Study of PET scanner designs using clinical metrics to optimize the scanner axial FOV and crystal thickness

Abstract

The aim of this study is to understand the trade-off between crystal thickness and scanner axial FOV (AFOV) for clinical PET imaging. Clinical scanner design has evolved towards 20–25 mm thick crystals and 16–22 cm long scanner AFOV, as well as time-of-flight (TOF) imaging. While Monte Carlo studies demonstrate that longer AFOV and thicker crystals will lead to higher scanner sensitivity, cost has prohibited the building of commercial scanners with > 22 cm AFOV. In this study, we performed a series of system simulations to optimize the use of a given amount of crystal material by evaluating the impact on system sensitivity and NEC, as well image quality in terms of lesion detectability. We evaluated two crystal types (LSO and LaBr₃) and fixed the total crystal volume used for each type (8.2 liters of LSO and 17.1 liters of LaBr₃) while varying the crystal thickness and scanner AFOV. In addition, all imaging times were normalized so that the total scan time needed to scan a 100 cm long object with multiple bed positions was kept constant. Our results show that the highest NEC/cm in a 35 cm diameter×70 cm long line source cylinder is achieved for an LSO scanner with 10 mm long crystals and AFOV of 36 cm while for LaBr₃ scanners, the highest NEC/cm is obtained with 20 mm long crystals and an AFOV of 38 cm. Lesion phantom simulations show best lesion detection performance is achieved in scanners with long AFOV (≥ 36 cm) and using thin crystals (≤ 10 mm of LSO and ≤ 20 mm of LaBr₃). This is due to a combination of improved NEC, as well as improved lesion contrast estimation due to better spatial resolution in thinner crystals. Alternatively, for lesion detection performance similar to that achieved in standard clinical scanner designs, the long AFOV scanners can be used to reduce the total scan time without increasing the amount of crystal used in the scanner. In addition, for LaBr₃ based scanners, the reduced lesion contrast relative to LSO based scanners requires improved timing resolution and longer scan times in order to achieve lesion detectability similar to that achieved in an LSO scanner with similar NEC/cm.

1. Introduction

The aim of this work is to study the trade-offs between crystal thickness versus PET scanner axial field-of-view (AFOV) to achieve high sensitivity and to optimize lesion detectability in whole-body imaging. We have included both LSO and LaBr₃ in this study since both scintillators can be used for time-offlight (TOF) PET scanners, but have significantly different stopping power for 511 keV photons. Commercially available TOF PET scanners (from GE, Philips, and Siemens) use 20–25 mm thick LSO or LYSO crystals and have axial FOV ranging from about 16–22 cm (Surti et al., 2007, Jakoby et al., 2011, Bettinardi et al., 2011). This choice of parameters is driven by performance, cost constraints, and marketing targets. In development of a research LaBr₃ based PET scanner (LaPET) (Daube-Witherspoon et al., 2010), we chose the scanner design to match the maximum NEC performance of an LSO scanner with 18 cm AFOV and 20 mm thick crystals by increasing both the AFOV (to 25 cm) and crystal thickness (to 30 mm) of LaBr₃ (Surti et al., 2004). The commercial LSO and LYSO scanners achieve timing resolution in the range of 550–600ps while our research LaBr₃ scanner has a timing resolution of about 375ps. Over the years, there has also been some interest in developing scanners with long AFOV with the goals being to achieve shorter imaging times for whole-body scans, as well as providing the ability to perform dynamic imaging and dosimetry studies to test and evaluate new radio-tracers. However, the cost of building such scanners is considered to be prohibitive. Also, while Monte Carlo studies have demonstrated that as expected longer AFOV scanners and thick crystals lead to higher scanner sensitivity and noise equivalent counts (NEC) (MacDonald et al., 2011, Badawi et al., 2000, Eriksson et al., 2011, Eriksson et al., 2007, Hunter et al., 2009, Poon et al., 2012), none of these studies used more complex imaging metrics (such as lesion detectability) that depend on reconstruction algorithm performance, in addition to intrinsic spatial resolution and sensitivity, for evaluation of scanner performance and design optimization. In our study we first use sensitivity and NEC metrics to help restrict our design choices, followed by an evaluation of the trade-offs between crystal thickness and scanner AFOV based on reconstructed images of lesion phantoms. For this work we use a fixed amount of crystal volume and assume that the cost/cc of the scintillator is fixed, without taking into account potential differences in manufacturing costs for different crystal thickness. We also do not take into account the increased cost of photo-detectors needed for longer AFOV scanners since that comparison is beyond the scope of this study. Photodetector cost can potentially be significant especially when using detectors such as silicon photomultipliers (SiPMs), but in current practice the cost of conventional photo-multiplier tubes (PMTs) is much less than the cost of the scintillator (< 20%).

