A framework of modeling detector systems for computed tomography simulations

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1 Home Search Collections Journals About Contact us My IOPscience A framework of modeling detector systems for computed tomography simulations This content has been downloaded from IOPscience. Please scroll down to see the full text. ( View the table of contents for this issue, or go to the journal homepage for more Download details: IP Address: This content was downloaded on 31/01/2016 at 22:24 Please note that terms and conditions apply.

2 17 th International Workshop on Radiation Imaging Detectors 28 June 2 July 2015, DESY, Hamburg, Germany Published by IOP Publishing for Sissa Medialab Received: September 25, 2015 Revised: November 23, 2015 Accepted: December 7, 2015 Published: January 29, 2016 A framework of modeling detector systems for computed tomography simulations1 H. Youn, a D. Kim, b S.H. Kim, b S. Kam, b H. Jeon, a J. Nam a and H.K. Kim b,c,2 a Department of Radiation Oncology, Pusan National University Yangsan Hospital, Yangsan , South Korea b School of Mechanical Engineering, Pusan National University, Busandaehak-ro 63beon-gil, Geumjeong-gu, Busan , South Korea c The Center for Advanced Medical Engineering Research, Pusan National University, Busandaehak-ro 63beon-gil, Geumjeong-gu, Busan , South Korea hokyung@pusan.ac.kr Abstract: Ultimate development in computed tomography (CT) technology may be a system that can provide images with excellent lesion conspicuity with the patient dose as low as possible. Imaging simulation tools have been cost-effectively used for these developments and will continue. For a more accurate and realistic imaging simulation, the signal and noise propagation through a CT detector system has been modeled in this study using the cascaded linear-systems theory. The simulation results are validated in comparisons with the measured results using a laboratory flat-panel micro-ct system. Although the image noise obtained from the simulations at higher exposures is slightly smaller than that obtained from the measurements, the difference between them is reasonably acceptable. According to the simulation results for various exposure levels and additive electronic noise levels, x-ray quantum noise is more dominant than the additive electronic noise. The framework of modeling a CT detector system suggested in this study will be helpful for the development of an accurate and realistic projection simulation model. Keywords: Computerized Tomography (CT) and Computed Radiography (CR); Detector modelling and simulations I (interaction of radiation with matter, interaction of photons with matter, interaction of hadrons with matter, etc) 1The original title, Effect of detector noise on low-dose tomography, with which the authors presented at the iworid 2015 conference, has been modified to more appropriately reflect the work done. 2Corresponding author. c 2016 IOP Publishing Ltd and Sissa Medialab srl doi: / /11/01/c01085

3 Contents 1 Introduction 1 2 Modeling framework 2 3 Materials and methods Phantoms and measurements Simulations and analysis 3 4 Results 4 5 Discussion and conclusion 7 1 Introduction Computed tomography (CT) technology has greatly evolved; for example, whole-body examinations within a couple of seconds and low-dose examinations with an effective dose less than 1 msv [1]. Those developments include both hardware (e.g, detector and scanner systems) and software (e.g., reconstruction algorithm), and are still ongoing to provide tomographic images with better conspicuity in further shorter scan time and lesser patient dose [2]. Imaging simulations have played great roles in the CT developments [3]. The concept of recent model-based image reconstruction [4] demands more accurate and realistic projection models [5], and the related low-dose CT simulations have become an important issue for the CT development [6 8]. In projections useful information is carved by x-ray photon interactions with patient anatomy but its interpretation can be interfered by noise associated with the stochastic nature of photon interactions (i.e., quantum noise). Imaging chain in a CT detector system, which typically consists of scintillator-coupled photodiode arrays and readout electronics [9], can further impair information interpretation from projections by increasing image noise. Electronics noise, which is usually uncorrelated with the x-ray interaction quantum noise, hence additive to the quantum noise, is an another quality degradation factor of projections and can cause artifacts in the reconstructed images [10]. Therefore, inclusion of the model describing the imaging chain of a CT detector system to imaging simulations can help the detector system design for a better CT as well as make projections more realistic. On the other hand, there has been little work on noise due to detector systems in the CT simulation developments. In this study, the authors present a simple framework describing the signal and noise transfers through a CT detector system based on the cascaded-linear systems theory. Similar to a previous study [5], the cascaded model is based on a pixel image (not a quantum image). However, the realization method of image noise is different from the method previously introduced. While in the previous study image noise was realized by re-distributing the pixel signals following 1

