Lack of knowledge of absorbed dose calculation uncertainties has been a factor that has impeded widespread uptake of dosimetry in MRT.
The EANM guidelines provide a schema of uncertainty propagation to evaluate the standard uncertainty in absorbed dose to a target. This schema was based on the recommendations described within the GUM [28] and necessarily involves formation of covariance matrices for several steps of the dosimetry process. In this work, we have applied the EANM guidelines to evaluate the uncertainty of tumour dosimetry calculations in PRRT. This study carried out, for the first time, the uncertainty analysis of the entire process of dosimetry calculation on a large sample of clinical cases compared to the existing scientific context. A total of 154 lesions were analyzed.
As shown in Fig. 2, the fractional uncertainty associated with the considered quantities (volume, CF, S-factor, etc.) was widespread around the median value, incurring a high inter-lesion variability. Volume and S-factor are the parameters with the highest uncertainty. These results confirmed that the uncertainty in absorbed dose is dominated by the uncertainty in the delineation of the VOI. For example, when contouring a volume, the uncertainty in edge definition due to the limited spatial resolution, together with the voxel width, involves errors in the assessment of the volume.
The uncertainty associated with the volume is then propagated to many of the other parameters (RC, Counts, Activity, Fitting, TIA, S-factor and Absorbed dose). The relationship between fractional absorbed dose uncertainty and tumour volume is evident in Fig. 4. The analytical power model for this relationship fitted the empirical data points well and this could be useful, in clinical practice, for a quick estimate of uncertainty without implementing the entire error propagation schema, which could be useful to select the lesions to be monitored for patient outcome assessment.
Fig. 7 shows the uncertainty in absorbed dose (black points) and the uncertainty in volume (blue line) on the same axis. This graph shows the "weight" of the uncertainty associated with the volume segmentation and other parameters on the accuracy of the dosimetric calculation. From a practical point of view, from Fig. 7 it is possible to deduce that uncertainty pertaining to a smaller lesion is mainly due to the volume delineation. For larger lesions, volume contouring impact is less significant and other parameters, such as random effects affecting the confidence of the fit parameters for the TAC, begin to dominate. As a result, data-points are increasingly distributed beyond the empirical function as the volume increases. It is also interesting to note that the fractional uncertainty in absorbed dose is lower than that of the volume uncertainty as covariance effects within the dosimetry chain reduce the overall uncertainty in absorbed dose. The accuracy of time-activity curve fitting depends on the number of data-points, the scan times and the theoretical model function employed. The optimal scan times to perform dosimetry in PRRT are yet to be determined. Sandstrom et al. [29] proposed to use a late time-point at 7 days, the EANM dosimetry committee [30] suggested to use at least three time-points, while Del Prete et al. [31] and Hänscheid et al. [32] proposed simplified dosimetry protocols based on two time-points and one time-point, respectively. It is evident that the greater the number of time-points, the more uncertainty will be reduced. However, an evaluation in terms of cost/benefits should be performed to determine the optimal solution. The average 177Lu-DOTATATE tumour effective half-life was found to be between 77 h and 110 h [31-33]. As a consequence, tumour uptake at 70 h p.i. (last acquisition time-point based on our clinical protocol) is about 60% of the maximum value. Further SPECT/CT studies, especially at late time-points, are probably to increase the accuracy of the activity curve determination. However, it is inconvenient for patients, especially those out-of-city patients who would need to prolong their stay. Therefore, we opted for four-time points. In this study, 141 tumours with four time-points (1, 24, 40 and 70 h p.i.) and 13 tumours with three time-points (1, 24, 70 h p.i.) were analyzed. Our data suggest that the use of four time-points reduces the uncertainty of the TAC fitting by 4% compared to using three time-points (12% to 16%). Moreover, it should be noted that it is undesirable to fit three data-points with a three parameters bi-exponential curve like the one in Eq. 3. From a pure mathematical point of view, this will result in an unreliable model with no test of goodness of fit and so with no possibility of checking the parameters. However, with early time-points acquisition (1 h p.i.), we often saw evidence of the initial uptake phase before the time-activity curve started to decrease in mono-exponential washout. Hence, using a mono-exponential curve to model the time-activity decay may not be the optimal choice. The potential impact on the accuracy of absorbed dose need to be investigated, however it goes beyond the aim of this study. In this work, time-activity points were fitted by using either mono- or bi-exponential curves. The optimal fit function should be chosen for each case based on the number and the distribution of available data-points, possibly by using model selection criteria as discussed by Kletting et al. [34].