2. Methods

2.1. Simulated scanner geometry

We performed EGS4-based system simulations (Surti et al., 2004) for a cylindrical PET scanner geometry using pixelated crystals. The choice of EGS4 over GATE (Jan et al., 2004) is driven by our experience with using this simulation over many years to study trends using generalized (cylindrical) scanner designs. While GATE provides the ability to simulate more specific scanner geometry and sophisticated phantoms that can be useful in certain scenarios, the flexibility and speed of the EGS4 simulation is desirable when obtaining generalized system design results with simple, but realistic, activity distributions. Two different types of crystals, LSO and LaBr₃, were chosen in order to evaluate performance of TOF PET scanners. The crystal cross-section for both was chosen to be 4x4 mm², while the scanner energy resolution was simulated to be 12% for LSO and 7% for LaBr₃ scanners. The lower energy threshold was fixed at 440 keV for both crystals. With 7% energy resolution we could raise the lower energy threshold to 470 keV with LaBr₃ as we do on the LaPET scanner (Daube-Witherspoon et al., 2010), but for this study we kept it fixed for both scintillators and ignored the effect of differences in the scatter fraction. The rationale for choosing 4x4 mm² crystal cross-section for this work was to be consistent with what is currently used in whole-body PET scanners. A fixed number of back-to-back (coincident) 511 keV photon emissions were simulated for each scanner design. The simulation output is a list-mode data set with TOF information. The simulated scanner design had a ring diameter of 84 cm, and the scanner AFOV was varied between 7–100 cm while the crystal thickness was varied between 5 and 50 mm.

For NEC evaluation, simulations were limited to scanner designs using a fixed volume of crystal. We fixed the crystal volume at 8.2 liters for LSO scanners and 17.1 liters for LaBr₃ scanners. These numbers are based on our standard scanner geometries in this study, which have previously been shown to achieve similar maximum NEC rate (Surti et al., 2004).

For imaging performance (spatial resolution and lesion detectability), our scanner designs were further restricted to a subset of four geometries per crystal type while using a fixed amount of crystal (8.2 liters for LSO scanners and 17.1 liters for LaBr₃ scanners). Table 1 summarizes the specifications and the scanner design label for these eight scanner configurations. Note that the specifications for the Standard LSO and LaBr₃ scanners are similar, but not identical, to the Philips Gemini TF and LaPET scanners respectively. In Table 2 we show the coincidence detection efficiency for the different crystal thickness that we chose for our scanner design in Table 1. These numbers are for all events within the photo-peak (deposited energy > 440 keV). For each scanner design we simulated Non-TOF and TOF capability, where the timing resolution was chosen to be 300ps and 600ps for LSO scanners, and 150ps and 300ps for LaBr₃ scanners; these choices represent current performance and potential future performance of these crystals. Commercial LSO and LYSO scanners that use light sharing detector design with large PMTs achieve timing resolution values in the range of 550–600ps (Surti et al., 2007, Jakoby et al., 2011, Bettinardi et al., 2011). New detector designs using 1-1 coupling of thinner LYSO scintillators to new photo-detectors such as the silicon photomultipliers (SiPMs) (Kim et al., 2011, Gola et al., 2012) show a timing resolution in the range of 300ps. Hence, we chose timing resolution of 300ps and 600ps for the simulated LSO scanners. Similarly, our LaBr₃-based LaPET scanner has a measured system timing resolution of 375ps that is limited by electronics calibration (Daube-Witherspoon et al., 2010), and for which laboratory measurements show a timing resolution of 300ps (Kuhn et al., 2006). In addition, measurements performed with thinner LaBr₃ crystals 1-1 coupled to a photo-detector show a coincidence timing resolution of less than 150ps (Wiener et al., 2011). Thus, we chose 150ps and 300ps for the timing resolution of the simulated LaBr₃ scanners.

