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Handbook of computed tomography x-ray spectra
... Voltage ( (Fewell et al., 1981;Cosslett, 1961, 1968;Poludniowski, 2007;Tucker et al., 1991). angles and a wide range of X-ray tube potentials. ...
... Comparison between measured, computed and data obtained from the literature are presented in the Fig. 4. This figure shows values of the characteristic-to-total spectrum ratio, R, calculated from experimental data measured by Fewell et al. (1981), from theoretical calculation done by Cosslett (1961, 1968), from semiempirical approach evaluated by Tucker et al. (1991), from Monte Carlo calculations done by Poludniowski (2007), and from our experimental data obtained using 3.04 mmAl of additional filter. Fig. 5 shows the ratio of characteristic-to-total spectrum for measured and computed X-ray spectra using different additional filters. ...
... This is reflected in Tables 2 and 3, since the differences of the first HVLs and mean energies values between measured and computed results, they increases at high tube potentials. Fig. 4 illustrates that the largest discrepancy in the R value (18% at 110 kV) between experimental results at 3.04 mmAl and published data occur with the Fewell results (Fewell et al., 1981). This discrepancy is attributed to the differences in the anode composition of the two X-ray generator tubes. ...
... Early attempts at predicting diagnostic x-ray spectra were undertaken by Kramers (1923). This pioneering work was sustained by several investigators and many research groups are still trying to find an accurate method for computer simulation of x-ray spectra owing to the fact that experimental measurement of x-ray spectra requires special equipment which is available only in a limited number of laboratories (Fewell and Shuping 1978, Fewell et al 1981, Laitano et al 1991, Antonuk et al 1997, Dance et al 2000, Wilkinson et al 2001). Fewell et al measured x-ray spectra with different target/filter combinations for over two decades and have published several measured spectra (Fewell and Shuping 1977, 1978, Fewell et al 1981). ...
... This pioneering work was sustained by several investigators and many research groups are still trying to find an accurate method for computer simulation of x-ray spectra owing to the fact that experimental measurement of x-ray spectra requires special equipment which is available only in a limited number of laboratories (Fewell and Shuping 1978, Fewell et al 1981, Laitano et al 1991, Antonuk et al 1997, Dance et al 2000, Wilkinson et al 2001). Fewell et al measured x-ray spectra with different target/filter combinations for over two decades and have published several measured spectra (Fewell and Shuping 1977, 1978, Fewell et al 1981). Since experimental measurement of x-ray spectra is time consuming and remains difficult, different methods for spectra prediction have been presented. ...
... as an international standard for coupled particle transport having the best condensed history electron physics package and remarkable tally capabilities in addition to a powerful reporting system of statistical checks (Briesmeister 2000, Mercier et al 2000). The validity of MCNP4C simulated data was checked by comparing the calculated spectra, transmission curves and heel effect with the IPEM report number 78 (Cranley et al 1997), measured data (Fewell et al 1981, Pernieka et al 1997) and EGS4-based Monte Carlo simulations (Bhat et al 1999), respectively. ...
The general purpose Monte Carlo N-particle radiation transport computer code (MCNP4C) was used for the simulation of x-ray spectra in diagnostic radiology and mammography. The electrons were transported until they slow down and stop in the target. Both bremsstrahlung and characteristic x-ray production were considered in this work. We focus on the simulation of various target/filter combinations to investigate the effect of tube voltage, target material and filter thickness on x-ray spectra in the diagnostic radiology and mammography energy ranges. The simulated x-ray spectra were compared with experimental measurements and spectra calculated by IPEM report number 78. In addition, the anode heel effect and off-axis x-ray spectra were assessed for different anode angles and target materials and the results were compared with EGS4-based Monte Carlo simulations and measured data. Quantitative evaluation of the differences between our Monte Carlo simulated and comparison spectra was performed using student's t-test statistical analysis. Generally, there is a good agreement between the simulated x-ray and comparison spectra, although there are systematic differences between the simulated and reference spectra especially in the K-characteristic x-rays intensity. Nevertheless, no statistically significant differences have been observed between IPEM spectra and the simulated spectra. It has been shown that the difference between MCNP simulated spectra and IPEM spectra in the low energy range is the result of the overestimation of characteristic photons following the normalization procedure. The transmission curves produced by MCNP4C have good agreement with the IPEM report especially for tube voltages of 50 kV and 80 kV. The systematic discrepancy for higher tube voltages is the result of systematic differences between the corresponding spectra.
... During the interactive running of PHACOM and MATSIM1, the information supplied includes incident spectrum data, elemental compositions (with atomic number of elements and weight by fraction), density and thickness of tissue phantoms, aluminium and steel. The constant-potential spectra data used as incident spectra were those published for 70, 80, 90, 100, 110, 120, 130 and 140 kVcp in Fewell et al. 10 for General Electric Maxiray 125B with tungsten as target. For all these, the inherent filter is equivalent to 1.3 mm Al and added filter is 1.5 mm Al. ...
... Simpkin 11 had used this set of incident spectra data to generate exposure transmission curves that are in reasonable agreement with measured three-phase X-ray transmission data reported in literature 12,13 . The first HVL values of the incident beams used in this study are as presented in Table 1 of this text (after Fewell et al. 10 ). These incident spectra are considered to accurately represent output from modern diagnostic X-ray machine that produces more intense and penetrating photon beams 11 . ...
... Using these computer packages, a good match was also observed for HVL values obtained using these packages for spectra transmitted by aluminium, copper and yttrium at equivalent thicknesses (Table V of Jennings 5 ). In this study, based on exposure reduction, the HVL values of incident spectra that were obtained from Fewell et al. 10 were calculated using the computer packages. The results of these calculations which are in agreement with experimental HVL values reported by Fewell et al. 10 are given in Table 1 of this text. ...
In the estimation of additional shielding requirements for primary beam apart from that provided by patient and hardware in the x-ray beam, there is the need to distinguish between attenuation and hardening properties of materials in comparison. In this work, numerical comparison of attenuation and hardening properties of phantom (Lucite, soft tissue, water) and hardware (aluminum and steel) materials with those of lead have been carried out. Results presented show that the shielding affordable by lead attenuation equivalent thicknesses (LAE) and lead hardening equivalent thicknesses (LHE) is not strictly equivalent to that affordable by thicknesses of substitutes (phantom materials, aluminum and steel) when there are differences in attenuation and hardening properties. Even though beams through LAE that are not "exact" have equal exposure values, the half value layers are higher than those through thicknesses of lead substitutes. Example calculations show that the use of lead thickness (LAE) that are not "exact" to account for the shielding afforded by the thickness of the patient (water phantom) produces lesser reduction of the primary radiation level in the area indicated for shielding. The "exact" LAE that will reduce the primary radiation level equally as the patient and radiographic table may be higher by close to 20% or more of that which is not "exact."
... The aim of this work was to develop an indirect transmission measurement-based spectrum estimation method using only raw projection data of a physical phantom with known density to estimate the corresponding spectrum of a CT scanner. To determine the x-ray spectrum of a CT scanner, energy-resolved detectors such as cadmium zinc telluride (CdZnTe) (Miyajima et al., 2002;Fritz et al., 2011), cadmium telluride (CdTe) (Miyajima, 2003;Redus et al., 2009) or high purity germanium (Fewell et al., 1981) are often used to directly measure the spectra. However, due to the limited count rate of these detectors and the high photon flux of CT scanners, it is not easy to directly measure the spectrum of a CT scanner because of the detector pile-up effect. ...
... The model spectra were generated using Geant4-based MC simulation tool-kit and were binned to 1 keV intervals. However, the raw spectra were generated using the Spektr software which is based on the TASMIP model (Boone and Seibert, 1997;Sisniega et al., 2013)and the TASMIP model is further based completely on interpolation of Fewell's direct spectroscopy measurements results (Fewell et al., 1981), which were tabulated at intervals of 2 keV. Thus, even though the raw Spektr values were interpolated to 1 keV intervals, it is difficult for the estimated spectrum to match the raw analytical spectra at the characteristic peak exactly. ...
The characteristics of an x-ray spectrum can greatly influence imaging and related tasks. In practice, due to the pile-up effect of the detector, it’s difficult to directly measure the spectrum of a CT scanner using an energy resolved detector. An alternative solution is to estimate the spectrum using transmission measurements with a step phantom or another CT phantom. In this work, we present a new spectrum estimation method based on indirect transmission measurement and a model spectra mixture approach. The estimated x-ray spectrum was expressed as a weighted summation of a set of model spectra, which can significantly reduce the degrees of freedom of the spectrum estimation problem. Next, an estimated projection was calculated with the assumed spectrum. By iteratively updating the unknown weights, we minimized the difference between the estimated projection data and the raw projection data. The final spectrum was calculated with these calibrated weights and the model spectra. Both simulation and experimental data were used to evaluate the proposed method. In the simulation study, the estimated spectra were compared to the raw spectra which were used to generate the raw projection data. For the experimental study, the ground truth measurement of the raw x-ray spectrum was not available. Therefore, the estimated spectrum was compared against the spectra generated using the SpekCalc software with tube configurations provided by the scanner manufacturer. The results show the proposed method has the potential to accurately estimate x-ray spectra using the raw projection data. The difference between the mean energy of the raw spectra and the mean energy of the estimated spectra was less than 0.5 keV for both the simulation and experimental data. Further tests show the method was robust with respect to the model spectra generator.
