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Examples are shown in Fig. 3.8 for the case of a 48-ring scanner in one particular 2D configuration, with planes added up to a maximum ring difference of ± 4 rings, and in a 3D acquisition configuration, where there are 482 (= 2,304) possible planes of response, but in this case the maximum acceptance angle between rings in limited to a ring difference of 40, with up to five axial lines of response being combined into a single plane.

The entire motivation for 3D PET is to increase sensitivity. While radionuclide emission imaging techniques in general use minute tracer amounts (usually micrograms or less), the proportion of the available signal detected is still relatively poor. A radiotracer in most cases distributes throughout the body with only a small fraction localizing in the target organ (if one exists), and collimation, attenuation, and scattering preclude many emitted photons from being detected. A conventional PET camera with interplane septa in 2D mode detects around 4,000-5,000 coincidence events per 106 (~0.5%) positron emissions with approximately uniform sensitivity over the axial profile, apart from the less sensitive end planes (Fig. 3.9). A gamma

Figure 3.8. Michelograms representing the plane combinations for a 48-ring scanner are shown for the 2D case (left) and the 3D case (right). The x and y axes represent ring numbers on opposing sides of the scanner. Each point on the graph defines a unique plane of response (e.g., all lines-of-response in ring 1 in combination with ring 2).The diagonal lines joining individual dots indicate that the planes of response are combined (added together) thus losing information about each individual point's polar acquisition angle. This form of combination of data from different planes represents a "lossy" compression scheme.

Figure 3.8. Michelograms representing the plane combinations for a 48-ring scanner are shown for the 2D case (left) and the 3D case (right). The x and y axes represent ring numbers on opposing sides of the scanner. Each point on the graph defines a unique plane of response (e.g., all lines-of-response in ring 1 in combination with ring 2).The diagonal lines joining individual dots indicate that the planes of response are combined (added together) thus losing information about each individual point's polar acquisition angle. This form of combination of data from different planes represents a "lossy" compression scheme.

Figure 3.9. The 2D axial sensitivity profile for a line source in air on a 16-ring tomograph (CTI ECAT 951R) demonstrates both the bimodal pattern resulting from the two blocks used in this camera and the sinogram-to-sinogram variation arising from the combination of either three (odd-numbered sinograms) or four (even-numbered sinograms) axial lines-of-response in forming the sinogram. The end sinograms, which contain only one axial line-of-response, are only 20% as efficient as the sinograms formed in the center of the block detector.

15 20

Sinogram

camera, with its inefficient lead collimator, detects only around 200 of every 106 photons emitted. In spite of this modest efficiency, PET remains the most sensitive emission tomographic modality.

Constraining the allowed coincidences to a narrow plane orthogonal to the z axis of the PET camera severely restricts the overall sensitivity of the technique. Historically, the reasons for this restriction were twofold: the lack of appropriate 3D reconstruction software, and to keep the scatter fraction low. When the interplane septa are removed and all possible lines-of-response within the field-of-view are acquired in 3D, sensitivity is increased by two factors:

(i) the increased number of lines-of-response that it is now possible to acquire without the septa in place, and,

(ii) the amount by which the detector crystals are "shadowed" by the septa when they are in place [7-9]. The 3D acquisition mode leads to a nonuniform axial sensitivity profile, though, as shown in Fig. 3.10 for a 16-ring scanner and a distributed source.

In a 16-ring tomograph the sensitivity gain can be up to around thirty times greater in the center of the scanner compared to the end planes. The "average" gain over the entire axial feld-of-view is around five- to sevenfold. It is possible to separate the contributions of the two factors indicated above by scanning the same source in 2D mode both with and without the interplane septa using the usual 2D configurations of plane-defining lines-of-response. This demonstrates the effect due to septal shadowing alone, seen in Fig. 3.11.

The shadowing effect of the septa is greater when the plane definition utilizes cross-planes as is usually done in a conventional 2D acquisition, as would be expected. The average sensitivity improvement due to shadowing is a factor of approximately 2.2. In the studies with a maximum ring difference (dmax) of zero, the component of sensitivity lost due to the thickness of the septa themselves (1 mm), and the amount of the detector that this covers is seen in isolation. The second component of the increase in sensitivity is the greater number of lines-of-response that can be accepted in 3D. When the 16 direct rings only are used (dmax = 0), this corresponds to 16 planes-of-response accepted; with the usual 31 plane definition for 2D acquisitions (ring difference d = 0, ±2 for odd-numbered planes (apart from the end detectors) and d = ±1, ±3 for even-numbered planes) this becomes a total of 100 planes-of-response. In a full 3D acquisition this would become 16 x 16 for this tomograph, i.e., 256 planes-of-response, as now each ring is in coincidence with every other ring on the opposing fan. This gives a factor of 256/100 = 2.56 increase in sensitivity due to the increased numbers of planes accepted compared with conventional 2D mode. However, there is a concomitant increase in the acceptance of scattered events axially as well.

