The influence of triple energy window scatter correction on activity quantification for ^1 7 7Lu molecular radiotherapy

The phantom data were reconstructed using a clinical OSEM reconstruction algorithm (GE OSEM) with 10 subsets and 4 iterations on a GE Xeleris 2 workstation. Narrow beam attenuation correction (AC) was applied with the Xeleris 2 workstation, using Hawkeye CT data acquired as part of the scan protocol. The use of attenuation maps generated from CT imaging using the camera manufacturer's own software for attenuation correction for ${{}^{1\,7\,7}}$Lu is highly recommended (Ljungberg et al 2015). The SPECT data were reconstructed with parameters corresponding to a clinical protocol for ${{}^{1\,7\,7}}$Lu MRT dosimetry. Data were reconstructed for individual photopeaks (EM1 and EM2) with (1) AC and no scatter correction (AC) and (2) AC and the standard TEW scatter correction (AC)(TEW) applied prior to reconstruction. The application of scatter correction outside of the reconstruction algorithm, whilst sub-optimal, is a common procedure in commercial clinical reconstruction algorithms. A Hann prefilter (0.9) and Butterworth low-pass post-reconstruction filter with order 10 and normalized cutoff frequency 0.5, were applied to all reconstructed images. It should be noted that any filtering is generally applied based on the specific objectives of the study and will have an effect on quantification and partial volume contributions.

A calibration factor, cf, can be defined which relates the count rate (counts per second, cps) in a reconstructed SPECT image to the known total activity (MBq) in a phantom or insert,

$$\begin{eqnarray}&&\text{cf}=\text{counts}/\left(\text{Activity}\times \text{time}\right).\end{eqnarray} \tag{ 2 }$$

The whole body sensitivity (WBS) phantom measurement was used to determine calibration factors for the total counts in the SPECT camera field-of-view. The small volume sensitivity (SVS) phantom measurements were used to determine calibration factors for a volume-of-interest (VOI) corresponding to a 10 ml phantom insert. A VOI defining the 10 ml phantom insert was manually outlined using the Hawkeye CT data and transferred to the SPECT image. Partial volume effects in the final reconstructed images, leading to the loss of apparent activity due to the limited resolution of the SPECT camera, can be compensated for by using a sensitivity factor specific to the volume in which the activity is being quantified (Dewaraja et al 2012). This approach is typically used in clinical protocols. Whilst an anatomy based partial volume correction can provide a more robust approach, there is currently no widely accepted, well-validated method (Dewaraja et al 2012). In the present work, the SPECT images for calibration used the same reconstruction, attenuation correction and TEW scatter correction parameters as were used for the images being quantified to ensure accurate activity quantification.

For a known activity in a phantom volume an activity recovery factor (RF) is defined as,

$$\begin{eqnarray}&&\text{RF}=1.0-\left(\frac{{{A}_{\text{admin}}}-{{A}_{\text{quantified}}}}{{{A}_{\text{admin}}}}\right)\end{eqnarray} \tag{ 3 }$$

where A_admin is the known administered activity in a phantom volume and A_quantified is the quantified activity calculated for a specific calibration factor (equation (2)) appropriate to the volume being considered. Thus, for a specific calibration factor (cf) a recovery factor less than 1.0 corresponds to an underestimation of the quantified activity in the phantom, whilst conversely values greater than 1.0 represent an overestimation of the administered activity.

The count losses due to dead time in a SPECT camera system for ${{}^{1\,7\,7}}$Lu are small due to the low yield of gamma rays from the decay of ${{}^{1\,7\,7}}$Lu. Dead time effects are highly camera-specific and must be corrected for each individual photopeak and projection before reconstruction. The total activities used in this work were selected to be below the level at which deadtime effects are observed for the camera system used in this work (>2.5 GBq total activity).

The simulation described in section 2.3 was used to generate event-by-event data for detected gamma rays for both the full activity imaged in each experiment described in table 1 and for the SVS and WBS calibration scans. The simulations were performed on a computer cluster containing 200 CPU cores (Intel Xeon E5260—2.4 GHz). A dedicated analysis package has been developed (written in C + +) to produce projection data sets from the raw MC simulation output (stored in a ROOT tree (Brun and Rademakers 1997)) in an interfile format compatible with the Xeleris workstation software (GE Healthcare). This software allowed a general set of conditions to be placed on the parameters of the detected emission when generating the projections (i.e. energy window, particle type, interaction history). Simulated projection data sets were generated corresponding to the tomographic data for each energy window acquired with the Infinia-Hawkeye-4 camera. The MC projection data were imported into the Xeleris 2 workstation and reconstructed using the same OSEM algorithm, attenuation correction and reconstruction parameters as the experimental phantom data described in section 2.2.1.

