- Email: [email protected]
P in mammography: GEANT4 validation
ORIGINALARBEIT
PSF, LSF and S/P in mammography: GEANT4 validation Varlen Grabski1, Maria-Ester Brandan1, Cesar Ruiz-Trejo1, Yolanda Villaseñor2 1 Instituto de Física UNAM, A.P. 20-364, 01000 DF, Mexico 2 Instituto Nacional de Cancerología, Avda. San Fernando 22, Tlalpan, 14080 DF, Mexico
Abstract The main goal of this study was to validate the predictions of GEANT4, a Monte Carlo code originally developed for high-energy physics, for low-energy (10–40 keV) photon transmission and scattering through matter similar to biological tissue. We compared GEANT4 calculations with existing phantom data relevant for the mammographic imaging technique. This work showed that scattered-toprimary ratio data can be simulated using GEANT4 with a deviation smaller than 5%. At the same time, we encountered a limitation in the small-angle region description by the code, which is important for point- and line-spread function calculations. The comparison with forward angle data showed that the GEANT4 models, known as “G4 Low Energy” and “G4 Penelope”, describe the measurements for X-ray beams typically used in mammography better than 10% for angles above 10 degrees, and that “G4 Low Energy” is preferable to “G4 Penelope”. The results confirm the possible use of GEANT4 for the optimization of applications based on low-energy photon transmission and scattering.
Keywords: Monte Carlo simulation, GEANT4, validation, mammography, PSF, LSF, scatter-to-primary ratio
Introduction The detection of an object in a radiological image depends on the X-ray transmission and scattering properties. Thus, a detailed description of the photon scattering in the medium is of importance to fully understand the information contained in the image. Mammographic images are particularly difficult to interpret due to the small contrast between breast tissues and small size of structures of interest.
298
PSF, LSF und S/P in der Mammographie: GEANT4-Gültigkeitserklärung Zusammenfassung Unser Hauptziel war das Studium der Gültigkeit von GEANT4, einem Monte-Carlo-Programm, ursprünglich für die Hochenergiephysik entwickelt, im Vorhersagen der Emission und Streuung niederenergetischer Photonen (10–40 KeV) durch Materie, die biologischem Gewebe ähnelt. Wir haben die Simulationsergebnisse von GEANT4 mit vorhandenen Phantomdaten verglichen, die für die Mammographiebelichtungstechnik wichtig sind. Diese Arbeit hat gezeigt, dass die Verhältnisse von gestreuten zu primären Photonen mit Abweichungen kleiner als 5% mit GEANT4 simuliert werden können. In der Beschreibung der Kleinwinkelregion haben wir aber eine Limitierung des Programms gefunden, die wichtig für die Berechnung von Punkt- und Linienverbreitungsfunktionen ist. Der Vergleich mit Vorwärtswinkeldaten hat gezeigt, dass die GEANT4-Modelle, bekannt als „G4 Low Energy“ und „G4 Penelope“, die typisch in der Mammographie benutzte Messungen von Röntgenstrahlen über 10 Grad, besser als zu 10% beschreiben und dass das G4 „Low Energy“Modell dem „G4 Penelope“-Modell vorzuziehen ist. Diese Ergebnisse bestätigen den möglichen Gebrauch von GEANT4 für die Optimierung von Anwendungen, die auf niederenergetischer Photontransmission und -streuung basieren. Schlüsselwörter: Monte-Carlo-Methode, GEANT4, Gültigkeitserklärung, Mammographie, PSF, LSF, Streu-zu-Primärstrahl-Verhältnis
The optimization of the application, as well as the determination of different characteristics of a mammographic image can often be done by means of Monte Carlo (MC) calculations [36]. The choice of the appropriate Monte Carlo code essentially depends on the required accuracy for the given task. At present, a large selection of sufficiently good and complex programs [1, 3, 9, 30] exist, describing the experimental data with an accuracy of the order of several percent. For low-energy photon processes, the description of
Z. Med. Phys. 16 (2006) 298–306 http://www.elsevier.de/zmedphys
PSF, LSF and S/P in mammography: GEANT4 validation
the mass-attenuation coefficients above 10 keV photon energy is similar for all these codes [2, 35]. For Compton scattering attenuation coefficients, the difference among MC programs can reach up to 10% for elements with large Z values and photon energies around 10 keV. Below 10 keV, the discrepancy among codes in the description of coherent scattering mass-attenuation coefficients increases [35] as the energy decreases, due to differences between the XCOM [17] and EPDL [18] data bases. For mammography images, energies
Figure 1 Setup for the forward scattering simulations. PMMA represents an empty polymethyl metacrylate cylindrical volume around the 2 cm thick polyethylene target. HPGe are high-purity germanium detectors.
