Development of a Monte Carlo Simulation Code and Its Test Results for Optimal Design of a Digital Radiographic System Based on a CMOS Image Sensor

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1 Journal of the Korean Physical Society, Vol. 46, No. 2, February 2005, pp Development of a Monte Carlo Simulation Code and Its Test Results for Optimal Design of a Digital Radiographic System Based on a CMOS Image Sensor Hyosung Cho Basic Atomic Energy Research Institute and Department of Radiological Science, Yonsei University, Wonju Manhee Jeong and Bongsoo Han Basic Atomic Energy Research Institute, Yonsei University, Wonju Sin Kim Department of Nuclear & Energy Engineering, Cheju National University, Jeju Bongsoo Lee School of Biomedical Engineering, Konkuk University, Chungju Byongrae Park Department of Radiological Science, Pusan Catholic University, Busan (Received 15 September 2004) We have developed a Monte Carlo simulation code, the so-called Monte Carlo Simulation for Digital Imager (MCSDI), using the Visual C ++ programming language for the optimal design of a digital radiographic system. The MCSDI code has emulated a variety of test conditions for X-ray energy distributions (bremsstrahlung and characteristic X-rays) and exposure levels, beam shapes (parallel or cone-shaped), and scintillator types and structures (Gd 2O 2S : Tb or CsI(Tl), and flat or columnar), and a variety of test phantoms. In this paper, we describe the image characteristics of a digital radiographic system based on a CMOS image sensor using the MCSDI code in terms of the contrast-to-noise ratio (CNR), the modulation transfer function (MTF), the noise power spectrum (NPS), and the detective quantum efficiency (DQE). This code is expected to be useful in designing the optimal components for a digital radiographic system with respect to the detector pixel size, the scintillator type and thickness, the tube voltage, the exposure level, and so on. PACS numbers: Mc; Wk Keywords: Monte carlo simulation, Digital radiography, Scintillator, X-ray beam, CMOS imager, CNR, MTF, NPS, DQE I. INTRODUCTION We have developed a Monte Carlo simulation code, the so-called Monte Carlo Simulation for Digital Imager (MCSDI), using the Visual C ++ programming language for optimal design of the digital X-ray image system based on a CMOS image sensor. In our design of a portable (battery-operated) digital X-ray image system, we consider a CMOS pixel array as a digital X-ray sensor owing to its much lower power consumptioncompared with a charge-coupled device (CCD), which allows bslee@kku.ac.kr; Tel: ; Fax: a portable digital X-ray image system to run longer, and its highly-integrated architecture, which also allows a system-on-chip (SOC) design and, thus, makes its manufacturing cost ultimately cheaper for a large-area imaging applications [1,2]. The MCSDI code has emulated a variety of test conditions, X-ray energy distributions (bremsstrahlung and characteristic X-rays), beam shapes (parallel or coneshaped), scintillator types and structures (Gd 2 O 2 S : Tb or CsI(Tl), and flat or columnar structure), and a variety of test phantoms. In the code, a 2D parallel grid is included to simulate general test conditions, and simulation algorithms, such as the interactions among X-ray beams, test phantoms, a grid, and a scintillator, and the behavior of lights generated in the scintillator and their

