Computerized Tomography for Industrial Applications and Image Processing in Radiology March 15-17, 1999, Berlin, Germany DGZfP Proceedings BB 67-CD Paper 17 X-ray simulation and applications P. Hugonnard, A. Glière LETI - CEA - Technologies Avancées CEA Grenoble 17, rue des Martyrs F 38054 Grenoble Cedex 9 France Abstract This paper describes Sindbad, a X-ray simulation tool which has been developed in our laboratory. Firstly, we briefly present the general characteristics of the program and explain in more details the model implemented in order to simulate the radiation flux scattered in the examined sample. In a second part, the paper discusses an application of X-ray simulation to the design of a dual-energy computed tomography facility. Introduction The Monte Carlo method is the most regularly used numerical technique addressing the problem of X-ray matter interaction simulation. Its basic idea is to follow the path of individual particles (photons and electrons) by randomly sampling the probability law describing the real particle behavior. In order to reduce the statistical noise to an acceptable level, and to accurately correlate with experimental results, the number of photon histories must usually be large, hence leading to a heavy computational load, still generally not acceptable in an applied research or industrial application context. For this kind of problems, especially in the field of nondestructive evaluation (NDE), the necessity to have practical simulation tools at disposal lead to the development of alternative solutions based on analytical models, ray tracing techniques, computer aided design (CAD) of the examined sample and graphical user interface (GUI). The Federal Institute for Materials Research and Testing (BAM, Germany) has developed [1] a NDE simulation tool and coupled it to a CAD interface. Special attention has been placed on the realistic description of complicated shape defects. A scattered radiation model has been added in collaboration with the Institute of Applied Physics of Belarussian Academy of Science. The Center for Non-Destructive Evaluation (CNDE, USA) built along the years a complete and sophisticated simulation program family [2], featuring a X-ray source model, the CAD description of the inspected object (several CAD formats are accepted), a scattered flux model and a number of radiation detector models such as X-ray film and image intensifier. The Laboratoire d Electronique et de Techniques d Instrumentation (CEA-LETI, France) is involved in the development of high performance radiographic or DGZfP Proceedings BB 67-CD 103 Paper 17
tomographic facilities, radiation detectors design and radiation image processing techniques. In this context, the availability of a radiographic devices simulation tool is essential. The necessity to fully understand the implemented models, as well as the permanent evolution of our needs, lead, a few years ago, to the decision to develop our own simulation software package, which we call Sindbad [3]. This paper is organized as follows. We begin by a short description of the models used in Sindbad, emphasizing our recent work on scattered radiation modeling. Then we discuss an interesting application of the program to the design of a dual-energy computed tomography (CT) facility. Models The physics of the radiographic inspection process can be divided into three separate parts, namely the X-ray beam generation in the source, the beam interaction with the examined sample, and the imaging process (detection of the remaining photon flux and transformation into a measured signal). The implemented X-ray tube model, which can be used between 30 and 450 kv, semi-empirically simulates the physical phenomena involved in bremsstrahlung and characteristic photon production. It takes into account the anode angle and composition, the inherent and additional filtration and the photons exit angle. Experiments performed at LETI show an agreement better than 20% between calculated and measured doses. The uncollided flux simulation relies on the computation of the attenuation of the incident flux, binned in narrow energy channels, by the examined sample. This is performed by tracing rays from the source point to every pixel of the detector through the sample model, built with BRL-CAD [4], and by calculating the energy dependent attenuation due to the crossed materials. Detectors are modeled in two successive steps. The first one, common to all types of detectors computes the energy deposition in the sensing part of the detector using the energy absorption attenuation coefficients. The second one, specific to each type of detector, simulates the successive physical phenomena involved in the energy to signal transformation. For instance, in the case of a scintillating screen viewed by a CCD camera, it accounts for energy to light photons transformation, light photon absorption in the screen and optical coupling system, and photon to electron conversion in the CCD device. Details on the characteristics of our program have been previously reported [3]. We focus hereafter our attention on a recent improvement, namely the simulation of the radiation scattered in the examined sample. Other new features, such as a X-ray film detector model, a geometric collimator model, a modulation transfer function based blurring model and a pixelated gamma camera simulator are currently under development. Scattered flux model The scattered flux, which can cause significant degradation to the radiographic image, and hence is an important modeling issue, is usually estimated using build-up factors or more accurately computed by the means of Monte Carlo techniques. An alternative method has been used by Gray and coworkers [5] who modeled the incoherent (Compton) scattered flux by the means of a deterministic numerical procedure. DGZfP Proceedings BB 67-CD 104 Paper 17
