Abstract

A Monte-Carlo radiation transport simulation program, EGS4 Nova, and a Computer Aided Design software, BRL-CAD, have been coupled within the framework of Sindbad, a X-Ray Nondestructive Evaluation (NDE) simulation system, in order to simulate the images of the uncollided and scattered photon fluxes in a single NDE software environment.

We present an experimental validation performed in a 40 - 140 keV energy range, comparing simulation and experimental data acquired on a setup designed for 2D Dual Energy X-Ray absorptiometry, and equipped with a 2D digital flat panel. The agreement between experimental and simulated data is good if we correct the signal from scattering effects inside the detector.

1 Introduction

A Monte Carlo radiation transport simulation program, EGS4 Nova (1), and a Computer Aided Design software, BRL-CAD, have been coupled (2) within the framework of Sindbad (3-4), a X-Ray Nondestructive Evaluation (NDE) simulation system. The code allows to simulate images of the uncollided and scattered photon fluxes in a single NDE software environment, without having to switch a Monte Carlo code parameters set. The main restriction is that the scattering effects are taken into account only in the object under evaluation, not in the detector.

An experimental validation of the code has been performed within the 40-150 keV range. We chose as experimental set-up a 2D dual-energy X-ray absorptiometry system (5) which provides quantitative and accurate measurements for medical applications.

2 Description of the experiment

2.1 Experimental set-up
The X-ray tube delivers X-ray beams of 70 kV (LE) or 140 kV (HE), with appropriate filters for a good spectrum separation (see fig. 1 typical spectra). The LE spectrum is centered on photoelectric energies whereas the HE spectrum is centered on Compton energies for human tissues. The tube intensities are 7 mA and 3 mA respectively. The beam is collimated by a square collimator in order to match the detector size. The dose delivered by the beam was measured with an ionization chamber (6).

Fig 1: Typical double-exposure dual-energy source X-ray spectra (simulation).

The 2D detector is a digital flat panel which consists of a Lanex scintillator coupled to a grid of amorphous silicon photodiodes. The equivalent thickness of Lanex is 0.170 mm Gd₂O₂S. There is an aluminium filter for protection in front of the sensitive layer. The pixel size is 0.4 x 0.4 mm (512x512 pixels). The signal is coded on 16 bits. The image is acquired during several pulses. The equivalent duration is 0.8 s. The phantoms to be studied lay on a 8 mm thick Lucite bed (see fig. 2)

Fig 2: Experimental bench principle.

2.2 Experimental tests
Simple phantoms have first been used for validation : Lucite (density = 1.185) plates or steps of various thicknesses (13 to 25 cm) and a PolyVinyleChloride (density = 1.4) stair with six steps whose thicknesses range from 3.2 mm to 16 mm.

2.3 Total image acquisition and correction
Raw acquisitions cannot be used directly as “total image” proportional to X-Ray dose deposition for each pixel of the detector. An usual offset and gain correction has to be applied on the raw images. Reference flat field images and offset or dark images are first acquired. The standard correction consists in computing the ratio of the current raw image corrected from offset image, and the flat field acquisition also corrected from offset image then in multiplying the ratio image by an average value of the flat field image (corrected from offset).

A conversion coefficient between energy deposit and experimental signal is inferred from experiments (same coefficient 34 keV/pixel/grey level for LE and HE measurements).

2.4 Scatter image acquisition and correction
Scatter fraction is estimated for each acquisition with the beam-stop approach that was proposed in (7) by using the acquisition with a grid of lead balls or beam stops (see fig. 2). Several positions of the grid are required to sample the scattered image on the whole field of the detector. Scatter is estimated only locally behind each ball on the uniformity corrected images (as total image acquisition) in order to get rid of spatial gain variation in the detector and beam inhomogeneities.

Fig 3: LE and HE profiles across a 15 cm lucite step (with standard correction, and with actual correction).

Fig. 3 shows the result of the scatter measurement with the beam-stops on LE and HE beams with a 13 cm Lucite step. The upper dots (diamonds) are corrected with the standard correction method. However this method measures both object scatter and scatter inside the detector itself. As we are interested only in the object scatter measurements for the validation of the simulation, the internal detector scatter is removed with a method which estimates this scatter contribution as proportional to the straight beam. Results are shown on figure 3 where we can see that the final corrected scatter profiles (for object contribution) (square dots) is more continuous.