Table 1.

Specifications and labels for eight different simulated scanner designs for evaluation of imaging performance.

	LSO		LaBr3
Scanner design	AFOV (cm)	Crystal thickness (mm)	AFOV (cm)	Crystal thickness (mm)
Long	72	5	75	10
Medium	36	10	38	20
Standard	18	20	25	30
Short	12	30	16	50

Table 2.

Coincidence stopping efficiency as a function of crystal thickness for LSO and LaBr₃ scintillators. Results are for events within the photo-peak (deposited energy > 440 keV).

LSO		LaBr3
Crystal thickness (mm)	Coincidence efficiency (%)	Crystal thickness (mm)	Coincidence efficiency (%)
5	3.5	10	2.8
10	17.0	20	12.5
20	45.3	30	25.8
30	66.2	50	52.3

2.2. Simulated phantoms

A point source in air was simulated at the center of the scanner to estimate the system sensitivity since it represents the intrinsic efficiency of the system for a singular source. For NEC evaluation, a 35 cm diameter by 70 cm long water cylinder with a hot line source at a radial position of 4.5 cm in the cylinder was simulated (line source phantom). This phantom is similar to the NEMA NU 2-2008 (NEMA 2008) NEC phantom but modified to better represent a large patient and also to be more consistent with the lesion phantom used for lesion detectability studies. A fixed number of coincident photon emissions were simulated for all scanner geometries. For spatial resolution evaluation, a point source in air was simulated at radial positions, r = 0, 1, 5, 10, 15, and 20 cm.

For lesion detectability evaluation, a 35 cm diameter by 70 cm long lesion phantom was simulated. The phantom had 16, 1 cm diameter hot lesions (spheres) placed in the central transverse slice with a water background. The lesion activity uptake ratio was set at 3:1 relative to the background. Lesion diameter of 1 cm was chosen because it represents the smallest lesion we typically evaluate for scanner performance characteristics and is loosely based on the premise that this size defines a good limit for scanners with spatial resolution in the range of 4–5 mm (using 4 mm wide crystals). We used a lesion activity uptake of 3:1 because it represents a challenging situation where the differences between the different scanner designs are well discriminated. The simulated activity concentration in the phantom background was 0.1 μCi/cc, which is typically what is present in clinical patients at start of a PET scan. Eight lesions were uniformly distributed at a radial position of 7 cm from the center while the other eight were uniformly distributed at a radial position of 13 cm from the center. We also simulated a 35 cm diameter by 70 cm long uniform water-filled phantom with an activity concentration that is the same as the lesion phantom background. Five independent data replicates were simulated for each phantom. In figure 1 we show reconstructed images of the central transverse slice for these two phantom simulations with very high count statistics (or scan time) in order to illustrate the distribution of lesions.

Figure 1.

Reconstructed images of the central transverse slices for the simulated lesion (Left) and uniform (Right) phantoms. Images are shown for data reconstructed with very high count statistics (or scan time). The distribution of 16, 1-cm diameter lesions at radial distances of 7 and 13 cm can be visualized in the Left image.

2.3. Simulated scan times and image reconstruction

For lesion detectability studies, we used fixed total scan times of 5, 10, and 20 minutes for a 100 cm long scan, which correspond to 25, 50, and 100 second scans per single bed position in the Standard LSO scanner design (assuming a 50% overlap between adjacent bed positions as routinely implemented on Philips and Siemens scanners). For the other scanner designs the scan time for the simulated single bed position was adjusted so that the total scan time for a 100 cm long scan would be constant at 5, 10, and 20 minutes. Note that the standard clinical protocol at our institution for imaging on the Gemini TF is 90, 120, and 180 seconds per bed position for patients with low (< 25), medium (25–30), and high (> 30) BMI, respectively.