Monte Carlo simulated data corresponding to the physical phantoms scans (described in section 2.3.1) were used to track photons and their interactions detected in the EM1 and EM2 photopeak windows through the MC simulation geometry. Simulations were also performed for an additional phantom geometry corresponding to the cylindrical NEMA PET phantom (6.9 l, 220 mm diameter and 183 mm height) with a large 278 ml cylindrical insert (44 mm diameter, 183 mm height), shown in figure 2(b), imaged with the same acquisition parameters (table 2).

Events detected in the SPECT camera were classified according to the number of Compton interactions (scattered and unscattered) and the physical origin of the emitted photon (from within phantom inserts or body). Projection data corresponding to these different classes of events were produced using the analysis software described in section 2.3.1. The projection data for each event class were reconstructed, using the method defined in section 2.2.1, allowing detected events to be selected which correspond to a 3D VOI within the reconstructed regime. The data were subsequently filtered by the 3D position of the detected event within the reconstructed regime. This allowed the composition of events in a photopeak window detected in a VOI defining a single cylindrical insert to be determined. This technique allowed event classes to be tracked through an iterative clinical reconstruction algorithm, providing unique information which can only be obtained from MC simulation.

Simulated data corresponding to the 'BG' phantom scans (table 1) were used to produce localized energy spectra for events detected in reconstructed VOIs corresponding to the individual 10 ml inserts (with varying activities). The total phantom energy spectrum, as measured by clinical SPECT systems, was also produced. Experimental measurements of localized energy spectra are not possible with conventional SPECT cameras and are a unique capability of MC simulation

The whole image activity recovery factor (RF), as defined in equation (3), for total reconstructed counts in the SPECT field-of-view is shown in figure 3 for the 'No BG' phantom data. RF values are calculated for EM1 (red line) and EM2 (green line) emission windows as a function of total activity with (1) attenuation correction only (AC) (solid line) and (2) attenuation correction and TEW scatter correction (AC)(TEW) (dashed line) applied to both the calibration scan and object scan. The data in figure 3 has been calibrated using the total reconstructed counts in (a) the WBS phantom data and (b) the highest activity scan 'No BG' cylindrical phantom scan (755 MBq).

Zoom In Zoom Out Reset image size

Figure 3(a) shows a clear overestimation of recovered activity ($\text{RF}>1.0$) at activities lower than 200 MBq when applying the TEW (dashed lines), to both calibration and object scans, in contrast to data with (AC) only (solid lines). The difference in activity recovery factor from 1.0 is improved for both (AC) and (AC)(TEW) when using calibration data with an identical geometry (figure 3(b)). However, there is still a significant overestimation of recovered activity when the TEW correction is applied at lower activities (<200 MBq), up to 51% and 25% for EM1 and EM2 respectively, (figure 3(b)).

The RF for ${{}^{1\,7\,7}}$Lu calculated for a VOI corresponding to the 10 ml phantom inserts (outlined on co-registered CT data) is shown in figure 4. The SVS scan data (226 MBq) was used for calibration and provided separate calibration factors for scans with (AC)(TEW) and without the standard TEW correction (AC) applied. Data is presented for (a) 'No BG' phantom data and (b) 'BG' phantom data. Recovery factors are shown for both data sets (AC) (solid line) and (AC)(TEW) (dashed line) as a function of insert activity. For the 'BG' data the insert to phantom body activity concentration ratio is indicated by the line color, $4:1$(green crosses), $13:1$ (pink circles), and $24:1$ (light blue squares).

Zoom In Zoom Out Reset image size

With and without scatter correction applied, there is minimal difference in the values of RF for the 'No BG' data (figure 4(a)). For both the EM1 and EM2 photopeaks the activity recovery varies from 90% to 97% with decreasing activity. However, the addition of activity into the phantom body, figure 4(b), significantly changes the activity recovery in the CT defined VOIs. For the highest insert-to-background activity ratios ($24:1$), the difference between recovered activity and known activity is 10% or less for EM1 and EM2 (blue lines) for both (AC) and (AC)(TEW) data. As the background activity increases relative to the insert activity the value of RF increases for both EM1 and EM2 (purple and green lines), up to a maximum of 1.8(3) ($80\pm 30\%$ overestimation) and 1.4(2) ($40\pm 20\%$ overestimation) for EM1 and EM2 respectively with (AC) only. When the TEW correction is applied the overestimated value of RF (for a $4:1$ insert-to-background activity ratio) is reduced to  ∼1.2 (20%) for EM1 and EM2, with the largest reduction for EM1 (which has higher underlying scatter).

