2.1.1. Pencil-beam simulations

A schematic geometry used to evaluate the effects of ICS-P is illustrated in Figure 1. A pencil-beam of ^99mTc irradiating central crystal element in combination with a section of the pixelated crystal is also shown. In order to assess the PDA, the collimator was deliberately removed, and PDA was quantified in various array configurations.

Fig. 1.Full-screen View

A schematic view of the simulation geometry including a pencil-beam of ^99mTc along with side view of three crystal pixels.

To model oblique gamma-rays facing the crystal, the pencil-beam was angled respecting normal vector of the crystal surface. Theoretically, there is a critical angle, above which the incident-beam can enter an adjacent crystal pixel, leading to an increase in contribution of neighbor pixels in radiation detection process. Such an angle is geometry-dependent, and can be fully determined by crystal pixel-size and pixel-gap. The critical angle, θ_c, can be expressed as follows:

where s is pixel-size, g is the pixel-gap, and l is the crystal length (fixed to 5 mm).

2.1.2. Point-source simulations

In real SPECT systems, the neighbor crystals are simultaneously irradiated as well. To take the contribution of these neighbor crystals in PDA into account, a set of point-source simulations was conducted for various CsI(Na)-based crystal configurations. For this, an 11×11 CsI(Na) crystal array was irradiated by a ^99mTc point-source located at a 60 mm source-to-crystal distance, and then the PDA was assessed. It should be noted that the collimator was removed.

2.3.1. Pencil-beam simulations

The GATE MC code was then used for detailed transport of ^99mTc photons originated from a pencil-beam toward the central pixel of the simulated geometry. Multiple simulations at different gamma-ray angles of incidence were performed, in order to investigate the effects of photon angles on ICS and penetration (parallax) phenomena. The beam-angles varied from 0° to 45° (5° steps) respecting normal vector of the crystal.

PDA, the ratio of detected photons in irradiated crystal to the total detected events, was defined, indicating how accurate is the signal positioning when a ^99mTc photon reaches with an oblique-angle. On the other hand, in absence of the collimator, the MC simulations could be dramatically shortened. Also, in an ideal imager, a PDA of unity would be expected.

The PDA was calculated for three common crystal materials, i.e. CsI(Na), NaI(Tl) and YAP(Ce), and various geometrical configurations of the crystal at a fixed crystal thickness of 5 mm. The pixel-size ranged from 0.5 mm×0.5 mm to 2 mm× 2 mm (0.5-mm steps). In addition, pixel-gap was assumed to be 0.1, 0.2 and 0.3 mm of Epoxy. Moreover, it was worth calculating the effect of photon energy on PDA quantification with ^99mTc, ¹¹¹In and ¹³¹I as low-, medium-, and high-energy tracers, respectively.

2.3.2. Point-source simulations

In the case of point-source evaluation, the PDA was redefined as follows: the ratio of the total number of photons reached all individual crystals and detected in the same crystals to the total detected counts. We note that such a definition would also be valid for the pencil-beam data and results in the same PDA values. This re-definition includes contribution of the neighbor pixels in calculating the PDA for different CsI(Na)-based configurations as for the pencil-beam simulations.

The point-source simulation also allows to study flood images by calculating peak-to-valley ratios (PVRs) using a line-profile of the images. The PVR well reflects crystal identification in pixelated detectors. In order to calculate the PVRs, spatial uncertainties in position estimation caused by the two PS-PMTs as well as our positioning-circuit is modeled as a 2D Gaussian function. Convolving the detector response with the 2D Gaussian function emulates the integrated effect of the PS-PMTs and the positioning-circuit, since we are extracting the PVRs from MC simulations. In order to mimic a more realistic SPECT simulation, electronic noise is added to the calculated flood images. However, this procedure neglects deteriorations in response at edges of the detection module commonly caused by the PS-PMTs readings.

3.2.1. Crystal material

PDA over all beam-angles for 1 mm×1 mm pixel-area and 0.2 mm Epoxy separator, with three common crystal materials of CsI(Na), NaI(Tl) and YAP(Ce) is plotted in Fig. 3. One sees that PDA decreases with increasing incident angles. The CsI(Na) crystal indicates the higher PDA over all beam-angles than the NaI(Tl) and YAP(Ce) types. Indeed, CsI(Na) possess the highest linear attenuation coefficient of the three crystals^[15], hence the highest probability of 140 keV photons detection, and a higher CI (i.e., the PDA). The CsI(Na) is benefited from a lower-cost and higher light output, as well^[16].

Fig. 3.Full-screen View

Position-detection-accuracy vs beam-angle for a 1 mm×1 mm pixel-area and 0.2 mm Epoxy gap configuration with different crystal materials.

For better visualization, only a portion of the crystal is plotted.

Figure 4 illustrates scatter plots of the detected counts for a 1 mm×1 mm pixel-area and 0.2 mm Epoxy separator array at 0° and 45° incidence. Contribution of adjacent crystals in detection process is clear in Fig. 4(b). The red arrows indicate registered counts in the irradiated crystal. We noted that only a portion of the pixelated crystal in depicted, for better visualization.

