Original article
A new PET resolution measurement method through Monte-Carlo simulations George E. Karpetasa, Christos M. Michailb, George P. Fountosb, Ioannis S. Kandarakisb and George S. Panayiotakisa Objective The aim of this study was to propose a novel method for image quality assessment in PET scanners through estimation of the modulation transfer function (MTF) of a plane source. The simulation was implemented using the previously validated Monte-Carlo model. A comparison of the proposed method with the more traditional technique, based on a line source, was also performed. Materials and methods The Geant4 application for tomographic emission (GATE) Monte-Carlo package was used for model development, and reconstructed images were obtained using software for tomographic image reconstruction (STIR) with cluster computing. A novel plane source consisting of a radioactive (18F-fluorodeoxyglucose) thin-layer chromatography plate was simulated (total source activity: 44.4 MBq) to assess image quality through the MTF. All images were reconstructed with the threedimensional filtered back projection (FBP3DRP) and ordered-subsets expectation maximization (OSEM) reprojection algorithms. Results The MTFs obtained using ordered-subsets expectation maximization show, in all cases, that higher frequencies are preserved compared with those obtained
Introduction Over the last few years functional nuclear medicine imaging has been further improved by the introduction of combined PET-computed tomography (PET/CT) scanners. The imaging performance of PET/CT scanners can be accurately modeled using Monte-Carlo simulation packages with the aim of designing high-quality scanners for improved image quantification. An open-source extension of the Geant4 [1] Monte-Carlo toolkit was the Geant4 application for tomographic emission (GATE) package, which was developed by the OpenGATE collaboration [2]. The overall purpose of this study was to propose a novel method for the assessment of the image quality performance of PET systems and particularly to predict the modulation transfer function (MTF) through the line spread function (LSF) of a plane source. To this aim, the GATE Monte-Carlo package was used in combination with the software for tomographic image reconstruction (STIR, version 2) to simulate: (i) a novel highly uniform 18 F-fluorodeoxyglucose (18F-FDG) plane source, based 0143-3636 © 2014 Wolters Kluwer Health | Lippincott Williams & Wilkins
using the FBP3DRP. In addition, the plane source method is less prone to noise than the conventional line source method (SD = 0.0031 and 0.0203, respectively). Conclusion The thin-layer chromatography-based plane source presented requires materials commonly found in a clinical environment and could be used to assess image quality in nuclear medicine departments and to further develop PET and single-photon emission computed tomography scanners through Monte-Carlo simulations. Nucl Med Commun 35:967–976 © 2014 Wolters Kluwer Health | Lippincott Williams & Wilkins. Nuclear Medicine Communications 2014, 35:967–976 Keywords: GATE, modulation transfer function, PET, plane source, software for tomographic image reconstruction a Department of Medical Physics, Faculty of Medicine, University of Patras, Patras and bDepartment of Biomedical Engineering, School of Technological Applications, Technological Educational Institute (TEI) of Athens, Athens, Greece
Correspondence to Ioannis S. Kandarakis, PhD, Department of Biomedical Engineering, School of Technological Applications, Technological Educational Institute of Athens, Egaleo, 12210 Athens, Greece Tel: + 30 10 5385 375; fax: + 30 10 5910 975; e-mail: [email protected] Received 17 December 2013 Revised 6 April 2014 Accepted 13 May 2014
on a thin-layer chromatography (TLC) plate, to obtain reconstructed plane source images and (ii) a conventional 18 F-FDG line source, to obtain the point spread function (PSF) of line source reconstructed images, for comparison. In the past few years, ongoing work on STIR reconstruction for large commercial PET scanners has been carried out [3–9]. None of these, however, simulate the GE Discovery ST scanner that is used in this study. In addition, PET image quality metrics have not been previously studied in terms of MTF by estimating the LSF of a plane source. To evaluate the performance of PET scanners, the PSF in a slice profile has traditionally been used [10,11]. The full width at half maximum (FWHM) of this function, which is used to measure the spatial resolution, lacks the possibility for complete system characterization and needs to be improved, as different PSF shapes may show equal FWHM values [12]. The response of the system to the incident signal amplitudes can be described by the MTF, which expresses the system’s response in the spatial frequency domain by taking the Fourier transform of the corresponding PSF from a reconstructed cross-sectional image. DOI: 10.1097/MNM.0000000000000151
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from the STIR software. The MTF was also assessed, in lines passing through the central axis of the PET scanner, by placing the plane source 3° to horizontal (parallel to coronal) and 3° to vertical (parallel to sagittal), allowing estimation from the center to the edges of the plane source. The proposed plane source phantom method, simulated in this work, serves as a useful tool that can be used in quality control procedures and also to characterize the performance of nuclear medicine imaging systems.
Fig. 1
Detector ring End shielding 88.6 cm
Crystal block BGO crystal
Module
Materials and methods Geometry of the modeled PET scanner
12
24 rings
6
PET scanner geometry.
Precise and accurate determinations of MTF are important for comparing the effects of different scan and reconstruction parameters, for comparison between different PET scanners, and especially for evaluating the accuracy of size and density measurements of fine details in medical images [13]. The use of the LSF for determining the MTF in tomographic imagers was initially introduced by Boone who applied this method for the evaluation of CT scanners [14]. This method is robust to aliasing when used for MTF calculation and is more resilient to noise because of greater data averaging when compared with the conventional point source method [14]. Fountos et al. [15] recently introduced a similar method for single-photon emission computed tomography (SPECT) scanners by immersing an Agfa MammoRay HDR Medical X-ray film in a solution of dithiothreitol/Tc-99m(III)-DMSA to obtain the MTF through the plane source method. Building on the work of Fountos and colleagues, this study introduces a plane source phantom to estimate the MTF through the LSF by simulating a thin-layer chromatography (TLC) plate, which can be implemented by a layer of silica gel on Al foil substrates, immersed in an 18 F-FDG bath solution. The idea of simulating TLC films as a plane source in PET imaging was first introduced by Heckathome et al. [16]. For comparison purposes, the MTF was also estimated by simulating a conventional 18F-FDG line source. Image quality was assessed by evaluating reconstructed images obtained
The PET scanner modeled in this study is the Discovery ST PET/CT, incorporating bismuth germinate oxide (BGO) crystals with dimensions of 6.3 × 6.3 × 30 mm in the tangential, axial, and radial directions, respectively (Fig. 1). The crystals were assembled into blocks of 6 × 6 crystals. Each block was coupled with a photomultiplier tube consisting of four square channels and is assembled in modules consisting of eight blocks (2 × 4) each. The detector ring finally comprises 35 modules – that is, 280 crystal blocks or 24 rings of 420 crystals (for a total of 10 080 BGO crystals). The dimensions of the ring are an 88.6 cm diameter, with 15.7 cm axial and 70 cm transaxial fields of view (FOVs). The scanner is designed to acquire images in both twodimensional (2D) and three-dimensional (3D) modes. In the 2D mode, collimation between image slices is achieved with retractable tungsten septa (54 mm long and 0.8 mm thick), which are used to reduce scattering, and every image plane counts events from ± 5 crystal rings (high-sensitivity mode). In the 3D mode, the septa are absent and the system allows oblique lines of responses with a maximum difference of 24 rings. The energy window width in both cases was set from 375 to 650 keV with a coincidence timing window of 11.7 ns. Physics processes, signal, and coincidence processing
GATE uses the standard and low-energy Geant-4 packages to simulate electromagnetic processes [17]. In this study, the standard energy package was used to model the photoelectric and Compton interactions and the low-energy package was used to simulate the Rayleigh interactions. To obtain a more realistic simulation, the positron range, the acolinearity effects, and the depth of interaction were taken into account, as all of these effects contribute to loss of resolution. X-rays and secondary electrons are not tracked, to speed up the simulation using 1 GeV for both X-rays and δ-rays with an electron range up to 30 cm. In every BGO crystal of the detector block, a Gaussian energy blur is applied with an average energy resolution of 17%, referenced at 511 keV. The quantum detection efficiency of the crystals was found to be 0.94 at 511 keV [18,19]. Thereafter, a 300-ns dead time value was applied on the single events in the BGO crystal [20,21] using a paralysable Deadtime
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A new PET resolution measurement method Karpetas et al. 969
module [22]. The sinogram output file (.ima), obtained from the ECAT system, was used by STIR as the input file for the reconstruction of the simulated plane source image. All the evaluations in this study were performed on the center slice of the reconstructed images. All simulations were performed using a computer cluster with 12 dual-core Intel(R) Xeon(TM) CPU 3.00 GHz processors (Supermicro SuperServer 6015B-UR/NTR, San Jose, California, USA).