Validation of simulated results by comparison to experimental measurements, is essential for all simulation techniques. Accurate validation is particularly important for MC simulation when using the output to provide insight into experimental phenomena which are not directly observable such as gamma ray tracking in a SPECT camera system. A comparison of the simulated (red line) and experimental (black line) energy spectrum from the Infinia-Hawkeye-4 PHA acquisition is shown in figure 5 for a water filled phantom with three 10 ml inserts containing ${{}^{1\,7\,7}}$Lu, acquired using MEGP collimators. The true scattered component of the simulated ${{}^{1\,7\,7}}$Lu emission spectrum (TS) is also shown (blue dashed line). Figure 5 shows good agreement both in the photo-peak and lower energy Compton scattered regions for the complex emission from ${{}^{1\,7\,7}}$Lu. In addition the simulation correctly reproduces the emission and detection of Pb x-rays. The close agreement with experiment, across the whole energy spectrum (when the measured low energy detector efficiency and cut off are included), supports the choice of physics processes in the simulation and validates the global photon transport in our model.

Zoom In Zoom Out Reset image size

Figure 6 shows; (a) a representative projection of the experimental data from the 'No BG' scans (with ${{}^{1\,7\,7}}$Lu) from the Infinia-Hawkeye SPECT camera and (b) the corresponding projection from our MC simulation. A horizontal profile through the inserts is shown (on both a linear and logarithmic scale) in figure 6(c) for the experimental (blue) and simulation (red dashed line). There is excellent agreement across the whole profile. The simulated 2D projection (figure 6(b)) closely reproduces that of the experiment with a peak-signal-to-noise ratio (PSNR) (Al-najjar and Soong 2012) of 71.2(1) dB for the two projection sets. Figure 6(d) shows the variation in total counts in each projection, corresponding to the head position for a tomographic acquisition. The variation in count rate, which depends on the specific source activity distribution and densities of the phantom and patient bed, is fully reproduced, further validating the geometry and material composition of our SPECT camera model for the full range of direct observables from a commercial SPECT camera.

Zoom In Zoom Out Reset image size

Table 3 shows the composition of events reconstructed within VOIs outlining the cylindrical inserts in the simulated 'BG' phantom data. Also shown is the corresponding event composition for the larger NEMA PET phantom data with 278 ml cylinder (described in section 2.3.2). The fraction of the total events detected in the EM1 and EM2 photopeak windows is classified according to the number of Compton interactions (scattered and unscattered) and the physical origin of the emitted photon (from phantom inserts or body). Data is presented for phantoms with variable insert to background activity ratios ($24:1,13:1$ and $4:1$) and also with no background activity (Calib). The largest contribution to the quoted uncertainty is due to iteratively reconstructing a subset of the total events detected in the photopeak. The fraction of events removed in each VOI by applying the standard TEW correction are also shown ('comparison with TEW correction'). For an ideal scatter correction this value should be equal to the total number of scattered events from the insert and body (shown as 'Total scattered events' in table 3). However, these data show an overestimation of scattered events when using the TEW. As an example, for the $4:1$ insert to body activity ratio data in the EM1 photopeak (column 5, table 3), the fraction of total scattered events (sum of 'insert scattered'  +  'body scattered') is $0.33\pm 3$ ($33\pm 3\%$). In contrast for the same data the TEW correction estimates that 40% of the total events are scattered ('TEW correction'), an overestimation of 7%. A similar level of overestimation is seen with the TEW scatter correction with increased insert-to-background ratio and for the larger 278 ml insert data, with reduced scatter for the EM2 window.

Table 3. Composition of events in photopeak windows reconstructed within a VOI corresponding to cylindrical inserts for MC simulated SPECT data.