below 10 keV are less significant because of the initial spectrum absorption before reaching the detector. In addition, the description of the scattered radiation angular characteristics is a complicated task due to coherent scattering. Detailed validation studies of the coherent scattering angular characteristics in the low-energy region do not exist for the above mentioned codes [1, 3, 9, 30]. We must mention that besides the best known programs [1, 3, 9, 30], others exist, already reported in medical physics literature, that are good enough for low-energy photon processes, but not easy for the public use [5, 11, 13]. Among the enumerated MC codes, GEANT4 [1] is a toolkit for simulation of the particle passage through matter. A set of processes have been developed to describe the electromagnetic interactions of photons and electrons with matter down to 250 eV. GEANT4 offers advantages for its use: it is free, is relatively well documented, has great capabilities for describing difficult and time-dependent geometrical shapes [31, 32], is flexible to use for different physical models, and allows visualization of the elementary events. The main disadvantage of GEANT4 is to be slower than EGSNRC [35] and thus, to require a large CPU time for generation of the required amount of statistics for radiological images. Tests of GEANT4 describing low-energy electromagnetic processes have a rather brief history and are mainly connected with medical physics [2, 10, 23, 24, 31–36]. It is possible to find test results not yet published at the GEANT4 low-energy site [19].
Figure 2 Experimental and simulation setups for PSF (a), edge detection S/P and LSF (b), and beam stopping S/P (c).
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PSF, LSF and S/P in mammography: GEANT4 validation
In mammography, the majority of the experimental results relate to integral characteristics, such as scatter-to-primary ratio (S/P) [4, 7, 12, 29, 38], and only a few measurements address differential characteristics, such as line spread function (LSF) [7, 12] and point-spread-function (PSF) [14]. In our opinion, these latter data can be more informative than the previous for the validation of the scattered radiation description by a given program. Also, there are few experimental data related to the low-energy photon forward scattering [25–28] for the 20–120 keV region, that can be used to test the small angle scattering description in a MC code. Our objective in this work is the validation of GEANT4 for 10–40 keV electromagnetic radiation, with a specific interest in determining the accuracy of predictions relevant for mammography [16].
Materials and Methods 1. Forward angle scattering An important and difficult part in the description of forward scattering is the coherent scattering dependence on the structure of the scattering medium. The accuracy of GEANT4 coherent scattering predictions can be checked against smallangle scattering data. Measurements of low-energy scattered photons in this angular region can be found in works of diffraction computed tomography (also called X-ray forwardscatter imaging) [25, 27, 28]. We have simulated the photon transmission using the experimental arrangements reported in [28]. Two setups were described in Ref. 28, having approximately equal separation (83.7 and 82.3 cm) from the focal spot of the X-ray tube to the target, and we have combined them into just one, shown in Figure 1, where all the geometrical sizes of the simulation arrangement are defined. For Xray photon generation, the measured spectrum for the transmitted photons from [28] is used. To recover the initial spectrum, the measurements were corrected by absorption in target and air, as well as by detector energy resolution and registration efficiency. Information on the chemical composition of materials and mass-attenuation coefficients was taken from the NIST database [20]. The simulation was performed using two models of GEANT4 version 4.6, “G4 Low Energy” and “G4 Penelope” [1]. All beam collimations after the target, as well as the solid angle and air absorption corrections, were performed during the data analysis process according to the experimental conditions [28].
thick disk with a 1 mm diameter hole. The scattering media are 4 cm thick polymethyl metacrilate (PMMA) plates with 20 × 20 cm2 transversal sizes. The X-ray tube high voltage was between 26 and 28 kVp, using the Mo/Mo anode/filter combination. The digital detector (~1913 × 2300 pixels, 100 μm sizes) is based on columnar CsI(Tl) scintillators. A GEANT4 simulation of the same experimental setup has been performed using the “G4 Low Energy” model. Edge profiles have been measured for different thicknesses and high voltages [5, 12]. The experimental setup for the edge profile measurements is presented in Figure 2b [12]. We have simulated this experimental setup for similar conditions. 3. Scatter-to-Primary ratio The S/P measurement has been the basic method, in the last 15 years, for the investigation of the scattered radiation influence on the quality of mammography images. Two main experimental methods, known as “beam stopping” (BS) [4] and “edge detection” (ED) [12], depicted in Figs. 2c and 2b, respectively, have been used. The work of Barnes and Brezovich [4] is one of the first and most accurate measurements of S/P carried out according to the BS method. In that work, the minimal transversal size of the scattering medium of a given thickness was determined experimentally. Unfortunately, the X-ray beam spectra were not published, making the detailed simulation difficult. A simulation of the data from Ref. 4, using their geometry and W/Al X-ray spectra calculated according to the method in Ref. [8], has been performed.
2. Point- and Line-spread functions The point spread function determines the significant size of the scattering medium region creating the image of a point. We have performed PSF measurements using a Senographe 2000D mammographic unit located at the National Institute of Cancerology in Mexico City. The experimental setup is presented in Figure 2a. The tungsten collimator is a 2 mm
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Figure 3 Transmitted photon energy spectrum for the geometry shown in Figure 1. Data in the figures (empty symbols) are from Ref. [28]. The spectrum is normalized to N0, the detected number of photons in the absence of the target.
PSF, LSF and S/P in mammography: GEANT4 validation
We have simulated the conditions of measurements reported in Ref. [12]. Here, besides the relatively small size of the scattering medium, the S/P determination method is based on the determination of the primary radiation by subtraction of the scattered radiation, a technique that, seemingly, doubles the systematic uncertainty.