... The pulse height distributions from the multichannel analyzer were unfolded into X-ray spectra incident at the face of the detector by deconvolving detector distortions (e.g., full energy peak eciency, Compton scatter events, Kescape events, backscatter events, and window attenuation) from the acquired data in spreadsheet matrices. Detector response estimators were calculated for the matrices using a well-known Monte Carlo technique 20 with an established Monte Carlo photon transport code, MCNP4b2. 12 Air kerma measurements, corrected for energy response and environmental conditions (e.g. ...
... The harder nature of the X-ray beam computed by BM model con®rms the ®ndings of other researchers. 20,21 The average dierences for the measured and calculated transmission curves is in the range of 1 to 6%. Both EST and TBC methods give a value of less than 2% at both 60 and 70 kV while with the BM and MoCa methods it was about 3%. ...
To compare the diagnostic X-ray spectra derived by different methods for a constant potential dental X-ray unit.
Five methods of deriving X-ray spectra for a constant potential dental X-ray unit were compared: measurement by spectrometer using cadmium-zinc-telluride (CZT) detector, calculation by Monte Carlo simulation, calculation by two different, semi-empirical methods and estimation from transmission data. The dental X-ray set was a Heliodent MD unit (Sirona, Charlotte, NC, USA) operable at 60 or 70 kV. A semiconductor detector was used in the spectrometer measurements and an ionization chamber dosimeter in the transmission measurements. From the five methods, photon-fluence spectra were derived. Based on the photon-fluence spectra, average energies and transmission curves in aluminum were calculated.
For all five methods, the average energies were within 2.4% of one another. Comparison of the transmission curves showed an average difference in the range of 1 to 6%.
All of the five methods of deriving spectra are in extremely good agreement with each other.
... We evaluated the goodness of fit of the compound Poisson distribution in a Monte Carlo simulation with 20 000 independent experiments for various values of NEQs. We employed the spectrum data provided by Boone and Seibert,7 where tungsten spectra were tabulated from 30 to 140 kVs considering the measures taken by Fewell et al. 19 and hardened to fit measured attenuation profiles (what Boone and Seibert denoted as modified Fewell spectra). The tissue attenuation was performed with a water-equivalent material for different thicknesses (0, 10, 20, and 30 cm). ...
Purpose
To provide a unifying statistical model that characterizes the integrated x‐ray intensity at the detector after logarithmic transformation and can be extended to the characterization of computed tomography (CT) numbers in the reconstructed image.
Methods
We study the statistical characteristics of polyenergetic x‐ray beams in the detector. Firstly, we consider the characterization of the integrated x‐ray intensity at the detector through a probabilistic model (compound Poisson) that describes its statistics. We analyze its properties and derive the probabilistic distribution after the logarithmic transformation analytically. Finally, we propose a more tractable probabilistic distribution with the same features observed in the characterization, the noncentral Gamma (nc‐Gamma). This distribution exhibits desirable properties for the statistical characterization across the reconstruction process. We assess the assumptions adopted in the derivation of the statistical models throughout Monte Carlo simulations and validate them with a water phantom and a lung phantom acquired in a Siemens clinical CT scan. We evaluate the statistical similarities between the theoretical distribution and the nc‐Gamma using a power analysis with a Kolmogorov–Smirnov test for a 95% confidence level.
Results
The Kolmogorov–Smirnov goodness‐of‐fit test obtained for the Monte Carlo simulation shows an extremely high agreement between the empirical distribution of the post‐logarithmic‐integrated x‐ray intensity and the nc‐Gamma. The experimental validation performed with both phantoms confirmed the excellent match between the theoretical distribution, the proposed nc‐Gamma, and sample distributions in all situations.
Conclusion
We derive an analytical model describing the post‐log distribution of the linear attenuation coefficient in the sensor for polychromatic CT scans. We also demonstrate that the nc‐Gamma distribution approximates well the theoretical distribution. This distribution also approximates well the CT numbers after reconstruction since it naturally extends across linear operations involved in filtered back projection reconstructions. This probabilistic model may provide the analytical foundation to define new likelihood‐based reconstruction methodologies for polychromatic scans.
... The initial X-ray energy spectra for a certain kilovoltage peak (kVp) setting was estimated using the Spektr Software, developed by Siewerdsen et al. [86]. The software is based on the Tungsten anode spectral model using interpolating polynomials (TASMIPs) [87], while the approach is completely empirical and based on straightforward interpolation techniques using a modified version of Fewell's measured spectra [88] as a data source. SPEKTR is consisted of Matlab™ library functions, a database of attenuation coefficients, and a user interface, allowing a user to obtain TASMIP spectra with an energy resolution of 1.0 keV from the TASMIP library. ...
Purpose:
The purpose of this study is to create an organ dose database for pediatric individuals undergoing chest, abdomen/pelvis, and head computed tomography (CT) examinations, and to report the differences in absorbed organ doses, when anatomical differences exist for pediatric patients.
Methods:
The GATE Monte Carlo (MC) toolkit was used to model the GE BrightSpeed Elite CT model. The simulated scanner model was validated with the standard Computed Tomography Dose Index (CTDI) head phantom. Twelve computational models (2.1-14 years old) were used. First, contributions to effective dose and absorbed doses per CTDIvol and per 100 mAs were estimated for all organs. Then, doses per CTDIvol were correlated with patient model weight for the organs inside the scan range for chest and abdomen/pelvis protocols. Finally, effective doses per dose-length product (DLP) were estimated and compared with the conventional conversion k-factors.
Results:
The system was validated against experimental CTDIw measurements. The doses per CTDIvol and per 100 mAs for selected organs were estimated. The magnitude of the dependency between the dose and the anatomical characteristics was calculated with the coefficient of determination at 0.5-0.7 for the internal scan organs for chest and abdomen/pelvis protocols. Finally, effective doses per DLP were compared with already published data, showing discrepancies between 13 and 29% and were correlated strongly with the total weight (R2 > 0.8) for the chest and abdomen protocols.
Conclusions:
Big differences in absorbed doses are reported even for patients of similar age or same gender, when anatomical differences exist on internal organs of the body.
... Other research groups determine spectra by means of transmission measurements (Duan et al. 2011;Lin et al. 2014) or half value thickness measurements (Randazzo and Tambasco 2015). Another option is the calculation of source spectra with mathematical models (Sandborg et al. 1994;Zhou and Boone 2008) or to use source spectra published in the literature or online (Fewell et al. 1981;Siemens Healthineers 2018). Some studies make use of energy spectra obtained from the manufacturer under non-disclosure agreements (DeMarco et al. 2005;Lin et al. 2014;Steuwe et al. 2018). ...