Spatial resolution images for point source in air list-mode data were generated by re-binning into a linearly-interpolated sinogram and reconstructing with a 3D-FRP reconstruction algorithm (Matej and Lewitt, 2001), which is a direct 3D Fourier reconstruction method with Fourier reprojection. Lesion and uniform phantom data were reconstructed into 2×2×2 mm³ voxel images using an optimized blob-based, list-mode OSEM algorithm (Hudson and Larkin, 1994) with Gaussian TOF kernel, 25 subsets, and normalization, attenuation, and scatter corrections built into the system model (Popescu, 2004). Attenuation images were generated analytically, and scatter estimate was obtained using a TOF-extended single scatter simulation correction (Werner et al., 2006) that is similar to the method implemented commercially by Philips as well as Siemens (Watson, 2007). Normalization data were generated by performing uniform phantom simulations (40 cm diameter and same length as the scanner AFOV) for each scanner design with a very high number of coincident events. This phantom size was chosen to be larger than the simulated lesion phantom and covering the entire AFOV of the scanner.

2.4. Image analysis

Scanner sensitivity was estimated from point source in air data as the ratio of the number of events detected in a scanner to the number of events generated in the point source. Relative scanner sensitivity, S, for each scanner AFOV and a crystal type was then calculated as a function of crystal thickness where 100% sensitivity represents a scanner with full, 4π solid angle coverage and a perfect (100%) efficiency scintillator for photo-peak events. From this we then calculated the change in relative sensitivity per crystal thickness ( dS / d(xtal _thick)) as a function of crystal thickness for each scanner AFOV and crystal type.

NEC in this study was calculated using the standard NEC formula for a fixed number of coincident photon emissions (same scan time), but only including the effect of true and scattered coincidences, and not random coincidences. However, for a line source both true and random coincidences will be proportional to scanner AFOV². Hence, the randoms to trues fraction will be approximately constant for all scanner axial lengths and so the relative difference in the NEC for the various scanner designs will not change after inclusion of the random coincidences. Data from the 35 cm diameter by 70 cm long water cylinder with a hot line source was used for this analysis. The phantom was centered axially in the scanner and simulations were performed for a single bed position. In a clinical oncology study performed in a fully-3D PET scanner, multiple overlapping bed positions are needed when scanning a long object in order to achieve a uniform sensitivity over the entire object length. For this work we assume a 50% bed overlap for adjacent bed positions and calculate the number of bed positions needed to image a 100 cm long object. In order to image a 100 cm long object in a fixed amount of total time, a scanner with shorter AFOV will require more bed positions with shorter scan times per bed position than a scanner with longer AFOV. We calculated the NEC/cm for the different scanner designs after adjusting for this change in scan time for a single bed position as a function of scanner AFOV (short scan time per bed position for short AFOV scanners).

Reconstructed point source in air images for spatial resolution studies were analyzed according to the NEMA NU 2-2008 standard (NEMA 2008). The average transverse resolution (fwhm) was calculated and reported as function of source radial position.

Lesion detectability was estimated using a generalized scan statistics model (Popescu and Lewitt, 2006). Briefly, we calculated the local contrast over multiple lesions in the lesion phantom images (5 image replicates * 16 lesions per image = 80 lesions) by using the ratio of mean counts in a circular ROI (diameter of 1 cm) and the mean counts in an annulus around the circular ROI (inner diameter of 1.2 cm, outer diameter of 4 cm). The lesion contrast distribution was fitted to a Gaussian to estimate the lesion contrast (or signal) probability density function (pdf). Local contrast distribution for noise nodules was calculated by scanning the uniform cylinder images (five image replicates), and calculating the contrast for ROIs centered over each image voxel. A Gaussian fit to the tails of the local contrast distribution for noise nodules is then used to estimate the pdf of the noise nodule contrast as described in (Popescu and Lewitt, 2006). The two (signal and noise) pdfs are used to calculate the ROC and LROC curves from first principles. For our analysis we chose to calculate the area under the LROC curve (ALROC) as the metric for lesion detection and localization since the primary difference in our different scanner designs is count statistics. ALROC values were calculated for the different scanner geometries and timing resolutions a function of the number of reconstruction iterations. The error in the ALROC value was determined as the standard deviation of the results over the 100 bootstrap data sets. The ALROC value changes as a function of the number of iterations of the reconstruction algorithm, and the maximum ALROC value is reached faster as the timing resolution improves in TOF scanners. All results shown here are for the iteration number at which the maximum ALROC value is achieved for a given scanner design.