Results 1. Forward angle scattering As the first test, the measured [28] energy spectrum of transmitted photons was compared with the simulated equivalent. As can be seen in Figure 3, the description of the data for a 2 cm thick polyethylene target, by use of both models of the code, is good. Small differences in the narrow structure description can be partially explained by coherent scattering mass-attenuation coefficient differences among the real experiment, the NIST data base, and the GEANT4 simulation. As it was expected, absorption coefficients in both GEANT4 models for the energy region 20–80 kV are similar [33], as displayed by the coincidence of both model results in Figure 3. Scattered photon energy distributions at two small angles are presented in Figures 4 and 5. It can be observed that the predictions from both GEANT4 models are not appropriate for quantitative descriptions. For mammography imaging simulations, this coherent scattering limitation in GEANT4 can affect the object edge profile shape description. GEANT4 predictions for low-energy scattered photons angular distributions can be compared with the data of Ref. 26, obtained by an experimental setup similar to that in Figure 1, and shown in the Figure 6 inset. In this experiment, the scattered photon flux relative to primary photons at the exit of the 4 cm thick Plexiglas phantom by use of I-125 Ka line
Figure 4 Energy distribution of photons scattered at 3 degrees. Symbols as in Figure 2.
Figure 5 Same as Figure 4, for 6 degrees.
Figure 6 Angular dependence of 27.3 keV monoenergetic photons scattered off a 4 cm thick PMMA plate as shown by the inset. Experimental data [26] (䊉), Monte Carlo: SIERRA [6] (dotted line), Chan & Doi [11] (solid line), the low-energy GEANT4 models described in the text (䊊 and 䊐) and experimental to simulation ratio (䉱).
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PSF, LSF and S/P in mammography: GEANT4 validation
photons (energy 27.3 keV) has been measured. Our results have been normalized at 50 degrees, where the contribution of coherent scattering is relatively small. The predictions of the “G4 Low Energy” model agree with the experiment within 5–15% depending on the angle, as shown by triangles in Figure 6. In Figure 6, the “G4 Penelope” predictions below
20 degrees are lower than “G4 Low Energy”, as already known [22]. 2. Point- and Line-spread functions Figure 7 presents our PSF data and simulation results. Since the simulation doesn’t include the detailed description of the photon detection process, the results have been corrected by multiple detection effects [15]. Two types of relative normal-
Figure 7 This work experimental and simulation PSF for a 4 cm thick PMMA phantom and 26 kVp Mo/Mo X-ray beam. Figure 9 Ratio of integrated PSF experimental and MonteCarlo values.
Figure 8 Ratio of experimental and Monte-Carlo PSF values shown in Figure 7, for two different normalizations, as explained in the text.
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Figure 10 Edge profiles as a function of phantom thicknesses. Data are from Refs. [7,12] and simulation was obtained by the “G4 low-energy” model.
PSF, LSF and S/P in mammography: GEANT4 validation
ization have been performed. One is by use of the experimental and simulation scattered radiation angular distribution integrals; the other (called “differential” normalization) uses values of the PSF angular distributions in the 45–50 degrees region, where the contribution form coherent scattering is small [10]. Figure 7 shows the simulated results normalized
by use of the angular distribution integrals. The ratios cdiff (r) = PSFexp (r)/PSFsim (r) of experimental data and simulation point-spread functions by use of the two normalization methods are presented in Figure 8. The almost perfect overlap among the data points in Figure 8 shows that the use of either type of normalization does not significantly change the quality of the description. The main shortcoming of the description is observed for radii smaller than 10 mm (i.e., scattering angles smaller than 15 degrees), where the difference between the experimental and simulation results can reach up to 50%. At large scattering angles, the statistical errors prevent drawing a conclusion about significant discrepancies between data and simulation. In practice, sometimes it is useful to compare the experiment and simulated PSF integrated over an area with radius size R, with an expression such as R
cdiff (R) = 兰 PSFexp (r) 0
/
R
兰PSFsim (r)dr. 0
Figure 11 LSF calculated from the edge profile data and simulations presented in Figure 10.
As it can be seen in Figures 8 and 9, the PSF integral values show better agreement between the calculation and the data; for R larger than 3 mm, the difference between the experimental and simulated integral PSF is less than 5%. This difference between data and simulation can also be seen in the profile description near the edge, where the smallangle region will have important contribution. Digitized data of profiles from [7, 12] are presented in Figure 10 together
Figure 12 S/P as a function of scattering medium lateral size, for two phantom thickness values. Data are from Ref. [4] and the simulation was obtained by the “G4 low-energy” model.
Figure 13 Ratios of simulation and experimental S/P as a function of the scattering medium thickness. Data are from Ref. [4] and the simulation was obtained by the “G4 lowenergy” model.
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PSF, LSF and S/P in mammography: GEANT4 validation
with our simulation results. To obtain LSF, the profile measurements and simulation have been fitted and their first derivatives, calculated. Results of LSF for both experimental and simulation for different phantom thickness are presented in Figure 11. As it can be seen from Figure 11, LSF extracted from experiment and simulation are symmetric functions and agreement between them is within 15%. The description of these data with other Monte Carlo programs [5] is within 8%.