In den letzten Jahrzehnten sind die Anzahl von Computertomographieaufnahmen und die damit einhergehende Strahlenbelastung für Patienten durch die größere Anzahl von Indikationen und die leichte Verfügbarkeit dieser Aufnahmen deutlich gestiegen. Ein gründliches Verständnis der Strahleneffekte der genutzten ionisierenden Röntgenstrahlung ist daher notwendig, um den Nutzen und die Risiken der Untersuchungen abschätzen und einordnen zu können. Röntgenstrahlung ist insbesondere bei hohen Strahlendosen (>100 mSv) krebserregend. Die gesundheitlichen Langzeiteffekte von niedrigen Dosen sind jedoch noch unbekannt. Um Computertomographieaufnahmen mit potenziellen Nebenwirkungen der Röntgenstrahlung zu korrelieren, sind Studien notwendig, bei denen die resultierende, räumlich aufgelöste Strahlendosis in großen Patientenkohorten über Jahrzehnte hinweg bestimmt werden muss. Die genaueste Möglichkeit, die effektive Dosis von Computertomographieaufnahmen zu untersuchen, um eine räumlich aufgelöste Verteilung der Dosis im Patienten oder in Prüfkörpern (Phantomen) zu erhalten, ohne Patienten oder Personal Röntgenstrahlung auszusetzen, bieten Monte Carlo Methoden. Es gibt bereits mehrere kommerzielle Monte Carlo Programme zur Dosisberechnung in der Computertomographie, allerdings schränken diese häufig den Nutzer durch vorgegebene Scanner- oder Phantomgeometrien, Röntgenspektren oder in der Datenauslese ein. Ziel dieser Arbeit war daher die Entwicklung einer Monte Carlo Software, die eine flexible Integration von Röntgenspektren, Scannergeometrien, und selbst gestalteten, geometrischen Abdomen- und digitalen Patientenphantomen ermöglicht, und gleichzeitig eine differenzierte Datenauswertung bereithält. Für die Simulation der physikalischen Prozesse in Phantomen bei Computertomographieaufnahmen wurde das Open-Source Toolkit Geant4 genutzt. Nach Anpassung und Weiterentwicklung des Toolkits war es möglich, Informationen (z.B. Position, Interaktionstypen) über die Energiedeposition von Röntgenstrahlung im Phantom zu erhalten und Expositionskarten zu erstellen. Das in dieser Arbeit entwickelte Computertomographiemodell verfügt über die Emission von Röntgenstrahlung mit optionaler Strahlformung, experimentellen und anthropomorphen Phantomen unterschiedlicher Komplexität sowie einem Photonendetektor. Unterschiedliche Aufnahmemöglichkeiten und Röhrenstrommodulation wurden zusätzlich implementiert. Digitalisierte Patientenphantome wurden aus Bilddatensätzen von Computertomographieaufnahmen erstellt, wofür die Datensätze schwellwertbasiert und manuell segmentiert wurden. Im ersten Schritt wurde die grundlegende Funktionalität des Monte Carlo Modells bezüglich der Strahlformungsmethoden und den spektralen Eigenschaften von 120 kVp-Photonenverteilungen evaluiert. Dieser Schritt war erforderlich, da Röntgenspektren von Computertomographen nur schwierig messbar und häufig proprietär sind, und daher oft simuliert oder aus mathematischen Modellen oder Computerprogrammen generiert werden müssen. Computertomographieaufnahmen werden auch oft bei anderen Röhrenspannungen und unter Zugabe von Kontrastmitteln akquiriert. Da Kontrastmittel Strahlenschäden verstärken können, sind fundierte Studien der Effekte von Kontrastmitteln auf die Energiedeposition von Röntgenstrahlung wichtig, insbesondere bei Materialübergängen von kontrastierten zu nichtkontrastierten Geweben. Daher wurde in einem zweiten Schritt der Einfluss der Röhrenspannung (80, 100, 120 kVp) und die Zugabe von jodhaltigen Kontrastmitteln auf die Gesamtenergiedeposition (Etotal) und deren räumlichen Verteilung (Espatial) in einem Boxphantom bei verschiedenen Jodkonzentrationen (1-15 mg/ml) untersucht. Die Auswertung des Boxphantoms war Grundlage weiterer Simulationen von Computertomographieaufnahmen eines geometrischen Abdomenphantoms und sechs digitalisierter Patientenphantomen mit unterschiedlicher Morphologie und Body-Mass-Index. Der Einfluss von Röhrenspannung und Kontrastmittel auf Etotal und Espatial wurde auch für die anthropomorphen Phantome (Abdomen- und Patientenphantome) bestimmt. Kontrastmittelverstärkte Gewebe waren dabei die Aorta, Nieren, Leber, Milz und Pankreas mit einer Jodkonzentration von 5 mg/ml. Die Energiedeposition wurde des Weiteren noch detaillierter an Gewebeübergängen analysiert. Die Ergebnisse der Arbeit zeigen, dass ein Monte Carlo Modell eines Computertomographen den Effekt des Strahlenformfilters korrekt darstellen muss und dass Röntgenspektren zwischen Geräteherstellern und -modellen austauschbar sind, solange die durchschnittliche Energie und die maximale Röhrenspannung übereinstimmen. Obwohl Etotal für die verschiedenen Röntgenspannungen im Boxphantom ähnlich war, so variierte Espatial erheblich, was die Notwendigkeit der räumlich aufgelösten Dosimetrie verdeutlicht. Für anthropomorphe Phantome mit einer abdominellen Scanabdeckung nahm die Energiedeposition der exponierten Gewebe (mit Ausnahme der Haut) mit geringerer Röhrenspannung ab. In der Haut nahm die Energiedeposition bei Senkung der Röhrenspannung von 120 auf 80 kVp um ~4% zu. Der Anstieg der Hautexposition ist im Vergleich zur generellen Abnahme der Gesamtenergiedeposition von ~9% vernachlässigbar, insbesondere wenn die geringe Strahlenempfindlichkeit der Haut mit einbezogen wird. Zugabe von Jod in Geweben erhöhte die Energiedeposition für kontrastverstärkte Gewebe in allen Phantomen (bis zu +50% bei einer Jodkonzentration von 5 mg/ml). Der relative Unterschied in der Energiedeposition zwischen kontrastverstärkten und nicht-kontrastierten Aufnahmen nahm mit zunehmender Jodkonzentration und Röhrenspannung zu. In den umliegenden nicht-kontrastierten Geweben nahm die Energiedeposition leicht ab. Ein Energieaufbaueffekt war bereits für nicht-kontrastierte Materialübergänge aufgrund von Unterschieden der physikalischen Dichten sichtbar. Bei Zugabe von Jod hat sich dieser Aufbaueffekt jedoch noch verstärkt. Im Gegensatz zu den relativen Unterschieden zwischen nicht-kontrastierten und kontrastierten Aufnahmen nahm der Aufbaueffekt mit abnehmender Röhrenspannung zu. Für geringere Röhrenspannungen (z.B. 80 kVp) werden größere Unterschiede in der Energiedeposition zwischen Organen und dem umliegenden Gewebe gemessen als für höhere Röhrenspannungen. Zusammenfassend ergibt sich, dass die entwickelte Software den Weg in Richtung individualisierter virtueller Dosimetrie für Patienten ebnet. Da die Verteilung der Energiedeposition von der Röhrenspannung, Kontrastmittelgabe und von Materialübergängen abhängt, ist die räumlich aufgelöste Dosimetrie für die korrekte Bestimmung der Strahlenbelastung notwendig. Individualisierte Dosimetrie ist erforderlich, um Unterschiede der Strahlenbelastung bei unterschiedlichen Patientenmorphologien zu verstehen, und um Abschätzungen der Strahlenschäden für häufig untersuchte Patienten zu ermöglichen. Ein tieferes Verständnis der Dosisdeposition im Körper wird dazu beitragen, technische Fortschritte in der Niedrig-Dosis-Computertomographie zu erreichen.
... Although the value of Q eff for the 0.5Ce:LBS10 glass is much lower than that of the 0.5Ce:LBS40 glass because of the generation of Ce 4+ species, the scintillation peak area of the 0.5Ce:LBS10 glass is higher than the peak areas of most 0.5Ce:LBSy glasses in Fig. S9. Figure 10(a) shows the total attenuation with coherent scattering of 0.5Ce:LBSy glasses, which was calculated using a previously published fomula 45 that takes into account the influence of Z eff . The energy spectrum of the X-rays used in the present study [46][47][48] is also shown in the figure with a scale given on the right axis. Here, the X-ray source is a conventional X-ray tube with a W target and a Be window. ...
The efficiency of X-ray-induced scintillation in glasses roughly depends on both the effective atomic number Zeff and the photoluminescence quantum efficiency Qeff of glass, which are useful tools for searching high-performance phosphors. Here, we demonstrate that the energy transfer from host to activators is also an important factor for attaining high scintillation efficiency in Ce-doped oxide glasses. The scintillation intensity of glasses with coexisting fractions of Ce3+ and Ce4+ species is found to be higher than that of a pure-Ce3+-containing glass with a lower Zeff value. Values of total attenuation of each sample indicate that there is a non-linear correlation between the scintillation intensity and the product of total attenuation and Qeff. The obtained results illustrate the difficulty in understanding the luminescence induced by ionizing radiation, including the energy absorption and subsequent energy transfer. Our findings may provide a new approach for synthesizing novel scintillators by tailoring the local structure.
... The model with the lowest RMSD value was identified as the most accurate. Following the model calibration, the proposed model was tested comparing the calculated K-characteristic lines with the spectrum models discussed in the introduction (Birch and Marshall, 1979;Tucker et al., 1991;Poludniowski, 2007) and with the independent data presented in the literature (Fewell and Shuping, 1977;Fewell et al., 1981;Bhat and Pattison, 1998). The data provided by these articles are organized in terms of bremsstrahlung and characteristic peaks, so it is possible for a direct comparison between their results and the proposed calculations. ...
Diagnostic x-ray beams are composed of bremsstrahlung and discrete fluorescence lines. The aim of this study is the development of an efficient model for the evaluation of the fluorescence lines. The most important electron ionization models are analyzed and implemented. The model results were compared with experimental data and with other independent spectra presented in the literature. The implemented peak models allow the discrimination between direct and indirect radiation emitted from tungsten anodes. The comparison with the independent literature spectra indicated a good agreement.
... For the scope of this study, a constant potential for accelerating source electrons from cathode to anode was simulated corresponding to a constant potential generator (zero-voltage ripple). 2 A wedge macrobody specification in MCNPX was used to define the anode composed of tungsten (95% by weight) and rhenium (5% by weight) at an angle of 12 • with respect to the z-axis. TASMIP, 2 which was based upon seminal laboratory measurements performed by Fewell et al. in the early 1980s, 8 utilized an anode composed of tungsten (90% by weight) and rhenium (10% by weight). Given that modern tungsten anode compositions vary in the amount of rhenium, depending on manufacturer/model and specific application, the present choice of rhenium (5% by weight) is simply the average of the TASMIP composition and no rhenium. ...
Purpose:
Monte Carlo methods were used to generate lightly filtered high resolution x-ray spectra spanning from 20 kV to 640 kV.
Methods:
X-ray spectra were simulated for a conventional tungsten anode. The Monte Carlo N-Particle eXtended radiation transport code (MCNPX 2.6.0) was used to produce 35 spectra over the tube potential range from 20 kV to 640 kV, and cubic spline interpolation procedures were used to create piecewise polynomials characterizing the photon fluence per energy bin as a function of x-ray tube potential. Using these basis spectra and the cubic spline interpolation, 621 spectra were generated at 1 kV intervals from 20 to 640 kV. The tungsten anode spectral model using interpolating cubic splines (TASMICS) produces minimally filtered (0.8 mm Be) x-ray spectra with 1 keV energy resolution. The TASMICS spectra were compared mathematically with other, previously reported spectra.
