary, when placed far away, there is loss of count statistics. For this reason, optimal position for placing the source has to be investigated. With the improvement in the instrumentation of radiation detection applications over the years, high count rate measurement accuracy is more crucial than ever. This is due to periodic measurement and new correction models for dead time. The aim of this study is to examine the performance of two gamma spectroscopic systems. The source detector distance dependence on dead time, peak-to-compton ratio, overall amplifier gain, FWHM, and voltage variation were investigated using American standard procedures (ANSI/IEE -325). Measurements were performed at five (5) different distances of detector cap for four (4) point sources (Co-60, Eu-152, Cs-137 and Ba-133). Source-to-detector distance at 25 cm was improved to avoid summing coincidence and dead time correction. The results obtained at 25 cm showed that the dead time was found less than 1% as compared to 4 cm. This will describe the stability of dead time. It also indicated that for both detectors the rise in biased voltage will yield a good resolution at 1332.5 KeV. This study is significant as it provides information to ensure that detectors are kept at optimal distance to achieve good dead time.

Pulse Height Analyzer with Coincidence Correction

A pulse height analyzer (PHA) is used to measure the frequency distribution of the signal output height of an event detector. However, the typical PHA algorithm has limitations in measurement; it cannot distinguish multiplet due to coincidence and singlet pulse. Coincidences will pile up the signals that make the pulse height value higher than it should be. Therefore, this study has developed a simple algorithm to calculate pulse height distribution with coincidence correction (PHA-CC). The developed algorithm firstly identified the coincidence pulse by considering its pulse width. The result shows that the developed algorithm could successfully distinguish multiplet and singlet pulses. The significance of pulse height distribution measured by the PHA-CC compared to regular PHA was also discussed in this paper.

648 Hilbert-space dimensionality in a biphoton frequency comb: entanglement of formation and Schmidt mode decomposition

Qudit entanglement is an indispensable resource for quantum information processing since increasing dimensionality provides a pathway to higher capacity and increased noise resilience in quantum communications, and cluster-state quantum computations. In continuous-variable time–frequency entanglement, encoding multiple qubits per photon is only limited by the frequency correlation bandwidth and detection timing jitter. Here, we focus on the discrete-variable time–frequency entanglement in a biphoton frequency comb (BFC), generating by filtering the signal and idler outputs with a fiber Fabry–Pérot cavity with 45.32 GHz free-spectral range (FSR) and 1.56 GHz full-width-at-half-maximum (FWHM) from a continuous-wave (cw)-pumped type-II spontaneous parametric downconverter (SPDC). We generate a BFC whose time-binned/frequency-binned Hilbert space dimensionality is at least 324, based on the assumption of a pure state. Such BFC’s dimensionality doubles up to 648, after combining with its post-selected polarization entanglement, indicating a potential 6.28 bits/photon classical-information capacity. The BFC exhibits recurring Hong–Ou–Mandel (HOM) dips over 61 time bins with a maximum visibility of 98.4% without correction for accidental coincidences. In a post-selected measurement, it violates the Clauser–Horne–Shimony–Holt (CHSH) inequality for polarization entanglement by up to 18.5 standard deviations with an S-parameter of up to 2.771. It has Franson interference recurrences in 16 time bins with a maximum visibility of 96.1% without correction for accidental coincidences. From the zeroth- to the third-order Franson interference, we infer an entanglement of formation (Eof) up to 1.89 ± 0.03 ebits—where 2 ebits is the maximal entanglement for a 4 × 4 dimensional biphoton—as a lower bound on the 61 time-bin BFC’s high-dimensional entanglement. To further characterize time-binned/frequency-binned BFCs we obtain Schmidt mode decompositions of BFCs generated using cavities with 45.32, 15.15, and 5.03 GHz FSRs. These decompositions confirm the time–frequency scaling from Fourier-transform duality. Moreover, we present the theory of conjugate Franson interferometry—because it is characterized by the state’s joint-temporal intensity (JTI)—which can further help to distinguish between pure-state BFC and mixed state entangled frequency pairs, although the experimental implementation is challenging and not yet available. In summary, our BFC serves as a platform for high-dimensional quantum information processing and high-dimensional quantum key distribution (QKD).