Photopeak	Event Origin	Compton Scattera	$3\times 10$ ml inserts and body activity				278 ml insert and body activity
			Insert to body activity ratio				Insert to body activity ratio
			Calibb	$4:1$	$13:1$	$24:1$	Calib	$4:1$	$13:1$	$24:1$
EM1	Insert	Unscattered	0.90(2)	0.43(2)	0.67(2)	0.75(2)	0.87(1)	0.66(1)	0.79(1)	0.83(1)
EM1	Body	Unscattered		0.23(2)	0.12(2)	0.09(2)		0.13(1)	0.05(1)	0.03(1)
EM1	Insert	Scattered	0.10(2)	0.04(2)	0.06(2)	0.07(2)	0.13(1)	0.10(1)	0.11(1)	0.12(1)
EM1	Body	Scattered		0.29(2)	0.15(2)	0.08(2)		0.11(1)	0.04(1)	0.02(1)
Total scattered events			0.10(2)	0.33(3)	0.21(3)	0.15(3)	0.13(1)	0.21(1)	0.15(1)	0.14(1)
Comparison with TEW correctionc			0.16(2)	0.40(2)	0.28(2)	0.21(2)	0.27(1)	0.36(1)	0.29(1)	0.28(1)
EM2	Insert	Unscattered	0.94(2)	0.55(2)	0.77(2)	0.83(2)	0.92(1)	0.78(1)	0.87(1)	0.89(1)
EM2	Body	Unscattered		0.31(2)	0.14(2)	0.09(2)		0.12(1)	0.04(1)	0.03(1)
EM2	Insert	Scattered	0.06(2)	0.03(2)	0.05(2)	0.05(2)	0.08(1)	0.07(1)	0.08(1)	0.08(1)
EM2	Body	Scattered		0.10(2)	0.05(2)	0.03(2)		0.03(1)	0.01(1)	0.01(1)
Total scattered events			0.06(2)	0.13(3)	0.10(3)	0.08(3)	0.08(1)	0.10(1)	0.09(1)	0.09(1)
Comparison with TEW correctionc			0.10(2)	0.21(2)	0.15(2)	0.12(2)	0.16(1)	0.17(1)	0.14(1)	0.14(1)

^aEvents classified by number of Compton interaction (Unscattered  =  0, Scattered  >0). ^bNo background activity. ^cFraction of events removed by TEW correction. Note: The fraction of total events detected in the VOI are given (standard uncertainties referred to the corresponding last digits of the quoted result are quoted in parentheses).

Figure 7 presents data from table 3 filtered by the 3D position of the origin of the event detected within the reconstructed regime. The fraction of total events originating from the phantom body background activity, detected within an VOI outlining the cylindrical inserts, is shown as a function of distance from the VOI (measured with 4.4 mm voxels). Data are shown for the EM1 and EM2 photopeaks for (a) 10 ml cylindrical insert (25 mm diameter) and (b) 278 ml cylindrical insert (44 mm diameter) with varying insert to background activity ratios. The contribution of unscattered background activity events (solid lines) and Compton scattered events (dashed lines) is also indicated. The different characteristics of these two event types is striking, the scattered events (dashed line) originate almost isotropically throughout the body of the phantom whilst the unscattered events (solid line) occur mainly in the voxels closest to the VOI and rapidly fall off with distance, suggesting these events are due to partial volume effects.

Zoom In Zoom Out Reset image size

The data presented in table 3 were used to calculate the contribution of scattered and unscattered events originating in the background to the change in activity recovery factor, $\Delta$RF (table 4). The contribution from scattered photons is seen to be due to incorrect estimation of the true scatter when using the TEW correction, in both the calibration and object scans. The contribution of unscattered background events is a result of incomplete partial volume effect compensation. As an example, for the $4:1$ insert to body activity ratio data in the EM1 photopeak (column 3, table 4) the contribution of scattered photons will reduce the recovery activity by 11% (line 1) whilst the partial volume contribution overestimates the recovery by 53% (line 2), resulting in a total overestimation of activity by 42% (line 3). The relative contribution of partial volume events to $\Delta$RF for the larger 278 ml cylinder data is significantly reduced, as might be expected, in comparison to a smaller 10 ml cylinder.

Table 4. Total change in activity recovery factor (RF, no units) for MC simulated data with phantom background activity^a.

	Photopeak	$3\times 10$ ml inserts and body activity			278 ml insert and body activity
		Insert to body activity ratio			Insert to body activity ratio
		$4:1$	$13:1$	$24:1$	$4:1$	$13:1$	$24:1$
$\Delta$RF from scattered photonsb	EM1	−0.11(2)	−0.06(2)	−0.03(2)	−0.08(1)	0.00(1)	0.00(1)
$\Delta$RF from PVEc	EM1	0.53(2)	0.18(2)	0.13(2)	0.20(1)	0.06(1)	0.03(1)
$\Delta$RF Total	EM1	0.42(3)	0.12(3)	0.10(3)	0.12(1)	0.06(1)	0.03(1)
$\Delta$RF from scattered photonsb	EM2	−0.10(2)	−0.04(2)	−0.01(2)	−0.02(1)	0.02(1)	0.02(1)
$\Delta$RF from PVEc	EM2	0.56(2)	0.18(2)	0.10(2)	0.16(1)	0.05(1)	0.03(1)
$\Delta$RF total	EM2	0.46(3)	0.14(3)	0.09(3)	0.14(1)	0.7(1)	0.05(1)

^aFrom data presented in table 3. ^bDue to incorrect estimate of scatter from TEW correction. ^cDue to unscattered events originating in phantom body. Note: The table shows the contributions from scattered photons and partial volume events (standard uncertainties referred to the corresponding last digits of the quoted result are quoted in parentheses)^a.