Limiting ourselves to the computation of the singly scattered flux (i.e. the scattered photons which have experienced only one scattering), but extending the model to the simulation of coherent (Rayleigh) scattering and annihilation photons created after pair production events, we have followed a similar approach. Firstly, the examined sample is divided into a mesh of cubic volume elements (voxels). Material properties are assumed to be constant in each voxel. Then, the photon flux leaving the X-ray source, attenuated along its path to each voxel, is computed. The voxel center becomes in turn a scattered photon source, whose magnitude and directional intensity depends on the scattering interaction crosssection. Eventually, the possibly energy shifted, scattered photons are attenuated on their way to the detector pixels, where they deposit their energy. This process is repeated in nested loops on source energy channels, mesh voxels and detector pixels. The scattered flux incident to one detector pixel is given by : Φ s = µ ( E). dlb E dl d E µ ( ). a σθ (, ) b a 3 Φ0( E). e.. e dω. d V. de dω Energy Volume In the previous formula, the b and a indexes stand for before and after scattering, Φ 0 is the source photon flux, E and E are the photon energies before and after scattering, µ is the total attenuation coefficient, dσ/dω is the considered scattering phenomena differential cross-section, Ω and θ are the solid angle and scattering angle to the pixel. Each scattering phenomena involves a different processing strategy : The coherent scattering differential cross-section is computed with the Thomson formula. After a coherent scattering event, the photon energy remains unchanged. The incoherent scattering differential cross-section is computed with the Klein and Nishina formula. The scattered photon energy shift is computed with the Compton formula. The pair-production cross-sections is calculated from the pair-production attenuation coefficient. After a pair-production event, the outgoing positron is supposed to be locally annihilated and a couple of back to back 511 kev photons are emitted isotropically. Results of the model have been compared with Monte Carlo computations on the following validation case. An aluminum cylinder is placed between a monochromatic 122 kev photon source and a planar detector. The height of the cylinder is kept constant (30 mm) and its radius is varied. The test case geometry, as well as scattering profiles drawn from the detector s center, obtained with the EGS4 Monte Carlo program [6] and our model are presented on Figure 1. They show a good qualitative agreement. The remaining difference can probably be explained by multiple scattering events which are not accounted for in our model. DGZfP Proceedings BB 67-CD 105 Paper 17
X-ray source Scattered energy (arb. units) Aluminum cylinder 5 4 3 2 Detector 1 0 Radius (mm) 0 1 2 3 4 5 6 7 8 9 10 Figure 1 : Simulation conditions (left) and results (right). Comparison of our scattering model (smooth curves) with EGS4 computations (staircase curves). The pairs of curves are obtained with cylinders of height 30 mm and respective radii 1 mm (black), 15 mm (red) and 100 mm (blue). Applications As in others fields of physics, the initial goal of X-ray matter interaction modeling was to understand and explain experimental results. However, the computational burden has long been too important and the programs use too specialized for simulation to leave the academic research laboratories. Over the last decades, computers became more powerful, program interfaces more user friendly and dedicated simulation techniques appeared, leading to the emergence of application in the fields of NDE and medical imaging. X-ray simulation tools are nowadays successfully used during the design stage of radiographic facilities, when they help choose the fundamental parameters, such as X-ray tube voltage and filtration, detector choice, bench geometry, and predict performances of the future device. They are also helpful during evaluation and test of advanced radiation image processing techniques, such as CT or tomosynthesis, when they provide simulated data before the device is actually built. The application we focus on in the next paragraph shows the major role undertaken by simulation during an advanced imaging system design. In a near future, simulation tools will address industrial production applications, either during the design cycle of mechanical parts (inspectability evaluation and probability of detection, definition of the inspection scenario), or during the part production (automated flaw detection using synthetic images). Use of simulation during a dual-energy CT bench design Extensive use of X-ray simulation has been made during the design of the MACAC dual-energy CT bench at CEA-LETI. Three examples are presented hereafter. This 4mx4mx3m device, dedicated to the estimation of the matrix attenuation in radioactive waste drums in the 59.5 kev to1.4 MeV energy range, has been built and tested at CEA-LETI. It will soon be transferred to its end users. Results have been reported in [7]. Gamma spectroscopy measurements of activity in radioactive waste drums must be corrected for the attenuation due to the waste matrix, which depends on its density and effective atomic number. These parameters can be determined by the means of DGZfP Proceedings BB 67-CD 106 Paper 17