Results:
Using pairedt-test analyses, no statistically significant difference (i.e., p > 0.05) was observed between compared spectra over energy bins above 1% of peak bremsstrahlung fluence. For all energy bins, the correlation of determination (R(2)) demonstrated good correlation for all spectral comparisons. The mean overall difference (MOD) and mean absolute difference (MAD) were computed over energy bins (above 1% of peak bremsstrahlung fluence) and over all the kV permutations compared. MOD and MAD comparisons with previously reported spectra were 2.7% and 9.7%, respectively (TASMIP), 0.1% and 12.0%, respectively [R. Birch and M. Marshall, "Computation of bremsstrahlung x-ray spectra and comparison with spectra measured with a Ge(Li) detector," Phys. Med. Biol. 24, 505-517 (1979)], 0.4% and 8.1%, respectively (Poludniowski), and 0.4% and 8.1%, respectively (AAPM TG 195). The effective energy of TASMICS spectra with 2.5 mm of added Al filtration ranged from 17 keV (at 20 kV) to 138 keV (at 640 kV); with 0.2 mm of added Cu filtration the effective energy was 9 keV at 20 kV and 169 keV at 640 kV.
Conclusions:
Ranging from 20 kV to 640 kV, 621 x-ray spectra were produced and are available at 1 kV tube potential intervals. The spectra are tabulated at 1 keV intervals. TASMICS spectra were shown to be largely equivalent to published spectral models and are available in spreadsheet format for interested users by emailing the corresponding author (JMB).
... To simulate the generation of projection data, 11 the emitting spectrum of the x ray source S (ε) [see Fig. 2(a)] 42 and the absorption spectrum of CsI x ray detector Q (ε) (see Fig. 2(b)) 43 are given. The spectra used for the projection simulation and beam-hardening correction are completely the same. ...
In medical x ray computed tomography (CT) imaging devices, the x ray tube usually emits a polychromatic spectrum of photons resulting in beam-hardening artifacts in the reconstructed images. The bone-correction method has been widely adopted to compensate for beam-hardening artifacts. However, its correction performance is highly dependent on the empirical determination of a scaling factor, which is used to adjust the ratio of the reconstructed value in the bone region to the actual mass density of bone-tissue. A significant problem with bone-correction is that a large number of physical experiments are routinely required to accurately calibrate the scaling factor. In this article, an improved bone-correction method is proposed, based on the projection data consistency condition, to automatically determine the scaling factor. Extensive numerical simulations have verified the existence of an optimal scaling factor, the sensitivity of bone-correction to the scaling factor, and the efficiency of the proposed method for the beam-hardening correction.
... ( ) i S ε , the emitting energy spectrum of the x-ray source, and ( ) i Q ε , the absorption energy spectrum of CsI detector, are taken from [5], [6], and are shown in Fig. 2. uniformly acquired for a full scan. Noise is simulated by assuming 3 × 10 6 photons for each x-ray penetrating path. ...
In the medical diagnostic computed tomography (CT) systems, the x-ray tube usually emits photons with a polychromatic spectrum, resulting in beam hardening artifacts in the reconstructed images. Although the bone correction method is extensively used to compensate for the beam hardening artifacts, its performance crucially depends on the empirical choice of a scaling factor. To overcome this shortcoming, here we propose two adaptive correction methods, which utilize the Helgasson-Ludwig (H-L) consistency condition to determine the optimal scaling factor and the corresponding coefficient vector. Our numerical simulation results demonstrate the effectiveness of the proposed methods.
... This aim can be reached with the knowledge of the diagnostic x-ray energy spectra, which provide a complete description of the x-ray beam. Since Kramers' first attempt in 1923, several research groups are working to find an accurate method for predicting x-ray spectra, which would be very useful because experimental measurement of x-ray spectra[1,2] is time consuming and requires special equipment which is available only in some laboratories. ...
The open-source object-oriented toolkit GEANT4 was used to simulate x-ray spectra in diagnostic radiology and mammography. The simulations were performed using different combinations of target, filters and tube voltages. All the relevant physical processes were included in the calculations: Compton scattering, photoelectric effect, Rayleigh scattering, bremsstrahlung and ionization. The analyzed energy range is from 10 keV to 150 keV. Both Penelope and Low Energy physical models included in the Low Energy extensions of GEANT4 toolkit were used in this work. Range cuts for electron and gamma were set to 500 nm and 3000 nm, respectively. The simulated x-ray spectra using both physics models were compared with calculated spectra generated by the IPEM report number 78. Results show good agreement for the bremsstrahlung intensity for the spectra with tube voltages 40 kV, 100 kV and 150 kV, while the bremsstrahlung intensity is larger for the simulated spectra with 25 kV and 30 kV. Simulated characteristic peaks present lower intensities all spectra. These discrepancies should be related with the ionization process and/or the atomic relaxation implemented in the code. The cross section tables for electrons used in the simulations should be checked.
... Our group has previously used the MCNP4C general-purpose Monte Carlo code running on Pentium-based PC to simulate diagnostic radiology and mammography x-ray tubes with the aim of predicting the x-ray spectra for different target/filter combinations [3]. It has been shown through comparison of simulated and measured spectra that the MCNP4C general purpose Monte Carlo code with some slight adjustment in the appropriate MCNP cards is a useful tool for generating diagnostic radiology and mammography x-ray spectra [7]. The condensed history electron transport algorithm used in MCNP4C is derived from ITS3.0, which is a well validated code for coupled electron/photon transport. ...
The random walk for electron transport in the MCNP4C general purpose Monte Carlo code is derived from ITS3.0, which is a well validated code for coupled electron/photon transport. The continuous slowing down approximation energy loss model is used for electron transport where the MCNP4C code breaks the electron's path into many steps. In this study, the influence of substeps and choice of electron energy indexing algorithm for electron transport on the simulation of X-ray spectra in diagnostic radiology and mammography energy range is investigated. For the simulation of X-ray spectra for tungsten (W) and molybdenum (Mo) targets at different tube voltages, the code was run in photon and electron mode with different substeps and energy indexing algorithms using default values for PHYS:P and PHYS:E cards. The simulated x-ray spectra were compared with the spectra calculated by IPEM report number 78. An average relative difference (ARD) of 11.9%, 13.7% and 14.1% were calculated between the simulated W target spectra using MCNP and ITS energy indexing algorithms at tube voltages of 80, 100 and 120 kVp, respectively. The ARD for Mo target spectra at tube voltages of 25 and 30 kVp was 16.6% and 16.7%, respectively. There is no noticeable difference between the spectra simulated using different substeps in both mammography and radiology energy range; however the simulation time increased by 43.8% and 44.2% when the substeps are set to twice the default value for W and Mo targets, respectively. Generally, there is a good agreement between the simulated and IPEM spectra, although the results suggest slight differences between the simulated spectra using different energy indexing algorithms and electron substeps which tend to be reduced by the normalization process. It is concluded that the energy indexing algorithm and electron substeps have limited influence on electron transport in MCNP4C for the purpose of simulating X- ray spectra in diagnostic radiology and mammography.
... These error-free values are obtained by ensuring that the sum of the photons counted under different interaction processes (absorption and scattering) and those that do not interact (transmitted primary photons) are equal to the total number of incident photons in all the simulation runs. The unfiltered spectra distributions that were reported by Fewell et al. (1981) for 100, 120 and 140 kVp and listed as EI4, EI9 and EI8, respectively, were used as incident radiation. The scorings of the transmitted primary and scattered photons were simultaneously carried out in 2 keV energy bin widths during the simulations. ...
As a result of the differences in the attenuation properties, it is impossible for two different elemental filter material to transmit equal primary photon spectra with the same radiometric equivalence over the entire energy spectrum for the same incident spectrum. However, earlier work reported in the literature show that it is possible to approximately match the spectra shape of transmitted primary photons over a large range of energy spectrum. In this work, the relative differences in the cumulative transmitted primary photons of filter materials used in diagnostic radiology have been investigated using EGS4 Monte Carlo codes. The quantitative influence of these relative differences on parameters such as efficiency of filter, tube current, heat capacity, entrance air kerma and exposure are presented. Simple comparative theoretical models were derived for these differences.
... In their work, Ay et al. [5] compared X-ray spectra calculated by computational and MC codes with measured X-ray spectra obtained in Fewell et al. [21]. We have compared the X-ray spectra generated by the EGSnrc/BEAM code with X-ray spectra calculated by some of these computational codes. ...