3. Results

3.1. System sensitivity

In figure 2 we show the relative sensitivity for a point source of activity as a function of crystal thickness for each scanner AFOV, crystal thickness, and crystal type. For the LSO scanners, the increase in sensitivity with increasing crystal thickness is slow as the crystal thickness increases due to the higher stopping power of this crystal. In figure 3 we show the change in relative sensitivity per crystal thickness (gradient of the plot shown in figure 2) as a function of crystal thickness for each scanner AFOV, crystal thickness, and crystal type. For both LSO as well as LaBr₃ there is a value for crystal thickness where the change in relative sensitivity per crystal thickness achieves a maximal value and is relatively independent of the scanner AFOV.

Figure 2.

Relative sensitivity for a point source as a function of crystal thickness for (a) LSO and (b) LaBr₃ scanners with varying AFOV.

Figure 3.

Change in relative sensitivity per crystal thickness for a point source as a function of crystal thickness for (a) LSO and (b) LaBr₃ scanners with varying AFOV.

This occurs at a crystal thickness of 15 mm for LSO and 25 mm for LaBr₃ due to the differences in intrinsic sensitivity of the two crystal types. These results indicate that for a fixed amount of crystal volume, one should use 15 mm thick LSO or 25 mm thick LaBr₃, which then automatically determines the scanner AFOV in our study. However, the point source in air sensitivity results as shown here do not include the effect of scatter (or random) coincidences on the collected data, which can change as a function of scanner FOV. Hence, for a fixed crystal volume, system NEC may not be optimal with 15 mm thick LSO or 25 mm thick LaBr₃.

3.2. System NEC

In figure 4a we show the calculated NEC (after including scatter) in the line source phantom as a function of crystal thickness for scanner designs using a fixed crystal volume (8.2 liters of LSO and 17.1 liters of LaBr₃). This result corresponds to a fixed scan time for a single bed position study. As the crystal thickness increases, the corresponding scanner AFOV is lower as shown in figure 4b. From figure 4a we find that the highest total NEC for LSO based scanners is achieved with 10 mm thick crystals leading to a scanner AFOV of 36 cm. For LaBr₃ based scanners there is a slowly changing peak NEC with highest NEC achieved in scanners using 20 or 25 mm thick crystals with corresponding AFOV values 38 cm and 30 cm, respectively. This shift towards slightly thinner crystals and longer AFOV (for a fixed crystal volume) than what we anticipated from sensitivity calculations for a point source in air (figure 3), is due to a small relative increase in the scatter fraction but a larger gain in sensitivity due to collection of oblique lines-of-response (LORs) in long AFOV scanners. In figure 4a we also observe that the NEC for a scanner with 30 mm long LaBr₃ and 25 cm AFOV is similar to that achieved in a scanner with 20 mm long LSO and 18 cm AFOV, as previously shown in our work (Surti et al., 2004) about the equivalency of these two systems.

Fig. 4.

(a) Total NEC as a function of crystal thickness for scanner designs using a fixed amount of crystal (8.2 liters of LSO and 17.1 liters of LaBr₃). As the crystal thickness increases, the corresponding scanner AFOV is lower. This result corresponds to a fixed scan time for a single bed position study. (b) Simulated scanner AFOV for a given crystal thickness when using a fixed amount of crystal (8.2 liters of LSO and 17.1 liters of LaBr₃) for different scanner designs.

3.3. System NEC/cm for a constant scan duration per 100 cm long scan

While the NEC results shown in figure 4 were calculated for a single bed position and fixed scan time, in clinical studies multiple overlapping bed positions are used to image a long object. In figure 5a we plot the relative scan time per bed position (assuming 50% bed overlap) for scanner designs using different combinations of crystal thickness and scanner AFOV while keeping the total crystal volume used in the scanner constant. All scan times are shown relative to an 18 cm long LSO scanner with 20 mm thick crystals (Standard LSO scanner design in table 1). The scan times per bed position as shown in this plot were used in the imaging simulation studies performed with the lesion phantom.

Figure 5.

(a) Relative scan time per bed position for scanner designs using different combinations of crystal thickness and scanner AFOV while keeping the total crystal volume used in the scanner constant. Scan times are shown relative to an 18 cm long LSO scanner with 20 mm thick crystals (b) NEC/cm for performing a 100 cm long scan in a fixed total scan time of 10 minutes. All results are shown for a 35 cm diameter line source phantom.

