PET SPATIAL RESOLUTION LIMITATIONS

Spatial resolution is a measure of an imaging system’s ability to accurately distinguish between two close together objects and observe their details [69]. The point spread function (PSF) is used to describe the response of the imaging system to a point source. Spatial resolution is typically described by the full width half maximum (FWHM) of the PSF at various positions within the FOV [70]. Figure 1.5 shows an ideal point source and its frequency spectrum (green lines): all spatial frequencies are required for an accurate point source representation [71]. A detection system with a typical Gaussian PSF would produce the PSF shown by the red lines in Figure 1.5. Its frequency spectrum shows the loss of high frequency components, which results in the loss of fine detail in the reconstructed images.

Figure 1.5: Point source in spatial and frequency domains

There are a number of factors that affect the spatial resolution of PET images.

1.6.1 Emission Process

The distance travelled by a positron prior to annihilation introduces an inherent spatial resolution limitation. Coincidence detection relates to the site of annihilation rather than the site of the positron’s parent nucleus. Higher energy radionuclides have greater positron ranges in tissue than lower energy radionuclides. For example, 18_{F (0.6mm mean positron}

range) will produce images with better spatial resolution than 15_{O (1.5mm mean positron}

range).

A second inherent spatial resolution limitation results from non-colinearity of the annihilation photons. Positrons typically have some residual momentum at the point of annihilation. This causes a small deviation from 180° between the anti-parallel annihilation photons, which in turn causes the LOR between the two detectors to be slightly displaced from the point of annihilation. The maximum deviation from 180° is ±0.25° [72]. The effect of non-colinearity worsens as the size of the detector ring increases. For an 80cm FOV, non-colinearity amounts to ≈ 1.8mm [61].

1.6.2 Detection Process

The size of the scintillation detector elements has a major impact on spatial resolution: smaller detectors create thinner, more precise and more numerous LORs, improving sampling of the object in the imaging FOV. Smaller detectors can therefore increase spatial resolution [73]; however, this must be optimised with respect to sensitivity [74]. Furthermore, detector response to a point source is dependent on the source’s position within the FOV, as shown in Figure 1.6 (A). The response to a point source mid-way between two detectors is triangular, with a FWHM equal to half of the detector width. The response worsens as the point source moves towards either of the two detectors (i.e. closer to the FOV edge) and becomes trapezoidal in shape, with a FWHM matching the detector width [29], [75]. Therefore, for a detector width d, resolution is ≈ d/2 at the centre of the FOV and ≈ d at the face of the detectors.

Figure 1.6: Detector effects on spatial resolution

Parallax effects, or radial elongation, also contribute to spatial resolution variability throughout the FOV, as shown in Figure 1.6 (B). Photons incident perpendicularly on a particular crystal are more likely to be absorbed within that crystal (shown in green), producing a true LOR. However, photons that enter a particular crystal at an acute angle are more likely to penetrate into the neighbouring crystal(s) before being absorbed (shown in pink). The depth-of-interaction (DOI) within the crystals is unknown and is not accounted for, resulting in an incorrect LOR (dotted line). The FWHM of point sources located nearer the FOV edges are therefore broadened.

1.6.3 Partial Volume Effects

Partial Volume (PV) effects refer to phenomena that cause voxel intensities to differ from what they should be: smaller objects can appear to have lower activity concentrations than larger objects with equal activity concentrations [28]. PV effects lead to underestimation of the activity concentration of lesions smaller than twice the system spatial resolution FWHM [17], [32]. The extent of PV effects depend on the lesion size, the contrast between the lesion and its background, and the system spatial resolution [76]. The term ‘partial volume effect’ typically refers to two distinct phenomena [77]:

1. Three-dimensional image blurring introduced by the finite spatial resolution of the imaging system

Image blurring as a result of limited spatial resolution causes ‘spillover’ between regions, which in turn causes small sources to appear larger and less intense. As spatial resolution degrades towards the edges of the FOV, PV effects also become more significant at FOV edges [17].

Sampling the radiotracer distribution onto a voxel grid also causes PV effects. Most voxels will contain different types of tissues (tissue fraction effect [77]). Each voxel’s signal intensity is the average of all underlying tissues within the voxel. Voxels around the edge of a source will contain both source and background tissue. Large voxels are more likely to contain a mixture of different tissue types than small voxels. Averaging source and background tissue signals causes the source to appear larger and less intense than it should be, which contributes to the ‘spilling out’ effect. Activity from background tissue can also ‘spill in’ to the source tissue, which may partially compensate for the ‘spill out’ effect, depending on the background activity concentration.

The use of smaller voxels reduces the tissue fraction effect, and therefore minimises PV effects; however, this must be balanced with the associated increase in statistical noise. Motion correction techniques, such as respiratory and cardiac gating, can be used during acquisition to minimise blurring caused by physiological movement. There are many methods for PV correction currently under investigation, but these are yet to gain widespread acceptance in clinical PET imaging. PV correction can be applied as part of the reconstruction algorithm: for example, the detector PSF response can be modelled and incorporated into the reconstruction algorithm. This type of correction is described in more detail later in this chapter. Alternatively, PV correction can be applied as a post- reconstruction technique: for example, high-resolution structural images (such as CT images) can be used to transfer high frequency information [78].