Phantom study
At the outset this study was planned with only the routinely applied QSPECT reconstruction without post-filtering [18, 21] in order to eventually apply the same reconstruction for tumor dosimetry as for kidney dosimetry. The 'valley' artefact observed in Fig. 1a, however, reduces the maximum and the peak values in the ø37 sphere to values below those of the ø28 sphere as shown in Fig. 2a. This carries on to lower the fixed-percentage thresholds and in turn influences values derived from the threshold-generated VOIs. The artefact can probably be ascribed to Gibbs-like ringing artefacts in performing point-spread function correction as discussed by Kangasmaa et al. [19]. The artefact is not visible in Fig. 1d-f, where the transition from spheres to background is less sharp due to the presence of 177Lu in the background volume. The smoothing by a Gaussian post-filter removes the artefact, and a more regular behavior can be seen in Fig. 1b and in Fig. 2c-d, where the mean and peak values for the ø37 sphere are larger than or equal to the values for the other spheres. With the Bayesian reconstruction, the voxel values are similar in voxels with similar Hounsfield Units in the CT scan. Indeed, in Fig. 1c, the voxel values across the spheres vary less than in the OSEM reconstructions and there is a sharp edge to the background.
As shown in Fig. 3, the accuracy is very good for the five largest spheres using the QSPECT reconstruction, which also means that despite the 'valley'-artefact, the total counts are maintained within the ø37 sphere. For the filtered QSPECT reconstruction, the negative deviation is due to counts found outside the VOIdia+15 spheres as a consequence of the smoothing. For the Bayesian reconstruction the deviation is within 10% over the entire range of sphere sizes.
The contrast shown in Fig. 4 is 100% for all reconstructions and all sphere sizes for P∞, however, once background activity is introduced the values drop below the theoretical values in particular for the smallest spheres. Visually judged from the reconstructed images, the presence of a sphere, or tumor, cannot be recognized once the contrast is below about 0.2 (compare Fig. 1d-f and Fig. 4). The RCs in Fig. 4 show a regular behavior for P∞, but for the other phantoms the presence of activity in the background volume causes the RCs of the smallest spheres to become larger than the RCs of some of the larger spheres. For the Bayesian reconstruction the picture is even inverted, such that the RCs for P2.7 and P5.0 are generally above those of P9.5 and P∞.
One method for calculating tumor dose is based on the mean concentration in small spherical VOIs, for which data are shown in Fig. 5. The mean is within about 40% of the true value only for the largest sphere using the QSPECT reconstruction, but for the two largest spheres using the filtered QSPECT reconstruction and for the three largest using the Bayesian reconstruction. The variation of the obtained mean with 177Lu content in the background is largest for the QSPECT reconstruction and smallest for the Bayesian reconstruction. The variation with chosen small VOI diameter can be observed from the series of three displaced data points for the same phantom and sphere diameter. Generally the mean decreases with increasing VOI diameter, as expected from the profiles in Fig. 1, where the voxel values vary across the sphere, being largest in the center, except in the presence of the 'valley'-artefact. For the smaller spheres the mean values are generally quite low as compared to the true value, which can be explained by the low RCs and that the spherical VOIs probe a large fraction of the sphere volume.
For the method based on threshold-generated VOIs, the uncorrected data presented in Fig. 6 (a, c, e) and Fig. 7 (a, c, e) show that for the QSPECT reconstruction, values within 50% of the true are obtained, while the mean is generally underestimated for the other two reconstructions except for the ø37 sphere. The means in VOIs generated by a percentage of the peak value were expected to be less susceptible to noise than those generated from the maximum in a single voxel, however, no appreciable difference in standard deviation of the mean is seen between the two. The volumes probed by the VOIs, as shown in Fig. 6 (b, d, f) and Fig. 7 (b, d, f), vary significantly with the level of 177Lu background activity, and in particular for the Bayesian reconstruction the volume may extend outside the sphere volume.
With correction for the partial volume effect, as presented in Fig. 8 and Fig. 9, the QSPECT reconstruction performs surprisingly bad. The Bayesian reconstruction on the other hand is very stable across all sphere sizes as compared to the other reconstructions. The values for the filtered QSPECT reconstruction with a threshold at 40% of the maximum are quite reasonable for P∞ with a sphere diameter of 22 mm and larger. This is in line with the procedure applied by Ilan et al. [8], using a 42% threshold and a similar QSPECT procedure, with the same number of iterations and subsets in the OSEM reconstruction as here and a Hanning filter with cutoff at 0.85 cycles/cm. Once 177Lu activity is introduced to the background volume, the corrected mean drops significantly for the ø22 sphere (P9.5) or the threshold-based VOI even extends beyond limits (P5.0 and P2.7), while for the ø28 and ø37 spheres the mean remains within about 40% of the true.
For tumor dosimetry, we assume that the mean tumor dose is calculated from the mean 177Lu activity concentration in a tumor in sequential post-treatment scans, and that the beta-radiation is completely absorbed within the tumor.