NaI cubic detector full-energy peak efficiency, including coincidence and self-absorption corrections for rectangular sources using analytical method

Low activities of radionuclides in environmental and occupational samples demand for the lower detection limits of the measuring system, which can be achieved by minimizing the source-to-detector distance. Analytical technique to calculate full-energy peak efficiency and total efficiency, self-absorption of sources and a coincidence factor of the NaI cubic scintillation detector with rectangular cavity for rectangular source have been derived. The photon path length of the volumetric sources calculated and determined source self-absorption. The photon attention by rectangular sources and detector cap materials is also calculated. In the experiments gamma aqueous source containing Eu-152 radionuclide covering range from 121 to 1408 keV was used. By comparison analytical method for calculating the full energy peak efficiency and the corrected experimental efficiency values are in good a agreement.

Random coincidence and angular correlation corrections in the sum-peak method using Monte Carlo simulations

The sum-peak method is a technique for measuring the absolute activity of gamma cascade emitting sources with a single gamma spectrometer. The effects of angular correlations and random coincidences, if not taken into account, can significantly reduce the accuracy of the method. However, we show that Monte Carlo simulations can reproduce the spectral data with a sufficient quality to perform the required corrections. In this work, we introduced a novel approach for data corrections for angular correlations and pile-up using Monte Carlo simulations. Furthermore, the new method for forming the count rate equations leads to a new formula for the sum-peak method, including random coincidences of any order.

In quest of the optimal coincidence resolving time in TDCR LSC

This paper presents studies of the influence of the coincidence resolving time on the activity calculated by the Triple-to-Double Coincidences Ratio (TDCR) method in Liquid Scintillation (LS) counting. Recently, published methods for the correction for accidental coincidences in TDCR counting open the possibility to use resolving times up to several μs, long enough not to miss true coincidences and to study the effects of delayed fluorescence.3H, 14C, 55Fe and 63Ni LS-sources in UltimaGold (UG), UG LLT and Toluene+PPO cocktails were measured using a TDCR counter connected to a digitizer working in list-mode. The necessary resolving time to include 99.9% of the logical sum of double (D) coincidences was found to be 1.2 μs for 3H, 1 μs for 55Fe and 500 ns for 63Ni in UG. The activity of all LS-sources was calculated using the TDCR method for resolving times from 10 ns to 2 μs and a significant dependence between the calculated activity and resolving time was observed. A dedicated Monte Carlo (MC) code was used to simulate list-mode data from TDCR measurements. The simulation results suggest that the 3H activity calculated by the TDCR method is overestimated regardless of the used resolving time if delayed fluorescence is present which is not described by the used ionization quenching function.Efficiency variation measurements of 3H in UG LLT show a strong dependence of the optimal kB parameter on the used resolving time: 85 μm/MeV at 40 ns and 110 μm/MeV at 200 ns, leading to 2.5% difference in calculated activity. In the framework of this study the efficiency variation methods by chemical quenching and gray filters were compared and a difference of 60 μm/MeV between the two was observed. The results from this article demonstrate that regardless of the available corrections for accidental coincidences, it is not advisable to increase the resolving time beyond what is necessary to register all prompt fluorescence events. Moreover, even for short coincidence resolving times, delayed fluorescence could have a significant influence on the activities calculated by the TDCR method.

A time-dependent Monte Carlo approach to chance coincidence summing correction factor calculation for high-purity Ge gamma-ray spectroscopy

The chance (random) coincidence correction factor (CCCF) for the counting geometry of a 137Cs point source placed very close to the end cap of a high-purity Ge coaxial detector with 50% relative efficiency was evaluated by a time-dependent Monte Carlo approach. The probability distributions of gamma-ray and X-ray energy depositions in the detector crystal were obtained by use of the MCNPX code. The signal resolving time of the electronic parts, one of the parameters needed for time-dependent Monte Carlo simulation, was evaluated experimentally by the moving-source method. Another parameter also needed for the simulation is the signal pile-up rejection time interval. A random pulse generator was replaced with the detector for this purpose and the value was calculated iteratively by comparing the spectrum obtained experimentally with the spectrum obtained from the time-dependent Monte Carlo simulation of the random pulse generator. A pulse train with a Poisson distribution in time was created, and these parameters with energy deposition probability distributions were used for theoretical determination of the high-count-rate spectrum and the low-count-rate spectrum. The CCCF for the experiment was calculated as 0.92 by our comparing these two theoretical spectra and agrees well with the experimental result, 0.94.Also, the results of paralyzable and nonparalyzable model approaches for dead time calculations were compared with the experimental results.