purposes with the 3D OSEM reprojection algorithms [23–26]. The sinogram was defined by 47 segments, bin size 0.3195 cm, 221 arc-corrected and 249 non-arccorrected bins, span 3, and mashing 1. The images were obtained using STIR with perfect scatter rejection. Attenuation correction was performed by applying the attenuation correction factors of the created attenuation map on the reconstructed image [27]. Line source phantom simulation
Simulation of the MTF test object Plane source phantom simulation
The plane source, which is introduced in this study following the works of Boone [14] for CT and Fountos et al. [15] for SPECT systems, is based on the excellent binding of 18F-FDG to TLC plates. The plate of the plane source was implemented as a layer of silica gel on Al foil substrates (Al density 2.7 g/cm3). The dimension of the TLC plate was 5 ± 10 cm2, with a total source activity of 44.4 MBq (18F-FDG; Fig. 2). The total source thickness was 145.58 μm (Al thickness 102.1 μm and silica thickness 43.38 μm). The MTF test object (plane source; i.e., the radioactive plate) was simulated within a phantom, consisting of two semicylindrical polyethylene blocks with a 20 cm diameter and a 70 cm length, in the horizontal (parallel to coronal) and vertical (parallel to sagittal) directions. From the three colored cross-sectional lines (Fig. 2), the LSFs can be obtained for MTF estimation in three planes, in lines passing though the central axis. The plane source was also simulated with a dimension of 18 × 10 cm2 to investigate the effect of the field size on the MTF of the transaxial FOV.
To simulate the thin line source, the following procedure was followed: a cylindrical glass capillary with a 1 mm internal diameter, a 2 mm external diameter, and a 4 cm length was modeled [14]. The radioactivity of the line source occupies 3 cm of the 4 cm glass capillary. The source was simulated passing through the center of the FOV, in the axial direction. The line source phantom was filled with 18F-FDG (activity 0.37 MBq). For the purpose of the present study and to obtain an appropriate simulation that could be reproducible in clinical practice, the capillary tube was simulated inside the 76–823 PET/SPECT Performance Phantom (Fluke Biomedical, Everett, Washington, USA), filled with water. The dimensions of the phantom are as follows: internal diameter 20.3 cm, external diameter 21.59 cm, and length 30.5 cm (Fig. 3). A transverse slice image of the line source was acquired from STIR after reconstruction of the sinogram data with the 3D FBP (FBP3DRP) and with the OSEM reprojection algorithms [25]. Fig. 3
Plane source images were acquired from STIR, after reconstruction of the arc-corrected sinogram data with the commonly used Kinahan and Rogers three-dimensional filtered back projection (FBP3DRP) and for comparison 3 cm Fig. 2
21.59 cm
30.5 cm 1cm
Simulation of the plane source for the MTF measurement (Left). (a) The source is placed horizontally; transverse and sagittal lines for the MTF calculation (Right). (b) The source is placed vertically (parallel to sagittal); transverse and coronal lines for the MTF calculation. MTF, modulation transfer function.
Line source phantom simulation for the measurement of the MTF through PSF. The radioactivity of the source occupies 3 cm of the glass capillary. MTF, modulation transfer function; PSF, point spread function.
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defining the rectangular edges. ix, iy are the pixel coordinates in the horizontal and vertical axes, respectively, in the transverse, sagittal, or coronal image slices, respectively, of Fig. 2, ranging as follows: x1 ≤ ix ≤ x2, y1 ≤ iy ≤ y2 [28].
Fig. 4
(x1, y2)
The average LSF profile was calculated as follows [28]: G ix ; iy
y2 x2 P P
(x2, y2)
LSF ðxÞ ¼
ix ¼x1 iy ¼y1 y2 x2 P P
(x1, y1)
ð1Þ 1
ix ¼x1 iy ¼y1
(x2, y1) Schematic representation of the line profile selection.
Modulation transfer function
In addition to the commonly used FWHM from slice profiles of point source images, image quality was further assessed in terms of the spatial frequency dependent MTF. MTF was obtained in lines passing through the central axis of the PET scanner; by placing the plane source horizontally, transverse and sagittal images of the source can be obtained. In these images the source appears as a line. From these lines the LSF can be calculated. By changing the orientation of the plane source from horizontal to vertical, a coronal slice image of the plane source can be obtained, in which the source will appear as a line (Fig. 2). In this way the MTF of a PET scanner can be estimated in three dimensions.
where ξ = tan(θ), ix = iy, and θ is the angle between the line image and the horizontal or vertical axis. In this study, the MTF of the PET scanner was estimated by averaging the line profiles across the length of the plane source transverse image (defined by X1, X2 in Fig. 4). Further, the spatial variation in the MTF was investigated at radial offsets from the center to the edge of the large plane source, successively in 2 cm spaces, allowing the investigation of the image resolution off center, in a specific rectangular region of interest inside the FOV. This is one of the advantages of the present method, as compared with the conventional line source method, as spatial resolution of a PET scanner can be fully investigated from the center to the edges of the FOV, with a single source. The average LSF was fitted using four different functions: a Gaussian function [Eq. (2)], the sum of two Gaussian functions [Eq. (3)], a Lorentzian function [Eq. (4)], and a hybrid (sum) of a Gaussian and a Lorentzian function [Eq. (5)]: fG ðxÞ ¼ a eðððxbÞ=c ÞÞ
2
ð2Þ
Plane source method
In the plane source method, the source was simulated at a 3° angle with respect to the horizontal (parallel to coronal) or vertical (parallel to sagittal) axis. This technique was followed to avoid aliasing effects, which are caused by discrete data sampling, as the effective sampling distance becomes much smaller than the original and thus the effect of aliasing on the MTF calculations can be eliminated, as described in the Fujita technique [28]. In this technique the source should be placed at angles ranging from 2° to 8°. For angles greater than 8°, the dimensions of the vertical LSFs will be different from those of the true LSFs by more than 1%, and geometrical corrections should then be applied [14]. Since the plane source was positioned either clockwise or counter clockwise in a 3° angle, a custom-made software was used for angle correction [15,29]. The final LSF was obtained by averaging all line LSF profiles after angle correction. Angle correction was performed following the procedure described by Boone et al. [15]. The line profile can be obtained from the pixel value G [ix,iy], where G represents the pixel value image matrix in a rectangular region of interest (Fig. 4). x1, x2, y1, and y2 are the coordinates (Fig. 4)
f2G ðxÞ ¼ a1 eðððxb1 Þ=c1 ÞÞ þa2 eðððxb2 Þ=c2 ÞÞ 2
f L ð xÞ ¼ a
1 1þððxbÞ=c Þ2
fGL ðxÞ ¼ a1 eðððxb1 Þ=c1 ÞÞ þa2 1= 1þ ððxb2 Þ=c2 Þ2
2
ð3Þ ð4Þ
2
ð5Þ
where the parameters ai, bi, and ci are the amplitude, the position of the center of the peak, and the spread of the curve, respectively, calculated by the custom-made software. The fitting function providing the optimum correlation coefficient (R2) was selected. Fourier transformation and subsequent normalization were then applied to the final LSF to compute the MTF [14] according to Eq. (6): MTF ¼ F½LSF
ð6Þ
Line source method
MTF was also obtained through the PSF method using a line source method as described by Boone et al. [15]. The
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A new PET resolution measurement method Karpetas et al. 971
center of the point image was determined (x0, y0 coordinates), and line profiles passing from this point were obtained, covering various angles ranging from 0° to 180° with a 2° angle step.