3. Scatter-to-Primary ratio Data [4] and simulation results are presented in Figures 12 and 13. Figure 12 shows the dependence of S/P on the scattering medium transversal size, and the difference between experimental data and simulation increases as the scattering medium size decreases. This can be a consequence of the small-angle GEANT4 PSF description problem, mentioned
Figure 14 S/P dependence on phantom thickness and high voltage. Data are from Ref. [12] and the simulation was obtained by the “G4 low-energy” model. The line is a linear fit to the simulation results.
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PSF, LSF and S/P in mammography: GEANT4 validation
in Results section 2. The observed agreement in Figure 12, in the region of large scattering medium size, is better than 5%. This level of agreement can be explained by statistical errors and the probable existence of small systematic differences between the photon spectra. Figure 13 shows that the quality of the description doesn’t worsen with the increase of the scattering medium thickness, and the agreement remains within the 5% level. Concerning the consistency among different sets of S/P data, the measurements in Ref. [4] agree with the analogous independent data in Refs. [29, 38] within the experimental errors, but the comparison against others [6,12] shows differences that slightly exceed the statistical uncertainties. The S/P results of Monte Carlo calculations, together with the data [12], are shown in Figure 14 as a function of the scattering medium thickness for different kVp values. For all kVp values, the simulated S/P depend linearly on the thickness, a result already encountered in the Barnes and Bre-
zovich measurements [4]. The agreement between MonteCarlo and experiment for the S/P is presented in Figure 15. The ratios in Figure 15 almost don’t depend on the phantom thickness and on the average calculations values exceed the data by 10%, except at 24 kVp. The observed systematic difference between our calculations and data from Ref. [12] can be understood as related to the particular experimental conditions of this measurement. Unfortunately, the data uncertainties (only statistical) don’t permit to establish a thickness and kVp dependence in the comparison. One would expect the experimental systematic errors to increase as a function of scattering medium thickness.
Conclusions This work has shown that S/P mammography data obtained under accurately defined conditions can be simulated using GEANT4 with a discrepancy smaller than 5%.
Figure 15 Ratios of simulation and experimental S/P as a function of the phantom thickness and kVp. Data are from Ref. [12] and the simulation was obtained using the “G4 low-energy” model.
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PSF, LSF and S/P in mammography: GEANT4 validation
We have encountered a limitation in the small-angle region description by GEANT4, relevant for PSF and LSF calculations. At angles below 10 degrees, predictions show a sharper angular dependence, and therefore, the scatter reduction estimations for mammography are expected to be smaller than those in a real situation. This also implies that GEANT predictions for diffraction computed tomography will be only approximate. The comparison with forward angle data has shown that both GEANT4 models describe the measurements for X-ray beams typically used in mammography, better than 10% for angles above 10 degrees, and that “G4 Low Energy” is preferable compared with “G4 Penelope”.
Acknowledgments Authors thank medical physicist Flavio Trujillo and radiological technicians Silvia Ayala and Norma Becerril, at the National Institute of Cancerology, for their assistance in this research. This work has been partially funded by PAPIITUNAM IN 109302.
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[16] Grabski, V., Brandan, M.-E.: The influence of scattered photons on the accurate determination of microcalcification thickness in digital mammography, arXiv:physics/physics/0403041 [17] http://physics.nist.gov/PhysRefData/Xcom/html/xcom1.html [18] http://reddog1.llnl.gov/homepage.red/photon.htm [19] http://www.ge.infn.it/geant4/lowE/ [20] http://physics.nist.gov/PhysRefData/XrayMassCoef/ [21] http://wwwasd.web.cern.ch/wwwasd/geant4/G4UsersDocuments/ UsersGuides/ PhysicsReferenceManal [22] http://wwwasd.web.cern.ch/wwwasd/geant4/geant4.html [23] Jane, S., et al.: GATE: A simulation toolkit for PET and SPECT, Phys. Med. Biol. 49 (2004) 4543–4561 [24] Jiang, H., Paganetti, H.: Adaptation of GEANT4 to Monte Carlo dose calculations based on CT data. Med. Phys. 31 (2004) 2811–2818 [25] Kidane, G., et al.: X-ray scatter signatures for normal and neoplastic breast tissues. Phys. Med. Biol. 44 (1999) 1791–1802 [26] Klein, D.J.. et al.: Experimental and theoretical energy and angular dependencies of scattered radiation in the mammography energy range. Med. Phys. 10 (1983) 664–668 [27] Leclair, R.J., Johns, P.C.: A semianalytic model to investigate the potential applications of X-ray scatter imaging. Med. Phys. 25 (1998) 1008–1020 [28] Leclair, R.J., Johns, P.C.: X-ray forward-scatter imaging: Experimental validation of model. Med. Phys. 28 (2001) 210–219 [29] Moeckli, R., et al.: Influence of scatter reduction method and monochromatic beams on image quality and dose in mammography. Med. Phys. 30 (2003) 3156–3164 [30] Nelson, W.R., Hirayama, H., Rogers, D.W.O.: The EGS4 Code System. Report No SLAC-265 Stanford California (1985) [31] Paganetti, H.: Four dimensional Monte Carlo simulation of time dependent geometries. Phys. Med. Biol. 49 (2004) N75–81 [32] Paganetti, H., et al.: Monte Carlo simulation with time-dependent geometries to investigate effects of organ motion with high temporal resolution. Int. J. Radiat. Oncol., Biol., Phys. 60 (2004) 942–950 [33] Paganetti, H., et al.: Accurate