We have evaluated the utilization of five X-ray spectra codes for Monte Carlo (MC) simulations of computed tomography (CT) examinations. Four codes (Xcomp5r, X-raytbc, X-rayb&m and Srs-78) are semi-empiricals and one is based on MC methods (EGSnrc/BEAM Monte Carlo code). The X-ray spectra calculated by the semi-empirical codes were compared with the X-ray spectrum calculated by the EGSnrc/BEAM MC code. The absorbed doses to each organ or tissue were also compared. The calculated doses, and its respective organs, for which occurs the greatest disagreement, as well as the calculated doses for the testes and red bone marrow (two important organs used for calculating effective dose) were presented. The results obtained in this work are in good agreement with those obtained by Ay [M.R. Ay, S. Sarkar, M. Shahriari, D. Sardari, H. Zaidi, Assessment of different computational models for generation of X-ray spectra in diagnostic radiology and mammography, Med. Phys. 32 (2005) 1660], mainly for the bremsstrahlung distribution. Also, it was noted that the total characteristic X-rays produced by the EGSnrc/BEAM MC code increases with the increase of voltage more intensely than with the Xcomp5r, X-raytbc and Srs-78 codes. Comparison between the absorbed dose to each organ or tissue showed that, for X-ray spectra with additional filtration, the code based on Tucker et al. is in agreement with EGSnrc/BEAM MC code. But, for X-ray spectra without additional filtration the code based on Tucker et al. model presented the strong disagreement with EGSnrc/BEAM MC code.
... 23 The model included an x-ray spectrum computed using the Spektr toolkit 24 implementation of the TASMIP model of Boone and Seibert. 25 The spectrum calculations were modified empirically to account for variations in anode angle and aging [Tungsten (W) deposition on the exit window] between the actual x-ray tube used in the experimental benchtop emulating the scanner geometry (detailed below) and that implicit in TASMIP (namely, the tube in Fewell and Shupings' original measurements 26 ). To this end, mR=mAs and HVL were measured at 90 and 120 kVp beams (with added filtration of 0.3 mm Cu and 4 mm Al) using an Accu-Pro 9096 multipurpose exposure meter (Radcal Corp., Monrovia, CA). ...
This paper reports on the design and initial imaging performance of a dedicated cone-beam CT (CBCT) system for musculoskeletal (MSK) extremities. The system complements conventional CT and MR and offers a variety of potential clinical and logistical advantages that are likely to be of benefit to diagnosis, treatment planning, and assessment of therapy response in MSK radiology, orthopaedic surgery, and rheumatology.
The scanner design incorporated a host of clinical requirements (e.g., ability to scan the weight-bearing knee in a natural stance) and was guided by theoretical and experimental analysis of image quality and dose. Such criteria identified the following basic scanner components and system configuration: a flat-panel detector (FPD, Varian 3030+, 0.194 mm pixels); and a low-power, fixed anode x-ray source with 0.5 mm focal spot (SourceRay XRS-125-7K-P, 0.875 kW) mounted on a retractable C-arm allowing for two scanning orientations with the capability for side entry, viz. a standing configuration for imaging of weight-bearing lower extremities and a sitting configuration for imaging of tensioned upper extremity and unloaded lower extremity. Theoretical modeling employed cascaded systems analysis of modulation transfer function (MTF) and detective quantum efficiency (DQE) computed as a function of system geometry, kVp and filtration, dose, source power, etc. Physical experimentation utilized an imaging bench simulating the scanner geometry for verification of theoretical results and investigation of other factors, such as antiscatter grid selection and 3D image quality in phantom and cadaver, including qualitative comparison to conventional CT.
Theoretical modeling and benchtop experimentation confirmed the basic suitability of the FPD and x-ray source mentioned above. Clinical requirements combined with analysis of MTF and DQE yielded the following system geometry: a -55 cm source-to-detector distance; 1.3 magnification; a 20 cm diameter bore (20 x 20 x 20 cm3 field of view); total acquisition arc of -240 degrees. The system MTF declines to 50% at -1.3 mm(-1) and to 10% at -2.7 mm(-1), consistent with sub-millimeter spatial resolution. Analysis of DQE suggested a nominal technique of 90 kVp (+0.3 mm Cu added filtration) to provide high imaging performance from -500 projections at less than -0.5 kW power, implying -6.4 mGy (0.064 mSv) for low-dose protocols and -15 mGy (0.15 mSv) for high-quality protocols. The experimental studies show improved image uniformity and contrast-to-noise ratio (without increase in dose) through incorporation of a custom 10:1 GR antiscatter grid. Cadaver images demonstrate exquisite bone detail, visualization of articular morphology, and soft-tissue visibility comparable to diagnostic CT (10-20 HU contrast resolution).
The results indicate that the proposed system will deliver volumetric images of the extremities with soft-tissue contrast resolution comparable to diagnostic CT and improved spatial resolution at potentially reduced dose. Cascaded systems analysis provided a useful basis for system design and optimization without costly repeated experimentation. A combined process of design specification, image quality analysis, clinical feedback, and revision yielded a prototype that is now awaiting clinical pilot studies. Potential advantages of the proposed system include reduced space and cost, imaging of load-bearing extremities, and combined volumetric imaging with real-time fluoroscopy and digital radiography.
... The simulation software used in this work was compared to the state-of-the-art and validated Monte Carlo code (Poludniowski et al 2009). However, the available experimental x-ray spectra were measured long time ago with old x-ray systems and detectors (Fewell et al 1981). It is clear that more experimental x-ray spectra are needed to tabulate more accurate x-ray spectral data. ...
Compact, room temperature x-ray spectroscopy detectors are of interest in many areas including diagnostic x-ray imaging, radiation protection and dosimetry. Room temperature cadmium zinc telluride (CZT) semiconductor detectors are promising candidates for these applications. One of the major problems for CZT detectors is low-energy tailing of the energy spectrum due to hole trapping. Spectral post-correction methods to correct the tailing effect do not work well for a number of reasons; thus it is advisable to eliminate the hole trapping effect in CZT using physical methods rather than correcting an already deteriorated energy spectrum. One method is using a CZT detector with an electrode configuration which modifies the electric field in the CZT volume to decrease low-energy tailing. Another method is to irradiate the CZT surface at a tilted angle, which modifies depth of interaction to decrease low-energy tailing. Neither method alone, however, eliminates the tailing effect. In this work, we have investigated the combination of modified electric field and tilted angle irradiation in a single detector to further decrease spectral tailing. A planar CZT detector with 10 × 10 × 3 mm³ size and CZT detector with 5 × 5 × 5 mm³ size and cap-shaped electrode were used in this study. The cap-shaped electrode (referred to as CAPture technology) modifies the electric field distribution in the CZT volume and decreases the spectral tailing effect. The detectors were investigated at 90° (normal) and 30° (tilted angle) irradiation modes. Two isotope sources with 59.6 and 122 keV photon energies were used for gamma-ray spectroscopy experiments. X-ray spectroscopy was performed using collimated beams at 60, 80 and 120 kVp tube voltages, in both normal and tilted angle irradiation. Measured x-ray spectra were corrected for K x-ray escape fractions that were calculated using Monte Carlo methods. The x-ray spectra measured with tilted angle CAPture detector at 60, 80 and 120 kVp tube voltages were compared to corresponding theoretical spectra. The low-energy tailing was nearly completely eliminated from 59.6 and 122 keV isotope spectra, and 60, 80 and 120 kVp x-ray spectra, when CAPture detector was used with 30° tilted angle irradiation. It is concluded that using a CZT detector with modified electric field in tilted angle configuration resolves problem of the tailing effect in CZT detectors, opening promising possibilities in gamma-ray and x-ray spectroscopy applications.
... The x-ray spectra show significant molybdenum K x-rays at energies of 17.4 and 19.6 keV as well as the more pronounced tungsten K x-rays at 57.9, 59.3, 67.2, and 69.1 keV. Table I compares our spectral data with the data published for an Eimac x-ray tube by Fewell et al. 11 The Eimac x-ray tube had a 12.5°tungsten target, rotating anode and nominal inherent filtration of 1.2 mm Al eq . These parameters matched closely with the Toshiba x-ray tube used in the current study. ...
A number of computer codes, developed using semi-empirical models, are available to compute x-ray spectra from a tungsten target for different tube parameters. In this study x-ray spectra measured with a high-purity germanium detector are compared with those computed using the empirical models and previously published measured data. The computer codes used to generate the spectra are based on models proposed by Birch et al. and Tucker et al. The measured x-ray spectra agreed well with the computed x-ray spectra using the model of Tucker et al. whereas the model of Birch et al. produced a "harder" x-ray spectrum compared to the measured spectra. Our measured x-ray spectra compared well with the previously published measured spectral data of Fewell et al.
... The high purity germanium ͑HP-Ge͒ semiconductor detector is known widely for measuring photon energy spectra. [1][2][3] While this detector is excellent in energy resolution ͓e.g., 419 eV for the 59.5 keV peak of the 241 Am ␥ rays, see Fig. 1͑a͔͒ it is necessary to cool the Ge crystal and the field effect transistor ͑FET͒ of the pre-amplifier by liquid nitrogen. The equipment, therefore, becomes large and hard to move. ...