4 Figure 1. Block diagram describing the imaging chain of the CT detector: x-ray photon detection (α), x-ray-to-optical photon conversion ( β), optical photon spreading (κ), optical photon-to-electron conversion (η), and addition of electronic noise (σ add ). the probability density function (PDF) governing given stage, in the current study each pixel value is randomly determined by the governing PDF. This approach requires more computational efforts but it is expected to provide more reasonable results. The simulated projections and their reconstructed images are compared with those obtained from the measurements. Using the developed model, the effects of quantum and electronic noise on the reconstructed images are discussed. The modeling framework described in this study will be helpful to CT imaging simulations. 2 Modeling framework To describe the imaging chain of the CT detector, the cascaded linear-systems model was used, as shown in figure 1. Conventional cascaded linear-systems model tracks x-ray and secondary quantum (e.g., optical photons and/or electrons) interactions in a virtual detector volume or at a plane to account for correlation between interactions [11]. And then, before the stage describing the addition of electronic noise, the model usually performs the secondary quantum detection by pixels using the aperture integration operation. In this study, however, each stage is assumed to be a pixel image, and this assumption is probably reasonable because the CT detector array uses an anti-scatter grid and each scintillator pixel is surrounded by optical reflection layers [9]. q describes the number of x-ray photons attenuated through the patient. The cascaded model of the CT detector, as shown in figure 1, consists of the following stages: (1) binomial x-ray photon detection with a probability of α equal to the quantum efficiency of the scintillator, (2) Poissonian production of secondary optical quanta (Gaussian for a large number of optical photons) with an average gain of β secondary optical quanta per x-ray detection, (3) random secondary optical quanta relocation with a PDF κ, (4) binomial conversion of secondary optical quanta into electrons with a probability of η in photodiodes, and (5) addition of electronic noise (σ add in units of electrons). This cascaded model eventually results in the averaged pixel value d in units of electrons. Unlike the other processes, the quantum relocation was performed in a deterministic way: i.e., the convolution of detector spreading function, which could be characterized by the modulationtransfer function (MTF), with the image. The effect of this non-stochastic quantum relocation model on image noise will become severe when the detector MTF is poor. Excluding this process, each pixel value at each stage is determined by the random values as described above, hence the stochastic nature of interactions is well reflected into the resultant image. 2