2 Development of a Monte Carlo Simulation Code and Hyosung Cho et al collection in the CMOS pixel array, were coded by using the Monte Carlo method. The scintillator thickness and the CMOS pixel pitch were set as 50 m and 48 m, respectively, and the pixel format was assumed to be Using the MCSDI code, we obtained X-ray images under various simulation conditions and evaluated their image qualities by calculating the contrast-to-noise ratio (CNR), the modulation transfer function (MTF), the noise power spectrum (NPS), and the detective quantum efficiency (DQE). The MCSDI code developed in this study may be applied to a variety of digital X-ray imaging systems and is expected to be useful for the design optimization of a digital X-ray imaging system by estimating the dependence of its image performance on various design parameters. II. SIMULATION CONDITIONS AND CODE ALGORITHM Fig. 2. Example of an X-ray energy spectrum for the RQA5 test condition from the SRS-78 program. Figure 1 shows the GUI of the MCSDI code, which includes a parameter input window, a used X-ray energy spectrum, a cross-sectional view of the imaging system, and the resulting image window. The total linear attenuation coefficients ( t ) for the used materials in the code were obtained from the web site of the National Institute of Standards and Technology (NIST) [3]. The target material for the used X-ray generator was tungsten, and the X-rays coming from the target were filtered by using an aluminum filter according to the RQA5 condition (2.5Al + 21Al(mmAl), HVL(mmAl) = 7.047, kv p = 74, E ave (kev) = 54) [4]. The X-ray spectrum mixed with both bremstrahlung and characteristic X-rays at a given test condition was obtained from the SRS-78 program [5]. Figure 2 shows an example X-ray energy spectrum for Fig. 3. Relative exposure measured with source-todetector distance (SDD), which obeys an inverse-square law well. Fig. 1. The GUI of the MCSDI code which includes a parameter input window, used X-ray energy spectrum, a crosssectional view of the imaging system, and the resulting image window. the RQA5 test condition calculated from the SRS-78 program. From the spectrum, the probability energy density function (PEDF) is obtained for the selection of an incident X-ray energy. In order to simulate a cone-beamtype X-ray generator, we restricted the incident X-ray angle, w z, to lie in the range from 1 (vertical direction to the test phantom) to 0 (horizontal direction to the test phantom). Here, w z is the z-component of the directional unit vector w. Figure 3 shows that the relative exposure as a function of the source-to-detector distance (SDD) obeys an inverse-square law well [6]. As scintillation materials,

3 -420- Journal of the Korean Physical Society, Vol. 46, No. 2, February 2005 both Gd 2 O 2 S : Tb and CsI(Tl) were used in the simulation, and both were 50-µm thick. The visible photons generated by the interactions of X-rays with the scintillators were assumed to be emitted isotropically, and the numbers of photons generated were E x and E x, respectively [7]. Here, E x is the X-ray energy deposited in the scintillation material in units of MeV. We also assumed that the main interactions between X-rays and other materials were limited to photoelectric absorption (PA) and Compton scattering (CS) and that other interactions, such as coherent scattering (CHS) and pair production (PP), were negligible due to their relatively low interaction probabilities for the diagnostic X-ray energy range. The details of the code algorithms are given below; 2. Selection of Interaction Type If the position of the next interaction is inside the test phantom, the interaction type should be determined. In the code, we use the simple rejection technique [8]: after generating a random number (ζ), if ζ is smaller than or p(e) equal to t (E), then the interaction type is considered to be photoelectric absorption on that position. Otherwise, Compton scattering is assumed to happen. Here, p (E) and t (E) are the linear attenuation coefficients for photoelectric absorption and total interactions, respectively. 