Ubicación de la Catequesis entre las funciones eclesiales

Conventional wisdom dictates that, when all other reconstruction parameters are kept constant, noise in the 256 matrix images should exceed that of the 192 matrix, which should in turn exceed that of the 128 matrix, because smaller voxels have increased statistical noise (as discussed in Chapter 1). However, the previous section demonstrated that Image Roughness appeared to decrease as the matrix size increased. These results were therefore analysed further to determine if there were any confounding effects caused by combinations of reconstruction parameters.

Figure 6.8 illustrates the relationship between matrix size and Gaussian filter FWHM for Image Roughness. Each row in Figure 6.8 represents a different combination of the remaining reconstruction parameters (reconstruction method, z-axis filter weight and effective iterations). There are 80 different combinations of reconstruction method, z-axis filter and effective iterations in the dataset used for this chapter. All 80 combinations were produced; while only four of these plots (selected at random) are presented in this chapter for brevity, all 80 plots demonstrated the same pattern of results shown in Figure 6.8. The dotted line on the plots indicates the 4mm Gaussian filter width, which is suggested by GEMS for clinical imaging.

At low filter widths (up to approximately 2mm FWHM), Image Roughness results are as one would expect: the 256 matrix produces the greatest Image Roughness whilst the 128 matrix produces the lowest Image Roughness. As the filter width increases, Image Roughness of the larger matrices begin to reduce at a lower filter FWHM than the smaller matrices:

• 256 matrix requires FWHM > 1mm to reduce Image Roughness • 192 matrix requires FWHM ≈ 2mm to reduce Image Roughness • 128 matrix requires FWHM ≈ 3mm to reduce Image Roughness

One would expect this to be the case; wider Gaussian filter widths are required to impact the filtered values of larger voxels. One would also expect the smallest voxels to continue to produce the greatest noise levels regardless of the filter applied, until such point that the filter width is large enough to produce similar results for all matrix sizes. However, as the filter width increases beyond approximately 3mm, the relative Image Roughness pattern of the three matrix sizes begins to follow an unexpected pattern:

• 256 matrix Image Roughness falls below 192 matrix at FWHM ≈ 3mm • 256 matrix Image Roughness falls below 128 matrix at FWHM ≈ 4mm • 192 matrix Image Roughness falls below 128 matrix at FWHM ≈ 4.5mm

Figure 6.8: Unexpected relationship between Image Roughness, Gaussian filter width and matrix size

Each row represents a different combination of remaining reconstruction parameters. Dotted lines indicate GEMS recommended Gaussian filter width for clinical imaging.

At filter widths greater than ≈ 4.5mm, the expected Image Roughness noise pattern is entirely reversed: the smallest voxels produce the lowest Image Roughness, while the largest voxels produce the greatest Image Roughness. At larger filter widths (≈ 9mm), all three matrix sizes produce very similar results.

As this relationship between Image Roughness, matrix size and filter width was an unexpected finding, an additional analysis was performed on a subset of the reconstruction using Matlab instead of Hermes Hybrid Viewer, in order to rule out any problem with the measurement technique. The Matlab analysis produced the same relationship between noise, matrix size and Gaussian filter width.

6.4.2.1

_{F-FDG Patient Liver Noise Analysis}

A small retrospective patient study was performed to verify this unexpected relationship between noise, matrix size and Gaussian filter width wasn’t limited to the 68_{Ge cylindrical}

phantom experiment. Ten consecutive patients reported to have no liver abnormalities were selected. All patients were fasted for at least 6 hours and received intravenous injections of 400MBq +/- 10%. Imaging was performed 60 minutes post-injection. Patient BMIs ranged from 20.6 to 35.4. Each set of patient data was retro-reconstructed 33 times, as follows: • Gaussian filter FWHM: varied from 0mm to 10mm, in 1mm increments

• All three matrix sizes: 128, 192, 256

• Remaining reconstruction parameters kept constant: HD reconstruction, 54 effective iterations, and no z-axis filter applied. Transaxial FOV kept constant at 700mm. These reconstruction parameters matched those of the first graph in Figure 6.8.

Image Roughness for each patient liver was analysed by placing three 3cm diameter ROIs on three consecutive transaxial slices of the liver. The ROIs were positioned in visibly uniform areas of the liver, avoiding major blood vessels. This method of liver noise analysis has previously been used in studies by Akamatsu et al [132], [134], [146] and Taniguchi et al [145].

Figure 6.9 shows a transaxial liver slice from the patients with the smallest and largest BMI, as well as their Image Roughness versus Gaussian FWHM plots. All ten patient analyses demonstrated similar findings: the unexpected relationship between noise, matrix size and Gaussian filter width is also observed for patient data. As one would expect, Figure 6.9 also demonstrates the noise in the larger patient is greater than that of the smaller patient, both qualitatively and quantitatively.

Small Patient BMI = 20.6

Large Patient BMI = 35.4

Figure 6.9: Patient liver images and Image Roughness results Example reconstruction images used 4mm FWHM Gaussian filter and 192 matrix.