A further effect produces a gain in coincidence count rates in 3D PET compared with 2D in addition to septal shadowing and acquiring more lines-of-response at greater polar acceptance angle. It has been shown that the 3D mode of acquisition is more efficient at converting single events into an annihilation pair which are both detected [9]. Measurements on a first-generation 2D/3D PET system have shown that the conversion rate

Figure 3.10. The axial sensitivity variation for the 3D acquisition geometry of 16-ring PET camera is shown. The center of the scanner is sampled around 32 times more than the end planes, where all possible planes of response are accepted. The plot is normalized to the first plane. Restricting the maximum acceptance angle (ring difference in this example with discrete detectors) will "flatten" the profile between defined limits (broken line), thereby achieving more uniform sampling in the central axial region of the scanner.

Plane Location

Figure 3.10. The axial sensitivity variation for the 3D acquisition geometry of 16-ring PET camera is shown. The center of the scanner is sampled around 32 times more than the end planes, where all possible planes of response are accepted. The plot is normalized to the first plane. Restricting the maximum acceptance angle (ring difference in this example with discrete detectors) will "flatten" the profile between defined limits (broken line), thereby achieving more uniform sampling in the central axial region of the scanner.

from single events to coincidences for a line source measured in air (i.e., no scatter) was 6.7% in 2D and 10.2% in 3D. For the same source measured in a 20 cm-diameter water-filled cylinder, the conversion rate in 2D was 2.4% and 4.8% in 3D. The ratio of these results show that, without scatter, the increase in conversion from single photons to coincidences for 3D compared to 2D is over 50% (10.2/6.7) higher, and in a scattering medium approaches 100% (4.8/2.4), although many of these events will be scattered events. The explanation is simple: more single photons can now form coincidence pairs in 3D where, in 2D, one or both would have been lost to the system by virtue of the flight angle (outside the allowed maximum ring difference) or by attenuation by the septa.

The non-uniform axial sampling in 3D, however, causes truncation of the projections, which is potentially a far greater problem for reconstruction than an axial variation in sensitivity (Fig. 3.12). This problem was solved, however, in 1989 with the development of the "reprojection" algorithm [6, 7]. This method exploits the fact that the data contains redundancy and the volume can be adequately reconstructed from the direct ring data (dmax = 0). The first step in this algo

Direct+cross planes

Direct+cross planes

Figure 3.11. Sensitivity improvement due to removal of septa alone is demonstrated. The results are for direct planes only (solid line) and for conventional 2D planes where cross-planes contributions are included (broken line). The "dip" towards the center is at the block boundary of this two-block (axial) tomograph. This shows the effect purely due to septal shadowing.

B 9 Ring

B 9 Ring

Figure 3.11. Sensitivity improvement due to removal of septa alone is demonstrated. The results are for direct planes only (solid line) and for conventional 2D planes where cross-planes contributions are included (broken line). The "dip" towards the center is at the block boundary of this two-block (axial) tomograph. This shows the effect purely due to septal shadowing.

Figure 3.12. In the 3D acquisition case truncation of the projections occurs for those polar angles > 0°. At the top (d = 0) the entire field of view is sampled -this is the usual 2D case. When the ring difference is increased there is truncation of the axial field of view resulting in loss of data corresponding to the ends of the tomograph (center). In the limiting case (bottom) it results in severe truncation of the object.

Figure 3.12. In the 3D acquisition case truncation of the projections occurs for those polar angles > 0°. At the top (d = 0) the entire field of view is sampled -this is the usual 2D case. When the ring difference is increased there is truncation of the axial field of view resulting in loss of data corresponding to the ends of the tomograph (center). In the limiting case (bottom) it results in severe truncation of the object.

rithm is to reconstruct the volume from the conventional 2D data sinograms. The unmeasured, or missing, data are then synthesized by forward projection through this volume. After this the data are complete and shift-invariant, and a fully 3D reconstruction algorithm can be used. This algorithm is discussed in depth in the next chapter.

From Projections to Reconstructed Images

Finally in this section, a brief description of how the data discussed are used to reconstruct images in positron tomography is included. The theory of reconstruction is dealt with in detail in the next chapter.

The steps involved and the different data sets required for producing accurate reconstructed images in 2D PET are shown in Fig. 3.13. All data (apart from the reconstructions) are shown as sinograms (i.e., the coordinates are (s,^)). The usual data required are:

(i) the emission scan which is to be reconstructed,

(ii) a set of normalization sinograms (one per plane in 2D) to correct for differential detector efficiencies and geometric effects related to the ring detector, or a series of individual components from which such a normalization can be constructed (see Ch. 6), and,

(iii) a set of sinograms of attenuation correction factors to correct for photon attenuation (self-absorption or scattering) by the object.

The normalization factor singrams can include a global scaling component to account for the plane-to-plane variations seen in Fig. 3.9. The attenuation factor sinograms are derived from a "transmission" scan of the object and a transmission scan without the object in place (often called a "blank" or reference scan); the ratio of blank to transmission gives the attenuation correction factors. The most common method for acquiring the transmission and blank scans is with either a ring or rotating rod(s) of a long-lived positron emitter such as 68Ge/68Ga, with which the object is irradiated [10]. The emission sinograms are first corrected for attenuation and normalized for different crystal efficiencies, and then reconstructed using the filtered back-projection process. During the final step, scalar corrections for dead time and decay may also be applied.

Figure 3.13. The steps involved in producing a 2D PET image are shown using filtered back-projection. Typically 31-95 planes of data are reconstructed in transverse section.

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