5 3 Materials and methods 3.1 Phantoms and measurements Two voxel phantoms were considered; one was for microtomography (micro-ct) and the other for medical-ct. The phantoms were only different from their sizes. The medical-ct phantom was 10 larger than the micro-ct phantom. For the micro-ct voxel phantom, a commercial contrast phantom (QRM-MircoCT-HA, QRM GmbH, Germany) was considered to compare with the measurement results as described below. The phantom included five cylindrical inserts with the same diameter of 5 mm. The inserts were composed of hydoxyapatite with different densities (1.13, 1.16, 1.26, 1.64, and 1.90 g cm 3 ). The micro-ct simulation was performed for an additional phantom design which included eight different-size inserts ( mm in diameters) with the same density of 1.26 g cm 3. To validate the image noise model described in this study, the experimental micro-ct phantom was scanned by using the home-made laboratory micro-ct system with a flat-panel detector (FPD). The micro-ct system employed the object rotation during x-ray irradiation. The x-ray source (Series 5000 XTF5011, Oxford Instruments, Inc., U.S.A.) employed a tungsten anode and could operate up to the maximum power of 50 Watts. According to the manufacturer, the nominal focal-spot size was mm. The FPD (Shad-o-Box 1548 HS, Teledyne Rad-icon Imaging Corp., Sunnyvale, CA) used a Gd 2 O 2 S:Tb-based phosphor ( 68 mg cm 2 ) for x-ray detection, and the optical photons from the phosphor were detected by a photodiode array made by complementary metal-oxide-semiconductor (CMOS) process. The CMOS photodiode had mm sized pixels arranged in a format. Although the maximum frame rate for reading out x-ray images was 20 frames per second (fps), the detector was operated at 5 fps in this study. The applied tube voltage was 45 kvp. 3.2 Simulations and analysis q was determined using the analytic algorithms introduced in a previous study [5]. Tungsten x-ray spectral model was used. The image blur due to the focal spot with a finite size was considered by using a transfer function in the Fourier domain assuming that the geometrical focal-spot distribution followed the Gaussian distribution. For ray tracing (i.e., x-ray photon attenuation through a patient or a phantom), which occupied the most computation time, the thickness projections of internal materials consisting of the voxel phantom were first calculated. Energy-dependent linear attenuation coefficients were then assigned to the thickness projections using simple arithmetic operations. While the conventional ray tracing may require the total number of operations of N voxel (the number of phantom voxels) N pixel (the number of detector pixels) N bin (the number of energy bins), the method considered in this study requires approximately N voxel N pixel. The x-ray scatter in the phantom was not considered in this study. However, the x-ray scatter can be simulated with a relatively less effort by solving the analytic first-order transport equation with the assumption that the multiple scattering contributes only to the DC value in the spatial distribution [12]. The micro-ct simulation obtained 360 projections for a single scan whereas the medical-ct simulation obtained 1200 projections. For the medical-ct simulation, a single-slice CT detector array with 1-mm pitch pixels arranged in format was considered. A 5-mm thick Gd 2 O 2 S:Tb crystal with a density of 4.85 g cm 3 was considered as a detector. Assuming that an abdomen CT 3

6 imaging protocol was 120 kvp and 260 ma, the exposure was varied from 6.5 mas to 65 mas for low-dose imaging. To calculate β, the W -value, known as the average energy required to create a single optical photon, of kev for Gd2 O2 S:Tb scintillator was assumed. The photodiode quantum efficiency η was assumed to be 0.6 for both the micro- and medical-ct detector systems. The additive electronic noise of the micro-ct detector system was assumed to be 103 electrons, whereas that of the medical-ct detector system was varied from 102 to 104 electrons. For quantitative evaluations of image quality, signal-to-noise ratio (SNR) and contrast-to-noise ratio (CNR) for specified regions of interest (ROIs) and their neighboring background regions (BGNs) in the reconstructed images were respectively calculated by SNR = and d ROI σroi d ROI d BGN CNR = q, 2 2 σroi + σbgn (3.1) (3.2) where d and σ denote the pixel mean value and its standard deviation, respectively. 4 Results Figures 2(a) and 2(b) show the simulated and measured projections obtained for the micro-ct phantom, respectively. Respective pixel-value profiles extracted from the projections are compared in figures 2(c) and 2(d). Because the units of pixel values were different to each other (i.e., the number of electrons for simulation and digital numbers for measurement), the pixel values were normalized their own mean values. As shown in figures 2(c) and 2(d), the levels of pixel values and the degrees of their fluctuations were the almost same. Reconstructed images for the micro-ct phantom with respect to various exposure levels are shown in figure 3. The images are displayed with the levels of their mean values and the windows 4 Figure 2. Projection images obtained from (a) the simulation and (b) the measurement for micro-ct, and the profiles extracted from (c) the simulated and (d) measured projections.