In figure 5b we show the NEC/cm in the line source phantom for performing a 100 cm long scan in a fixed total scan time of 10 minutes (corresponds to a 50 second scan per bed position in the Standard LSO scanner design). Maximum NEC/cm is obtained for an LSO scanner with 10 mm long crystals and AFOV of 36 cm (Medium LSO scanner design in table 1). Similarly, for LaBr₃ scanners, maximum (or close to maximum) NEC/cm is obtained between 20–30 mm long crystals and AFOV of 25–38 cm (Standard and Medium LaBr₃ scanner designs in table 1). These results agree with what we observed for the total system NEC in figure 4a.

3.4. Point source spatial resolution

In figure 6 we show the average transverse spatial resolution (FWHM) (average over both dimensions) as a function of source radial position for varying scanner geometries. Point source in air data were reconstructed using the 3D-FRP algorithm and analyzed according to the NU 2-2008 standard (NEMA 2008). The improved (smaller) spatial resolution right at the center of the scanner is due to the excellent sampling of the data at the geometric center of the scanner. From this plot we say that as the scanner AFOV increases, and correspondingly the crystal thickness decreases, the spatial resolution improves due to reduced Compton scatter in thin crystals. This result holds true as the source position increases radially indicating parallax error in longer AFOV scanner using thin crystals is less than in shorter AFOV scanners using thick crystals.

Figure 6.

Average transverse spatial resolution (FWHM) measured in varying scanner designs. Results are shown separately for source radial positions between (a) 0–5 cm and (b) 5–20 cm. The scanner AFOV (in cm) and crystal thickness (in mm) are listed for each scanner design.

3.5. Lesion contrast

In figure 7 we plot the mean lesion contrast (averaged over 80 lesions) as a function of iteration number (OSEM reconstruction algorithm) for varying scanner geometries and 300ps timing resolution. The rate of convergence of contrast to it maximum value is faster as the scanner timing resolution improves, but the maximum contrast value does not change. In figure 7, we see that as the scanner AFOV increases, and correspondingly the crystal thickness is reduced, the measured lesion contrast is higher. This result is explained by the improved spatial resolution achieved in scanners with longer AFOV but using thin crystals (see figure 6).

Figure 7.

Measured lesion contrast values as a function of iteration number for varying scanner designs with a timing resolution of 300ps for both LSO and LaBr₃. Note, that the simulated lesion uptake was 3:1 with respect to the background. The scanner AFOV (in cm) and crystal thickness (in mm) are listed for each scanner design.

3.6. Lesion detectability

Impact of scanner design and timing resolution on lesion detection

In figure 8 we show results for ALROC values calculated using the generalized scan statistics technique for LSO and LaBr₃ based scanner designs as a function of timing resolution. The total scan time was fixed at 10 minutes for imaging a 100 cm long object. From these results we see that for both crystal types, the Long and Medium scanners have the highest and similar ALROC values for a fixed timing resolution. With TOF information, all scanners show an increase in the ALROC values, with the differences between the different LSO scanners being reduced as timing resolution improves to 300ps due to a very high value of ALROC. The ALROC values for the LaBr₃ scanners are also noticeably lower than those achieved by the LSO scanners and better timing resolution is needed to achieve performance similar to that of the LSO scanners. In general, Short scanner designs need better timing resolution to achieve the same performance as the Standard or Long/Medium scanners.

Figure 8.

ALROC values as calculated using the generalized scan statistic technique for (a) LSO and (b) LaBr₃ scanners as a function of timing resolution. The total scan time was fixed at 10 minutes for imaging a 100 cm long object. The scanner AFOV (in cm) and crystal thickness (in mm) are listed for each scanner design.

Impact of scanner design and scan time on lesion detection

In figure 9 we show the ALROC values for varying scanner designs as a function of total scan time for imaging a 100 cm long object, while using timing resolution of 600ps and 300ps for LSO and LaBr₃ scanners, respectively. Again the Long and Medium scanners have the highest and similar ALROC values and, as expected, longer scan times lead to higher ALROC values for all scanners. In general, Short scanner designs need about four times the total scan time (after 20 mins) to achieve the same performance as in Long/Medium scanners (after 5 mins), while the Standard scanner designs typically need to double the scan time (after 10 mins) to achieve performance similar to the Long/Medium scanners (after 5 mins). Hence, for an optimized scanner geometry and fixed system timing resolution, we can reduce the total scan time without a significant degradation in performance.

