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BASIC SCIENCE INVESTIGATIONS |
Clinical PET Center, University Hospital Vrije Universiteit, Amsterdam, The Netherlands
| ABSTRACT |
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Key Words: iterative reconstruction dynamic PET quantitative accuracy kinetic modeling
| INTRODUCTION |
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Maximum likelihood expectation maximization (MLEM) iterative reconstruction for emission tomography was first developed by Shepp and Vardi (1). Hudson and Larkin (2) proposed an ordered-subset expectation maximization (OSEM) implementation of the algorithm. Introduction of the latter algorithm decreased the reconstruction time considerably and made it feasible to apply OSEM in daily clinical routine.
Several studies have evaluated the characteristics of the expectation maximization algorithm for use in PET (312). Miller and Wallis (8) performed phantom studies to assess the effect of MLEM on PET and SPECT image contrast, resolution, and noise as a function of the number of iterations. The studies showed that MLEM resulted in improved image contrast and SNR depending on the number of iterations. Liow et al. (6) showed that, for three-dimensional PET, MLEM reconstructions resulted in better resolution than did FBP. Reader et al. (9) compared several three-dimensional reconstruction techniques for PET, showing that, compared with FBP, three-dimensional OSEM gave the best contrast at the cost of increased noise. Disadvantages of OSEM, however, included its relatively slow convergence, amplification of noise with increasing number of iterations, and the dependence of its characteristics on source distribution. The number of iterations required to achieve reliable quantitative results while keeping noise within acceptable levels should be carefully selected, as described by Wang et al. (11) and de Jonge and Blokland (13). A clinical evaluation of OSEM for attenuation-corrected whole-body PET studies was performed by Lonneux et al. (7). This study revealed that AC-OSEM images were less noisy and easier to interpret than FBP images.
Although the characteristics of OSEM have been investigated extensively and its superior image quality compared with FBP is well documented (7), most studies have focused on image quality of OSEM for static diagnostic whole-body PET studies. Data on the performance of OSEM for dynamic quantitative PET studies are limited. Katoh et al. (5) observed higher reproducibility and lower variability in the metabolic parameters obtained from iterative median root prior reconstructed images compared with those obtained from FBP images. They recommended use of median root prior reconstructions for quantitative myocardial 15O PET studies. The application of iterative reconstruction techniques for dynamic PET studies of different organs, however, still needs to be evaluated.
Recently, an OSEM algorithm has become widely available as part of commercial software for the ECAT HR+ PET scanner (CTI/Siemens, Knoxville, TN). Consequently, increased use of OSEM can be expected. Therefore, an analysis of the performance of OSEM is needed to warrant its use in quantitative dynamic PET studies. In this study, the quantitative accuracy and SNR of this commercially available OSEM algorithm will be compared with those of FBP. First, phantom studies were performed to assess the quantitative accuracy and SNR of reconstructed emission scans as a function of noise equivalent counts (14) of emission and transmission scans, phantom size, and source distribution. Next, effects of OSEM versus FBP on tissue activity concentration and kinetic modeling were evaluated for a variety of 18F-FDG studies. Finally, use of image-derived input functions obtained from OSEM reconstructed data were addressed.
| MATERIALS AND METHODS |
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Phantom Studies
Acquisitions.
Dynamic phantom studies were acquired in two-dimensional mode as dynamic emission (Ex) scans with 10-min frames and 20-min intervals over a 14-h period. Emission scans were performed for the following phantoms: homogeneous phantoms of 2-, 5-, 10-, and 20-cm diameter, initially filled with an 18F solution of high concentration (300 kBq/mL); NEMA phantom (20-cm diameter) filled with an 18F solution (300 kBq/mL) and cold 5-cm-diameter inserts; and NEMA phantom filled with a moderate 18F background (40 kBq/mL) and a high-activity 11C insert (450 kBq/mL). Because of the 20-min half-life of 11C, an emission scan was acquired for 5 h only for the last phantom. All phantoms were positioned at 1 cm from the center of the field of view. After activity had decayed to background level, Tx scans of 2, 5, 10, 15, 30, and 60 min were acquired.
In addition to these phantom measurements, line spread functions (LSFs) were obtained by scanning a line source of 1-mm thickness positioned at 1 cm from the center of the field of view. These latter measurements were performed for comparison with apparent resolution measured with the NEMA phantom insert studies, as it has been shown that that resolution convergence is object dependent and that, therefore, the line spread function may not represent the resolution in more realistic emission distributions (18,19).
Reconstructions.
