Australas Phys Eng Sci Med (2014) 37:551–557 DOI 10.1007/s13246-014-0287-4
SCIENTIFIC PAPER
Spatial resolution is dependent on image content for SPECT with iterative reconstruction incorporating distance dependent resolution (DDR) correction Daniel Badger • Leighton Barnden
Received: 8 April 2014 / Accepted: 21 June 2014 / Published online: 9 July 2014 Ó Australasian College of Physical Scientists and Engineers in Medicine 2014
Abstract The aim of this study is to determine the dependence of single photon emission computed tomography (SPECT) spatial resolution on the content of images for iterative reconstruction with distance dependent resolution (DDR) correction. An experiment was performed using a perturbation technique to measure change in resolution of line sources in simple and complex images with iterative reconstruction with increasing iteration. Projections of the line sources were reconstructed alone and again after the addition of projections of a uniform flood or a complex phantom. An alternative experiment used images of a realistic brain phantom and evaluated an effective spatial resolution by matching the images to the digital version of the phantom convolved with 3D Gaussian kernels. The experiments were performed using ordered subset expectation maximisation iterative reconstruction with and without the use of DDR correction. The results show a significant difference in reconstructed resolution between images of line sources depending on the content of the added image. The full width at half maximum of images of a line source reconstructed using DDR correction increased by 20–30 % when the added image was complex. Without DDR this difference was much smaller and disappeared with increasing iteration. Reported SPECT resolution should be taken as indicative only with regard to clinical imaging if the measurement is made using a point or line source alone and an iterative reconstruction algorithm is used. Keywords SPECT OSEM Distance dependent resolution Spatial resolution D. Badger (&) L. Barnden The Queen Elizabeth Hospital, 28 Woodville Rd, Woodville South, SA 5011, Australia e-mail:
[email protected]
Introduction Single photon emission computed tomography (SPECT) is based on the reconstruction of 3D tomographic sections from the 2D projections acquired by the gamma camera. Iterative reconstruction can incorporate a number of corrections for distortions that occur during the imaging process. One of these is distance dependent resolution (DDR), which takes into account geometric blurring in the projections which increases with distance of the radioactive source from the collimator. Modelling this effect during iterative image reconstruction improves the final tomographic image quality, at the expense of a large increase in the computation required for the reconstruction. Reconstruction with ordered subset expectation maximisation (OSEM) including DDR correction is now universally available in clinical SPECT systems, but it appears very little work has been done to quantify the benefit of the additional processing power required when incorporating the correction in iterative reconstruction. SPECT spatial resolution is commonly measured by imaging a point or line source in air. This theoretically gives an image of the response function of the combination of the camera system and the reconstruction algorithm. However maximum likelihood expectation maximisation (MLEM)-like reconstruction algorithms may be non-linear [1], in which case the spatial resolution will also depend on the image content. This means the reported resolution of the system obtained using simple point or line sources may not correspond to the actual resolution of clinical images. Yokoi et al. [2] investigated DDR correction by simulating the effects of the collimator on projections with software, then reconstructing them with OSEM, including the DDR correction. The full width at half maximum (FWHM) of point sources at the centre of rotation
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improved from 14.7 mm when reconstructed with filtered back-projection (FBP) to 8.1 mm when reconstructed with OSEM using DDR correction. They also demonstrated that DDR caused a marked reduction in noise as measured by the mean square error (MSE) difference between the true values and reconstructions of a brain phantom with OSEM without DDR correction. Several clinical investigations have assessed reconstruction techniques visually, using groups of observers [3– 6]. They generally conclude that OSEM with DDR correction improves the images over plain OSEM or FBP. DDR correction is also commonly used in (visual) comparisons of OSEM to FBP reconstruction, for example, Dickson et al. [7] or Knoll et al. [8], where the reconstruction algorithms of three different gamma camera vendors (using DDR correction) showed varying improvements in resolution when compared to FBP, although it was noted that vendors recommended settings were not always those that produced the best results. O’Mahoney and Murray [9] compared standard (no DDR) OSEM reconstruction with the ‘Astonish’ reconstruction algorithm (which incorporates DDR correction) on images of a triple line source in water and found an improvement in FWHM from 15 to 8 mm. They also noted evidence of edge enhancement artefacts in the images with DDR correction which over-enhanced small sources. A major reason for the paucity of quantitative measures of spatial resolution with DDR may be the non-linear nature of MLEM like reconstruction algorithms that means that the final image quality depends on the characteristics of what is being imaged [1, 10]. Thus resolution improvements seen using point or line sources in air, which can indicate spatial resolutions similar to or better than positron emission tomography (PET), may not be indicative of spatial resolution in clinical SPECT images. In this paper we use two approaches to estimate SPECT spatial resolution in clinical conditions when DDR correction is applied in iterative reconstruction. The first uses simple line sources effectively superimposed on two different extended phantoms, one with simple, and one with complex image content. This ‘perturbation’ method as described by Erlandsson et al. [11] combines the convenience of point or line sources for spatial resolution measurement with a ‘background’ image extent that is typical of clinical images. It thereby minimises the distortions otherwise introduced by MLEM non-linearity in isolated line or point sources. Fakhri et al. [12] validated a similar technique in PET time of flight (TOF) imaging. The second uses a realistic brain phantom for which an accurate digital representation (here called the ‘digital phantom’) is available [13]. The digital phantom is convolved with point spread functions of different widths to find the best fit to the DDR reconstructed physical phantom.