Fig. 5
The PSF profile can be written as PSF(ξ) = G[xi,yi], where G[ix,iy] are the image pixel values [28]. xi, yi are the pixel coordinates in the horizontal and vertical axes, respectively, fulfilling the line equation criteria.
xi
yi
where ξ is the pixel position in the horizontal axis. The average PSF was fitted using Eqs (2)–(5). The fitting function providing the optimum R2 was again selected. Fourier transformation and subsequent normalization were then applied on the final LSF to compute the MTF [14].
Results Modulation transfer function
Figure 5 shows the reconstructed slice profiles of the plane source and the corresponding point profiles of the line source images obtained from the STIR software. The first column shows the FBP3DRP reconstructed images in both horizontal (parallel to coronal) and vertical (parallel to sagittal) directions (tilted by 3°), as well as the point profiles of the line source 3D image at the bottom. The second column shows the corresponding OSEM (horizontal, vertical, and point) reconstructed images (21 subsets, two iterations). Finally, the third (right) column shows the large (18 cm) plane sources that were used to examine resolution of the PET scanner in a large part of the field of view, in FBP3DRP (top) and OSEM (bottom).
Reconstructed line and point images obtained from the STIR software. (a) The first column shows the FBP3DRP reconstructed images in both horizontal and vertical (parallel to sagittal) directions (tilted by 3°), and the point 3D image at the bottom. (b) The second column shows the OSEM reconstructed images (21 subsets, two iterations), and (c) the third (right) column shows the large (18 cm) plane sources in FBP3DRP (up) and OSEM (down). 3D, three dimensional; FBP3DRP, three-dimensional filtered back projection; STIR, software for tomographic image reconstruction; OSEM, ordered-subsets expectation maximization.
Fig. 6
1.0 Modulation transfer function (MTF)
Almost all applications of the PSF, as a generalized descriptor of tomographic system performance, follow the assumption of rotational symmetry; therefore, the PSF profiles in the radial directions can be averaged to produce a one-dimensional PSF profile, which is calculated as follows [30,31]: PP G½xi ; yi xi y i PP PSF ðxÞ ¼ ð7Þ 1
Plane source horizontal FBP 3D Plane source horizontal OSEM 3D 2 Iter, 21 subsets Plane source horizontal OSEM 3D 8 Iter, 21 subsets Plane source horizontal OSEM 3D 20 Iter, 21 subsets
0.8
0.6
0.4
0.2
0.0 0.00
0.02
0.04
0.06
0.08
Spatial frequency (cycles/mm) Comparison between the MTFs obtained using the plane source method, from the horizontal plane source reconstructed image with the FBP3DRP and the OSEM (21 subsets, two, eight, and 20 iterations) algorithms, respectively. 3D, three dimensional; Iter, iteration; FBP3DRP, three-dimensional filtered back projection; MTF, modulation transfer function; OSEM, ordered-subsets expectation maximization.
Plane source
Figure 6 shows a comparison between the MTFs obtained by the plane source method, from the horizontal plane source reconstructed images, with the FBP3DRP and the OSEM reconstruction algorithms. The influence of different numbers of iterations of the OSEM image reconstruction on the imaging performance of the GE Discovery ST was also investigated. To obtain these curves, the number of subsets was kept fixed (21 subsets) and the number of iterations was allowed to vary (two, eight, and 20). In every case, MTF was found to increase as the number of iterations increased. Further, the MTF curves of the OSEM reconstructed images show that
higher frequencies are preserved compared with those in FBP3DRP, in the whole spatial frequency range. This finding justifies the observations in Fig. 5 with regard to the uniformity of resolution. On inspection of the large (18 cm) plane source images (Fig. 5), which are reconstructed using the 3D filtered back projection algorithm, it can be observed that resolution is degraded off-center. Quantification of the above observations is shown in Fig. 7, which shows the MTFs obtained using the plane
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972 Nuclear Medicine Communications 2014, Vol 35 No 9
Fig. 7
Fig. 8
0.8 Plane source FBP 3D 0−2 cm
0.6 Plane source FBP 3D 2−4 cm
0.4
0.2
Plane source FBP 3D total
Plane source FBP 3D 4−6 cm
Plane source FBP 3D 6−8 cm
0.0 0.00
0.02 0.04 0.06 Spatial frequency (cycles/mm)
source method, from the large plane source reconstructed image, with the FBP3DRP. MTFs were obtained every 2 cm from the center to the edge of the plane source to investigate image resolution off center. Figure 7 and Table 1 show that the possible spatial frequencies (in cycles/mm) that can be resolved are gradually reduced from the center toward the edge of the FOV. This is due to the streak artifacts and the parallax effect that are present in the images [32,33]. Using the plane source method, spatial resolution was assessed by examining MTF in a large part of the FOV. Line source
Figure 8 shows a comparison between the MTFs obtained from PSF using the line source method, from the reconstructed point images, with the FBP3DRP and OSEM (21 subsets, two iterations) algorithms, respectively. MTF values of the OSEM reconstructed image are higher than those of FBP3DRP by 20.32%. Figure 9 shows a comparison between the two methods (plane and line source) for the assessment of the MTF. Both MTF curves were obtained after FBP 3D image reconstruction. The MTFs are shown along with their Image resolution of the large plane sources at 5% MTF
Radial distance (cm) 18 0–2 2–4 4–6 6–8
FBP3DRP (cycles/mm) 0.0571 0.0624 0.0613 0.0581 0.0446
3D, three dimensional; FBP3DRP, three-dimensional filtered back projection; MTF, modulation transfer function.
Line source FBP 3D Line source OSEM 3D 0.8
0.6
0.4
0.2
0.0 0.00
0.08
Comparison between the MTFs obtained using the plane source method, from the large (18 cm) horizontal plane source FBP3DRP reconstructed image. 3D, three dimensional; FBP3DRP, threedimensional filtered back projection; MTF, modulation transfer function.
Table 1
Modulation transfer function (MTF)
1.0
0.02 0.04 0.06 Spatial frequency (cycles/mm)
0.08
Comparison between the MTFs obtained through point sources with the FBP3DRP and the OSEM (21 subsets, two iterations) algorithms, respectively. 3D, three dimensional; FBP3DRP, three-dimensional filtered back projection; MTF, modulation transfer function; OSEM, ordered-subsets expectation maximization.
Fig. 9
1.0 Modulation transfer function (MTF)
Modulation transfer function (MTF)
1.0
Plane source method FBP 3D Line source method FBP 3D
0.8
0.6
0.4
0.2
0.0 0.00
0.02
0.04
0.06
0.08
Spatial frequency (cycles/mm) Comparison between the MTFs obtained through the plane source and the line source methods (FBP3DRP) with the corresponding SD values. FBP3DRP, three-dimensional filtered back projection; MTF, modulation transfer function.