The analysis of x‐ray spectra is important for quality assurance (QA) and quality control (QC) of radiographic systems. The aim of this study is to measure the diagnostic x‐ray spectra under clinical conditions using a high‐resolution Schottky CdTe detector. Under clinical conditions, the direct measurement of a diagnostic spectrum is difficult because of the high photon fluence rates that cause significant detector photon pile‐up. An alternative way of measuring the output spectra from a tube is first to measure the 90 deg Compton scattered photons from a given sample. With this set‐up detector, pile‐up is not a problem. From the scattered spectrum one can then use an energy correction and the Klein–Nishina function to reconstruct the actual spectrum incident upon the scattering sample. The verification of whether our spectra measured by the Compton method are accurate was accomplished by comparing exposure rates calculated from the reconstructed spectra to those measured with an ionization chamber. We used aluminum (Al) filtration ranging in thickness from 0 to 6 mm. The half value layers (HVLs) obtained for a 70 kV beam were 2.78 mm via the ionization chamber measurements and 2.93 mm via the spectral measurements. For a 100 kV beam we obtained 3.98 and 4.32 mm. The small differences in HVLs obtained by both techniques suggest that Compton scatter spectroscopy with a Schottky CdTe detector is suitable for measuring the diagnostic x‐ray spectra and useful for QA and QC of clinical x‐ray equipment.
This work presents a comprehensive catalogue of x-ray spectra measured from x-ray tubes with tungsten, molybdenum, and rhodium anodes generated at tube potentials between 10 kV and 50 kV in steps of 1 kV. They can serve as an input for dose calculations, image quality calculations, investigations of detector features, and validations of computational spectral models, among other things. The measurements are performed by means of a high-purity germanium detector-based spectrometer 1 m from the x-ray sources without any added filtration. The x-ray tubes are characterised by thin Beryllium exit windows (0.15 mm to 4 mm); thus, for energies above 15 keV, the spectra recorded can be considered approximately unfiltered. This allows users of the catalogue to computationally add any filter to the spectra and create radiation qualities of their choice. To validate this option, a small number of spectra are recorded with filter materials in place whose purity and thickness are known with high precision. These spectra agree very well to the corresponding spectra from the catalogue with computationally added filters. Several typical mammographic radiation qualities are selected to compare the spectra with spectra obtained from other catalogues published by Boone et al. [Boone, Fewell, and Jennings, Medical Physics 24 (1997) 1863-1874] and Hernandez et al. [Hernandez et al., Medical Physics 44 (2017) 2148-2160], which rely partly or fully on calculations. A quantitative comparison is made by means of typical x-ray quality descriptors such as the mean energy and the first and second half-value layer. The results obtained from the Boone catalogue match those of the current catalogue sufficiently well for the Mo- and Rh-anode-based spectra. However, significant differences up to 10 times the estimated uncertainties are found for the quality descriptors evaluated from the spectra of Hernandez et al. and the W-anode based spectra of Boone et al.
Purpose
To develop a tool to produce accurate, well‐validated x‐ray spectra for standalone use or for use in an open‐access x‐ray/CT simulation tool. Spectrum models will be developed for tube voltages in the range of 80 kVp through 140 kVp and for anode takeoff angles in the range of 5° to 9°.
Methods
Spectra were initialized based on physics models, then refined using empirical measurements, as follows. A new spectrum‐parameterization method was developed, including 13 spline knots to represent the bremsstrahlung component and 4 values to represent characteristic lines. Initial spectra at 80, 100, 120, and 140 kVp and at takeoff angles from 5° to 9° were produced using physics‐based spectrum estimation tools XSPECT and SpekPy. Empirical experiments were systematically designed with careful selection of attenuator materials and thicknesses, and by reducing measurement contamination from scatter to <1%. Measurements were made on a 64‐row CT scanner using the scanner’s detector and using multiple layers of polymethylmethacrylate (PMMA), aluminum, titanium, tin, and neodymium. Measurements were made at 80, 100, 120, and 140 kVp and covering the entire 64‐row detector (takeoff angles from 5° to 9°); a total of 6,144 unique measurements were made. After accounting for the detector’s energy response, parameterized representations of the initial spectra were refined for best agreement with measurements using two proposed optimization schemes: based on modulation and based on gradient descent. X‐ray transmission errors were computed for measurements vs calculations using the nonoptimized and optimized spectra. Half‐value, tenth‐value, and hundredth‐value layers for PMMA, Al, and Ti were calculated.
Results
Spectra before and after parameterization were in excellent agreement (e.g., R² values of 0.995 and 0.997). Empirical measurements produced smoothly varying curves with x‐ray transmission covering a range of up to 3.5 orders of magnitude. Spectra from the two optimization schemes, compared with the unoptimized physic‐based spectra, each improved agreement with measurements by twofold through tenfold, for both postlog transmission data and for fractional value layers.
Conclusion
The resulting well‐validated spectra are appropriate for use in the open‐access x‐ray/CT simulator under development, the x‐ray‐based Cancer Imaging Toolkit (XCIST), or for standalone use. These spectra can be readily interpolated to produce spectra at arbitrary kVps over the range of 80 to 140 kVp and arbitrary takeoff angles over the range of 5° to 9°. Furthermore, interpolated spectra over these ranges can be obtained by applying the standalone Matlab function available at https://github.com/xcist/documentation/blob/master/XCISTspectrum.m.
Purpose:A computational toolkit (spektr 3.0) has been developed to calculate x-ray spectra based on the tungsten anode spectral model using interpolating cubic splines (TASMICS) algorithm, updating previous work based on the tungsten anode spectral model using interpolating polynomials (TASMIP) spectral model. The toolkit includes a matlab (The Mathworks, Natick, MA) function library and improved user interface (UI) along with an optimization algorithm to match calculated beam quality with measurements.
Methods:The spektr code generates x-ray spectra (photons/mm2/mAs at 100 cm from the source) using TASMICS as default (with TASMIP as an option) in 1 keV energy bins over beam energies 20–150 kV, extensible to 640 kV using the TASMICS spectra. An optimization tool was implemented to compute the added filtration (Al and W) that provides a best match between calculated and measured x-ray tube output (mGy/mAs or mR/mAs) for individual x-ray tubes that may differ from that assumed in TASMICS or TASMIP and to account for factors such as anode angle.
Results:The median percent difference in photon counts for a TASMICS and TASMIP spectrum was 4.15% for tube potentials in the range 30–140 kV with the largest percentage difference arising in the low and high energy bins due to measurement errors in the empirically based TASMIP model and inaccurate polynomial fitting. The optimization tool reported a close agreement between measured and calculated spectra with a Pearson coefficient of 0.98.
Conclusions:The computational toolkit, spektr, has been updated to version 3.0, validated against measurements and existing models, and made available as open source code. Video tutorials for the spektr function library, UI, and optimization tool are available.
This entry treats sources of only ionizing radiation, such as electrons, protons, high-energy photons, neutrons, and similar radiations that have the ability to cause ionization, either directly or indirectly, and, thus, to induce chemical and physical changes along their passages through materials. Not included are sources of relatively lower frequency electromagnetic radiation from radio waves to ultraviolet light.
A Monte Carlo-based tungsten anode spectral model, conceptually similar to the previously-developed TASMIP model,
was developed. This new model provides essentially unfiltered x-ray spectra with better energy resolution and
significantly extends the range of tube potentials for available spectra. MCNPX was used to simulate x-ray spectra as a
function of tube potential for a conventional x-ray tube configuration with several anode compositions. Thirty five x-ray
spectra were simulated and used as the basis of interpolating a complete set of tungsten x-ray spectra (at 1 kV intervals)
from 20 to 640 kV. Additionally, Rh and Mo anode x-ray spectra were simulated from 20 to 60 kV. Cubic splines were
used to construct piecewise polynomials that interpolate the photon fluence per energy bin as a function of tube potential
for each anode material. The tungsten anode spectral model using interpolating cubic splines (TASMICS) generates
minimally-filtered (0.8 mm Be) x-ray spectra from 20 to 640 kV with 1 keV energy bins. The rhodium and molybdenum
anode spectral models (RASMICS and MASMICS, respectively) generate minimally-filtered x-ray spectra from 20 to 60
kV with 1 keV energy bins. TASMICS spectra showed no statistically significant differences when compared with the
empirical TASMIP model, the semi-empirical Birch and Marshall model, and a Monte Carlo spectrum reported in AAPM
TG 195. The RASMICS and MASMICS spectra showed no statistically significant differences when compared with
their counterpart RASMIP and MASMIP models. Spectra from the TASMICS, MASMICS, and RASMICS models are
available in spreadsheet format for interested users.
The Practical Peak Voltage-PPV has been adopted to measure the voltage
applied to an X-ray tube. The PPV was recommended by the IEC document
and accepted and published in the TRS no. 457 code of practice. The PPV
is defined and applied to all forms of waves and is related to the
spectral distribution of X-rays and to the properties of the image. The
calibration of X-rays tubes was performed using the MCNPX Monte Carlo
code. An X-ray tube for Dental Radiology (operated from a single phase
power supply) and an X-ray tube used as a reference (supplied from a
constant potential power supply) were used in simulations across the
energy range of interest of 40 kV to 100 kV. Results obtained indicated
a linear relationship between the tubes involved.