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Materials and methods SPECT projections were acquired for a number of configurations of a line source phantom, a cylindrical container and the Hoffman Brain phantom on two different gamma cameras using 99mTc and a low energy high resolution collimator. Some of these configurations are shown in Fig. 1. The line source phantom consisted of three 1 mm ID tubes which were parallel and configured in a Perspex frame at the corners of an isosceles right triangle with 100 mm shorter sides. The line at the right angle was located along the centre of rotation of the camera. The ends of the tubes were fitted with taps so the tubes could be filled with 99mTc solution. This triple line phantom could be mounted within a cylindrical container to allow imaging in water. The Hoffman brain phantom contains polycarbonate sections precision-milled from digital grey and white matter templates derived from a magnetic resonance imaging (MRI) scan of an individual human brain. At the spatial resolution of a SPECT (or PET) camera the phantom design yields a grey matter to white matter specific activity of 4:1. The digital templates (digital phantom) therefore constitute the ‘truth’ which, after appropriate reslicing (voxel size adjustment) and coregistration to the reconstructed physical phantom, can be used to quantify the accuracy of the physical phantom reconstruction. Iterative reconstruction was performed with version 5.1 of the Macquarie University OSEM package [14] for 1, 2, 3, 4, 8 and 16 iterations without DDR correction and for 2, 4, 8, 12, 32, and 64 iterations with DDR correction. For each of this ‘standard set’ of 11 tomographic images, SPECT spatial resolution was evaluated as follows: Perturbation method The aim of this approach was to assess the SPECT spatial resolution within an activity distribution of clinical extent. A previous implementation scanned a chest phantom before and after insertion of a point source [11]. After reconstruction and subtraction the FWHM of the point source was measured. Here, as with the approach validated by Fakhri et al. [12], we acquired projections of an extended phantom and the line sources independently, and then added them to simulate insertion of the lines within the extended phantom. The triple line source was assessed in two different perturbation experiments, firstly combined with a uniform source, the cylindrical container phantom, and secondly with a complex source, the Hoffman brain phantom. In each case the phantoms were carefully co-located for the sequential acquisitions.
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Fig. 1 Images of some the reconstructed image sets used in these experiments: a shows the line source imaged in air; b shows the cylindrical phantom; c shows an image reconstructed from projections which were the sum of the projections of (a) and (b); d shows an image reconstructed from the addition of the projections of the line source and the Hoffman Phantom in experiment A.2; e shows a cross-section of the image in d showing the three line sources—note the elongation of the lateral (lat) line source compared the central (cen) and posterior (post) lines
Line source—flood phantom experiment (Exp. A.1)
Line source—brain phantom experiment (Exp.A.2)
The line source phantom was first imaged in air with 100 MBq of 99mTc solution in each tube, with the tubes aligned in the z-direction of the camera (shown in Fig. 1a). The centre line source was positioned along the centre of rotation of the camera, and the two other line sources were located 75 mm radially out from the centre line, so their cross sections formed the vertices of a right triangle with the centre source. The line phantom was then imaged inside a 223 mm diameter cylindrical container, filled with non-radioactive water to act as a scatter medium. Attenuation correction was performed using a uniform map generated from a preliminary reconstruction using the method of Barnden et al. [15]. Because lower window scatter subtraction was used, the narrow beam attenuation coefficient of 0.15/cm was used. Images were also obtained of the container of water after the addition of 100 MBq of 99m Tc solution (shown in Fig. 1b). In each instance 120 projections with matrix size 128 9 128 were acquired for 12 s each over 360° on an Irix triple-head camera (40 angles for each of the three detectors) at a radius of 15 cm. Two perturbed image sets were produced by adding the projections of the line source in air and the projections of the line source in water separately to the projections of the container (the former is shown in Fig. 1c). The relative count rates of the projections were adjusted to give a 1:4 background to line source ratio. The ‘standard set’ of OSEM reconstructions were performed with eight subsets.