3 Simulation conditions

The LE and HE spectra are simulated using the usual Birch & Marshall model (8), with Tucker model (9) for the lines on the HE spectrum. The spectra are homothetically fit to the experimental dose measurements.

The scattering effects (Compton scattering and Rayleigh effects) are taken into account only in the object (phantom + collimator + bed). The secondary electrons are not followed. The fluorescence effect is not available in the present version of the code. The pixellated detector is simulated through its filter transmission and the stopping power of the Gd₂O₂S layer. The code computes the energy deposition in the sensitive layer of the detector using the energy absorption coefficients. Air is taken into account. Figure 4 shows the scene visualization, a facility of the code.

Fig 4: Scene visualization.

One can store either the total image or the uncollided, scattered and total images. A normalization is done on the MC images to be consistent with the actual number of photons in the spectrum. This is checked by comparison between the analytical image and the MC uncollided image (see the profiles on a Lucite step at HE on figure 5). The scattered image can be split into an image including all events with the first scattering and an image with events including several scatterings (see the decomposition on fig. 6 for the case of fig.5).

Fig 5: Simulated profiles on a 13 cm step HE: total, direct, and scattered. Y-axis : detector energy deposit (keV/pixel).

Fig 6: Simulated scattered profiles on a 13 cm step HE : 1: total, 2: 1st scattered, 3 : several times scattered. Y-axis : (keV/pixel).

4 Comparison simulation - experimentation

4.1 Step phantoms
4.1.1 Total profiles
Figure 7 shows the comparison between total experimental and simulated profiles for the 1^st step. The uncollided and scattered simulated profiles are also shown. The experimental edge is not very sharp, probably due to the blur of scattering inside the detector rather than due to misalignement.

Fig 7: Experimental total (with standard correction) and simulated total, uncollided and scattered profiles on a 13 cm Lucite step (LE (left) and HE(right)).

4.1.2 Scattered profiles
The agreement between simulated and experimental data is good, as for instance on fig. 8, the profiles across 13 and 23 cm Lucite steps, especially with a LE beam. If the central beam stop is aligned with the edge of the step, the measurement on this ball is not reliable. There is a slight discrepancy for the HE beam, as for the total profile.

Fig 8: LE (left) and HE (right) scattering profiles across 13 cm (step1) and 23 cm (step 3) Lucite steps.

4.2 Stair phantom
4.2.1 Total profiles
We can see on figure 9 the experimental profiles across the stair and the simulated profiles. The experimental profile has been corrected in the usual way. The simulated profiles are the MC uncollided, scattered and total ones.

Fig 9: Experimental total profiles and simulated (direct, scattered and total ) profiles at LE (up) and HE (down) across the stair.

4.2.2 Comparison on scattered profiles. Rayleigh effect
Figure 10 shows the comparison between simulated and experimental scattered profiles across the stair. Two simulated profiles have been shown, one without Rayleigh effect, one with Rayleigh effect to emphasize the amount of Rayleigh effect. Both of them take air into account.

Fig 10: Profiles on a PVC stair (LE and HE). Simulation with air and with and without Rayleigh effect.

5 Discussion and conclusion

A validation of the code was done at two energies and on two kinds of objects. The agreement between experimental and simulated data is good, when we add some correction taking scattering effects inside the detector into account. The same factor between simulated and experimental data was used on LE and HE data with a good result, especially on LE data. The slight discrepancy for HE data may come either from a unperfect model for the spectrum or from the detector response. To be complete, a full calibration of the detector should be done with the same experimental conditions.

Further validation will be done with more complex objects on this bench and at higher energy ranges on other set-ups. When fully validated, the code will be very valuable in a NDE and medical instrumentation laboratory context. Improvements to accelerate the code are under development or planned in a near future.

Acknowledgments

We thank JM. Dinten, M. Darboux, G. Gonon, C. Robert-Coutant, B. Buzaré for their help in experiments and in interpretation, and P. Hugonnard and J. Tabary for their contributions in simulation software.

References

1. J.C. Satterthwaite: http://www.nemc.org/nova.
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5. JM. Dinten, C. Robert-Coutant, M. Darboux, “Dual-Energy X-ray absorptiometry using a 2D digital radiography detector. Application to Bone Densitometry”, SPIE Med. Im., San Diego, USA, 2001.
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9. D.M. Tucker, G.T. Barnes, D.P. Chakraborty, “Semiempirical model for generating tungsten x-ray spectra.”, Med. Phys. 18 (2), 1991.

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