In this work, the Monte Carlo (MC) code PENELOPE was employed for simulation of x-ray spectra in mammography and contrast-enhanced digital mammography (CEDM). Spectra for Mo, Rh and W anodes were obtained for tube potentials between 24-36 kV, for mammography, and between 45-49 kV, for CEDM. The spectra obtained from the simulations were analytically filtered to correspond to the anode/filter combinations usually employed in each technique (Mo/Mo, Rh/Rh and W/Rh for mammography and Mo/Cu, Rh/Cu and W/Cu for CEDM). For the Mo/Mo combination, the simulated spectra were compared with those obtained experimentally, and for spectra for the W anode, with experimental data from the literature, through comparison of distribution shape, average energies, half-value layers (HVL) and transmission curves. For all combinations evaluated, the simulated spectra were also compared with those provided by different models from the literature. Results showed that the code PENELOPE provides mammographic x-ray spectra in good agreement with those experimentally measured and those from the literature. The differences in the values of HVL ranged between 2-7%, for anode/filter combinations and tube potentials employed in mammography, and they were less than 5% for those employed in CEDM. The transmission curves for the spectra obtained also showed good agreement compared to those computed from reference spectra, with average relative differences less than 12% for mammography and CEDM. These results show that the code PENELOPE can be a useful tool to generate x-ray spectra for studies in mammography and CEDM, and also for evaluation of new x-ray tube designs and new anode materials.
Purpose:
The availability of accurate and simple models for the estimation of x-ray spectra is of great importance for system simulation, optimization, or inclusion of photon energy information into data processing. There is a variety of publicly available tools for estimation of x-ray spectra in radiology and mammography. However, most of these models cannot be used directly for modeling microfocus x-ray sources due to differences in inherent filtration, energy range and/or anode material. For this reason the authors propose in this work a new model for the simulation of microfocus spectra based on existing models for mammography and radiology, modified to compensate for the effects of inherent filtration and energy range.
Methods:
The authors used the radiology and mammography versions of an existing empirical model [tungsten anode spectral model interpolating polynomials (TASMIP)] as the basis of the microfocus model. First, the authors estimated the inherent filtration included in the radiology model by comparing the shape of the spectra with spectra from the mammography model. Afterwards, the authors built a unified spectra dataset by combining both models and, finally, they estimated the parameters of the new version of TASMIP for microfocus sources by calibrating against experimental exposure data from a microfocus x-ray source. The model was validated by comparing estimated and experimental exposure and attenuation data for different attenuating materials and x-ray beam peak energy values, using two different x-ray tubes.
Results:
Inherent filtration for the radiology spectra from TASMIP was found to be equivalent to 1.68 mm Al, as compared to spectra obtained from the mammography model. To match the experimentally measured exposure data the combined dataset required to apply a negative filtration of about 0.21 mm Al and an anode roughness of 0.003 mm W. The validation of the model against real acquired data showed errors in exposure and attenuation in line with those reported for other models for radiology or mammography.
Conclusions:
A new version of the TASMIP model for the estimation of x-ray spectra in microfocus x-ray sources has been developed and validated experimentally. Similarly to other versions of TASMIP, the estimation of spectra is very simple, involving only the evaluation of polynomial expressions.
A theoretical description for the production of characteristic X-rays (CX) is reviewed highlighting features that enhance the CX intensity. These are incorporated into the design of a secondary target system for excitation by white radiation produced by an industrial X-ray tube; Philips MCN-166, capable of continuous operation at up to 160 kVp and 1.6 kW. Results are presented for the measured spatial profile, CX intensity at 8-75 keV and spectral purity as a function of accelerating voltage. The beam is a narrow fan with half height (horizontal by vertical) 200 mm by 50 mm at 1 m from the source. The beam intensity is presented in units ph/s/mm2 at 1 m per kW and is equivalent to an isotope source with activities 100-300 mCi per kW deposited in the anode. The source provides variable intensity and the ability to change energy by simply exchanging the target material.
A Monte Carlo method was used to calculate the emission of bremsstrahlung and characteristic K X-rays, and the backscattering of electrons, from thick tungsten irradiated by electrons with energies between 500 and 50 keV, incident on the target surface at many angles, from perpendicular to almost grazing. An extensive database was produced consisting of the spectra of emitted X-rays, and of reflected electrons, emerging in many directions. This database is available on a compact disk. Auxiliary calculations were developed to take into account the modification of the X-ray spectra by filters, and to determine quantities which characterize the X-ray output: (1) the fraction of the incident electron energy that is converted to emitted X-ray energy; (2) the exposure rate (in roentgen per second) per unit power input, and per unit rate of energy deposition in the target.
The formation principle of X-ray computed tomography (CT) beam hardening and the effect law of noise on the correction result were studied. The suppression methods of noise impact in the process of beam hardening correction were presented from the following three aspects: First of all, aiming at the adverse factors of original beam hardening data, such as noise and measurement error, a method of simplifying beam hardening data was proposed based on histogram statistics of traversing lengths, which removing noise while ensuring the data density uniformity; Secondly, according to the basic characteristics of hardening curve, a new fitting function with good stability of curve shape was constructed, further enhancing the anti-noise capability of hardening model; Finally, an improved calculating method of beam hardening correction was proposed to primarily eliminate cupping artifacts and at the same time, to control the image noises at the original level. CT simulation result shows that these methods are well stable in the computing process of beam hardening correction for CT images contained serious noises, and the correction result is good.
A virtual experimentation combining computational fluid dynamics (CFD) and computed tomography (CT) simulations was presented to evaluate the beam hardening effect in the CT application to multiphase flow measurement. A semi-industrial scale circulating fluidized bed (CFB) reactor was simulated with a multiscale CFD approach, and its computed flow fields was taken as the dynamic phantom for CT. By this means, a 3rd generation X-ray CT with different filter parameters was simulated. Since the computed flow fields can be manipulated in detail and reproduced at will, this virtual approach enables quantitative evaluation of the beam hardening effect and helps establish the optimal filter parameters for CT measurement of multiphase flow.
As multidetector computed tomography (MDCT) scanning is routinely performed for treatment planning in radiation oncology, understanding the characteristics of the MDCT x-ray beam is essential to accurately estimate patient dose. The purpose of this study is to characterize the x-ray beams of two commercial MDCT simulators widely used in radiation oncology by Monte Carlo (MC) simulations.
X-ray tube systems of two wide bore MDCT scanners (GE LightSpeed RT 4 and Philips Brilliance Big Bore) were modeled in the BEAMNRC/EGSNRC MC system. All the tube components were modeled from targets to bowtie filters. To validate our MC models, the authors measured half-value layers (HVL) using aluminum sheets and multifunctional radiation detectors and compared them to those obtained from MC simulations for 120 kVp beams. The authors also compared x-ray spectra obtained from MC simulation to the data provided by manufacturers. Additionally, lateral/axial beam profiles were measured in-air using radiochromic films and compared to the MC results. To understand the scatter effect, the authors also derived the scatter-to-primary energy fluence ratio (SPR) profiles and calculated the total SPR for each CT system with the CT dose index (CTDI) head and body phantoms using the BEAMNRC system.
The authors found that the HVL, x-ray spectrum and beam profiles of the MC simulations agreed well with the manufacturer-specified data within 1%-10% on average for both scanners. The total SPR were ranged from 7.8 to 13.7% for the head phantom and from 10.7 to 18.9% for the body phantom.
The authors demonstrate the full MC simulations of two commercial MDCT simulators to characterize their x-ray beams. This study may be useful to establish a patient-specific dosimetry for the MDCT systems.
A novel water equivalent formulation of PRESAGE dosimeter more suitable for radiotherapy applications has been introduced and its radiological water equivalency has been investigated. Furthermore, its radiological properties have been compared with an existing PRESAGE formulation over an energy range from 10 to 20 MeV. Monte Carlo simulation method has been implemented to determine and compare depth dose profiles in both of the PRESAGE formulations at two different photon energies (140 KV(P) and 6 MV). The results show that our proposed PRESAGE formulation is more water equivalent than its known formulation especially for low photon energy beams.
Monte Carlo simulation is a very useful tool for radiotherapy and diagnostic radiology. Yet even with the latest PCs, simulation of photon spectra emitted by an x-ray tube is a time-consuming task, potentially reducing the possibility to obtain relevant data such as dose evaluations, simulation of geometric settings, or monitor detector efficiency. This study developed and validated a method to generate random numbers for realistic beams in terms of photon spectrum and intensity to simulate x-ray tubes via Monte Carlo algorithms.
Starting from literature data, the most common semiempirical models of bremsstrahlung are analyzed and implemented, adjusting their formulation to describe a large irradiation area (i.e., large field of view) and to take account of the heel effect as in common practice during patient examinations.
Simulation results show that Birch and Marshall's model is the fastest and most accurate for the aims of this work. Correction of the geometric size of the beam and validation of the intensity variation (heel effect) yielded excellent results with differences between experimental and simulated data of less than 6%.
The results of validation and execution time showed that the tube simulator calculates the x-ray photons quickly and efficiently and is perfectly capable of considering all the phenomena occurring in a real beam (total filtration, focal spot size, and heel effect), so it can be used in a wide range of applications such as industry, medical physics, or quality assurance.