Pushing Cherenkov PET with BGO via coincidence time resolution classification and correction

Bismuth germanate (BGO) shows good properties for positron emission tomography (PET) applications, but was substituted by the development of faster crystals like lutetium oxyorthosilicate (LSO) for time-of-flight PET (TOF-PET). Recent improvements in silicon photomultipliers (SiPMs) and fast readout electronics make it possible to access the Cherenkov photon signal produced upon 511 keV interaction, which makes BGO a cost-effective candidate for TOF-PET.Tails in the time-delay distribution, however, remain a challenge. These are mainly caused by the high statistical fluctuation on the Cherenkov photons detected. To select fast events with a high detected Cherenkov photon number, the signal rise time of the SiPM was used for discrimination. The charge, time delay and signal rise time was measured for two different lengths of BGO crystals coupled to FBK NUV-HD SiPMs and high frequency readout in a coincidence time resolution setup. The recorded events were divided into 5 × 5 categories based on the signal rise time, and time resolutions of 200 ± 3 ps for 2 × 2 × 20 mm3 and 117 ± 3 ps for 2 × 2 × 3 mm3 were measured for the fastest 20% of the events (4% in coincidence). These good timing events can provide additional information for the image reconstruction in order to increase the SNR significantly, without spoiling the detector sensitivity. Putting all photopeak events together and correcting for the time bias introduced by different numbers of Cherenkov photons detected, time resolutions of 259 ± 3 ps for 20 mm long and 151 ± 3 ps for 3 mm long crystals were measured. For a small fraction of events sub-100 ps coincidence time resolution with BGO was reached for a 3 mm short pixel.

小流量高浓度颗粒物光学计数及重叠校正方法研究

小流量高浓度颗粒物光学计数及重叠校正方法研究

Coincidence summing correction for a voluminous 152Eu source

A code is developed to correct for the coincidence summing effect in detecting a voluminous gamma source, and this code is applied to a152Eu standard source as a test case. The source is 1000 mL of liquid in a cylindrical shape. To calculate the coincidence summing effect, the cylindrical source is considered as 10(radial) × 8(height) sectional sources. For each sectional source, the peak efficiency and total efficiency are obtained by Monte Carlo simulation at each energy for 10 energies between 50 keV and 2000 keV. The efficiencies of each sector are then expressed as polynomials of gamma energy. To calculate the correction coefficients for the coincidence summing effect, the KORSUM code is used after modification. The magnitudes of correction are 4%–17% for the standard 152Eu source measured in this study. The relative deviation of 4.7% before the coincidence correction is reduced to 0.8% after the correction is applied to the efficiency based on the measured gamma line. Hence, this study has shown that a new method has been developed that is applicable for correcting the coincidence effect in a voluminous source, and the method is applied to the measured data of a standard 152Eu cylinder source.

Design and Validation of a Holographic Particle Counter.

An in-line holographic particle counter concept is presented and validated where multiple micrometer sized particles are detected in a three dimensional sampling volume, all at once. The proposed Particle Imaging Unit is capable of detecting holograms of particles which sizes are in the lower m- range. The detection and counting principle is based on common image processing techniques using a customized Hough Transform with a result directly relating to the particle number concentration in the recorded sampling volume. The proposed counting unit is mounted ontop of a Condensation Nucleus Magnifier for comparison with a commercial TSI-3775 Condensation Particle Counter (CPC). The concept does not only allow for a precise in-situ determination of low particle number concentrations but also enables easy upscaling to higher particle densities (e.g., ) through its linear expandability and option of cascading. The impact of coincidence at higher particle densities is shown and two coincidence correction approaches are presented where, at last, its analogy to the coincidence correction methods used in state-of-the-art CPCs is identified.