7 of four times their standard deviations. Dark streaks between the inserts with higher densities were regarded as the photon-starvation artifacts. The simulations showed faster reduction speed of relative image noise with increasing exposure than the measurements. For more quantitative investigations between the simulation and measurement results, the pixel-value profiles and the SNR analysis are shown in figure 3. As expected from the reconstructed images, the SNR in the simulation images was more quickly enhanced with increasing exposure than that in the measurements. As shown in the pixel-value profile plots, the different SNR trends between the simulations and measurements were due to noise with exposure rather than signal. The reason can be explained by the scattered xray photons in the measurements. In the cone-beam geometry, detection of scattered x-ray photons emitted from the phantom is inevitable. The scattered x-ray photons are known to play a role as an additive noise in images. Therefore, they reduce the image SNR. The simulation results for the micro-ct phantom with different-size inserts for the exposure level of 0.18 mas are shown in figure 4. The insert visibility degraded with decreasing insert diameter. The SNR plot as a function of insert diameter describes this observation more quantitatively, as shown in figure 4. The largest insert exhibited a SNR value deviated from the overall tendency. Although the reason is unclear, the authors suspect the influence of cupping artifacts on the signal level. The simulation results for the medical-ct phantom for various exposure levels and additive electronic noise levels are shown in figure 5. The photon-starvation artifacts were much less apparent because of use of a higher kvp. For all simulation conditions, the insert 5 with the smallest density was not visually discernible. On the other hand, the insert 4 was hardly discernible for the exposure 5 Figure 3. Comparisons of the cross-sectional images obtained from the measurements and simulations for various exposure levels. For their quantitative evaluations, the plots describing the SNR and pixel-value profiles for the exposure levels of 0.02 mas and 0.18 mas are shown. The SNR was calculated in the region designated by the solid-line box and the profiles were extracted along the designated dotted circle.

8 Figure 5. Cross-sectional images reconstructed from the simulated projections for the medical-ct phantom for various exposure levels and electronic noise levels. The display level/window are respectively 0 HU/1600 HU. CNR plots calculated for three inserts (1, 2, and 3) and their neighboring regions as a function of additive noise level are also shown for the exposure levels of 6.5, 13, and 65 mas. level of 6.5 mas. The CNR of inserts was nearly independent of the electronic noise level when the exposure level was 65 mas. On the other hand, the CNR of the inserts 1 and 2 was decreased with increasing electronic noise for the the exposure levels less than 26 ma. At the exposure level of 6.5 mas, for example, the CNR of the insert 1 with the electronic noise level of 104 electrons was decreased by about 50%. Figure 6 shows the effect of the detector system model described in this study on the reconstructed image noise. Figure 6(a) was obtained without the detector system model whereas figure 6(b) included the detector system model in the simulations. Inclusion of the detector system model to the imaging simulations resulted in 50% in the SNR reduction [relative noise values were ± and ± for the central regions of figures 6(a) and 6(b), respectively]. 6 Figure 4. A cross-sectional image obtained from the micro-ct simulation for a phantom with different-size inserts and a graph describing the SNR values calculated for each insert. Error bars indicate the average standard deviation of the calculated SNR values for 12 slices.