dual-energy CT. The principle is to successively record a low energy and a high energy projection sets, using two different tube voltages and filtration. After a calibration process, which allows to correct for beam polychromaticity, tomographic image reconstruction are performed, which produce an attenuation map at the required energy. Tube settings choice The low energy and the high energy measurements must be obtained with two non overlapping spectra, one which mean energy is located in the photoelectric domain of the examined materials and the other which mean energy is in the Compton domain. The photon flux must also remain compatible with the required signal to noise ratio and examination time. An application of the simulation has been to help to choose the correct X-ray tube voltages and filtration. The tube spectrum modeling, completed with materials attenuation simulations, led us to choose 80 kv with a 0.5 mm tungsten filtration for the low energy measurement and 350 kv with a 5 mm copper and 7 mm lead filtration for the high energy measurement (Figure 2). photon/sr/ma/s Figure 2 : Low (blue line) and high (red line) energy computed X-ray tube spectra (Mean energies : 62 kev and 290 kev). Influence of beam polychromaticity Dual-energy measurements rely on the assumption that, in the energy range of interest, the energy dependent attenuation coefficient µ(e), sum of a photoelectric and a Compton component, can be expressed as a function of the effective atomic number Z and the mass density r of the materials : µ ( E) = ρ. Z m. α( E) + ρ. β( E) In this formula, m is a constant and α(e) and β(e) are functions of the photon energy. The validity of this model has been checked for our experimental conditions using numerical regression performed over the attenuation database. The simulation code has then been used to quantify the effect of the beam polychromaticity, which has been shown to remain acceptable for the low atomic numbers (Z<20). kev DGZfP Proceedings BB 67-CD 107 Paper 17
Test of the tomographic image reconstruction The simulation has eventually been used to test the tomographic image reconstruction, adapted to the helical motion of the drum, before actually building the bench. The results, presented in Figure 3, have been obtained as follows. The test object is a cylindrical iron drum (450 mm diameter, 1 mm thickness) filled with cellulose, in which four cylinders (100 mm diameter) made of aluminum, silica, Plexiglas and polyvinyl have been inserted. The simulated detector is composed of 20 BGO scintillating crystals coupled with photo-multipliers, covering 35 on the arc of a circle. Thirty equally spaced projections have been computed with the two spectra. The low energy and high energy images have been obtained with a filtered backprojection reconstruction. The four inserted cylinders are clearly visible in both images when the drum wall can only be seen in the low energy image. Figure 3 :Reconstructed low energy (left) and high energy (right) images. The aluminum, silica, Plexiglas and polyvinyl cylinders are placed clockwise from the upper left of the images. Conclusion This paper presents the general principles used by Sindbad, a X-ray simulation tool based on analytical methods. It focuses on a recent improvement, namely the simulation of the radiation scattered in the examined sample. The program is routinely used in our laboratory to help design high performance X- ray devices. Among others applications, it has been used during the development the MACAC dual-energy CT facility, which is able to estimate the gamma ray attenuation in radioactive waste drums. Sindbad has continuously been improved since its first release. New features, such as a X-ray film detector model, a geometric collimator model, a modulation transfer function based blurring model and a pixelated gamma camera simulator are currently under development. Acknowledgements The authors thank A. Koenig and J. Nectoux for their help improving the program, C. Robert-Coutant and R. Sauze for their valuable assistance providing the dual-energy CT dataset, and P. Desproges "Dieu me tripote". DGZfP Proceedings BB 67-CD 108 Paper 17
References 1. C. Bellon, G.R. Tillack, C. Nockemann, L. Stenzel, "Computer simulation of X-ray NDE process coupled with CAD interface", Review of Progress in Non-destructive Evaluation, Vol. 16, 1997. 2. T. Jensen, J.N. Gray, "RTSIM: a computer model of real time radiography", Review of Progress in Non-destructive Evaluation, Vol. 14, 1995. 3. A. Glière, "Sindbad. From CAD model to synthetic radiographs", Review of Progress in Quantitative Nondestructive Evaluation, Vol. 17A, 1998. 4. P.C. Dykstra, M.J. Muus, " The BRL-CAD Package: An overview", USENIX, Proceedings of the Fourth Computer Graphics Workshop, Oct. 1987. 5. F. Inanc, J.N. Gray, "Scattering simulation in radiography", Applied Radiation and Isotopes, Vol. 48, 1997. 6. W.R. Nelson, H. Hirayama and D.W.O. Rogers, "The EGS4 code system", Stanford Linear Accelerator report, SLAC-265, 1985. 7. C. Robert-Coutant, V. Moulin, R. Sauze, P. Rizo, "Estimation of the matrix attenuation in heterogeneous radioactive waste drums using dual-energy computed tomography", Nuclear Instr. and Meth. in Phys. Res. Sect. A, Vol 422, pp 949-956, 1999. DGZfP Proceedings BB 67-CD 109 Paper 17