This experiment was performed on a different gamma camera because the camera used in experiment A.1 had been replaced with a Phillips Brightview. The Hoffman phantom loaded with 250 MBq 99mTc was acquired first. This was then removed and the triple line phantom, loaded with 170 MBq 99mTc, was carefully positioned with its central line where the centre of the brain phantom had been, and acquired in air. For each, 180 256 9 256 projections were acquired for 60 s with radius = 150 mm. Count rates were near 8 k/s. Perturbed projections were generated by adding the brain phantom projections to the triple-line phantom projections after the latter had been scaled to render their maximum values about the same (shown in Fig. 1d and in cross-section in Fig. 1e). The ‘standard set’ of OSEM reconstructions were performed with 12 subsets. The FWHM of the line sources was measured for each of the reconstructed image sets in experiments A.1 and A.2: in air, in water (for experiment A.1 only) and for the perturbed image sets, by fitting a Gaussian to X and Y profiles from transaxial sections. The Gaussian fit optionally included an offset to cater for the line profiles being superimposed on a background from the extended ‘perturbation’ phantom. In the case of experiment A.1 the lines were not well aligned with the Z axis and FWHM of X- and Y-profiles at eleven different sections were measured and their mean computed. In the case of experiment A.2 the lines were well aligned with Z and 20 sections were summed before generating the X and Y profiles.
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Matching of digital brain phantom (Exp. B) The Hoffman phantom was filled with 360 MBq 99mTc and acquired on an Irix triple-head camera with LEHR collimators and a circular orbit with r = 140 mm, for 360° for each head. Each head recorded 120 128 9 128 projections of 30 s duration with magnification 1.33 (pixel size 3.5 9 3.5 mm). To minimise the influence of noise on the assessment of SPECT spatial resolution capability, very high count levels were acquired. Head 1 acquired a total of 29 million counts and only this head was used in the analysis to avoid errors due to sensitivity differences between heads. After imaging, the Hoffman phantom projections were reconstructed into tomographic slices using (lower window) scatter and attenuation corrections, with OSEM with and without DDR correction. The digital Hoffman phantom was coregistered to a preliminary FBP reconstruction using an affine transformation with 9° of freedom and the same transformation was applied to the ‘known’ attenuation map constructed from the digital phantom (attenuation coefficients of 0.153 for water and 0.175 for polycarbonate) for the purpose of attenuation correction in the iterative algorithm [16]. The coregistration step incorporated ‘re-slicing’ to convert the 0.975 9 0.975 9 6.13 mm voxels of the native digital Hoffman images to the 3.5 9 3.5 9 3.5 mm voxel size of the reconstructions. The reconstruction was performed using the ‘standard set’ of iterations and eight subsets. Each of the 11 tomographic images was then compared to the co-registered digital phantom [14] that had been smoothed with varying width 3D Gaussian kernels. The amplitude of the
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difference between them was evaluated using the normalised mean square error (NMSE) P 1 ðxi yi Þ2 NMSE ¼ 1 Pi 1 P N N i xi N i yi where the xi and yi are matching voxel values for all N voxels of the smoothed digital phantom images and the reconstructed images of the physical phantom. This calculated NMSE should reduce with differences between the images, and with noise. A cubic polynomial fit to the FWHM versus NMSE plot was used to estimate a value for the width of the smoothing kernel which produced minimum NMSE (the ‘effective resolution’) for each reconstructed image. For plotting, the FWHM of this kernel was converted from pixels to mm using the pixel size of the image.
Results Figure 2 shows, for experiment A.1, a comparison of the mean of 11 measurements of FWHM of the central line source in images with and without perturbation by background activity, reconstructed with and without DDR correction, in air and in water. FWHM in reconstructed images of the line source phantom both in air and water with DDR correction decreased (i.e., spatial resolution improved) with iteration up to the maximum of 64 iterations. In the uncorrected image sets the resolution improved with iteration until four iterations were reached, but more iteration did not decrease FWHM. The overall resolution was improved when the DDR correction was applied after
Fig. 2 Mean FWHM from X and Y profiles through the central line for different numbers of iterations for the simple perturbed image set (experiment A.1) compared to line sources with no background added, in air and in water, with (left) and without (right) DDR correction
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Fig. 3 Mean FWHM from X and Y profiles through the central line in air for different numbers of iterations for the complex perturbed image set (experiment A.2) compared to the central line with no background, with (left) and without (right) DDR correction
sufficient (8) iterations had been performed. The perturbed data sets showed significant increases in FWHM at the same number of iterations. For images uncorrected for DDR (No DDR), there was no difference after four iterations, while for images with DDR correction the improvement persisted up to the maximum of 64 iterations. In all cases there was no significant difference between measurements made in the x- and y- directions. Figure 3 shows, for experiment A.2, the central line source in air with no perturbation, and in air but perturbed by complex background activity (the brain phantom), the mean measured FWHM in X and Y, with and without DDR correction. The DDR data shows progressive improvement in spatial resolution to 64 iterations, while without DDR, increasing iteration made no improvement. With DDR the spatial resolution when the reconstruction was perturbed by a complex background phantom was markedly worse (larger FWHM) than when the line sources in air were reconstructed unperturbed. Spatial resolutions of the three different lines were similar, with the lateral line showing slightly better values. Inspection of the measured FWHM in X and Y separately indicated the X values were lower than Y (e.g. for 16 iterations FWHM was 7.3 mm for X and 9.0 mm for Y). This elongation of the lateral line can be seen in the cross section image (Fig. 1e). The lateral line, which lies outside of the brain activity, is markedly asymmetric with X (radial) width less than the Y (circumferential) width and less than the X and Y widths of the centre and posterior lines. The off-centre posterior line that lies within the background activity of the brain phantom is much more symmetric.