3. Direction of Compton Scattered X-ray 1. Determination of Interaction Distance and Direction Incident or scattered X-rays in the test phantom may interact or be transmitted outside the phantom boundary. If this process is to be simulated, the interaction distance between the current position and the next interaction position must be calculated. If an X-ray having an energy E moves a distance s from the current position, the probability of having any interaction between s and s + ds, p(s)ds, can be expressed as p(s) = t (E)e t (E)s ds. (1) Integrating p(s) from s = 0 to infinity gives unity; thus, p(s) is the probability density function (PDF), and the cumulative distribution function (CDF) corresponding to this PDF is calculated as P (s) = s 0 p(s )ds = 1 e t (E)s. (2) If an X-ray interacts with the test phantom by photoelectric absorption, its energy is totally absorbed to the phantom. Otherwise, the X-ray loses a part of its energy and is scattered in another direction. Thus, we calculate a new direction, w(ω x, ω y, ω z ), and a new energy, E, for the scattered X-ray by using Klein-Nishina s formulaand an analytic formula, respectively [9]. Figure 4 shows both the angular distribution of the Compton scattered X-rays for three different X-ray energies, 10 kev, 140 kev, and 1 MeV, which were obtained by using the MCSDI code, and the forward scattering direction with the X-ray energy. The reduced energy of the scattered X-ray, E, is calculated analytically by using E = m 0 c 2 1 µ + 1/α, (5) where m 0 c 2 is the rest mass energy of the electron (0.511 MeV) and α is the energy of the incident X-ray in electric With the inverse transformation method [8], the next interaction distance, s, can be calculated: s = P 1 (ζ) = 1 ln ξ, 0 < ζ 1, (3) t where ζ is a random variable. If an X-ray is scattered at the position r 1 (x 1, y 1, z 1 ) with the direction w(ω x, ω y, ω z ), the next interaction position can be calculated to be x 2 = x 1 + sω x, y 2 = y 1 + sω y, z 2 = z 1 + sω z, (4) where ω x, ω y, and ω z are the x, y, and z components of the directional unit vector w. If r 2 (x 2, y 2, z 2 ) is outside the phantom boundary, then the calculation for the distance and the direction is stopped, and a new pass starts. Fig. 4. Angular distribution of the Compton scattered X- rays for three different X-ray energies, 10 kev, 140 kev, and 1 MeV, obtained by using the MCSDI code.

4 Development of a Monte Carlo Simulation Code and Hyosung Cho et al Fig. 6. Example of an X-ray image simulated at the RQA5 test condition for a 10-mm diameter, 4-mm-thick disk lead phantom to evaluate the CNR. Simplified flow chart for the MCSDI code algo- Fig. 5. rithm. Fig. 7. Relative noise level versus exposure at the RQA5 test condition for the Gd 2O 2S : Tb and the CsI(Tl). Both the abscissa and the ordinate are on a logarithmic scale. rest-mass energy units. Figure 5 shows a simplified flow chart for the MCSDI code algorithm. III. SIMULATION RESULTS AND DISCUSSION 1. Contrast-to-Noise Ratio (CNR) Noise in X-ray images means indeterminacy or inaccuracy in image signals and can be typically divided into two sources: quantum mottle and electronic readout circuit. The former source becomes manifest when the number of photons contributing to the X-ray image formation is quite a few whereas the detection probability of the image signal increases as the photon number increases. For code simplicity, the latter source was not considered in the current code, but will be included soon for more accurate image simulations. Figure 6 shows an example of an X-ray image simulated at the RQA5 test condition for a 10-mm-diameter, 4-mm-thick disk lead phantom to evaluate the contrastto-noise ration (CNR). The image contrast, C, is defined as the difference between the average object intensity (I disk ) and the average background intensity (I back ) divided by the background intensity: C = (I back I disk )/I back. (6) For a uniform X-ray exposure to the background, the background noise N is also definedas the ratio of the background standard deviation (σ) to the average background intensity (I back ): N = σ/i back. (7) Therefore, the CNR, defined as the ratio of the image contrast to the random fluctuation in the background intensity, is given by CNR = (I back I disk )/σ. (8) Figure 7 shows the image noise level measured as a function of exposure at the RQA5 test condition for the Gd 2 O 2 S : Tb and the CsI(Tl) scintillators. Note that