The proper use of imaging equipment in radiological units is based on an appropriate knowledge of the physical characteristics of the X-ray beam used. The FLUXEN PROJECT is working on a portable apparatus which, together with dedicated software, is able to perform an exact spectral reconstruction of the radiation produced in diagnostic X-ray tubes. The apparatus characterizes the energy spectrum of radiological tubes and also provides a measurement of the emitted flux. The acquisition system is based on a commercial CZT detector (3×3×2 mm<sup>3</sup>), produced by AMPTEK, cooled by a Peltier cell, with a high efficiency in the diagnostic X-ray energy range and modified in the shaping electronics so as to obtain a faster response. The acquiring section lies on a NuDAQ I/O card with a sampling frequency of up to 20 MHz. The signal produced by the X-ray tube is wholly acquired and an off-line analysis is made so as to make possible an accurate recognition of pile-up events and a reconstruction of the emitted spectra. The reconstructed spectra of a General Electric Senographe DMR mammographic X-ray tube are shown.
It has been generally expected that, as X-ray tube-voltage ripple increases, the X-ray spectrum shifts to the low photon-energy side, and therefore the mean energy decreases, i.e. the beam quality is softened. This is the normal order. Previous calculation (Birch et al., 1979), however, showed that the beam quality generated by 100% ripple was harder than that by 50% ripple. This is the reverse order, against general expectation. To verify the reverse order, X-ray spectra are measured using a germanium detector system. The measurements are performed with various thicknesses of aluminium object. To obtain large ripples at small tube currents, small-capacity high-voltage cables are made. To perform efficient measurements, the homogeneous sensitive region of the germanium crystal is determined, and detector-collimators with various diameters are prepared. As a result, experimental verification of the reverse order is performed for various thicknesses of object. The reverse order also appears in photon spectra and mean energies calculated using three models from previous work (Kramer, 1923; Birch and Marshall, 1979; Tucker et al., 1991) by inserting the tube-voltage waveforms measured with the authors' system. The experimental results agree well with the results using the Birch-Marshall model. Mean energies reach the minimum levels for the three models at 20-60% ripple, as do the experimental results. The reason for the phenomenon is clarified by qualitative illustration.
Estimated photon energy spectra are derived from transmission measurements using aluminium, copper, and sodium iodide absorbers. Two spectral models are proposed. One is based on a previously published model that analyzes the electron's penetration into the anode, and the production and attenuation of bremsstrahlung photons. The second model does not include details regarding the underlying physics, but treats the spectrum as a sum of delta functions. A nonlinear regularization method is used to overcome ill conditioning in the second model. Both models fit the transmission data to an accuracy of 0.30%, which is consistent with the experimental error. A quantitative comparison of the models is made by calculating the average and variance (over the derived energy spectra) of several relevant mass attenuation coefficients. The maximum variation in the average and variance was 1.5% and 3.2%, respectively, indicating that the spectra exhibit similar attenuation and beam hardening properties. The spectra were tested with a simulation that predicts scanner CT numbers for phantom measurements consisting of dilutions of sodium iodide in a water equivalent background. The agreement between simulation and experiment ranged from 1.5% at 220 HU to 4.4% at 1700 HU.
A tungsten anode spectral model using interpolating polynomials (TASMIP) was used to compute x-ray spectra at 1 keV intervals over the range from 30 kV to 140 kV. The TASMIP is not semi-empirical and uses no physical assumptions regarding x-ray production, but rather interpolates measured constant potential x-ray spectra published by Fewell et al. [Handbook of Computed Tomography X-ray Spectra (U.S. Government Printing Office, Washington, D.C., 1981)]. X-ray output measurements (mR/mAs measured at 1 m) were made on a calibrated constant potential generator in our laboratory from 50 kV to 124 kV, and with 0-5 mm added aluminum filtration. The Fewell spectra were slightly modified (numerically hardened) and normalized based on the attenuation and output characteristics of a constant potential generator and metal-insert x-ray tube in our laboratory. Then, using the modified Fewell spectra of different kVs, the photon fluence phi at each 1 keV energy bin (E) over energies from 10 keV to 140 keV was characterized using polynomial functions of the form phi (E) = a0[E] + a1[E] kV + a2[E] kV2 + ... + a(n)[E] kVn. A total of 131 polynomial functions were used to calculate accurate x-ray spectra, each function requiring between two and four terms. The resulting TASMIP algorithm produced x-ray spectra that match both the quality and quantity characteristics of the x-ray system in our laboratory. For photon fluences above 10% of the peak fluence in the spectrum, the average percent difference (and standard deviation) between the modified Fewell spectra and the TASMIP photon fluence was -1.43% (3.8%) for the 50 kV spectrum, -0.89% (1.37%) for the 70 kV spectrum, and for the 80, 90, 100, 110, 120, 130 and 140 kV spectra, the mean differences between spectra were all less than 0.20% and the standard deviations were less than approximately 1.1%. The model was also extended to include the effects of generator-induced kV ripple. Finally, the x-ray photon fluence in the units of photons/mm2 per mR was calculated as a function of HVL, kV, and ripple factor, for various (water-equivalent) patient thicknesses (0, 10, 20, and 30 cm). These values may be useful for computing the detective quantum efficiency, DQE(f), of x-ray detector systems. The TASMIP algorithm and ancillary data are made available on line at http:/(/)www.aip.org/epaps/epaps.html.
Theoretical x-ray spectra calculated by four different codes for the same tube parameters are compared by calculating and measuring doses to computed tomography (CT) body and head phantoms. The effect on the 120 kV spectrum, and hence on the calculated dose, of varying the anode angle, tube voltage, and total filtration of the x-ray tube is investigated. Codes used were those of Nowotny and Höfer (XCOMP), Boone, Iles, and Tucker et al. The code based on the work of Tucker et al. produced calculated doses noticeably lower than the other codes and compared best to the measured value. The variation in calculated dose between the Tucker code and the others is of the same order as the variation introduced by uncertainties in total filtration of about 20%, in peak tube voltage of +/- 4 kV, and in change of anode angle from 7 degrees to 13 degrees.
While the equivalence of different filter materials commonly considered useful in diagnostic radiology can be obtained in terms of the overall transmitted primary photons, the scattering characteristics are not the same. In this work, comparative models that relate the scattered photons produced from one-filter material with those from another have been developed. The comparison of the results of simulation of the scattering properties of these equivalent filter materials using the Monte Carlo technique with those from the models developed in the study are in reasonable agreement.
Present interest is in the shielding of diagnostic X-ray units. Numerical comparison has been made of the attenuation and hardening properties of lead and some particular alternative materials: steel, plate glass and gypsum wallboard. Results show, for particular choices of thickness, that lead and steel can be made to provide closely similar attenuation and spectral hardening, values of lead attenuation equivalent (LAE) and lead hardening equivalent (LHE) thicknesses being nearly the same. Significant differences in the attenuation and hardening properties of lead are found in comparison with plate glass and gypsum wallboard. LAE produces better matching of exposure for lead-plate glass and lead-gypsum wallboard than LHE.
In routine applications, information about the photon flux of x-ray tubes is obtained from exposure measurements and cataloged spectra. This approach relies mainly on the assumption that the real spectrum is correctly approximated by the cataloged one, once the main characteristics of the tube such as voltage, target material, anode angle, and filters are taken account of. In practice, all this information is not always available. Moreover, x-ray tubes with the same characteristics may have different spectra. We describe an apparatus that should be useful for quality control in hospitals and for characterizing new radiographic systems. The apparatus analyzes the spectrum generated by an x-ray mammographic unit. It is based on a commercial CZT produced by AMPTEK Inc. and a set of tungsten collimator disks. The electronics of the CZT are modified so as to obtain a faster response. The signal is digitized using an analog to digital converter with a sampling frequency of up to 20 MHz. The whole signal produced by the x-ray tube is acquired and analyzed off-line in order to accurately recognize pile-up events and reconstruct the emitted spectrum. The energy resolution has been determined using a calibrated x-ray source. Spectra were validated by comparison of the HVL measured using an ionization chamber.
Different computational methods based on empirical or semi‐empirical models and sophisticated Monte Carlo calculations have been proposed for prediction of x‐ray spectra both in diagnostic radiology and mammography. In this work, the x‐ray spectra predicted by various computational models used in the diagnostic radiology and mammography energy range have been assessed by comparison with measured spectra and their effect on the calculation of absorbed dose and effective dose (ED) imparted to the adult ORNL hermaphroditic phantom quantified. This includes empirical models (TASMIP and MASMIP), semi‐empirical models (X‐rayb&m, X‐raytbc, XCOMP, IPEM, Tucker et al., and Blough et al.), and Monte Carlo modeling (EGS4, ITS3.0, and MCNP4C). As part of the comparative assessment, the K x‐ray yield, transmission curves, and half value layers (HVLs) have been calculated for the spectra generated with all computational models at different tube voltages. The measured x‐ray spectra agreed well with the generated spectra when using X‐raytbc and IPEM in diagnostic radiology and mammography energy ranges, respectively. Despite the systematic differences between the simulated and reference spectra for some models, the student's t‐test statistical analysis showed there is no statistically significant difference between measured and generated spectra for all computational models investigated in this study. The MCNP4C‐based Monte Carlo calculations showed there is no discernable discrepancy in the calculation of absorbed dose and ED in the adult ORNL hermaphroditic phantom when using different computational models for generating the x‐ray spectra. Nevertheless, given the limited flexibility of the empirical and semi‐empirical models, the spectra obtained through Monte Carlo modeling offer several advantages by providing detailed information about the interactions in the target and filters, which is relevant for the design of new target and filter combinations and optimization of radiological imaging protocols.
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