All Ex data were reconstructed with measured attenuation using FBP with a Hanning filter at 0.5 of the Nyquist frequency and OSEM reconstructions (CTI version 7.1.1) with various numbers of iterations and subsets (2 x 12, 3 x 24, and occasionally 5 x 12, 5 x 24, and 12 x 24). OSEM with 2 x 12 iterations was used as default. With OSEM reconstruction a nonnegativity constraint is applied, which means that negative line of response (LOR) values (because of randoms correction) and negative pixel values are set to zero. The 60-min Tx scan was used for all reconstructions except when analyzing the contribution of Ex and Tx noise equivalent counts (NECs) to image noise, which were reconstructed using all measured Tx scans. Attenuation correction was performed by multiplying the emission sinograms with attenuation correction factors before reconstruction. To improve statistics of the attenuation correction, transmission scan data were smoothed with an 8-mm full width at half maximum (FWHM) Gaussian filter, as implemented by the manufacturer (CTI/Siemens).
Analyses.
For each dynamic scan, image noise or pixel heterogeneity and quantitative accuracy were derived from region-of- interest (ROI) analysis. Image noise was defined as the coefficient of variation (COV, 100 x SD/mean [%]) of the pixel values within a homogeneous ROI. Bias was defined as the deviation of the mean pixel value within an ROI from the actual activity concentration. The actual activity concentration was obtained by taking samples from the phantom and measuring these in a cross-calibrated well counter, which had an estimated accuracy within 2%. For the homogeneous phantoms a circular ROI with half the diameter of the phantom was positioned centrally in the phantom. A potential drawback of using large ROIs could be that small low-frequency nonuniformities in the phantom could contribute to the COV, thereby overestimating image noise. An evaluation using the mean COV of several smaller ROIs, however, illustrated that the effects of nonuniformities were negligible (<2%). For the NEMA phantoms (with both cold and 11C inserts) an ROI of 5-cm diameter was positioned centrally within the background area and 2-cm-diameter ROIs were positioned centrally within the inserts. ROIs were placed in planes 657, excluding the first and last five planes at the edges of the axial field of view, because of the larger variation in scanner sensitivity in the first and last five planes. For all scans, logfiles of the acquisition were generated, listing the number of counts (both random and true) for each frame, thus enabling calculation of whole-scanner NEC. Data were analyzed as a function of whole-scanner NEC or activity concentration. The relationship between image noise and the NEC of Ex and Tx scans can be described by:
![]() | (Eq. 1) |
![]() | (Eq. 2) |
![]() | (Eq. 3) |
For NECTx the contribution of scattered coincidences was assumed to be negligible because rod windowing was used during transmission scanning. In addition, the relationship between image noise and NECEx as a function of the number of iterations of OSEM was studied. For the latter analysis a 60-min transmission scan was used for which the NEC contribution to the image noise is negligible. The relationship between image noise and emission NEC can now be described by:
![]() | (Eq. 4) |
In addition to noise and bias analyses, activity profiles across the edge of insert and background of the NEMA phantom were generated. The shapes of these activity profiles were analyzed as functions of the number of iterations of OSEM and compared with the FBP data. This latter analysis was performed for comparison with resolutions measured with the LSF studies.
Patient Studies
Acquisitions.
Two-dimensional FDG dynamic emission scans for five cardiac, three lung tumor, and three brain studies were used. For the lung tumor studies three separate lesions were imaged on average, thus allowing an OSEMFBP comparison for a total of nine separate tumors of different shape and size. After the patient was positioned, a 15-min Tx scan was acquired for the purpose of attenuation correction of the subsequent Ex scan. This two-dimensional dynamic emission scan was started simultaneously with injection of 370 MBq FDG and consisted of 39 frames with durations ranging from 5 s at the beginning to 300 s at the end of the scan. For heart and brain studies, input functions were measured using a continuous flow-through automatic blood sampling device (21).
Reconstructions.
Patient data were reconstructed using FBP with a Hanning filter at 0.5 of the Nyquist frequency, OSEM with 2 iterations of 12 subsets and 4 iterations of 16 subsets, and the same OSEM reconstructions but with 5-mm FWHM Gaussian postsmoothing of the reconstructed image. Smoothing was performed to reduce the image resolution from about 5-mm to about 7-mm FWHM, thereby matching it to that of the image resolution obtained with FBP Hanning 0.5. Resolution matching was required to assess the extent to which differences between reconstructions could be explained by resolution effects, as shown by Carson et al. (22). The size of the kernel was determined by smoothing the OSEM images of the last frame of each dynamic scan with 3-, 4-, 5-, 6-, and 7-mm FWHM Gaussian filters. ROI values (provided in the following paragraph) derived from smoothed OSEM and FBP images for all studied patients showed best agreement when a 5-mm FWHM Gaussian filter was used. The 5-mm FWHM filter was applied for all studies, though slightly smaller or larger filter sizes may have been more appropriate for individual cases, because resolution is not uniform throughout the image (16) and is object dependent for OSEM reconstructions (9,19). In practice, however, use of a varying postsmoothing filter is not feasible. For the lung tumor studies only OSEM with 2 x 12 iterations was used, because image quality was too poor for 4 x 16 iterations.