These results may be useful to provide the user with an indication about the typical expected uncertainty while performing dosimetry. Assuming an acceptable absorbed dose uncertainty of 40% as reference, which is the typical absorbed dose uncertainty on clinical cases as reported by Grassi et al., the correspondent cut-off tumour volume is around 33 mL. Consequently, it can be concluded that absorbed doses to lesions with volumes smaller than 33 mL cannot be determined to a sufficient level of confidence to make the result meaningful. However, it should be noted that these values depend on the spatial resolution of the imaging system and on the method used to contour the VOI. In this study, the VOIs were manually contoured on the SPECT images.
Figs. 5 and 6 show the impact of spatial resolution on final uncertainty evaluated by postulating a different FWHM for each of the imaging systems. These results have demonstrated that uncertainty would be significantly reduced by increasing the spatial resolution. This effect would be particularly significant in the case of small volumes. Hence, a minimal acceptable volume cut-off should be set, depending on the spatial resolution of the system available in the site. A standard gamma camera, combined with an iterative reconstruction algorithm that includes attenuation, scatter and collimator-detector response, provides images with a spatial resolution around 1 cm for 177Lu, as reported in [25].
In this study, 128 lesions (out of 154) had a volume smaller than 33 mL. All 154 lesions were considered of clinical importance in the trial and were used in the treatment planning. It should be noted that for this analysis a tumour volume cut-off was not introduced (consequently also lesions with very small volumes were analysed) to provide worthy results in the whole clinical range of volumes.
Anyway exclusion of tumours below 33 mL is undesirable as they may be of clinical importance, rather, the improvement of spatial resolution and VOIs delineation is desirable. The accuracy of VOI delineation may be improved by using the appropriate acquisition/reconstruction protocol (accounting for acquisition statistics, matrix, collimator type, reconstruction settings) to obtain images with a spatial resolution as high as possible. Lesions may be delineated using contrast enhanced CT or 68Ga-PET where feasible, which are characterized by a better spatial resolution than SPECT imaging. Contouring on images with spatial resolution of 5 mm (typical of PET images) would provide a cut-off tumour volume of 4 mL (considering an absorbed dose uncertainty equal to 40%). Almost all the lesions provided absorbed dose uncertainty smaller than 40% if a spatial resolution equal to 0.5 mm (typical of CT images) was used. In that case, an absorbed dose uncertainty cut-off lower than 40% may be set in order to increase the significance of absorbed dose calculations. For example, a cut-off volume of 4 mL would provide a confidence level of absorbed dose calculation around 20%. However, the possibility of using CT in place of SPECT or PET is to be evaluated, maybe combining both the morphological and functional information. Uncertainty of volume evaluation might be further reduced by averaging VOIs delineated by different operators. However, this approach may be difficult to be applied in clinics.
This study had some limitations because some sources of uncertainty were not included in this analysis. VOIs were outlined using a standard threshold when possible, however in some cases the threshold was adapted by the physicians in order to adequately contour the tumour volume in relation to the tumour uptake and the activity of the surrounding tissues. For that reason, uncertainty of volume determination is operator-dependent, but in this study that component was not taken into account. Errors due to image mis-registration were not included in this analysis. Misalignment of VOIs with the tumours was assumed to be negligible as each VOIs was visually checked and manually adjusted in case of need. Activities were corrected for partial volume effect using pre-calculated RCs based on phantom measurements. This method makes some approximations: it is assumed lesions to have a spherical shape and counts do not spill-in from surrounding tissues. These approximations affect accuracy of partial volume effect correction; however they were not considered in this study. Following the MIRD schema, it was assumed that the tumour tissue was homogeneous, the tumours had spherical shapes and the target volumes were the sources activity volumes (i.e. the contribution of absorbed dose from the surrounding organs was not considered). There are uncertainties associated with deviations between these assumptions and reality, but there are outside the scope of this framework.