SD values for the whole spatial frequency range. To obtain the curves in Fig. 9, the whole procedure was repeated 10 times and the SD was calculated. The differences between the two methods, in the MTF calculation, could be attributed to the fact that the points and lines that were used in this study were assumed to have physical dimensions, to simulate experimental conditions, and were not ideal points; hence, they could not be
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A new PET resolution measurement method Karpetas et al. 973
Table 2
Spatial resolution comparison Published data
FWHM (mm) 3D Radial Tangential
6.11b 6.11b
6.29c 6.29c
Average of published data
Plane source methoda
Line source methoda
6.29 ± 0.175 6.29 ± 0.175
6.33 ± 0.022 6.30 ± 0.014
5.03 ± 0.117
6.46d 6.46d
a
This work. Mawlawi et al. [39]. Bettinardi et al. [41]. d Sharma et al. [42]. b c
applied in quality assurance procedures [34]. The PSF measured at a particular area in the image will depend on the emitter and attenuation distribution in the whole scanner due to detector dead time, scatter, positron range, photon noncollinearity, and possibly on other physical effects. Further, different reconstruction algorithms may have nonlinearities that depend in different ways on the source distribution, especially for nonlinear iterative reconstruction algorithms. The plane source method is less prone to noise because of the benefits of averaging larger amounts of data, using more samples [14,15] (line profiles), yielding a mean SD of SD ¼ 0:0031, in contrast to the line source method, which showed a mean SD of SD ¼ 0:0203 with regard to the MTF calculation of the PET plane source images. This may be the principal benefit of the proposed technique in the context of the spatial resolution assessment of clinical PET images because of the following: from the images of the plane source proposed in this work, a significant number of pixels, over the entire LSF, are averaged to estimate the MTF. This is an advantage over conventional PSF methods, as the point sources appearing in PET images with typical dimensions of 128 × 128, 256 × 256, or 512 × 512 will incorporate only a few pixels, which may be insufficient to correctly characterize image contrast [35,36]. The limitations of MTF calculation using the line source method arise from the assumption of rotational symmetry in the spatial resolution, which has also been adopted in previous work [37]. Following this assumption, the PSF profiles could be averaged in radial directions, taking into consideration the fact that the PSF has a complicated, nonseparable 3D shape, as has been reported for spiral CTs [37]. Further, PSF and LSF may not fulfill the shift invariance condition of the linear systems theory and thus, they may depend on the position within the image [38]. Table 2 shows a comparison between the spatial resolution, in terms of FWHM of the PSFs, from the plane and line sources, in all three orthogonal directions, obtained from the GATE simulations along with their SD values and published experimental data (average of radial and tangential values), obtained in accordance with the NEMA NU 2-2001 protocol [39–42]. Spatial resolution was assessed in the transverse slice. The differences
between simulated results and averaged experimental FWHM data range from 0.21 to 0.69%.
Discussion The contribution of the MTF measurement in PET image resolution estimation can arise from the following considerations. For each spatial frequency (which corresponds to a particular object size in the spatial domain), MTF gives the corresponding amplitude of useful signal – that is, the contrast level in the final image of the particular object size. Thus a single MTF analysis in the spatial frequency domain can be used to predict the system performance for all possible structure sizes. In the line source-based MTF estimation method presented here, the possibility for inaccurate estimation of the resolution is reduced, as compared with the FWHM method, because of the following reason: irregular (e.g. oblong) PSF shapes, often found in the peripheral areas of the FOV, may overestimate or underestimate axial and transverse image resolution. In contrast, in this study, averaged PSF profiles are obtained after integration of line profiles passing through the center of the point image and covering various angles ranging from 0° to 180° with a 2° angle step. The FWHM as a measure of spatial resolution lacks the possibility for correct and complete system characterization, as different PSF shapes may show equal FWHM values [12]. Further, the plane source method proposed in the present work has advantages over the traditional point source method, in which the point sources are positioned at various points in the FOV of the scanner. Taking into account that these point sources are placed at certain positions, the available resolution information is restricted only to particular coordinates, excluding intermediate values. Thus, possible non-uniformities within these regions of interest may not be revealed. This is also the case when multiple point sources can be positioned across the FOV, thus increasing the difficulty in assessing resolution with custom-made phantoms, hence making the use of commercialized phantoms necessary [43]. The method proposed in this work, when applied in PET quality control procedures, could obtain image resolution using only one plane source, covering a relatively large portion of the FOV instead of using numerous point sources.
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The point sources in glass capillaries free from air could be affected by the range of the positrons emitted by the source because of the finite source size, whereas methods that use cylindrical phantoms as attenuation media do not have this dependence. Measuring spatial resolution from a sharp interface (such as the plane source presented here) that produces a line response function may become increasingly important as the spatial resolution of PET systems improves. Such measurements have been widely investigated in other areas of medical imaging. Examples of similar work can be also found in CT [14] and SPECT [15] imaging. Moreover, the proposed method provides the ability to obtain image resolution in three dimensions by placing the source only horizontally and vertically (parallel to sagittal). Further, the poor spatial resolution of PET systems is a limiting factor for the accurate quantitative estimation of the PSF of structures more than three times smaller than the FWHM (partial volume effect) of the reconstructed image resolution [36]. The partial volume effect alternates the pixel values of a structure, by forcing lower activity peripheral tissues to gain uptake with higher activities from hot lesions spreading to the surrounding (spill-out effect) [44]. Thus, hot lesions will appear with reduced maximum values and the PSF will appear broader, with low-intensity tails. In the latter case, the low-intensity values dominating the shape of the PSF necessitate the estimation of the full width at tenth maximum, along with the FWHM, to assess the positron range effects on spatial resolution [45]. The plane source MTF method proposed in this work provides complete image resolution characterization compared with the single-value image quality metrics of FWHM and full width at tenth maximum. In conclusion, the broadening of the PSF, along with the finite number of image pixels available within the PSF area, may also lead to erroneous estimation of the FWHM, also taking into account that the width of a PSF does not track well with the perception of the individual performing the measurement [46,47]. Because of the aforementioned, MTF could be useful for comparing the effects of different scan and reconstruction parameters (FBP, OSEM, etc.), for quality control of PET scanners, and especially for evaluating the accuracy of size and density measurements of fine details in nuclear imaging [13]. In addition, it can be used as a longterm quality control method to identify the system’s performance stability. Further, this method could be useful for comparing different PET scanners in multicenter PET studies and, in particular, for the accurate determination of image resolution of new technology PET scanners incorporating high-resolution detectors [44,46,48]. Scatter and streak artifacts could be possible disadvantages of the plane source method in comparison
with the line source method. In this sense, the plane source method could be considered as more realistic, with respect to clinical practice, as both scattering and streak artifacts are present in PET in-vivo clinical imaging. One of the challenges of assessing spatial resolution with a clinical PET scanner is that iterative reconstruction algorithms, which are offered in most clinical systems, are nonlinear and difficult to evaluate [49,50]. However, as resolution is object-dependent, because of the nonlinear nature of iterative reconstruction algorithms, the use of a plane source to assess resolution will potentially lead to different resolution results from those obtained using a point source, and in turn both sources (plane and point) will potentially provide different resolution results from a realistic object, such as a patient, in different parts of the image [50]. For this reason, standardized measurement geometries of the method presented here are of practical importance when comparing clinical reconstruction protocols. The possible challenges for the implementation of the plane source method for routine PET quality control may be related to the following: (a) the total time required for the preparation of the source, (b) the total dose that will be received by the personnel, and the precautions that should be undertaken to avoid contamination during implementation and the quality control procedure, (c) the specific radioactivity of the solution in which the plane source should be immersed, (d) the uniformity distribution of the 18F-FDG radiopharmaceutical on the plane source, (e) the requirement of a cylindrical polymethyl methacrylate phantom consisting of two D-shaped parts from the positioning in between the plane source, (f) placing and holding of the phantom on the bed, as well as the orientation of the plane source in a slight angle ranging from 3° to 8° to avoid aliasing effects, and (g) the necessity for a software for MTF determination; this software can be freely distributed on demand by our group.
Conclusion The MTF, which could be useful in the characterization of the spatial resolution of a PET system, was determined by the simulation of a novel plane source using the Monte-Carlo method. This method is based on a thin plane source filled with 18F-FDG. The MTFs of the OSEM image reconstruction preserve are, in all cases, of higher frequencies than those found by FBP. MTFs of the OSEM were found to increase as the number of iterations increased. FBP-reconstructed images obtained from large horizontal plane sources showed that MTFs were degraded from the center of the FOV to the edges. The method modeled and simulated in this work can be experimentally implemented and used for routine PET quality control. Further, the method is less prone to noise and provides the ability to estimate MTF in three dimensions using a simplified procedure that involves
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A new PET resolution measurement method Karpetas et al. 975
placing the thin plane source phantom horizontally (parallel to coronal) and vertically (parallel to sagittal).
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Acknowledgements
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The authors thank Dr Ross Schmidtlein for the support on GATE development. They also thank Dr Kris Thielemans (senior lecturer, University College London) and Dr Harris Tsoubas (Lecturer, University of Leeds) for the helpful discussions concerning STIR reconstruction (http://stir.sourceforge.net).
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Conflicts of interest
There are no conflicts of interest.