5 -422- Journal of the Korean Physical Society, Vol. 46, No. 2, February 2005 Fig. 8. Image noise level measured with exposure at the RQA5 test condition for the Gd 2O 2S : Tb and the CsI(Tl). Fig D presampled MTFs for the Gd 2O 2S : Tb, the CsI(Tl), and an ideal system (sinc(b f)). both the ordinate and the abscissa are plotted on a logarithmic scale. The simulated data were least-squares fitted to straight lines, as shown in Fig. 7, with slopes of 0.51 for the Gd 2 O 2 S : Tb and 0.43 for the CsI(Tl). Since the slopes of the straight lines agreed with the theoretical values expected for an imaging system whose noise is determined by quantum mottle, these simulation results may be taken to be quantum-noise limited over the complete dynamic range investigated [10]. Figure 8 shows the corresponding CNRas a function of exposure. The CNR values sharply increased as the exposure was increased up to 0.1 mr and then leveled off; the values were about 47 and 30 at an exposure level of 1 mr for the Gd 2 O 2 S : Tb and the CsI(Tl), respectively. technique [11] and is the Fourier transformation (FT) of the line spread function (LSF) which is the derivative of the edge spread function (ESF) from the edge images in Fig. 9 [12 14]: [ ] d MT F (f) = F T [ESF (x)]. (9) dx Figure 10 shows the 1D presampled MTFs for the Gd 2 O 2 S : Tb and the CsI(Tl) and for the sinc(b f) function of an the ideal system. Here, b is the pixel size, and f is the spatial frequency. The spatial frequencies measured at 10 % MTF values were about 6.0 and 6.5 lp/mm for the Gd 2 O 2 S : Tb and the CsI(Tl), respectively. 2. Modulation Transfer Function (MTF) The modulation transfer function (MTF) is used to characterize the image resolution properties of a digital X-ray imaging system and its components. The 1D presampled MTF was measured using the angled edge Fig. 9. Edge images of (a) the Gd 2O 2S : Tb and (b) the CsI(Tl) for extracting the edge spread function (ESF). 3. Noise Power Spectrum (NPS) The Noise power spectrum (NPS) is an estimate for the effect of quantization noise. The system NPS was measured from uniformly exposed radiographs by using a 2D Fourier analysis. In this method, the central portion of each image, except the image boundary, was divided into multiple non-overlapping regions of in pixel size. The image data for each region were converted to a relative noise unit, dividing the data by its mean value, and the noise spectrum of the relative fluctuation for each region was computed by using a 2D fast Fourier transformation (FFT). The spectra for all regions were averaged to obtain the overall 2D NPS. The NPSs in the horizontal, vertical, and diagonal directions were calculated by averaging the central ± 10 horizontal/vertical/diagonal lines from the 2D NPS [12 14]. Figure 11 shows the white images for each scintillator to obtain the 2D NPS, and Fig. 12 shows the normalized 1D NPS for the Gd 2 O 2 S : Tb and the CsI(Tl)

6 Development of a Monte Carlo Simulation Code and Hyosung Cho et al Fig. 11. White images of (a) the Gd 2O 2S : Tb and (b) the CsI(Tl) for obtaining the 2D NPS. Fig. 13. DQE curves calculated for the Gd 2O 2S : Tb and the CsI(Tl) at the RQA5 test condition and an exposure of 1 mr. at the detector input, the DQE can also be expressed, according to the IEC standard, as DQE(f) = MT F 2 (f) Φ. (11) NP S(f) Fig. 12. Normalized 1D NPS for the Gd 2O 2S : Tb and the CsI(Tl) at the RQA5 test condition and an exposure of 1 mr. at the RQA5 test condition and an exposure of 1 mr. The Gd 2 O 2 S : Tb-based image system was more sensitive to noise than the CsI(Tl)-based one. Because each scintillator has a different photon yield, the NPS curve for the Gd 2 O 2 S : Tb-based system