Simulated localized energy spectra for events detected in reconstructed VOIs outlining three 10 ml inserts, within a single phantom, with $24:1,13:1$ and $4:1$ insert to background ratios are shown in figure 8(a). The corresponding total phantom energy spectrum, as measured by clinical SPECT systems, is shown in figure 8(b). The peak-to-background ratio for the 113 and 208 keV photopeaks in figure 8(a) varies significantly with changes in background activity in contrast to the averaged total energy spectra from the sum of all three inserts which the SPECT camera records, shown in figure 8(b).

Zoom In Zoom Out Reset image size

Figure 3 demonstrates a significant overestimation in activity recovery for total counts in the SPECT field-of-view when a TEW scatter correction is applied at low activities ($\leqslant$200 MBq total activity). These activities correspond to clinically observed total activities in the SPECT field-of-view for day 3 and day 6 NET patient ${{}^{1\,7\,7}}$Lu MRT imaging. In contrast the (AC) only data shows consistent activity recovery for an order of magnitude change in activity with an increase in RF of  <10% below 200 MBq (see figures 3(a) and (b)). This overestimation of recovered activity when TEW correction is applied is present even when using an identical calibration scan, a best case scenario which is only possible with phantom data (see figure 3(b)).

As activity reduces in the phantom the total counts in the measured energy spectrum (figure 5) will be reduced, assuming a fixed acquisition duration. The integrated counts in the adjacent TEW scatter windows will reach zero much quicker than in the photopeak window as the activity is reduced. For low total activities the number of voxels where this condition is met, and hence no scatter correction occurs, will rise significantly. When this condition occurs the scatter window distribution no longer represents the background in the photopeak window and the TEW subtraction correction will no longer be valid. This leads to an overestimation of recovered activity when using a single calibration factor for all imaging time points, as observed in figure 3.

The large increase in activity recovery observed when applying the TEW at low activities, in contrast to using (AC) only, suggests that automatic application of a TEW scatter correction for whole image activity quantification should be undertaken with caution. This is of particularly clinical relevance when performing dosimetry using a single SPECT image in combination with a sequence of whole body scans.

When considering activity recovery for a CT defined VOI outlining a phantom insert containing activity (figure 4), it is typically the voxels with highest count rates within the image which are being considered. As a consequence the condition when the TEW no longer represents the scatter distribution (as previously discussed for whole image activity recovery), is unlikely to occur in the voxels within the VOI due to their higher number of statistics. Therefore, there is good activity recovery with the 'No BG' data for both the (AC) and (AC)(TEW) data using the SVS calibration factor. Figure 4(a) shows activity recovery factors ranging from 90–97% for both EM1 and EM2—analogous with the results seen for higher whole image activities, shown in figure 3. The value of RF provides a benchmark for the accuracy of activity recovery when using a relative calibration technique with calibration factors which correspond exactly to the volume being considered (calculated for a specific reconstruction protocol). The increase in RF with decreasing activity seen in figures 4(a) and (b) for both (AC) and (AC)(TEW) data is a result of the increased influence of noise at lower activities. For example, the noise level for the 'No BG' 250 MBq per insert scan (0.3%, measured using a VOI placed away from the insert) will correspond to a noise level of  ∼9% in the lowest 7 MBq per insert scans. This is comparable to the 7(2)% increase in RF between the highest and lowest activity scans shown in figure 4(a).

The observed overestimation of activity recovery for a phantom insert with the introduction of background activity to a phantom may not be entirely unexpected. Exact activity localization can only be achieved with perfect compensation for scatter, partial volume and attenuation correction, whilst clinical SPECT imaging, by necessity, relies on approximate corrections. Whilst the TEW scatter correction provides improved values of RF, in comparison to using (AC) only, there is still a significant overestimation of recovered activity (see figure 4(b)). The underlying source of this overestimation is discussed in detail below in section 4.2.