6.4.2.2 Correspondence with GEMS Engineers

Dr Charles Stearns, the senior engineer at GEMS, was contacted directly about these unexpected findings (personal correspondence, 1st _{August 2016). As Dr Stearns had not}

encountered this phenomenon before, he performed his own simulation of the GEMS Gaussian filter operation for different matrix sizes and filter FWHMs, and produced the same unexpected relationship between noise, matrix size and filter FWHM demonstrated by the work in this chapter.

Dr Stearns explained the Discovery 690’s Gaussian filter is implemented by creating a Gaussian curve of the specified FWHM and selecting samples from the curve at intervals that correspond to the voxel widths. The filter is truncated to ± 4σ, where σ is the standard deviation, with a minimum of three points in the kernel, normalised to give a total of 1.0. As a result of this implementation method, the filter is close to [0 1 0] at lower filter widths. As the filter width increases, it operates more like a three-point averaging filter instead of a true

Gaussian. The Gaussian filter is therefore not a true Gaussian. The sampling of the Gaussian curve using the voxel width causes the unexpected relationship between noise, matrix size and filter FWHM.

Dr Stearns simulated the Image Roughness results that would be obtained using an ideal Gaussian filter, shown in Figure 6.10 below. The ideal filter is designed as the integral under the Gaussian for each voxel, instead of simply sampling a point from the Gaussian curve for each voxel. This implementation produced the expected relationship between different matrix sizes; noise in the larger matrices always exceeded that of the smaller matrices until such point that the filter width is large enough to produce similar noise results for all matrices.

Figure 6.10: GEMS sampled Gaussian filter versus ideal Gaussian filter Adapted from simulations provided by Dr Charles Stearns (personal communications, 1st _{August 2016).}

6.5 Discussion

Although the effects of effective OSEM iterations, filtering, voxel size, PSF and TOF upon PET image noise had been widely assessed in the literature, no single study had examined the effects of all of these parameters in combination. In particular, the combined effect of matrix size and filters on PET image noise had not yet been evaluated fully. Furthermore, there remains no universally agreed approach to clinically relevant noise assessment in PET imaging. This chapter therefore aimed to characterise the combined effects of these reconstruction parameters on both pixel-to-pixel noise (Image Roughness) and region-to- region noise (Background Variation) in a clinically relevant manner and assessed the use of the widely available 20cm diameter uniform 68_{Ge phantom for this purpose.}

PSF was found to improve Image Roughness but had a small detrimental effect upon Background Variation, similar to results from previous studies [19], [86], [134], [135], [140].

This remained the case even when combined with TOF, when at least 54 effective iterations were applied. The clinical implications of this finding are difficult to determine by assessing noise in isolation; the effects of PSF noise characteristics upon lesion detection are examined later in this thesis. For example, human observers may not agree that the correlated background activity produced by PSF improves image quality with respect to lesion detection, even though the Image Roughness metric suggests an improvement. TOF was shown to produce similar, but increased, Image Roughness results to the HD reconstruction when up to 180 effective iterations were applied. While this effect is partly caused by the early convergence of TOF, the 20cm diameter of the uniform phantom is not large enough to fully demonstrate the advantages of using TOF [19], [133].

The assessment of the remaining reconstruction parameters largely agreed with previously published studies. The number of applied effective iterations had a significant effect upon both Image Roughness and Background Variability: both noise metrics increased as the number of effective iterations increased, as expected [43]. Both the Gaussian filter and the z-axis filter were shown to reduce image noise, also as one would expect [44]. Z-axis filtering was shown to have a greater effect on Background Variation than the Gaussian filter, while the Gaussian filter was shown to have a greater effect on Image Roughness than the Z-axis filter. This suggests the Z-axis filter should be given greater consideration in mitigating the detrimental effects of PSF on Background Variation. As discussed in Chapter 2, the effect of Z-axis filtering is not as widely discussed in the literature as filtering in the transaxial plane, as z-axis filtering has not been adopted by all vendors.

One would expect the use of larger matrices, and hence smaller voxels, to result in increased image noise, as discussed in Chapters 1 and 2. However, the effects of matrix size were not as expected; the larger matrix produced the smallest median results for Image Roughness. Only the outlying results, corresponding to reconstructions which used little or no filtering, followed the expected noise pattern as the matrix size increased. An unexpected relationship, previously unknown to even GEMS, was therefore identified after further analysis. At certain filter widths (between approximately 3mm and 9mm FWHM), Image Roughness in the larger voxels exceeds that of the smaller voxels. This may have clinical relevance as GEMS suggest using a 4mm filter with a 192 matrix for clinical image reconstruction. If an imaging centre who initially followed the GEMS suggested reconstruction strategy wished to increase the matrix size from 192 to 256, e.g. with a view to improving the spatial resolution of their images, they would expect the image noise to increase. The work in this chapter has shown that, in fact, the measured noise would decrease. This raises questions as to how the change in matrix size would affect spatial resolution: if using smaller voxels unexpectedly improves the noise, could spatial resolution be unexpectedly worsened? Spatial resolution is investigated over the next two chapters.