Fig. 4.Full-screen View

Scatter plot of the detected photons at 0° and 45°incident-angle, for a 1 mm×1 mm pixel-area and 0.2 mm Epoxy configuration.

Considering a photon arrives at the crystal with an oblique angle. This photon may be geometrically entered an adjacent pixel without any interaction and can be detected in another element rather than the irradiated one. At this condition, a mispositioning of the signal occurs, leading to a decreased PDA. As the incident-angle increases, the problem becomes more rigorous. We limited our investigations to a maximum incident-angle of 45° because a photon with an incident-angle greater than such a limit may passed through multiple collimator septa, and this is practically impossible due to high photoelectric cross section of the collimator material (i.e., lead) at 140 keV.

3.2.2. Crystal pixel-size

Figure 5 provides a plot comparing PDAs for four pixel-sizes ranging from 0.5 mm×0.5 mm to 2 mm×2 mm all for a 0.2 mm Epoxy gap. The PDA increases with the crystal pixel dimension for a given fixed Epoxy separator. Fig. 5 proves that the higher the crystal pixel-sizes, the higher the PDA, because the ^99mTc photons travel longer distances in the same crystal element, and thereby have higher likelihood to be detected in the element at oblique angles. In other words, increasing crystal pixel-size reduces fraction of those photons experienced ICS-P and detected in neighbor elements. For example, the PDA drops from 0.44 to 0.14 when the pixel-size reduces from 2 mm×2 mm to 0.5 mm×0.5 mm, respectively. Although, from Figure 1, crystal length can control CI in the same manner, but in this study we assumed a fixed-length (i.e., 5 mm) crystal configuration. Figure 5 is also an evident that increasing the pixel-size consequently increases the critical-angle.

Fig. 5.Full-screen View

Normalized position-detection-accuracy vs. beam incident-angle for pixel-sizes of 1 mm×1 mm to 2 mm×2 mm, at 0.2 mm Epoxy gap.

For 1 mm×1 mm pixel-area and 0.2 mm Epoxy separator crystal geometry, Fig. 6 shows the percentage of detected photons in one adjacent pixel of the irradiated element for the CsI(Na), which is useful for investigating parallax artifact. As the photon incident-angle is getting greater (beyond the critical-angle), the counts in the adjacent pixel significantly increase so that the beam entirely passes the adjacent pixel, a second critical-angle (for example, 20° for 1 mm×1 mm pixel-area and 0.2 mm gap configuration). Further increasing the incident-angle results in fewer counts, because the next neighbor is now involved in detecting 140 keV primary photons.

Fig. 6.Full-screen View

Percentage of detected photons in 1 mm×1 mm pixel-area and 0.2 mm pixel-gap for crystals of different crystal materials.

3.2.3. Crystal pixel-gap

Influence of Epoxy gap between crystals as a function of beam-angle for pixel-gaps of 0.1, 0.2 and 0.3 mm is revealed in Fig. 7(a), for 1 mm×1 mm pixel-area configuration. As for pixel-size, the pixel-gap behaviors as the same manner. Fig.7(b) compares PDA values of various CsI(Na) crystal configurations at 45° incident-angle. The positioning accuracy increases with either pixel-size or pixel-gap.

Fig. 7.Full-screen View

Normalized position-detection-accuracy for (a) different beam-angles at 1 mm×1 mm pixel-area and (b) different crystal configurations at 45° incidence, with pixel-gaps of 0.1, 0.2 and 0.3 mm Epoxy.

Likewise, as pixel-gap increases, a ^99mTc photon has a higher probability to be attenuated within the Epoxy separator, and therefore, resulting in lesser counts in an adjacent pixel. In addition, more light photons produced within the crystal element were reflected off the pixel-gap. Quantitatively, a maximum reduction of 13% in PDA occurs when the pixel-gap varies from 0.3 mm to 0.1 mm for a 1 mm×1 mm pixel-area crystal configuration. However, influence of pixel-size on PDA is more severe than pixel-space, as it is evident from Fig. 5. As can be understood from the results, below the critical angles, for example 8° for a 1 mm× 1 mm pixel-area and 0.2 mm gap geometry, quantitative variations of the detected photons are negligible and beyond such critical angles, the PDA falls dramatically off.

3.2.4. Photon’s energy

Fig.8 shows how probe’s energy affects CI for 1 mm×1 mmm² pixel-area and 0.2 mm Epoxy-gap CsI(Na) configuration. Three probes of ^99mTc, ¹¹¹In and ¹³¹I were used. As can be observed, the PDA decreases with increasing energy, due to an increase in scattered and penetrated components in the detected signal. In more detail, the CsI(Na) crystal owns mass attenuation coefficients of 0.990, 0.291 and 0.144 cm²·g⁻¹ at 140, 245 and 364 keV, respectively^[15]. Therefore, a lower-energy SPECT probe automatically leads to a more accurate SPECT imaging from CI point-of-view. In other words, the parallax artifact is more serious when a high-energy SPECT scan is requested.

Fig.8.Full-screen View

Normalized PDA for ^99mTc, ¹¹¹In, and ¹³¹I, with CsI(Na) crystal of 1 mm×1 mm pixel-area and 0.2 mm Epoxy gap.