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A new PET resolution measurement method through Monte-Carlo simulations George E. Karpetasa, Christos M. Michailb, George P. Fountosb, Ioannis S. Kandarakisb and George S. Panayiotakisa Objective The aim of this study was to propose a novel method for image quality assessment in PET scanners through estimation of the modulation transfer function (MTF) of a plane source. The simulation was implemented using the previously validated Monte-Carlo model. A comparison of the proposed method with the more traditional technique, based on a line source, was also performed. Materials and methods The Geant4 application for tomographic emission (GATE) Monte-Carlo package was used for model development, and reconstructed images were obtained using software for tomographic image reconstruction (STIR) with cluster computing. A novel plane source consisting of a radioactive (18F-fluorodeoxyglucose) thin-layer chromatography plate was simulated (total source activity: 44.4 MBq) to assess image quality through the MTF. All images were reconstructed with the threedimensional filtered back projection (FBP3DRP) and ordered-subsets expectation maximization (OSEM) reprojection algorithms. Results The MTFs obtained using ordered-subsets expectation maximization show, in all cases, that higher frequencies are preserved compared with those obtained
Introduction Over the last few years functional nuclear medicine imaging has been further improved by the introduction of combined PET-computed tomography (PET/CT) scanners. The imaging performance of PET/CT scanners can be accurately modeled using Monte-Carlo simulation packages with the aim of designing high-quality scanners for improved image quantification. An open-source extension of the Geant4 [1] Monte-Carlo toolkit was the Geant4 application for tomographic emission (GATE) package, which was developed by the OpenGATE collaboration [2]. The overall purpose of this study was to propose a novel method for the assessment of the image quality performance of PET systems and particularly to predict the modulation transfer function (MTF) through the line spread function (LSF) of a plane source. To this aim, the GATE Monte-Carlo package was used in combination with the software for tomographic image reconstruction (STIR, version 2) to simulate: (i) a novel highly uniform 18 F-fluorodeoxyglucose (18F-FDG) plane source, based 0143-3636 © 2014 Wolters Kluwer Health | Lippincott Williams & Wilkins
using the FBP3DRP. In addition, the plane source method is less prone to noise than the conventional line source method (SD = 0.0031 and 0.0203, respectively). Conclusion The thin-layer chromatography-based plane source presented requires materials commonly found in a clinical environment and could be used to assess image quality in nuclear medicine departments and to further develop PET and single-photon emission computed tomography scanners through Monte-Carlo simulations. Nucl Med Commun 35:967–976 © 2014 Wolters Kluwer Health | Lippincott Williams & Wilkins. Nuclear Medicine Communications 2014, 35:967–976 Keywords: GATE, modulation transfer function, PET, plane source, software for tomographic image reconstruction a Department of Medical Physics, Faculty of Medicine, University of Patras, Patras and bDepartment of Biomedical Engineering, School of Technological Applications, Technological Educational Institute (TEI) of Athens, Athens, Greece
Correspondence to Ioannis S. Kandarakis, PhD, Department of Biomedical Engineering, School of Technological Applications, Technological Educational Institute of Athens, Egaleo, 12210 Athens, Greece Tel: + 30 10 5385 375; fax: + 30 10 5910 975; e-mail: [email protected] Received 17 December 2013 Revised 6 April 2014 Accepted 13 May 2014
on a thin-layer chromatography (TLC) plate, to obtain reconstructed plane source images and (ii) a conventional 18 F-FDG line source, to obtain the point spread function (PSF) of line source reconstructed images, for comparison. In the past few years, ongoing work on STIR reconstruction for large commercial PET scanners has been carried out [3–9]. None of these, however, simulate the GE Discovery ST scanner that is used in this study. In addition, PET image quality metrics have not been previously studied in terms of MTF by estimating the LSF of a plane source. To evaluate the performance of PET scanners, the PSF in a slice profile has traditionally been used [10,11]. The full width at half maximum (FWHM) of this function, which is used to measure the spatial resolution, lacks the possibility for complete system characterization and needs to be improved, as different PSF shapes may show equal FWHM values [12]. The response of the system to the incident signal amplitudes can be described by the MTF, which expresses the system’s response in the spatial frequency domain by taking the Fourier transform of the corresponding PSF from a reconstructed cross-sectional image. DOI: 10.1097/MNM.0000000000000151
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from the STIR software. The MTF was also assessed, in lines passing through the central axis of the PET scanner, by placing the plane source 3° to horizontal (parallel to coronal) and 3° to vertical (parallel to sagittal), allowing estimation from the center to the edges of the plane source. The proposed plane source phantom method, simulated in this work, serves as a useful tool that can be used in quality control procedures and also to characterize the performance of nuclear medicine imaging systems.
Fig. 1
Detector ring End shielding 88.6 cm
Crystal block BGO crystal
Module
Materials and methods Geometry of the modeled PET scanner
12
24 rings
6
PET scanner geometry.
Precise and accurate determinations of MTF are important for comparing the effects of different scan and reconstruction parameters, for comparison between different PET scanners, and especially for evaluating the accuracy of size and density measurements of fine details in medical images [13]. The use of the LSF for determining the MTF in tomographic imagers was initially introduced by Boone who applied this method for the evaluation of CT scanners [14]. This method is robust to aliasing when used for MTF calculation and is more resilient to noise because of greater data averaging when compared with the conventional point source method [14]. Fountos et al. [15] recently introduced a similar method for single-photon emission computed tomography (SPECT) scanners by immersing an Agfa MammoRay HDR Medical X-ray film in a solution of dithiothreitol/Tc-99m(III)-DMSA to obtain the MTF through the plane source method. Building on the work of Fountos and colleagues, this study introduces a plane source phantom to estimate the MTF through the LSF by simulating a thin-layer chromatography (TLC) plate, which can be implemented by a layer of silica gel on Al foil substrates, immersed in an 18 F-FDG bath solution. The idea of simulating TLC films as a plane source in PET imaging was first introduced by Heckathome et al. [16]. For comparison purposes, the MTF was also estimated by simulating a conventional 18F-FDG line source. Image quality was assessed by evaluating reconstructed images obtained
The PET scanner modeled in this study is the Discovery ST PET/CT, incorporating bismuth germinate oxide (BGO) crystals with dimensions of 6.3 × 6.3 × 30 mm in the tangential, axial, and radial directions, respectively (Fig. 1). The crystals were assembled into blocks of 6 × 6 crystals. Each block was coupled with a photomultiplier tube consisting of four square channels and is assembled in modules consisting of eight blocks (2 × 4) each. The detector ring finally comprises 35 modules – that is, 280 crystal blocks or 24 rings of 420 crystals (for a total of 10 080 BGO crystals). The dimensions of the ring are an 88.6 cm diameter, with 15.7 cm axial and 70 cm transaxial fields of view (FOVs). The scanner is designed to acquire images in both twodimensional (2D) and three-dimensional (3D) modes. In the 2D mode, collimation between image slices is achieved with retractable tungsten septa (54 mm long and 0.8 mm thick), which are used to reduce scattering, and every image plane counts events from ± 5 crystal rings (high-sensitivity mode). In the 3D mode, the septa are absent and the system allows oblique lines of responses with a maximum difference of 24 rings. The energy window width in both cases was set from 375 to 650 keV with a coincidence timing window of 11.7 ns. Physics processes, signal, and coincidence processing
GATE uses the standard and low-energy Geant-4 packages to simulate electromagnetic processes [17]. In this study, the standard energy package was used to model the photoelectric and Compton interactions and the low-energy package was used to simulate the Rayleigh interactions. To obtain a more realistic simulation, the positron range, the acolinearity effects, and the depth of interaction were taken into account, as all of these effects contribute to loss of resolution. X-rays and secondary electrons are not tracked, to speed up the simulation using 1 GeV for both X-rays and δ-rays with an electron range up to 30 cm. In every BGO crystal of the detector block, a Gaussian energy blur is applied with an average energy resolution of 17%, referenced at 511 keV. The quantum detection efficiency of the crystals was found to be 0.94 at 511 keV [18,19]. Thereafter, a 300-ns dead time value was applied on the single events in the BGO crystal [20,21] using a paralysable Deadtime
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A new PET resolution measurement method Karpetas et al. 969
module [22]. The sinogram output file (.ima), obtained from the ECAT system, was used by STIR as the input file for the reconstruction of the simulated plane source image. All the evaluations in this study were performed on the center slice of the reconstructed images. All simulations were performed using a computer cluster with 12 dual-core Intel(R) Xeon(TM) CPU 3.00 GHz processors (Supermicro SuperServer 6015B-UR/NTR, San Jose, California, USA).