Plots of NMSE against the FWHM of the smoothing kernel for different iteration numbers of the Hoffman phantom images are compared in Fig. 4 for reconstructions without DDR (right) and with DDR (left). The mean NMSE level for each iteration plot increased with increasing iteration, less rapidly for the DDR corrected reconstruction. As seen in Figs. 2 and 3, spatial resolution (as indicated by the NMSE minimum) progressively improved with number of iterations, but so did the overall NMSE error. The effective resolution decreased with increasing iteration for each reconstruction method and this is shown in Fig. 5 along with the curves for line sources in air with perturbed background from experiments A.1 and A.2.
Discussion and conclusions The results demonstrate that the spatial resolution in images reconstructed using OSEM with DDR is highly dependent on image content. The FWHM of line sources in the perturbed images when DDR correction was used was appreciably larger than that of line sources alone, whether in air or in water. Thus spatial resolution values derived for DDR reconstruction with point or line sources in air during system acceptance testing and routine quality control are not indicative of spatial resolution in clinical practice, where distributed sources are imaged. Without DDR however, although resolution was poorer, it was largely independent of image content. Increasing iteration did not significantly change the relative effect of the image content in the perturbed data
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Fig. 4 NMSE against FWHM of the smoothing kernel for different numbers of iterations for images of the Hoffman phantom reconstructed with OSEM (8 subsets) with (left) and without (right) DDR correction
Fig. 5 Effective resolution of Hoffman phantom images (experiment B) compared to line sources in air perturbed by simple (experiment A.1) and complex (experiment A.2) backgrounds. Experiments A.1 and B applied 8 subsets/iteration while experiment A.2 used 12 subsets/iteration
sets, suggesting that the DDR non-linear effects are not iteration dependent. The ‘effective resolution’ from the digital brain phantom matching method (Fig. 4) improved with iteration whether the DDR correction was applied or not. However, without DDR correction both line source perturbation methods showed resolution unchanged or worsening at higher iteration numbers and worse on average. The effect of the coregistration of the digital image could not be quantified, but could be expected to degrade the resolution slightly in
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addition to the smoothing applied within the method. The measurements of FWHM for the Hoffman phantom at similar values of NMSE showed better resolution in the no DDR images at low DDR iteration numbers, but this reversed with increasing DDR iterations. The two perturbation methods were performed on different gamma camera systems. We compared SPECT spatial resolution for perturbed line sources in air with both. Better resolution was observed for the camera used with the flood perturbation (experiment A.1) than for the
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camera used with the brain phantom perturbation (experiment A.2). For example, with 32 DDR iterations the central line FWHM was 4.8 mm compared to 7.2 mm. Because similar resolution LEHR collimators were used (system resolution at 10 cm = 7.6 and 7.4 mm), it would appear the low complexity of the container compared to the brain phantom is the main effect here. This is supported by the digital phantom approach (experiment B) yielding effective FWHM = 7.4 mm on the same camera used in experiment A.1 (Fig. 3). The phantom acquisitions here were idealised with regard to count levels and radius of rotation. Clinical images seldom have the very high count levels used here. Therefore clinically, noise levels will be higher and, if clinical practice demands that smoothing be performed to provide acceptable image appearance, the resolutions obtained in the perturbation experiments will not be attainable. In particular the results obtained for line sources acquired in air will only be clinically relevant if accurate, low noise scatter subtraction is available in clinical image reconstruction with DDR. Similarly, clinical practicalities mean that radius of rotation will be greater than that used in these experiments. This can be expected to degrade the SPECT spatial resolution further, despite the use of DDR correction, and could be the subject of further work. Nevertheless, these results indicate the resolutions that would be attainable in ideal imaging situations with ideal scatter subtraction.
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