When the results of the phantom study are considered in the context of tumor dosimetry, some options and limitations become clear. The data obtained for P∞ in Fig. 3 show, that the 177Lu concentration in a well-isolated tumor even down to 13 mm diameter can be determined quite accurately using a large VOI around the tumor on the QSPECT reconstruction for determination of activity, and using other imaging methods, e.g. PET, CT or MR, for determination of the tumor volume. In clinical cases, typical quantification accuracy of 177Lu activity is about 10–20% [18, 21, 22], and the volume should be determined with a similar accuracy.
The methods based on a small VOI or a threshold-generated VOI can be applied not only for isolated tumors, but also if nearby activity is present, e.g. in other tumors or as physiological uptake in liver, spleen or kidneys. For these methods the best agreement is found for the two or three largest spheres for the filtered QSPECT and the Bayesian reconstruction, respectively, with the threshold set to 40% of the maximum.
By the nature of the Bayesian reconstruction, it critically depends on the alignment between SPECT and CT, and hence the relatively good performance in this phantom study cannot necessarily be translated to patient studies, e.g. an 'erratic fragmented appearance' of lesions was reported by Grootjans et al. [23], and the Bayesian reconstruction should only be used with caution. Hence, the small VOI or the threshold-generated VOI method are judged more robust and straightforward to apply using the filtered QSPECT reconstruction.
As a practical limit we suggest for both methods a tumor diameter > 30 mm. This is slightly larger than the ø28 sphere and thus a bit conservative to allow for some deviations from the idealized case of a phantom study. Tumors down to 22 mm diameter can also be included for analysis, if they are well isolated, using either the small-VOI method with a ø10 VOI or the threshold-based method. Tumor diameters are often reported as the longest diameter in the plane of measurement [24], while partial volume effects are expected to be most significant in the plane of the shortest axis of non-spherical volumes. Hence if the aspect ratio differs significantly from unity, e.g. as for very elongated tumors, the short axis should also be considered.
For all ø28 and ø37 spheres in all phantoms the measured contrast is > 0.2. This is, however, also at the limit where a tumor can be recognized, and as a practical limit for the small VOI method we propose a contrast > 0.3, or equivalently a tumor-to-background ratio larger than 2. Some variation of the mean concentration with small VOI diameter is found, particularly when no 177Lu background activity is present. A ø15 or ø20 diameter VOI may be preferable, as the concentration tends to be overestimated with a ø10 VOI, but a general optimal choice cannot be made as this depends on tumor diameter. A 20 mm diameter sphere was applied by Sandström and colleagues in kidney and spleen dosimetry [25], and adapted for tumor dosimetry by Del Prete et al. [11, 26]. The threshold-based method (40% of maximum) could only be applied to spheres for which the measured contrast was > 0.5 or equivalently the tumor-to-background ratio was larger than 3. The tumor-to-background ratio is likely to vary in the days following treatment, and the contrast criteria must be fulfilled for all post-treatment scans used for tumor dosimetry. Normally the treatment drug is retained longer in tumors than in organs, which means of course that if the tumor-to-background criterion is fulfilled at the first post-treatment scan, it is most likely also fulfilled at later scans.
With these criteria for selecting tumors for analysis by one of the three methods, it should be possible to determine the mean 177Lu concentration at the level of 40% accuracy, or better with the large VOI method. Other significant error sources can be the volume determination (large VOI method), the partial volume correction (threshold-generated VOI method) or errors in fitting sequential data points to an exponential decay [18]. In clinical practice, quantification errors larger than the 40% found here cannot be excluded, and as further error sources also contribute to the total error of the tumor dose, a realistic boundary on the possible error is not below 50%. If the estimated tumor dose is within 50% of the true, then the true is within + 100%/-33% of the estimated dose.
This seems perhaps unsatisfactory, but since tumor dosimetry is more difficult than kidney dosimetry, with its smaller volumes that are undiscernible on non-contrast CT, errors up to 50% are not surprising [27, 28]. For a symmetric triangular error distribution, a 50% maximal error corresponds to a standard deviation of 20% [18, 29], which can be compared to reported standard deviations in kidney dosimetry of 10–15% [18, 27].
This level of uncertainty in tumor dosimetry is lower than observed inter-patient or inter-tumor variability or the intra-patient variability through the course of a treatment series[11, 14, 30], and further the threshold-based method with partial volume correction has already been used to demonstrate tumor-dose response for pancreatic neuroendocrine tumors [8]. This holds promises that any of the methods with its associated restrictions is useful for e.g. dose response studies in PRRT and RLT using 177Lu.
These conclusions are based on a phantom study with spheres up to 37 mm diameter, but are also expected to hold for larger tumors where partial volume effects are smaller [7]. A consistency check of the methods can be made for tumors, when more than one of the methods are applicable. Sandström et al. [25] demonstrated a good correspondence between the small VOI and the threshold based method in dosimetry of the kidneys and the spleen.