purposes with the 3D OSEM reprojection algorithms [23–26]. The sinogram was defined by 47 segments, bin size 0.3195 cm, 221 arc-corrected and 249 non-arccorrected bins, span 3, and mashing 1. The images were obtained using STIR with perfect scatter rejection. Attenuation correction was performed by applying the attenuation correction factors of the created attenuation map on the reconstructed image [27]. Line source phantom simulation
Simulation of the MTF test object Plane source phantom simulation
The plane source, which is introduced in this study following the works of Boone [14] for CT and Fountos et al. [15] for SPECT systems, is based on the excellent binding of 18F-FDG to TLC plates. The plate of the plane source was implemented as a layer of silica gel on Al foil substrates (Al density 2.7 g/cm3). The dimension of the TLC plate was 5 ± 10 cm2, with a total source activity of 44.4 MBq (18F-FDG; Fig. 2). The total source thickness was 145.58 μm (Al thickness 102.1 μm and silica thickness 43.38 μm). The MTF test object (plane source; i.e., the radioactive plate) was simulated within a phantom, consisting of two semicylindrical polyethylene blocks with a 20 cm diameter and a 70 cm length, in the horizontal (parallel to coronal) and vertical (parallel to sagittal) directions. From the three colored cross-sectional lines (Fig. 2), the LSFs can be obtained for MTF estimation in three planes, in lines passing though the central axis. The plane source was also simulated with a dimension of 18 × 10 cm2 to investigate the effect of the field size on the MTF of the transaxial FOV.
To simulate the thin line source, the following procedure was followed: a cylindrical glass capillary with a 1 mm internal diameter, a 2 mm external diameter, and a 4 cm length was modeled [14]. The radioactivity of the line source occupies 3 cm of the 4 cm glass capillary. The source was simulated passing through the center of the FOV, in the axial direction. The line source phantom was filled with 18F-FDG (activity 0.37 MBq). For the purpose of the present study and to obtain an appropriate simulation that could be reproducible in clinical practice, the capillary tube was simulated inside the 76–823 PET/SPECT Performance Phantom (Fluke Biomedical, Everett, Washington, USA), filled with water. The dimensions of the phantom are as follows: internal diameter 20.3 cm, external diameter 21.59 cm, and length 30.5 cm (Fig. 3). A transverse slice image of the line source was acquired from STIR after reconstruction of the sinogram data with the 3D FBP (FBP3DRP) and with the OSEM reprojection algorithms [25]. Fig. 3
Plane source images were acquired from STIR, after reconstruction of the arc-corrected sinogram data with the commonly used Kinahan and Rogers three-dimensional filtered back projection (FBP3DRP) and for comparison 3 cm Fig. 2
21.59 cm
30.5 cm 1cm
Simulation of the plane source for the MTF measurement (Left). (a) The source is placed horizontally; transverse and sagittal lines for the MTF calculation (Right). (b) The source is placed vertically (parallel to sagittal); transverse and coronal lines for the MTF calculation. MTF, modulation transfer function.
Line source phantom simulation for the measurement of the MTF through PSF. The radioactivity of the source occupies 3 cm of the glass capillary. MTF, modulation transfer function; PSF, point spread function.
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defining the rectangular edges. ix, iy are the pixel coordinates in the horizontal and vertical axes, respectively, in the transverse, sagittal, or coronal image slices, respectively, of Fig. 2, ranging as follows: x1 ≤ ix ≤ x2, y1 ≤ iy ≤ y2 [28].
Fig. 4
(x1, y2)
The average LSF profile was calculated as follows [28]: G ix ; iy
y2 x2 P P
(x2, y2)
LSF ðxÞ ¼
ix ¼x1 iy ¼y1 y2 x2 P P
(x1, y1)
ð1Þ 1
ix ¼x1 iy ¼y1
(x2, y1) Schematic representation of the line profile selection.
Modulation transfer function
In addition to the commonly used FWHM from slice profiles of point source images, image quality was further assessed in terms of the spatial frequency dependent MTF. MTF was obtained in lines passing through the central axis of the PET scanner; by placing the plane source horizontally, transverse and sagittal images of the source can be obtained. In these images the source appears as a line. From these lines the LSF can be calculated. By changing the orientation of the plane source from horizontal to vertical, a coronal slice image of the plane source can be obtained, in which the source will appear as a line (Fig. 2). In this way the MTF of a PET scanner can be estimated in three dimensions.
where ξ = tan(θ), ix = iy, and θ is the angle between the line image and the horizontal or vertical axis. In this study, the MTF of the PET scanner was estimated by averaging the line profiles across the length of the plane source transverse image (defined by X1, X2 in Fig. 4). Further, the spatial variation in the MTF was investigated at radial offsets from the center to the edge of the large plane source, successively in 2 cm spaces, allowing the investigation of the image resolution off center, in a specific rectangular region of interest inside the FOV. This is one of the advantages of the present method, as compared with the conventional line source method, as spatial resolution of a PET scanner can be fully investigated from the center to the edges of the FOV, with a single source. The average LSF was fitted using four different functions: a Gaussian function [Eq. (2)], the sum of two Gaussian functions [Eq. (3)], a Lorentzian function [Eq. (4)], and a hybrid (sum) of a Gaussian and a Lorentzian function [Eq. (5)]: fG ðxÞ ¼ a eðððxbÞ=c ÞÞ
2
ð2Þ
Plane source method
In the plane source method, the source was simulated at a 3° angle with respect to the horizontal (parallel to coronal) or vertical (parallel to sagittal) axis. This technique was followed to avoid aliasing effects, which are caused by discrete data sampling, as the effective sampling distance becomes much smaller than the original and thus the effect of aliasing on the MTF calculations can be eliminated, as described in the Fujita technique [28]. In this technique the source should be placed at angles ranging from 2° to 8°. For angles greater than 8°, the dimensions of the vertical LSFs will be different from those of the true LSFs by more than 1%, and geometrical corrections should then be applied [14]. Since the plane source was positioned either clockwise or counter clockwise in a 3° angle, a custom-made software was used for angle correction [15,29]. The final LSF was obtained by averaging all line LSF profiles after angle correction. Angle correction was performed following the procedure described by Boone et al. [15]. The line profile can be obtained from the pixel value G [ix,iy], where G represents the pixel value image matrix in a rectangular region of interest (Fig. 4). x1, x2, y1, and y2 are the coordinates (Fig. 4)
f2G ðxÞ ¼ a1 eðððxb1 Þ=c1 ÞÞ þa2 eðððxb2 Þ=c2 ÞÞ 2
f L ð xÞ ¼ a
1 1þððxbÞ=c Þ2
fGL ðxÞ ¼ a1 eðððxb1 Þ=c1 ÞÞ þa2 1= 1þ ððxb2 Þ=c2 Þ2
2
ð3Þ ð4Þ
2
ð5Þ
where the parameters ai, bi, and ci are the amplitude, the position of the center of the peak, and the spread of the curve, respectively, calculated by the custom-made software. The fitting function providing the optimum correlation coefficient (R2) was selected. Fourier transformation and subsequent normalization were then applied to the final LSF to compute the MTF [14] according to Eq. (6): MTF ¼ F½LSF
ð6Þ
Line source method
MTF was also obtained through the PSF method using a line source method as described by Boone et al. [15]. The
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A new PET resolution measurement method Karpetas et al. 971
center of the point image was determined (x0, y0 coordinates), and line profiles passing from this point were obtained, covering various angles ranging from 0° to 180° with a 2° angle step.