Figure 9.

ALROC values as calculated using the generalized scan statistic technique for (a) LSO and (b) LaBr₃ scanners as a function of total scan time. The scan time was fixed at 600ps for LSO and 300ps for LaBr₃ scanner designs. The scanner AFOV (in cm) and crystal thickness (in mm) are listed for each scanner design.

Combined effect of timing resolution, scanner design, and scan time on lesion detection

In figure 10 we plot the ALROC values for selected scanner designs using LSO and LaBr₃ crystals and varying total scan times and timing resolution. Commercial LSO and LYSO scanners using 20–25 mm thick crystals achieve a timing resolution of 550–600ps, while a 375ps timing resolution has been measured in the LaPET scanner using 30 mm thick LaBr₃. From a detector design perspective, it is also well understood that shorter crystals can lead to improved timing resolution (Wiener et al., 2011). Hence, we chose a timing resolution of 600ps as being representative of what we can achieve in Standard LSO scanner designs, and 300ps for Long/Medium LSO scanners with thinner crystals. Similarly, we chose a timing resolution of 300ps as being representative of what we can achieve in Standard LaBr₃ scanner designs, and 150ps for Long/Medium LaBr₃ scanners. Note that the timing resolution values chosen for thinner crystals in this work do not necessarily suggest that a factor of two improvement can be measured in the laboratory with these crystal sizes, but are selected here to illustrate the maximum gain that can be expected in the future. From the plot in figure 10 we observe that the Long LSO scanners with 300ps timing resolution (and Medium with 300ps timing resolution, not shown here) have the potential to achieve very high performance for imaging a 100 cm long object in 5 minutes. In Standard LSO scanners with 600ps timing resolution, the scan time needs to be doubled to achieve similar performance. For LaBr₃ scanners, a total scan time in the range of 10–20 minutes as well as improved timing resolution are necessary to achieve ALROC values similar to that of the LSO scanners.

Figure 10.

ALROC values as calculated using the generalized scan statistic technique for selected LSO and LaBr₃ scanners for varying total scan time and timing resolution while imaging a 100 cm long object. The scanner AFOV (in cm) and crystal thickness (in mm) are listed for each scanner design.

In figure 11 we show a representative reconstructed central transverse slice of the lesion phantom obtained for the six different scanner designs shown in figure 10. Figure 11a and 11d show the results for LSO and LaBr₃ scanner designs with currently achievable timing resolution of 600ps and 300ps, respectively. While the ALROC results are similar, lower lesion contrast but improved noise characteristics (due to longer scan time and improved timing resolution) can be observed in the LaBr₃ image (figure 11d). By moving to Medium scanner designs and improved timing resolution that can be achieved with thin crystals, the scan time can be reduced to 5 minutes and 10 minutes with LSO and LaBr₃, respectively, to achieve similar or better ALROC relative to the corresponding Standard scanners (figures 11b and 11e). Finally, figures 11c and 11f show images from Medium scanner designs with improved timing resolution and longer scan times. This combination of parameters leads to the best imaging performance with maximum ALROC values.

Figure 11.

Reconstructed central slice of the lesion phantom from six different scanner designs. We also show the corresponding ALROC, contrast and NEC/cm values for each image.

4. Discussion and conclusions

In our investigations we see that the increase in relative scanner sensitivity per crystal thickness is maximal for 15 mm thick LSO and 25 mm thick LaBr₃ (shown in figure 3). For a fixed crystal volume, the Medium (AFOV of 36–38 cm) scanner designs using thinner 10 mm LSO or 20 mm LaBr₃ provide the maximal NEC/cm for imaging a 100 cm long object in a fixed amount of time (10 minutes, as simulated here) as shown in figure 5.

Our NEC/cm results indicate that Medium LSO and Medium/Standard LaBr₃ scanners should give the best performance (figure 5). Our NEC calculations did not include the effect of random coincidences, but as we explained earlier the randoms to trues fraction will be approximately constant for the different scanner axial lengths with a fixed type of crystal. Hence, the relative differences in NEC will be the same with or without randoms included. In fact by using a fixed randoms to trues fraction (1.0 which is typically seen in the Philips Gemini TF scanner at clinical rates) we have verified that this is true and the plot shown in figure 5b shifts lower on the vertical scale.

