Physical Distortions of PET

The physical distortions seen in PET images can be divided into two main groups. First, there are artifacts produced by the scanner geometry and the detection system itself, and second, distortions introduced by the various processing steps applied to the data before the final image is produced. The result of both types of distortions is images where the activity distribution is distorted, which in the end will affect how well the PET image volume can be coregistered to a second data set. Some of these physical distortions can to a great extent be minimized by proper data handling; however, some artifacts cannot be removed and must be considered in the registration algorithm.

2.1 Nonuniform Sampling

Most modern PET systems use a circular detector geometry where a large number of discrete detector elements make up the detector ring. A number of these detector rings are typically placed next to each other to cover an extended axial field of view (FOV), which allows imaging of an entire organ. In the latest generations of PET systems, the detectors are made sufficiently small that this geometry allows the collection of a complete tomographic data set without the need for any mechanical motion to improve spatial sampling. However, this geometry introduces a nonuniformity in spatial sampling that may introduce image artifacts if not corrected for in the chain of processing steps required in PET. In Fig. 1, nonuniform sampling is illustrated. In the center of the FOV, the lines of response (LOR) (or sampling lines) are approximately equidistant; however, toward the edge of the FOV, the sampling

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FIGURE 1 Nonuniform sampling across the FOV in a PET system using a circular detector geometry. At the center of the FOV the coincidence or sampling lines are approximately equidistant, whereas at the edge of the FOV (dashed circle) the sampling becomes more dense.

becomes denser. When the events collected by the PET scanner are sorted into the sinogram, the radial offset is not the absolute radial offset measure in distance but rather a relative offset measured in number of LORs from the center. Thus, if the assumption is made (in the reconstruction algorithm) that the distance between the LORs is the same, events towards the edge of the FOV are incorrectly positioned too far away from the center [12,15]. The resulting distortions from this effect for a set of circular objects in the reconstructed image are shown in Fig. 2. As can be seen, the source located at the edge of the FOV has become triangular in shape and the center of the object has also be shifted from the actual center.

This problem is less severe if the imaged object boundary is located within the center of the FOV (or ~ 1/4 of the system diameter). Therefore, this problem may not be easily visualized in, for instance, brain studies on PET systems designed to accommodate whole-body scans.

2.2 Nonuniform Spatial Resolution Variations

The nonuniform spatial resolution variation seen in PET systems is well understood and can be described by the physical characteristics of the specific scanner (e.g., system geometry, detector materials, collimation [14]). The geometrical component of resolution variation is mainly determined by the dimensions of detector elements and the detector diameter of the scanner. The resolution loss is typically limited to a widening of the line spread function at off-center positions in

FIGURE 2 Example of distortion seen if the data are not corrected for nonuniform sampling. (Top) The true positions of the circular objects across the FOV. (Bottom) The resulting image if uniform sampling is assumed in the image reconstruction. Note both the distortion in shape of the objects and a shift in the position towards the periphery. The sources are located at 0, 5,10,15,20, and 25 cm radial offsets in an 80-cm diameter system.

FIGURE 2 Example of distortion seen if the data are not corrected for nonuniform sampling. (Top) The true positions of the circular objects across the FOV. (Bottom) The resulting image if uniform sampling is assumed in the image reconstruction. Note both the distortion in shape of the objects and a shift in the position towards the periphery. The sources are located at 0, 5,10,15,20, and 25 cm radial offsets in an 80-cm diameter system.

the field of view. This widening is also symmetric around the center of the LSF and does not introduce any distortions of the reconstructed image that might produce any mispositioning of the data.

A more complex resolution loss to characterize in PET is the detector penetration or detector parallax problem [29]. This resolution loss occurs at radial off-center positions in the FOV, where the detector elements in the system are positioned at a slight angle relative to each other (see Fig. 1). When a photon enters the detector elements at these off-center positions, there is a high probability that the photon penetrates the detector and deposits its energy in a neighboring detector. The probability of this increases toward the edge of the FOV, since the path length through the primary detector becomes shorter. The result of the detector penetration is a resolution loss that is also asymmetrical. Because of this asymmetry the reconstructed images not only have a loss in resolution, but also have a spatial distortion where objects located in the periphery have a shift toward the center of the FOV.

2.3 Axial Sampling

In order to accurately register two data sets with a minimal loss of information, it is necessary that the two image volumes both be adequately sampled in all three spatial dimensions (sampling distance is less than ~ 1/2 the spatial resolution). For all tomographic image modalities, this is in general true in the transaxial direction; however, axially this is not always the case. For instance, in CT and MRI, the axial resolution may be on the order of 1-2 mm, whereas the separation of the planes may be of the order of several millimeters, in order to reduce scanning time and the amount of data produced. Although the axial sampling has improved in recent generations of PET scanners, it is only the high-resolution systems that fulfill the sampling criterion [5].

Most registration algorithms are, however, in general not very sensitive to coarse axial sampling and are capable of aligning the data sets to a precision on the order of 2-3 mm [1,2,27,39,42]. The reason for this accuracy is that most algorithms are based on the realignment of large structures or volumes (e.g., the whole brain, brain surface, gray and white matter), and any undersampling can be compensated by interpolation [42]. However, the interpolation cannot recover any anatomical information that is lost due to undersampling (i.e., structures that are located in the areas between the measured slices). It is therefore not unusual that, for a pair of perfectly spatially registered image volumes, smaller structures might be visualized in one image set and missing in the second. In Fig. 3 this is illustrated for a PET study where the two image rows are perfectly registered with a plane separation of 10 mm. The top row shows measured cross-sections, whereas the bottom row shows images that were generated by interpolation from slices between those in the top row. As one can see, there is an overall good agreement in the activity distribution; however there are differences in some of the finer details (e.g., cortex and basal ganglia).

2.4 Attenuation Correction

In PET (and also SPECT), correction for photon attenuation is necessary to provide images that reflect the true activity distribution in the subject. A transmission scan of the subject is typically acquired in addition to the emission scan to correct for photon attenuation. The ratio of a reference or blank scan and the transmission scan then forms the attenuation correction of the emission data for photon attenuation. In order to reduce the contamination of the emission data of statistical noise from the transmission scan, the blank-transmission ratio is filtered relatively heavily. This filtering does not in general introduce artifacts in the emission image where the attenuation is relatively homogenous. However, it has been shown that the filtering may introduce distortions in the activity distribution, in particular at boundaries where there is a large change in attenuation coefficient (e.g., lung and soft tissue, soft tissue and air [17,31]). Distortions due to the filtering can also be seen on reconstructed transmission images, where shifts in the location of boundaries between different tissue types could occur. This type of distortion may be of concern in registration algorithms where the transmission images are used for alignment [37].

Some algorithms for attenuation correction process the reconstructed transmission images rather than the blanktransmission sinogram. In these algorithms, the CT-like transmission image is segmented into three or more discrete tissue types with corresponding attenuation coefficients [16,31,43,44]. From the noise-free, segmented transmission images, the appropriate attenuation correction can be calculated for each LOR. To minimize distortions in the final emission image, it is necessary to take into account the nonuniformity in sampling described in Section 2.1. First, in the reconstruction of the transmission images, it is necessary to take the sampling nonuniformity into account to avoid a distortion in shape of the transmission image. Second, when the attenuation corrections are derived, these are calculated along the actual LORs of the system (i.e., the nonuniform samples) to avoid introduction of image artifacts. The same care should also be taken in calculated attenuation correction algorithms, where the attenuation is derived from an object of a simple geometrical shape (e.g., an ellipse) or the outline of the object derived from emission data.

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