Fig. 5
The PSF profile can be written as PSF(ξ) = G[xi,yi], where G[ix,iy] are the image pixel values [28]. xi, yi are the pixel coordinates in the horizontal and vertical axes, respectively, fulfilling the line equation criteria.
xi
yi
where ξ is the pixel position in the horizontal axis. The average PSF was fitted using Eqs (2)–(5). The fitting function providing the optimum R2 was again selected. Fourier transformation and subsequent normalization were then applied on the final LSF to compute the MTF [14].
Results Modulation transfer function
Figure 5 shows the reconstructed slice profiles of the plane source and the corresponding point profiles of the line source images obtained from the STIR software. The first column shows the FBP3DRP reconstructed images in both horizontal (parallel to coronal) and vertical (parallel to sagittal) directions (tilted by 3°), as well as the point profiles of the line source 3D image at the bottom. The second column shows the corresponding OSEM (horizontal, vertical, and point) reconstructed images (21 subsets, two iterations). Finally, the third (right) column shows the large (18 cm) plane sources that were used to examine resolution of the PET scanner in a large part of the field of view, in FBP3DRP (top) and OSEM (bottom).
Reconstructed line and point images obtained from the STIR software. (a) The first column shows the FBP3DRP reconstructed images in both horizontal and vertical (parallel to sagittal) directions (tilted by 3°), and the point 3D image at the bottom. (b) The second column shows the OSEM reconstructed images (21 subsets, two iterations), and (c) the third (right) column shows the large (18 cm) plane sources in FBP3DRP (up) and OSEM (down). 3D, three dimensional; FBP3DRP, three-dimensional filtered back projection; STIR, software for tomographic image reconstruction; OSEM, ordered-subsets expectation maximization.
Fig. 6
1.0 Modulation transfer function (MTF)
Almost all applications of the PSF, as a generalized descriptor of tomographic system performance, follow the assumption of rotational symmetry; therefore, the PSF profiles in the radial directions can be averaged to produce a one-dimensional PSF profile, which is calculated as follows [30,31]: PP G½xi ; yi xi y i PP PSF ðxÞ ¼ ð7Þ 1
Plane source horizontal FBP 3D Plane source horizontal OSEM 3D 2 Iter, 21 subsets Plane source horizontal OSEM 3D 8 Iter, 21 subsets Plane source horizontal OSEM 3D 20 Iter, 21 subsets
0.8
0.6
0.4
0.2
0.0 0.00
0.02
0.04
0.06
0.08
Spatial frequency (cycles/mm) Comparison between the MTFs obtained using the plane source method, from the horizontal plane source reconstructed image with the FBP3DRP and the OSEM (21 subsets, two, eight, and 20 iterations) algorithms, respectively. 3D, three dimensional; Iter, iteration; FBP3DRP, three-dimensional filtered back projection; MTF, modulation transfer function; OSEM, ordered-subsets expectation maximization.
Plane source
Figure 6 shows a comparison between the MTFs obtained by the plane source method, from the horizontal plane source reconstructed images, with the FBP3DRP and the OSEM reconstruction algorithms. The influence of different numbers of iterations of the OSEM image reconstruction on the imaging performance of the GE Discovery ST was also investigated. To obtain these curves, the number of subsets was kept fixed (21 subsets) and the number of iterations was allowed to vary (two, eight, and 20). In every case, MTF was found to increase as the number of iterations increased. Further, the MTF curves of the OSEM reconstructed images show that
higher frequencies are preserved compared with those in FBP3DRP, in the whole spatial frequency range. This finding justifies the observations in Fig. 5 with regard to the uniformity of resolution. On inspection of the large (18 cm) plane source images (Fig. 5), which are reconstructed using the 3D filtered back projection algorithm, it can be observed that resolution is degraded off-center. Quantification of the above observations is shown in Fig. 7, which shows the MTFs obtained using the plane
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972 Nuclear Medicine Communications 2014, Vol 35 No 9
Fig. 7
Fig. 8
0.8 Plane source FBP 3D 0−2 cm
0.6 Plane source FBP 3D 2−4 cm
0.4
0.2
Plane source FBP 3D total
Plane source FBP 3D 4−6 cm
Plane source FBP 3D 6−8 cm
0.0 0.00
0.02 0.04 0.06 Spatial frequency (cycles/mm)
source method, from the large plane source reconstructed image, with the FBP3DRP. MTFs were obtained every 2 cm from the center to the edge of the plane source to investigate image resolution off center. Figure 7 and Table 1 show that the possible spatial frequencies (in cycles/mm) that can be resolved are gradually reduced from the center toward the edge of the FOV. This is due to the streak artifacts and the parallax effect that are present in the images [32,33]. Using the plane source method, spatial resolution was assessed by examining MTF in a large part of the FOV. Line source
Figure 8 shows a comparison between the MTFs obtained from PSF using the line source method, from the reconstructed point images, with the FBP3DRP and OSEM (21 subsets, two iterations) algorithms, respectively. MTF values of the OSEM reconstructed image are higher than those of FBP3DRP by 20.32%. Figure 9 shows a comparison between the two methods (plane and line source) for the assessment of the MTF. Both MTF curves were obtained after FBP 3D image reconstruction. The MTFs are shown along with their Image resolution of the large plane sources at 5% MTF
Radial distance (cm) 18 0–2 2–4 4–6 6–8
FBP3DRP (cycles/mm) 0.0571 0.0624 0.0613 0.0581 0.0446
3D, three dimensional; FBP3DRP, three-dimensional filtered back projection; MTF, modulation transfer function.
Line source FBP 3D Line source OSEM 3D 0.8
0.6
0.4
0.2
0.0 0.00
0.08
Comparison between the MTFs obtained using the plane source method, from the large (18 cm) horizontal plane source FBP3DRP reconstructed image. 3D, three dimensional; FBP3DRP, threedimensional filtered back projection; MTF, modulation transfer function.
Table 1
Modulation transfer function (MTF)
1.0
0.02 0.04 0.06 Spatial frequency (cycles/mm)
0.08
Comparison between the MTFs obtained through point sources with the FBP3DRP and the OSEM (21 subsets, two iterations) algorithms, respectively. 3D, three dimensional; FBP3DRP, three-dimensional filtered back projection; MTF, modulation transfer function; OSEM, ordered-subsets expectation maximization.
Fig. 9
1.0 Modulation transfer function (MTF)
Modulation transfer function (MTF)
1.0
Plane source method FBP 3D Line source method FBP 3D
0.8
0.6
0.4
0.2
0.0 0.00
0.02
0.04
0.06
0.08
Spatial frequency (cycles/mm) Comparison between the MTFs obtained through the plane source and the line source methods (FBP3DRP) with the corresponding SD values. FBP3DRP, three-dimensional filtered back projection; MTF, modulation transfer function.