From our lesion detectability studies we find that the Long and Medium scanner designs perform the best with similar ALROC results (figure 8). This difference is explained by the fact that the longer scanners use shorter crystals, which leads to improved spatial resolution and hence, higher lesion contrast (observed in figures 6 and 7), thereby leading to improved lesion detectability. While the NEC/cm for the Standard LSO and LaBr₃ scanners is not significantly different, the ALROC result that takes lesion contrast into account is higher for the LSO design for the same scan time and timing resolution (see figure 8). Improved timing resolution (or longer scan time) is needed for the Standard LaBr₃ scanner to achieve ALROC similar to the Standard LSO scanner. This fact can once again be explained by the reduced lesion contrast of the Standard LaBr₃ scanners relative to the Standard LSO scanner (figure 7). Alternately, the lesion contrast, as well as the NEC/cm, in the Short LSO scanner and Long LaBr₃ scanners is very similar (see figures 5b and 7). As a result, for the same timing resolution, the Short LSO scanner has ALROC values that are similar to those achieved by the Long LaBr₃ scanner. Hence, while NEC/cm provides a measure of the statistical noise present in the image, it does not account for spatial resolution and correspondingly the lesion contrast, which is a significant contributing factor in the calculation of the ALROC values for lesion detectability in this study where we used 1 cm diameter lesion with low activity uptake (3:1 with respect to the background).

Our results in figures 8 and 9 indicate that for a fixed scan time and timing resolution, longer AFOV scanner designs (and correspondingly shorter crystals) have higher ALROC results. In particular, when comparing the Long/Medium and Short scanner designs, either the scan time needs to be quadrupled or the system timing resolution improved by a factor of four in Short scanners to achieve the same ALROC results as in the Long/Medium scanners. Since we know that improved timing resolution is correlated with shorter crystals (Wiener et al., 2011), we show a comparison in figure 10 of the Long LSO scanner with 300ps timing resolution scanners to the Standard LSO scanner with 600ps timing resolution that achieve similarly high ALROC values but with a factor of two difference in total scan time (5 minutes versus 10 minutes of total scan time for a 100 cm long object). Due to reduced NEC/cm and lower lesion contrast the Medium LaBr₃ scanner requires approximately 20 minutes total scan time (compared to 10 minutes) and a timing resolution of 150ps (compared to 300ps) to achieve performance similar to the best performing LSO scanners.

Both the NEC and lesion detectability studies in this work incorporated the effects of true and scattered coincidences, and the reconstructed images included full corrections for scattered coincidences. The scatter fraction when going from a 12–15 cm AFOV scanner to a 72–75 cm long scanner increases by about 15%. Random coincidences were not modeled in this work, but as explained earlier we do not expect a significant change in the conclusions. Also, for this study we fixed the lower energy threshold at 440 keV for both LSO and LaBr₃ scanners. In practice, improved energy resolution of LaBr₃ allows the use of a higher lower energy threshold (470 keV on the LaPET scanner (Daube-Witherspoon et al., 2010)). Therefore, the number of scattered and random coincidences in otherwise equivalent LSO and LaBr₃ scanner geometries will be lower in the LaBr₃ scanner, thereby improving the relative performance of these scanners to the LSO designs.

In conclusion, the use of shorter crystals in longer axial FOV scanners (Long and Medium designs as used in this study) can be beneficial, especially due to the potential for achieving improved timing resolution relative to what is currently achieved in current commercial and research PET scanners. Long scanner designs (such as the 72–75 cm long scanners evaluated here) with scintillator costs similar to the Standard scanner designs can also provide the capability for performing dosimetry studies and dynamic whole-body imaging. Such studies are not possible in shorter axial FOV scanners where multiple bed positions are necessary to image different body regions. Medium scanner designs (such as the 36–38 cm long scanners evaluated here), while performing as well as the Long designs, will have the advantage of reduced photo-detector cost, which will depend on the detector design and is a factor that was not considered in this work. Short crystals also lead to reduced parallax error and could allow the use of a smaller ring diameter for the scanner, which will improve system sensitivity further and can also provide the ability to develop a clinical PET insert for use in a PET/MR system.