9 5 Discussion and conclusion For the quantum relocation, this study adopted the image resolution-modification routine developed by Saunders and Samei [13]. This method was deterministic and basically shared the convolution operation, because the oversampled pixel image, to avoid sampling effect, was blurred by the detector MTF in the Fourier domain and then the blurred image was reduced to the original image format. However, it is known that use of the convolution integral underestimates noise in the blurred image [14]. This problem can be remedied by redistributing or relocating quanta according to the probability density distribution describing the blur [15]. Because the model described in this study is based on the pixel image not quantum image, the true quantum relocation could not be performed. Image noise in CT mainly consists of quantum noise due to stochastic nature of x-ray photon interactions and additive electronic noise. The latter may have a minor effect for the conventional CT routine, but its effect will become significant for the low-dose CT, as demonstrated in this study. It has been reported that for similar levels of noise in patient images, CT with a low-noise integrated detector system could reduce the patient dose by 20% compared to that with a conventional detector system with distributed electronics [16]. An experimental phantom imaging study (a 30-cm phantom scanned using 80 kvp) has showed that the low-noise detector system resulted in up to 50% in dose reduction to achieve equivalent image noise with the conventional detector system, or equivalently 40% reduction in noise [10]. Therefore, imaging simulation considering noise from a detector system is very crucial for the development of low-dose CT. Depth-dependent interaction of x-ray photons within a scintillator and its stochastic nature at the corresponding depth can cause an additional noise [17], known as the Lubberts effect [18]. This Lubberts effect usually results in the increase of noise-power spectral densities at higher spatial frequencies. In addition, secondary x-ray photon (i.e., scattered/fluorescent x-ray photon) interactions [19] and random optical photon transports [20] within a scintillator can give rise to variations in the measured signal, which was first identified by Swank [21]. For a more realistic simulation, these Lubberts effect and the Swank noise factor should be considered in the simulations. As shown in figure 6, this study showed that variations in signal transfers through the detector system were not negligible in the CT imaging simulations. On the other hand, the simulation method introduced in this study is computationally expensive. The binomial stages, such as x-ray quantum detection (α) and optical-to-electronic quantum conversion (η) stages, require relatively 7 Figure 6. Comparison of the reconstructed images for the medical-ct phantom (a) without the detector system model and (b) with the detector system model (with electronic noise of 103 electrons) for the exposure level of 130 mas. Insets are the enlarged views for the regions indicated by the boxes.

10 large computation times because each pixel-signal value is determined by counting the number of quanta with given conversion efficiencies. For generating a single projection, the elapsed computation times with a single-core PC (2.4-GHz CPU, 16-GB memory, and 64-bit operation system) were and 0.63 seconds for the micro- and medical-ct applications, respectively. Considering the complete CT acquisitions, larger computational efforts are required. Because the algorithms can be readily parallelized, however, the computation time is expected to be much reduced by using the graphics processing units or the parallel computers. Otherwise, our previous method [5], which re-distributes pixel signals using a governing PDF at a given signal-transfer stage in the detector system, may be an alternative because the previous method shows a SNR difference less than 10% compared to the method introduced in this study. For a more realistic CT simulation, signal and noise propagation through a CT detector system has been modeled using the cascaded linear-systems theory. The simulation results were validated with the experimental results using the laboratory micro-ct system, and the difference between them was reasonably acceptable. Although quantum noise dominantly affected the contrast and noise performance, the effect of electronic noise level was not negligible to the contrast and noise performance. This study will be useful to an accurate and realistic projection model development including the better design of CT detectors. Acknowledgments This work was supported by the National Research Foundation of Korea (NRF) grants funded by the Korean governments (MSIP) (No. 2013M2A2A and No. 2014R1A2A2A ). References [1] M.M. Lell, Evolution in computed tomography: The battle for speed and dose, Invest. Radiol. 50 (2015) 629. [2] G. Wang et al., An outlook on x-ray CT research and development, Med. Phys. 35 (2008) [3] W.P. Segars, Realistic CT simulation using the 4D XCAT phantom, Med. Phys. 35 (2008) [4] J. Nuyts et al., Modeling the physics in the iterative reconstruction for transmission computed tomography, Phys. Med. Biol. 58 (2013) R63. [5] H. Youn et al., Physics-based modeling of computed tomography systems, Proc. SPIE 9412 (2015) 94122N. [6] S. Žabić et al., A low dose simulation tool for CT systems with energy integrating detectors, Med. Phys. 40 (2013) [7] Muenzel et al., Validation of a low dose simulation technique for computed tomography images, PLoS One 9 (2014) e [8] C.W. Kim and J.H. Kim, Realistic simulation of reduced-dose CT with noise modeling and sinogram synthesis using DICOM CT images, Med. Phys. 41 (2014) [9] H. Youn et al., Optical crosstalk in CT detectors and its effects on CT images, Proc. SPIE 9033 (2014) 90334V. 8

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