All Image Roughness results were compared with the 15% COV limit recommended by European guidance. The results in this chapter demonstrated that the number of effective iterations, the Gaussian filter width and the use of PSF were the dominant parameters in terms of achieving this limit. At 54 effective iterations, as suggested by GEMS for clinical reconstructions, all Image Roughness results were below the 15% limit when PSF was used, even when no filtering was applied. The majority of PSF results at 90 effective iterations were also below this 15% limit (the limit was only breached when a Gaussian filter width of less than 4mm was combined with no z-axis filtering for PSF-only). The GEMS suggested reconstruction parameters for clinical imaging (54 effective iterations, PSF+TOF, 4mm Gaussian, “standard” z-axis filter and 192 matrix) produced 8.8% Image Roughness, below the 15% limit; this fell to 8.4% when a 256 matrix was used instead.

European guidance on 18_{F-FDG imaging, discussed in Section 2.1, state that matrix sizes}

and zoom factors should be chosen such that reconstructed voxel sizes should be between 3mm and 4mm in any direction. The reason for this is not explicitly stated but is presumably to achieve acceptable spatial resolution whilst suppressing noise in the reconstructed images. Whole-body imaging on the GEMS Discovery 690 typically requires a 700mm transaxial FOV (the z-axis FOV is fixed at 157mm, with axial sampling fixed at 3.34mm). This means that only the 192 matrix complies with this voxel size recommendation:

• 128 matrix produces voxel sizes 5.47mm x 5.47mm x 3.34mm • 192 matrix produces voxel sizes 3.65mm x 3.65mm x 3.34mm • 256 matrix produces voxel sizes 2.73mm x 2.73mm x 3.34mm

The EANM guidelines also state that the maximum Gaussian filter width should be 7mm; however, no recommendations are made in terms of combinations of filters and matrix size. The guidelines may therefore merit review as a result of the unexpected relationship between noise, filters and matrix size, particularly if the motivation for restricting voxel size was to limit image noise rather than reconstruction time. The use of the 256 matrix, and hence sub 3mm voxel sizes, may be more appropriate for whole-body imaging using the GEMS Discovery 690.

The major limitation of this study was the use of a single, relatively small phantom. A larger phantom is required to fully assess the effects of TOF upon image noise; larger phantoms would also provide more realistic representations of patient body habitus for whole-body PET imaging. A larger phantom will be inherently noisier; this will therefore also affect which reconstruction parameters achieve the 15% EANM noise limit. However, it should be noted that the count density of the phantom used in this chapter was conservative when compared to that of 18_{F-FDG patient livers, as discussed in Chapter 4; statistical noise levels within}

Furthermore, the results of this phantom may be applicable to other clinical applications, for example paediatric or head and neck imaging. Both Image Roughness and Background Variation are assessed using a larger phantom in Chapter 9 (alongside other image quality metrics). Patient data is also used to assess noise later in this thesis.

6.6 Conclusions

This chapter concludes that, with the exception of matrix size, the effects of the reconstruction parameters upon both Image Roughness and Background Variation were as expected, and consistent with the literature.

This chapter further concludes that an unexpected relationship exists between matrix size, Gaussian filter width and noise measurements on the GEMS Discovery 690 PET-CT imaging system. Although the effect is small, it may cause confusion when assessing the effects of increasing matrix sizes; for example, when attempting to improve spatial resolution of reconstructed images. Furthermore, this effect may be of clinical interest as it applies to the GEMS suggested Gaussian filter width (4mm). The reasons for this phenomenon, previously unknown to even the GEMS engineers, were confirmed by GEMS as being a result of the sampled Gaussian filter implementation.

Furthermore, this chapter concludes that the EANM guidelines for voxel sizes may merit review. To achieve the recommended voxel size of between 3mm and 4mm on the GEMS Discovery 690 when the full 700mm FOV is used requires the use of the 192 matrix, which can produce greater noise than the 256 matrix when combined with specific Gaussian filter widths. The effects of the GEMS Gaussian filter implementation discovered in this chapter may therefore undermine the intentions of this voxel size guideline.

Finally, this chapter concludes that the 20cm diameter cylindrical phantom is not large enough to fully demonstrate the effects of TOF when assessing image noise; however, the results remain applicable to imaging of smaller structures (e.g. head and neck or paediatrics). A larger phantom is used in the latter chapters of this thesis to assess noise in a manner which is more clinically relevant to liver imaging.

Further work should involve assessing the relationship between matrix size, filtering and image noise measurements using PET systems from other vendors. This would determine if the unexpected relationship observed in this chapter is unique to GEMS or more widespread throughout the PET imaging community.

It should also be noted the analysis in this chapter focussed on five image slices at the centre of the axial FOV, where sensitivity is at its maximum. Further assessment of the z- axis filter should involve assessing its effects within the low-sensitivity, higher-noise overlap area between bed positions.

An abstract based on some of this chapter’s work was accepted for a poster presentation at the 2016 Institute of Electrical and Electronic Engineers (IEEE) Medical Imaging Conference.

Chapter 7 : Development of Methodology for Clinical