SD values for the whole spatial frequency range. To obtain the curves in Fig. 9, the whole procedure was repeated 10 times and the SD was calculated. The differences between the two methods, in the MTF calculation, could be attributed to the fact that the points and lines that were used in this study were assumed to have physical dimensions, to simulate experimental conditions, and were not ideal points; hence, they could not be
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A new PET resolution measurement method Karpetas et al. 973
Table 2
Spatial resolution comparison Published data
FWHM (mm) 3D Radial Tangential
6.11b 6.11b
6.29c 6.29c
Average of published data
Plane source methoda
Line source methoda
6.29 ± 0.175 6.29 ± 0.175
6.33 ± 0.022 6.30 ± 0.014
5.03 ± 0.117
6.46d 6.46d
a
This work. Mawlawi et al. [39]. Bettinardi et al. [41]. d Sharma et al. [42]. b c
applied in quality assurance procedures [34]. The PSF measured at a particular area in the image will depend on the emitter and attenuation distribution in the whole scanner due to detector dead time, scatter, positron range, photon noncollinearity, and possibly on other physical effects. Further, different reconstruction algorithms may have nonlinearities that depend in different ways on the source distribution, especially for nonlinear iterative reconstruction algorithms. The plane source method is less prone to noise because of the benefits of averaging larger amounts of data, using more samples [14,15] (line profiles), yielding a mean SD of SD ¼ 0:0031, in contrast to the line source method, which showed a mean SD of SD ¼ 0:0203 with regard to the MTF calculation of the PET plane source images. This may be the principal benefit of the proposed technique in the context of the spatial resolution assessment of clinical PET images because of the following: from the images of the plane source proposed in this work, a significant number of pixels, over the entire LSF, are averaged to estimate the MTF. This is an advantage over conventional PSF methods, as the point sources appearing in PET images with typical dimensions of 128 × 128, 256 × 256, or 512 × 512 will incorporate only a few pixels, which may be insufficient to correctly characterize image contrast [35,36]. The limitations of MTF calculation using the line source method arise from the assumption of rotational symmetry in the spatial resolution, which has also been adopted in previous work [37]. Following this assumption, the PSF profiles could be averaged in radial directions, taking into consideration the fact that the PSF has a complicated, nonseparable 3D shape, as has been reported for spiral CTs [37]. Further, PSF and LSF may not fulfill the shift invariance condition of the linear systems theory and thus, they may depend on the position within the image [38]. Table 2 shows a comparison between the spatial resolution, in terms of FWHM of the PSFs, from the plane and line sources, in all three orthogonal directions, obtained from the GATE simulations along with their SD values and published experimental data (average of radial and tangential values), obtained in accordance with the NEMA NU 2-2001 protocol [39–42]. Spatial resolution was assessed in the transverse slice. The differences
between simulated results and averaged experimental FWHM data range from 0.21 to 0.69%.
Discussion The contribution of the MTF measurement in PET image resolution estimation can arise from the following considerations. For each spatial frequency (which corresponds to a particular object size in the spatial domain), MTF gives the corresponding amplitude of useful signal – that is, the contrast level in the final image of the particular object size. Thus a single MTF analysis in the spatial frequency domain can be used to predict the system performance for all possible structure sizes. In the line source-based MTF estimation method presented here, the possibility for inaccurate estimation of the resolution is reduced, as compared with the FWHM method, because of the following reason: irregular (e.g. oblong) PSF shapes, often found in the peripheral areas of the FOV, may overestimate or underestimate axial and transverse image resolution. In contrast, in this study, averaged PSF profiles are obtained after integration of line profiles passing through the center of the point image and covering various angles ranging from 0° to 180° with a 2° angle step. The FWHM as a measure of spatial resolution lacks the possibility for correct and complete system characterization, as different PSF shapes may show equal FWHM values [12]. Further, the plane source method proposed in the present work has advantages over the traditional point source method, in which the point sources are positioned at various points in the FOV of the scanner. Taking into account that these point sources are placed at certain positions, the available resolution information is restricted only to particular coordinates, excluding intermediate values. Thus, possible non-uniformities within these regions of interest may not be revealed. This is also the case when multiple point sources can be positioned across the FOV, thus increasing the difficulty in assessing resolution with custom-made phantoms, hence making the use of commercialized phantoms necessary [43]. The method proposed in this work, when applied in PET quality control procedures, could obtain image resolution using only one plane source, covering a relatively large portion of the FOV instead of using numerous point sources.
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974 Nuclear Medicine Communications 2014, Vol 35 No 9
The point sources in glass capillaries free from air could be affected by the range of the positrons emitted by the source because of the finite source size, whereas methods that use cylindrical phantoms as attenuation media do not have this dependence. Measuring spatial resolution from a sharp interface (such as the plane source presented here) that produces a line response function may become increasingly important as the spatial resolution of PET systems improves. Such measurements have been widely investigated in other areas of medical imaging. Examples of similar work can be also found in CT [14] and SPECT [15] imaging. Moreover, the proposed method provides the ability to obtain image resolution in three dimensions by placing the source only horizontally and vertically (parallel to sagittal). Further, the poor spatial resolution of PET systems is a limiting factor for the accurate quantitative estimation of the PSF of structures more than three times smaller than the FWHM (partial volume effect) of the reconstructed image resolution [36]. The partial volume effect alternates the pixel values of a structure, by forcing lower activity peripheral tissues to gain uptake with higher activities from hot lesions spreading to the surrounding (spill-out effect) [44]. Thus, hot lesions will appear with reduced maximum values and the PSF will appear broader, with low-intensity tails. In the latter case, the low-intensity values dominating the shape of the PSF necessitate the estimation of the full width at tenth maximum, along with the FWHM, to assess the positron range effects on spatial resolution [45]. The plane source MTF method proposed in this work provides complete image resolution characterization compared with the single-value image quality metrics of FWHM and full width at tenth maximum. In conclusion, the broadening of the PSF, along with the finite number of image pixels available within the PSF area, may also lead to erroneous estimation of the FWHM, also taking into account that the width of a PSF does not track well with the perception of the individual performing the measurement [46,47]. Because of the aforementioned, MTF could be useful for comparing the effects of different scan and reconstruction parameters (FBP, OSEM, etc.), for quality control of PET scanners, and especially for evaluating the accuracy of size and density measurements of fine details in nuclear imaging [13]. In addition, it can be used as a longterm quality control method to identify the system’s performance stability. Further, this method could be useful for comparing different PET scanners in multicenter PET studies and, in particular, for the accurate determination of image resolution of new technology PET scanners incorporating high-resolution detectors [44,46,48]. Scatter and streak artifacts could be possible disadvantages of the plane source method in comparison
with the line source method. In this sense, the plane source method could be considered as more realistic, with respect to clinical practice, as both scattering and streak artifacts are present in PET in-vivo clinical imaging. One of the challenges of assessing spatial resolution with a clinical PET scanner is that iterative reconstruction algorithms, which are offered in most clinical systems, are nonlinear and difficult to evaluate [49,50]. However, as resolution is object-dependent, because of the nonlinear nature of iterative reconstruction algorithms, the use of a plane source to assess resolution will potentially lead to different resolution results from those obtained using a point source, and in turn both sources (plane and point) will potentially provide different resolution results from a realistic object, such as a patient, in different parts of the image [50]. For this reason, standardized measurement geometries of the method presented here are of practical importance when comparing clinical reconstruction protocols. The possible challenges for the implementation of the plane source method for routine PET quality control may be related to the following: (a) the total time required for the preparation of the source, (b) the total dose that will be received by the personnel, and the precautions that should be undertaken to avoid contamination during implementation and the quality control procedure, (c) the specific radioactivity of the solution in which the plane source should be immersed, (d) the uniformity distribution of the 18F-FDG radiopharmaceutical on the plane source, (e) the requirement of a cylindrical polymethyl methacrylate phantom consisting of two D-shaped parts from the positioning in between the plane source, (f) placing and holding of the phantom on the bed, as well as the orientation of the plane source in a slight angle ranging from 3° to 8° to avoid aliasing effects, and (g) the necessity for a software for MTF determination; this software can be freely distributed on demand by our group.
Conclusion The MTF, which could be useful in the characterization of the spatial resolution of a PET system, was determined by the simulation of a novel plane source using the Monte-Carlo method. This method is based on a thin plane source filled with 18F-FDG. The MTFs of the OSEM image reconstruction preserve are, in all cases, of higher frequencies than those found by FBP. MTFs of the OSEM were found to increase as the number of iterations increased. FBP-reconstructed images obtained from large horizontal plane sources showed that MTFs were degraded from the center of the FOV to the edges. The method modeled and simulated in this work can be experimentally implemented and used for routine PET quality control. Further, the method is less prone to noise and provides the ability to estimate MTF in three dimensions using a simplified procedure that involves
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placing the thin plane source phantom horizontally (parallel to coronal) and vertically (parallel to sagittal).
19
Acknowledgements
20
The authors thank Dr Ross Schmidtlein for the support on GATE development. They also thank Dr Kris Thielemans (senior lecturer, University College London) and Dr Harris Tsoubas (Lecturer, University of Leeds) for the helpful discussions concerning STIR reconstruction (http://stir.sourceforge.net).
21
Conflicts of interest
There are no conflicts of interest.
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