Monte Carlo simulation for nozzle design, commissioning and quality assurance for a proton radiation therapy facility. Med. Phys. 31 (2004) 2107–2118 [34] Perez-Calatayud, J., et al.: Monte Carlo dosimetric characterization of the Cs-137 selection/LDR source: Evaluation of applicator attenuation and superposition approximation effects. Med. Phys. 31 (2004) 493–499 [35] Poon, E., Verhaegen, F.: Accuracy of the photon and electron physics in GEANT4 for radiotherapy applications. Med. Phys. 32 (2005) 1696–1711 [36] Rogers, D.W.O.: Monte Carlo techniques in Radiotherapy. Physics in Canada 58 (2002) 63–70 [37] Steven, L., et al.: Scatter/primary ratios for x-ray spectra modified to enhance iodine contrast in screen-film mammography. Med. Phys. 10 (1983) 866–870 [38] Yester, V., Barnes, G.T., King, M.A.: Experimental measurements of the scatter reduction obtained in mammography with a scanning multiple slot assembly. Med. Phys. 8 (1981) 158–162 Received 30. 01. 2006; accepted for publication 27. 02. 2006.
Correspondence to: Varlen Grabski Instituto de Fisica UNAM A.P. 20-364, 01000 Mexico D.F. C.P.: 01000 Tel.: 52 55 5622 5185 Fax: 52 55 5622 5009 e-mail: Varlen@[email protected]
PSF, LSF and S/P in mammography: GEANT4 validation Varlen Grabski1, Maria-Ester Brandan1, Cesar Ruiz-Trejo1, Yolanda Villaseñor2 1 Instituto de Física UNAM, A.P. 20-364, 01000 DF, Mexico 2 Instituto Nacional de Cancerología, Avda. San Fernando 22, Tlalpan, 14080 DF, Mexico
Abstract The main goal of this study was to validate the predictions of GEANT4, a Monte Carlo code originally developed for high-energy physics, for low-energy (10–40 keV) photon transmission and scattering through matter similar to biological tissue. We compared GEANT4 calculations with existing phantom data relevant for the mammographic imaging technique. This work showed that scattered-toprimary ratio data can be simulated using GEANT4 with a deviation smaller than 5%. At the same time, we encountered a limitation in the small-angle region description by the code, which is important for point- and line-spread function calculations. The comparison with forward angle data showed that the GEANT4 models, known as “G4 Low Energy” and “G4 Penelope”, describe the measurements for X-ray beams typically used in mammography better than 10% for angles above 10 degrees, and that “G4 Low Energy” is preferable to “G4 Penelope”. The results confirm the possible use of GEANT4 for the optimization of applications based on low-energy photon transmission and scattering.
Keywords: Monte Carlo simulation, GEANT4, validation, mammography, PSF, LSF, scatter-to-primary ratio
Introduction The detection of an object in a radiological image depends on the X-ray transmission and scattering properties. Thus, a detailed description of the photon scattering in the medium is of importance to fully understand the information contained in the image. Mammographic images are particularly difficult to interpret due to the small contrast between breast tissues and small size of structures of interest.
298
PSF, LSF und S/P in der Mammographie: GEANT4-Gültigkeitserklärung Zusammenfassung Unser Hauptziel war das Studium der Gültigkeit von GEANT4, einem Monte-Carlo-Programm, ursprünglich für die Hochenergiephysik entwickelt, im Vorhersagen der Emission und Streuung niederenergetischer Photonen (10–40 KeV) durch Materie, die biologischem Gewebe ähnelt. Wir haben die Simulationsergebnisse von GEANT4 mit vorhandenen Phantomdaten verglichen, die für die Mammographiebelichtungstechnik wichtig sind. Diese Arbeit hat gezeigt, dass die Verhältnisse von gestreuten zu primären Photonen mit Abweichungen kleiner als 5% mit GEANT4 simuliert werden können. In der Beschreibung der Kleinwinkelregion haben wir aber eine Limitierung des Programms gefunden, die wichtig für die Berechnung von Punkt- und Linienverbreitungsfunktionen ist. Der Vergleich mit Vorwärtswinkeldaten hat gezeigt, dass die GEANT4-Modelle, bekannt als „G4 Low Energy“ und „G4 Penelope“, die typisch in der Mammographie benutzte Messungen von Röntgenstrahlen über 10 Grad, besser als zu 10% beschreiben und dass das G4 „Low Energy“Modell dem „G4 Penelope“-Modell vorzuziehen ist. Diese Ergebnisse bestätigen den möglichen Gebrauch von GEANT4 für die Optimierung von Anwendungen, die auf niederenergetischer Photontransmission und -streuung basieren. Schlüsselwörter: Monte-Carlo-Methode, GEANT4, Gültigkeitserklärung, Mammographie, PSF, LSF, Streu-zu-Primärstrahl-Verhältnis
The optimization of the application, as well as the determination of different characteristics of a mammographic image can often be done by means of Monte Carlo (MC) calculations [36]. The choice of the appropriate Monte Carlo code essentially depends on the required accuracy for the given task. At present, a large selection of sufficiently good and complex programs [1, 3, 9, 30] exist, describing the experimental data with an accuracy of the order of several percent. For low-energy photon processes, the description of
Z. Med. Phys. 16 (2006) 298–306 http://www.elsevier.de/zmedphys
PSF, LSF and S/P in mammography: GEANT4 validation
the mass-attenuation coefficients above 10 keV photon energy is similar for all these codes [2, 35]. For Compton scattering attenuation coefficients, the difference among MC programs can reach up to 10% for elements with large Z values and photon energies around 10 keV. Below 10 keV, the discrepancy among codes in the description of coherent scattering mass-attenuation coefficients increases [35] as the energy decreases, due to differences between the XCOM [17] and EPDL [18] data bases. For mammography images, energies
Figure 1 Setup for the forward scattering simulations. PMMA represents an empty polymethyl metacrylate cylindrical volume around the 2 cm thick polyethylene target. HPGe are high-purity germanium detectors.