has a steeper slope and a higher magnitude than the CsI(Tl)-based one. 4. Detective Quantum Efficiency (DQE) The detective quantum efficiencies (DQEs) of the systems were calculated from the measured MTF, NPS, and exposure, X, along with an estimated value of the ideal SNR 2 per mr, q, as described in Refs: 12 14: DQE(f) = G2 MT F 2 (f) Φ NP S(f) = S2 MT F 2 (f) Φ NP S(f),(10) where G is the detector gain and Φ is the X-ray quanta per area at the detector input. Note that the second expression in Eq. (10), where S is the detector signal, applies only if the detector response is linear and has zero intercept. When the MTF and the NPS are obtained from images and linearized to the quanta per unit area Figure 13 shows the DQE curves for the Gd 2 O 2 S : Tb and the CsI(Tl) at the RQA5 test condition and an exposure of 1 mr. The DQE(0) value for the CsI(Tl)-based system was about 0.66 and that for the Gd 2 O 2 S : Tbbased system was about Since the CsI(Tl) scintillator is less sensitive to noise than the Gd 2 O 2 S : Tb one, the CsI(Tl)-based system has a higher DQE than the Gd 2 O 2 S : Tb-based one. IV. CONCLUSION We have developed a Monte Carlo simulation code using the Visual C ++ programming language for optimal design of a digital X-ray image system based on a CMOS image sensor. We describe, in terms of the contrastto-noise ratio (CNR), the modulation transfer function (MTF), the noise power spectrum (NPS), and the detective quantum efficiency (DQE), the image characteristics of our digital radiographic system based on a CMOS image sensor by using the MCSDI code for the RQA5 test condition. The CNR values sharply increased as the exposure was increased up to 0.1 mr and then leveled off; the values were about 47 and 30 at an exposure level of 1 mr for the Gd 2 O 2 S : Tb and the CsI(Tl), respectively. The spatial frequencies measured at 10 % MTF values were about 6.0 and 6.5 lp/mm for the Gd 2 O 2 S : Tb and the CsI(Tl), respectively. The Gd 2 O 2 S : Tbbased image system was more sensitive to noise than the

7 -424- Journal of the Korean Physical Society, Vol. 46, No. 2, February 2005 CsI(Tl)-based one. The DQE(0) value for the CsI(Tl)- based system was about 0.66 and that for the Gd 2 O 2 S : Tb-based one was about This code is expected to be useful in designing optimal components for a digital radiographic system [15,16]. ACKNOWLEDGMENTS This study was supported by the Basic Atomic Energy Research Institute (BAERI) program of the Ministry of Science & Technology (MOST) under contract No. M REFERENCES [1] Scott T. Smith, Daniel R. Bednarek, Donald C. Wobschall, Myoungki Jeong, Hyunkeun Kim and Stephen Rudin, Proc. SPIE 3659, 952 (1999). [2] Manhee Jeong, M.S. thesis, Yonsei University, (2004). [3] tab4.html. [4] Ehsan Samei and Michael J. Flynn, Med. Phys. 29, 447 (2002). [5] Andrew J Reilly, Report 78 Spectrum Processor, IPEM, (1997). [6] Bruce H. Hasegawa, Medical X-ray Imaging (Med. Phys. Publishing Co., Madison, 1991). [7] H. K. Lee, K. S. Shin, T. S. Shu and B. Y. Choe, IEEE Trans. Nucl. Sci. 2, 1262 (1997). [8] I. Lux and L. Koblinger, Monte Carlo Particle Transport Method: Neutron and Photon Calculations (CRC Press, Boca Raton, 1990). [9] R. D. Evans, The Atomic Nucleus (McGraw-Hill, New York, 1955). [10] Walter Huda, Anthony M. Sajewicz and Kent M. Ogden, Med. Phys. 30, 442 (2003). [11] Ehsan Samei and Michael J. Flynn, Med. Phys. 25, 102 (1998). [12] Ehsan Samei, Michael J. Flynn, Harrell G. Chotas and Jamse T. Dobbins III, Proc. SPIE 4320, 189 (2001). [13] Carla D. Bradford and Walter W. Peppler, Med. Phys. 26, 27 (1999). [14] James T. Dobbins III, David L. Ergun, Loise Rutz, Dean A. Hinshaw, Hartwig Blume and Dwayne C. Clark, Med. Phys. 22, 1581 (1995). [15] H. S. Cho, S. M. Kang, M. H. Jeong, D. K. Hong, J. Kadyk and J. G. Kim, J. Korean Phys. Soc. 39, 980 (2001). [16] H. S. Cho, H. R. Yoon, S. H. Han and H. K. Kim, J. Korean Phys. Soc. 42, 56 (2003).