Analyses.
Tissue timeactivity curves and activity concentrations were derived from manually positioned ROIs. For cardiac studies a template consisting of 13 ROIs (6 for the basal part, 6 for the distal part, and 1 for the apex) was positioned on short-axis slices. In addition, ROIs for septum, apex, and lateral wall of the myocardium were defined on transaxial slices. For the lung tumor studies 50% isocontours were applied. All isocontours of one tumor across multiple axial slices were grouped to obtain a volume of interest (VOI). This VOI was used to derive the tumor timeactivity curve. In total, nine tumor VOIs were defined in three patient studies. Finally, for the brain studies 1-cm circular ROIs were defined in representative areas of gray matter. In addition to arterial blood sampling, image-derived input functions were obtained for the cardiac studies. For lung studies only image-derived input functions were used. For cardiac studies VOIs were drawn on the aorta ascendens and left ventricle, which are the most commonly used structures for deriving input function, and for lung tumor studies VOIs were drawn as described elsewhere (23). The size of these VOIs was at most half the size of the dimensions of the vascular structure to minimize partial-volume and spillover effects.
First, OSEM-reconstructed activity concentrations were evaluated for data with high NEC values by comparing mean ROI values obtained with FBP with those obtained during the last 15 min of the PET scan (4560 min; last three sinograms were added before reconstruction). To evaluate the agreement of the reconstructed data for the entire PET scan, tissue timeactivity curves in combination with a measured arterial plasma curve (input function) were used to calculate the metabolic rate of glucose (MRglu) using both a standard two-tissue compartment model with blood volume parameter and Patlak analysis. Finally, the agreement of image-derived input functions using OSEM and FBP was evaluated. First, the area under the curve (AUC) was calculated for each image-derived input function. Second, the average ratio of activity concentration between OSEM and FBP for 2060 min of the PET scan was determined.
| RESULTS |
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Data of the NEMA phantom with the hot 11C insert were used to assess the quantitative accuracy as a function of image contrast. During this study the NECEx varied from about 107108 counts, which is better than normally encountered in clinical practice. The randoms/trues fraction ranged from 0.06 to 0.81. In Figure 4 the ratio of reconstructed and actual activity concentration is given for various OSEM reconstructions and FBP as a function of image contrast (ratio of true activity concentration between insert and background). For image contrasts <0.3, that is, for insert activity concentration < one-third of the background activity concentration, an increasing bias (up to a factor of 3) was observed. With an increasing number of iterations, bias decreased from a factor of 3 to a factor of 1.5 (for OSEM 2 x 12 and OSEM 5 x 24, respectively). No improvement of bias was observed with further increases of the number of iterations. In fact, occasionally bias increased with more iterations. The randoms/trues fraction was <0.12 for data with image contrast <0.3.
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| DISCUSSION |
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The data given in Table 1 reveal that the contribution of NECTx to noise COV was smaller for OSEM than for FBP, which is in close agreement with clinical data reported by Lonneux et al. (7). One can conclude that OSEM leads to improved image quality with respect to SNR for attenuation-corrected PET scans compared with FBP. Recently, weighted attenuation schemes for OSEM reconstruction have been developed (29) that incorporate the attenuation correction within the OSEM reconstruction. In this study, attenuation correction factors were applied before reconstruction. With the new weighted OSEM schemes, a further reduction of the contribution of noise in the Tx scan NEC to the image noise can be expected, which would further improve image quality for attenuation-corrected whole-body studies, potentially allowing shorter Tx scans. Further studies are required to quantify this potential improvement.
When the number of iterations was increased, the relationship between image noise and NECEx could no longer be described by a square root relation, as the PL coefficient of Equation 4 progressively deviated from 0.5. This effect indicates that noise amplification with increasing number of iterations is not equal for all NECEX but increases with decreasing NEC. This observation might be explained by the positivity constraint applied in OSEM; that is, the cutoff of negative values will limit the increase in COV, as explained by Qi and Leahy (30). This observation is in contradiction with that of Budinger (25). This may be caused by differences in NEC range because of the use of different PET scanners. In this study data were acquired with the ECAT HR+, which features small crystals that result in high resolution, but which also has a limited number of counts per LOR. Bayesian iterative reconstruction methods have been developed to avoid noise amplification with increasing iteration numbers. This may result in better convergence of reconstructed data while keeping image noise within acceptable levels (5,12,3137). Investigation of the usefulness of these new algorithms, however, is beyond the scope of this study.