below 10 keV are less significant because of the initial spectrum absorption before reaching the detector. In addition, the description of the scattered radiation angular characteristics is a complicated task due to coherent scattering. Detailed validation studies of the coherent scattering angular characteristics in the low-energy region do not exist for the above mentioned codes [1, 3, 9, 30]. We must mention that besides the best known programs [1, 3, 9, 30], others exist, already reported in medical physics literature, that are good enough for low-energy photon processes, but not easy for the public use [5, 11, 13]. Among the enumerated MC codes, GEANT4 [1] is a toolkit for simulation of the particle passage through matter. A set of processes have been developed to describe the electromagnetic interactions of photons and electrons with matter down to 250 eV. GEANT4 offers advantages for its use: it is free, is relatively well documented, has great capabilities for describing difficult and time-dependent geometrical shapes [31, 32], is flexible to use for different physical models, and allows visualization of the elementary events. The main disadvantage of GEANT4 is to be slower than EGSNRC [35] and thus, to require a large CPU time for generation of the required amount of statistics for radiological images. Tests of GEANT4 describing low-energy electromagnetic processes have a rather brief history and are mainly connected with medical physics [2, 10, 23, 24, 31–36]. It is possible to find test results not yet published at the GEANT4 low-energy site [19].
Figure 2 Experimental and simulation setups for PSF (a), edge detection S/P and LSF (b), and beam stopping S/P (c).
299
PSF, LSF and S/P in mammography: GEANT4 validation
In mammography, the majority of the experimental results relate to integral characteristics, such as scatter-to-primary ratio (S/P) [4, 7, 12, 29, 38], and only a few measurements address differential characteristics, such as line spread function (LSF) [7, 12] and point-spread-function (PSF) [14]. In our opinion, these latter data can be more informative than the previous for the validation of the scattered radiation description by a given program. Also, there are few experimental data related to the low-energy photon forward scattering [25–28] for the 20–120 keV region, that can be used to test the small angle scattering description in a MC code. Our objective in this work is the validation of GEANT4 for 10–40 keV electromagnetic radiation, with a specific interest in determining the accuracy of predictions relevant for mammography [16].
Materials and Methods 1. Forward angle scattering An important and difficult part in the description of forward scattering is the coherent scattering dependence on the structure of the scattering medium. The accuracy of GEANT4 coherent scattering predictions can be checked against smallangle scattering data. Measurements of low-energy scattered photons in this angular region can be found in works of diffraction computed tomography (also called X-ray forwardscatter imaging) [25, 27, 28]. We have simulated the photon transmission using the experimental arrangements reported in [28]. Two setups were described in Ref. 28, having approximately equal separation (83.7 and 82.3 cm) from the focal spot of the X-ray tube to the target, and we have combined them into just one, shown in Figure 1, where all the geometrical sizes of the simulation arrangement are defined. For Xray photon generation, the measured spectrum for the transmitted photons from [28] is used. To recover the initial spectrum, the measurements were corrected by absorption in target and air, as well as by detector energy resolution and registration efficiency. Information on the chemical composition of materials and mass-attenuation coefficients was taken from the NIST database [20]. The simulation was performed using two models of GEANT4 version 4.6, “G4 Low Energy” and “G4 Penelope” [1]. All beam collimations after the target, as well as the solid angle and air absorption corrections, were performed during the data analysis process according to the experimental conditions [28].