Impact of prompt gamma coincidence correction on absorbed dose estimation in differentiated thyroid cancer using 124I PET/CT imaging.

Iodine-124 positron emission tomography/computed tomography (I PET/CT) is increasingly being used in the absorbed dose estimation in the radioiodine treatment of differentiated thyroid cancer (DTC). However, the produced prompt gamma coincidences (PGCs) associated with the I decay result in a bias in the absorbed dose estimation. The impact of a sinogram-based PGC correction approach on the absorbed dose estimation in I PET/CT DTC imaging is investigated. I phantom and patient measurements were performed on a Siemens Biograph mCT PET/CT system. All images were reconstructed with (PGCon) and without PGC correction (PGCoff). The phantom contained seven spheres (diameters: 6.6-37 mm). The spheres and background compartment were filled with a I solution, resulting in a low (9.4 : 1) and a high sphere-to-background activity concentration ratio (750 : 1). Sphere recovery coefficient (RC) values were determined. In addition, the impact of PGC correction on measured lesion uptake and calculated lesion-absorbed dose was assessed for 66 lesions identified in 24 DTC patients. PGC correction systematically increased sphere RC values up to 71% for the smallest spheres. For the patient data, PGC correction significantly increased both the measured I uptake (P<0.005) and the calculated lesion-absorbed dose (P=0.008) by ∼3%. The percentage difference in the calculated lesion-absorbed dose ranged from -19% to 50%, showing that PGC correction had a variable and large impact for a few lesions. PGC correction resulted in significantly higher sphere RC values, I lesion uptake values and estimated lesion-absorbed doses.

Generalized equation for the sum-peak method, accounting for random coincidences

For gamma cascade emitting radionuclides, the source activity can be determined by a single spectrometer from the sum peak area. At high count rates, random coincidence corrections must be considered. Starting from the equations of the peak and total count rates that consider random summing, a new equation for measurement of the activity is deduced. The results of the new formula are verified by Monte Carlo simulations.

Node-Pore Coded Coincidence Correction: Coulter Counters, Code Design, and Sparse Deconvolution.

We present a novel method to perform individual particle (e.g. cells or viruses) coincidence correction through joint channel design and algorithmic methods. Inspired by multiple-user communication theory, we modulate the channel response, with Node-Pore Sensing, to give each particle a binary Barker code signature. When processed with our modified successive interference cancellation method, this signature enables both the separation of coincidence particles and a high sensitivity to small particles. We identify several sources of modeling error and mitigate most effects using a data-driven self-calibration step and robust regression. Additionally, we provide simulation analysis to highlight our robustness, as well as our limitations, to these sources of stochastic system model error. Finally, we conduct experimental validation of our techniques using several encoded devices to screen a heterogeneous sample of several size particles.

Calibration of the Absolute Efficiency of Well-Type NaI(Tl) Scintillation Detector in 0.121–1.408 MeV Energy Range

Well-type NaI(Tl) detectors are beneficial for low-level photon activity measurements because of the near 4π solid angle that can be gained with them. The detection efficiency can differ with the source-to-detector system geometries, the absorption of the photon in the detector material, and attenuation layers in front of the detector face. For these purposes, the absolute efficiency and the coincidence corrections of the well-type sodium iodide detector have been measured at 0.121–1.408 MeV energy range (obtained from 152Eu, 137Cs, and 60Co radioactive isotopes). The covenant between the experimental (present work) and the published theoretical values is good, with the high discrepancies being less than 1%.

Summing coincidence correction for [formula omitted]-ray measurements using the HPGe detector with a low background shielding system

A Monte Carlo method based on the GEANT4 toolkit has been developed to correct the full-energy peak (FEP) efficiencies of a high purity germanium (HPGe) detector equipped with a low background shielding system, and moreover evaluated using summing peaks in a numerical way. It is found that the FEP efficiencies of 60Co, 133Ba and 152Eu can be improved up to 18% by taking the calculated true summing coincidence factors (TSCFs) correction into account. Counts of summing coincidence γ peaks in the spectrum of 152Eu can be well reproduced using the corrected efficiency curve within an accuracy of 3%.