Holm et al. (26) and Pajevic et al. (28) showed that image noise depends on source distribution or phantom size for FBP reconstructions. In this study the geometric dependency of the relationship between image noise and NEC found for OSEM was different from that found for FBP. For small hot spot regions or phantoms OSEM resulted in higher image noise, whereas for large regions or phantoms OSEM resulted in lower image noise, as shown in Figure 3. This relationship between image noise and phantom size for OSEM might be explained by variation of resolution with phantom size or object-dependent resolution recovery, as shown by Yao et al. (19), Liow and Strother (18), and Pan et al. (38). The resolution experiment showed that OSEM has higher resolution for a line source (very small object), whereas it has poorer resolution for larger phantoms, as will be discussed later. The clinical relevance of this observation is that the improved image quality seen in whole-body studies is caused mainly by the improved noise reduction in the (large) background regions.
Quantitative accuracy for OSEM reconstruction was similar to that for FBP for most phantom studies. In general, accurate activity concentrations or ROI values within 3% were obtained. Furthermore, quantitative accuracy of hot spots of both OSEM and FBP did not depend on phantom size and NECEx. Large bias, however, was found for regions enclosed within a 5- to 10-fold hotter background. Part of this bias is explained by lack of convergence for a smaller number of iterations, as shown in Figure 4. Note also that for hot regions within a colder background, convergence is obtained earlier than for a cold region within a hotter background. The remaining bias for a large number of iterations might stem from the implementation of randoms correction as a precorrection in sinogram space. LORs intersecting the cold region have a limited number of prompts, whereas the hot background induces a relatively high randoms rate. Online correction of the randoms may then result in negative "trues" for these LORs. With OSEM these negative values are set to zero, resulting in bias specifically for regions enclosed within hotter backgrounds. In clinical studies OSEM should be used with care for cold regions enclosed within hotter areas, such as white matter regions in brain studies and the left ventricle in myocardial studies. New OSEM algorithms such as the shifted Poisson model (32), which can take the effects of randoms corrections into account, are currently under development. At present, these new algorithms are not yet widely available and their use has not been fully validated for PET studies.
Differences in resolution between data obtained with a rod source (LSF) and the NEMA phantom again indicate the difference in speed of convergence for small hot regions within a colder background compared with regions enclosed within a hotter background. Generally, it is assumed that improved resolution can be obtained with OSEM. The current data suggest that careful assessment of image noise versus convergence trade-off as a function of the number of iterations should be performed for each object or organ being scanned. This conclusion agrees with that of Reader et al. (9) and Yao et al. (19), who observed that the performance characteristics of OSEM depended on source distribution. However, in the study of Reader et al. (9), neither resolution nor the application of OSEM to dynamic studies was considered.
Patient Studies
For most studies, ROI value (4560 min), timeactivity curve, and MRglu analyses indicated that FBP and OSEM reconstructions after resolution matching resulted in essentially identical tissue ROIs, provided that sufficient iterations were applied. Use of template ROIs on short-axis slices for myocardial PET studies showed a somewhat different result. For these studies the effects of smoothing and number of iterations were very small because use of short-axis slices reduces resolution during the reorientation process and because use of template ROIs includes areas with high and low activity concentrations. Especially, partial inclusion of left ventricle voxels and spillover effects may mask the effects of resolution differences among various OSEM reconstructions. For brain studies OSEM with 4 x 16 iterations was required to obtain images with sufficient accuracy, that is, with full convergence. This result is in close agreement with the data obtained during the phantom study indicating that for heterogeneous activity distributions, such as cold regions within a hotter background, convergence is slower than for small hot regions within a colder background, such as tumors and myocardium. It can therefore be concluded that, for tissue ROIs, OSEM and FBP provide similar results and that OSEM without smoothing provides an opportunity to achieve higher resolution resulting in fewer partial-volume effects. Optimization of the number of iterations is, however, required for each organ being scanned, as previously shown by Yao et al. (19).
In contrast, use of image-derived input functions based on OSEM reconstructions seemed more problematic over the interval of 2060 min after injection. Input functions derived from the aorta ascendens and left ventricle showed 30% higher activity concentrations than in corresponding FBP data. The bias in activity concentration would cause a similar large effect on MRglu calculations. Van der Weerdt et al. (39) showed good agreement (within 5%) between image-derived input functions and arterial sampling using FBP. With OSEM this agreement would deteriorate to a difference of about 35%. Data presented in Figure 4 suggest that part of this bias can be explained by image contrast. These results indicate the limitation of the current OSEM method to obtain accurate quantitative results in the presence of high image contrasts. Other OSEM methods, such as the newly developed shifted Poisson model (32), that take the effects of randoms correction into account might improve the quantitative accuracy of OSEM reconstructions.
| CONCLUSION |
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| ACKNOWLEDGMENTS |
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| FOOTNOTES |
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For correspondence or reprints contact: Ronald Boellaard, MD, Clinical PET Center, University Hospital Vrije Universiteit, P.O. Box 7057, 1007 MB Amsterdam, The Netherlands.
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