thick disk with a 1 mm diameter hole. The scattering media are 4 cm thick polymethyl metacrilate (PMMA) plates with 20 × 20 cm2 transversal sizes. The X-ray tube high voltage was between 26 and 28 kVp, using the Mo/Mo anode/filter combination. The digital detector (~1913 × 2300 pixels, 100 μm sizes) is based on columnar CsI(Tl) scintillators. A GEANT4 simulation of the same experimental setup has been performed using the “G4 Low Energy” model. Edge profiles have been measured for different thicknesses and high voltages [5, 12]. The experimental setup for the edge profile measurements is presented in Figure 2b [12]. We have simulated this experimental setup for similar conditions. 3. Scatter-to-Primary ratio The S/P measurement has been the basic method, in the last 15 years, for the investigation of the scattered radiation influence on the quality of mammography images. Two main experimental methods, known as “beam stopping” (BS) [4] and “edge detection” (ED) [12], depicted in Figs. 2c and 2b, respectively, have been used. The work of Barnes and Brezovich [4] is one of the first and most accurate measurements of S/P carried out according to the BS method. In that work, the minimal transversal size of the scattering medium of a given thickness was determined experimentally. Unfortunately, the X-ray beam spectra were not published, making the detailed simulation difficult. A simulation of the data from Ref. 4, using their geometry and W/Al X-ray spectra calculated according to the method in Ref. [8], has been performed.
2. Point- and Line-spread functions The point spread function determines the significant size of the scattering medium region creating the image of a point. We have performed PSF measurements using a Senographe 2000D mammographic unit located at the National Institute of Cancerology in Mexico City. The experimental setup is presented in Figure 2a. The tungsten collimator is a 2 mm
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Figure 3 Transmitted photon energy spectrum for the geometry shown in Figure 1. Data in the figures (empty symbols) are from Ref. [28]. The spectrum is normalized to N0, the detected number of photons in the absence of the target.
PSF, LSF and S/P in mammography: GEANT4 validation
We have simulated the conditions of measurements reported in Ref. [12]. Here, besides the relatively small size of the scattering medium, the S/P determination method is based on the determination of the primary radiation by subtraction of the scattered radiation, a technique that, seemingly, doubles the systematic uncertainty.
Results 1. Forward angle scattering As the first test, the measured [28] energy spectrum of transmitted photons was compared with the simulated equivalent. As can be seen in Figure 3, the description of the data for a 2 cm thick polyethylene target, by use of both models of the code, is good. Small differences in the narrow structure description can be partially explained by coherent scattering mass-attenuation coefficient differences among the real experiment, the NIST data base, and the GEANT4 simulation. As it was expected, absorption coefficients in both GEANT4 models for the energy region 20–80 kV are similar [33], as displayed by the coincidence of both model results in Figure 3. Scattered photon energy distributions at two small angles are presented in Figures 4 and 5. It can be observed that the predictions from both GEANT4 models are not appropriate for quantitative descriptions. For mammography imaging simulations, this coherent scattering limitation in GEANT4 can affect the object edge profile shape description. GEANT4 predictions for low-energy scattered photons angular distributions can be compared with the data of Ref. 26, obtained by an experimental setup similar to that in Figure 1, and shown in the Figure 6 inset. In this experiment, the scattered photon flux relative to primary photons at the exit of the 4 cm thick Plexiglas phantom by use of I-125 Ka line
Figure 4 Energy distribution of photons scattered at 3 degrees. Symbols as in Figure 2.
Figure 5 Same as Figure 4, for 6 degrees.
Figure 6 Angular dependence of 27.3 keV monoenergetic photons scattered off a 4 cm thick PMMA plate as shown by the inset. Experimental data [26] (䊉), Monte Carlo: SIERRA [6] (dotted line), Chan & Doi [11] (solid line), the low-energy GEANT4 models described in the text (䊊 and 䊐) and experimental to simulation ratio (䉱).
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PSF, LSF and S/P in mammography: GEANT4 validation
photons (energy 27.3 keV) has been measured. Our results have been normalized at 50 degrees, where the contribution of coherent scattering is relatively small. The predictions of the “G4 Low Energy” model agree with the experiment within 5–15% depending on the angle, as shown by triangles in Figure 6. In Figure 6, the “G4 Penelope” predictions below
20 degrees are lower than “G4 Low Energy”, as already known [22]. 2. Point- and Line-spread functions Figure 7 presents our PSF data and simulation results. Since the simulation doesn’t include the detailed description of the photon detection process, the results have been corrected by multiple detection effects [15]. Two types of relative normal-
Figure 7 This work experimental and simulation PSF for a 4 cm thick PMMA phantom and 26 kVp Mo/Mo X-ray beam. Figure 9 Ratio of integrated PSF experimental and MonteCarlo values.
Figure 8 Ratio of experimental and Monte-Carlo PSF values shown in Figure 7, for two different normalizations, as explained in the text.
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Figure 10 Edge profiles as a function of phantom thicknesses. Data are from Refs. [7,12] and simulation was obtained by the “G4 low-energy” model.
PSF, LSF and S/P in mammography: GEANT4 validation
ization have been performed. One is by use of the experimental and simulation scattered radiation angular distribution integrals; the other (called “differential” normalization) uses values of the PSF angular distributions in the 45–50 degrees region, where the contribution form coherent scattering is small [10]. Figure 7 shows the simulated results normalized
by use of the angular distribution integrals. The ratios cdiff (r) = PSFexp (r)/PSFsim (r) of experimental data and simulation point-spread functions by use of the two normalization methods are presented in Figure 8. The almost perfect overlap among the data points in Figure 8 shows that the use of either type of normalization does not significantly change the quality of the description. The main shortcoming of the description is observed for radii smaller than 10 mm (i.e., scattering angles smaller than 15 degrees), where the difference between the experimental and simulation results can reach up to 50%. At large scattering angles, the statistical errors prevent drawing a conclusion about significant discrepancies between data and simulation. In practice, sometimes it is useful to compare the experiment and simulated PSF integrated over an area with radius size R, with an expression such as R
cdiff (R) = 兰 PSFexp (r) 0
/
R
兰PSFsim (r)dr. 0
Figure 11 LSF calculated from the edge profile data and simulations presented in Figure 10.
As it can be seen in Figures 8 and 9, the PSF integral values show better agreement between the calculation and the data; for R larger than 3 mm, the difference between the experimental and simulated integral PSF is less than 5%. This difference between data and simulation can also be seen in the profile description near the edge, where the smallangle region will have important contribution. Digitized data of profiles from [7, 12] are presented in Figure 10 together
Figure 12 S/P as a function of scattering medium lateral size, for two phantom thickness values. Data are from Ref. [4] and the simulation was obtained by the “G4 low-energy” model.
Figure 13 Ratios of simulation and experimental S/P as a function of the scattering medium thickness. Data are from Ref. [4] and the simulation was obtained by the “G4 lowenergy” model.
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PSF, LSF and S/P in mammography: GEANT4 validation
with our simulation results. To obtain LSF, the profile measurements and simulation have been fitted and their first derivatives, calculated. Results of LSF for both experimental and simulation for different phantom thickness are presented in Figure 11. As it can be seen from Figure 11, LSF extracted from experiment and simulation are symmetric functions and agreement between them is within 15%. The description of these data with other Monte Carlo programs [5] is within 8%.
3. Scatter-to-Primary ratio Data [4] and simulation results are presented in Figures 12 and 13. Figure 12 shows the dependence of S/P on the scattering medium transversal size, and the difference between experimental data and simulation increases as the scattering medium size decreases. This can be a consequence of the small-angle GEANT4 PSF description problem, mentioned
Figure 14 S/P dependence on phantom thickness and high voltage. Data are from Ref. [12] and the simulation was obtained by the “G4 low-energy” model. The line is a linear fit to the simulation results.
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PSF, LSF and S/P in mammography: GEANT4 validation
in Results section 2. The observed agreement in Figure 12, in the region of large scattering medium size, is better than 5%. This level of agreement can be explained by statistical errors and the probable existence of small systematic differences between the photon spectra. Figure 13 shows that the quality of the description doesn’t worsen with the increase of the scattering medium thickness, and the agreement remains within the 5% level. Concerning the consistency among different sets of S/P data, the measurements in Ref. [4] agree with the analogous independent data in Refs. [29, 38] within the experimental errors, but the comparison against others [6,12] shows differences that slightly exceed the statistical uncertainties. The S/P results of Monte Carlo calculations, together with the data [12], are shown in Figure 14 as a function of the scattering medium thickness for different kVp values. For all kVp values, the simulated S/P depend linearly on the thickness, a result already encountered in the Barnes and Bre-
zovich measurements [4]. The agreement between MonteCarlo and experiment for the S/P is presented in Figure 15. The ratios in Figure 15 almost don’t depend on the phantom thickness and on the average calculations values exceed the data by 10%, except at 24 kVp. The observed systematic difference between our calculations and data from Ref. [12] can be understood as related to the particular experimental conditions of this measurement. Unfortunately, the data uncertainties (only statistical) don’t permit to establish a thickness and kVp dependence in the comparison. One would expect the experimental systematic errors to increase as a function of scattering medium thickness.
Conclusions This work has shown that S/P mammography data obtained under accurately defined conditions can be simulated using GEANT4 with a discrepancy smaller than 5%.
Figure 15 Ratios of simulation and experimental S/P as a function of the phantom thickness and kVp. Data are from Ref. [12] and the simulation was obtained using the “G4 low-energy” model.
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PSF, LSF and S/P in mammography: GEANT4 validation
We have encountered a limitation in the small-angle region description by GEANT4, relevant for PSF and LSF calculations. At angles below 10 degrees, predictions show a sharper angular dependence, and therefore, the scatter reduction estimations for mammography are expected to be smaller than those in a real situation. This also implies that GEANT predictions for diffraction computed tomography will be only approximate. The comparison with forward angle data has shown that both GEANT4 models describe the measurements for X-ray beams typically used in mammography, better than 10% for angles above 10 degrees, and that “G4 Low Energy” is preferable compared with “G4 Penelope”.
Acknowledgments Authors thank medical physicist Flavio Trujillo and radiological technicians Silvia Ayala and Norma Becerril, at the National Institute of Cancerology, for their assistance in this research. This work has been partially funded by PAPIITUNAM IN 109302.
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Correspondence to: Varlen Grabski Instituto de Fisica UNAM A.P. 20-364, 01000 Mexico D.F. C.P.: 01000 Tel.: 52 55 5622 5185 Fax: 52 55 5622 5009 e-mail: Varlen@[email protected]