TCP post-radioembolization and TCP post-EBRT in HCC are similar and can be predicted using the in vitro radiosensitivity

Findings

This study confirms even on HCC, seldom investigated with metabolic tracers, the strong correlation between reduction of tumor metabolism and EUD. This had been previously observed in colorectal cancer liver metastases that are more diffusely investigated with FDG [12].

A novelty of the present observation is that this correlation holds true when mixing acetate and FDG data for the tumor metabolism assessment. This makes sense considering the fact that reduction of acetate or FDG uptake mainly results from the reduction of tumor living cells number. Indeed, proteins which constitute the metabolic engines are hugely radioresistant (Fig. 1a in [27]).

Beyond this dose–response confirmation, the main finding of the study is that the observed TCP as a function of the EUD in RE is very similar to that of EBRT. We already demonstrated [11] that 90Y TOF-PET-based EUD provided the same threshold to discriminate “responding” and “non-responding” patients in glass RE, resin RE and EBRT, i.e., 40 Gy. This is the major benefit versus using mean absorbed that can also provide similar dose correlation when tuning an efficacy factor to the treatment device used [6, 11, 28], i.e., resin spheres, glass spheres or EBRT.

Beside the scientific satisfaction to better understand the therapeutic efficiency of these different treatments, it opens the way to predict the efficiency, and toxicity, of not yet used device [29], e.g., different specific sphere activities obtained by glass spheres decaying, or obtained by using new isotopes, such the recent 166Ho.

EUD assessment and voxel size

With regard to the finite voxel size (4 mm3), one can ask whether it is possible to get a tumor with all voxels exhibiting high curative probability voxels dose (i.e., > 80 Gy), while cell subsets in some voxels get low curative probability doses (i.e., < 40 Gy). In the affirmative, current PET imaging could fail to provide a predictive EUD assessment. Amazingly, although that the dose kernel has been shown to quickly decrease by a two orders of magnitude in a 1 mm range [30], this scenario is impossible.

Indeed, the dose Ds (in Gy) at a distance r0 (in mm) to the edge of a sphere of activity A (in kBq) and of radius R (in mm) is already accurately modeled by the Russell’s dose kernel [31] when R < 1 mm (see Additional file 2: Appendix B for the demonstration):

$$D_ \left( } \right) = 0.989 A \frac } \right)^ }} \left( }}} \right)$$

(14)

Let us consider 2.5 kBq glass sphere which is the most challenging device in term of sub-voxel dose heterogeneity. The number of spheres needed inside a 4 mm3 voxel to get a dose of 80 Gy is 41. Assume the worst scenario in which all the spheres are fully compacted at the voxel center, then the cluster diameter is R = 0.061 mm (assuming a rigid sphere compaction factor, i.e., 0.6).

In this scenario, Eq. 14 predicts a huge dose of 27,036 Gy at the cluster contact, and a dose 4.8 Gy at the voxel corners which are 3.4 mm far to the cluster edge. However, as all the tumor voxels are assumed to exhibit curative doses, voxel corners are in fact irradiated by 8 surrounding clusters, located at similar distance, giving 8 × 4.8 = 38.4 Gy, and by 24 surrounding clusters distant of ≈ 6.325 mm giving 24 × 0.53 = 12.7 Gy.

As a result, the lowest cell dose in the voxel is 51 Gy, above the low curative 40 Gy dose. Note that 90% of the minimal dose within a voxel arises from the spheres trapped in the surrounding voxels. This shows that the minimal dose within a 4mm3 voxel in a tumor exhibiting no centimetric activity heterogeneities is rather independent to the sphere distribution within the voxel. So, the 4mm3 voxel size appears sufficiently small to address most of intra-voxel activity heterogeneity issues.

EUD assessment and PET FWHM

The 90Y dose kernel FWHM is narrower than that of PET systems [32]. A similar concern thus arises: could the PET FWHM hide an activity fluctuation having an amplitude and an extension sufficiently large to produce into a voxel a drop from an apparent curative dose to a real non-curative one. There is no simple theoretical argument to answer this question as 2 mechanisms are used to dump the PET PSF impact: the Richardson–Lucy PET PSF deconvolution and the use of an apparent radiosensitivity α* to get a predictive EUD. This last mechanism is especially difficult to theoretically predict due to the nonlinearity of the Jones–Hoban EUD (Eq. 3).

However, phantom studies supported that these 2 PSF compensations used together are sufficient to avoid such scenario as shown in Fig. 3: below a 3 mm scale activity pattern distribution, the EUD already reaches 90% of the mean absorbed dose value. In fact, centimetric heterogeneity activity patterns are typically met in sphere radioembolization (see Fig. 1 in [10]). This explains why 90Y TOF-PET-based EUD is able to rightly take into account the impact of the heterogeneity of the absorbed dose distribution.

Fig. 3figure 3

Comparison of the TOF-PET-based EUD for the 6 hot rod sectors of an ultra-deluxe Jaszczak phantom filled with 90Y (triangles, diamonds are without and with 6 mm-FWHM filtering, respectively) with the true sectors for a mean sector absorbed dose D of 50 Gy (blue) and 100 Gy (brown). Note that due to the nonlinearity of Eq. 3 the 100 Gy curves shapes are not similar to those of the 50 Gy setup. (reprinted from [10], true EUD computation was extended down to 3.2 mm by the present authors)

EUD assessment and tumor delineation

Tumors delineation in dosimetry study is always a major critical step, especially when heterogeneous large tumors are present. Beside the challenge to get an observer independent technique, the key point is in the definition of what is the actual tumor tissue. In dose–response correlation study, only the absorbed dose to the tumor tissue still able to proliferate has to be considered. This justifies our choice to exclude necrotic core using a simple PET uptake iso-contour. This simple method was already successfully used in previous studies [10, 11].

Figure 4 clearly shows a typical response in a large necrotic tumor: the left part of the tumor shell well targeted by the sphere responded, while a small non-targeted region in the right part quickly relapsed in a new necrotic tumor. In the same time, the initial necrotic core, although not targeted, remained stable, i.e. necrotic.

Fig. 4figure 4

Baseline (day 1) and follow-up (day 57) FDG TOF PET scan of the patient liver compared to the 90Y TOF PET raw activity distribution measured after 90Y-labeled SIR-Spheres therapy (day 15). A nice tumor response was noted in the region of high absorbed dose (104 Gy), while a tumor progression occurred in the region not targeted by the 90Y-labeled SIR-Spheres. Absorbed doses (AD) were computed using the 90Y 4-mm voxel S values with (spatial resolution deconvolution) SRD and in parentheses without SRD. (Reprinted from [20] with permission of Springer, yellow notations were added by the authors)

Radiosensitivity and TCP

In this study, we found an apparent radiosensitivity α* value of 0.035 Gy−1 for the computation of EUD. Note that this value not only depends on the imaging spatial resolution, but depends on the spatial resolution of the used dose distribution. When using the mean absorbed dose, this spatial resolution is de facto the tumor diameter, i.e., a few centimeters. This explains why studies using the mean dose [6] found apparent radiosensitivity tenfold lower.

Due to the huge number of cells present in a tumor, the Poisson model gave a step function for the TCP (Fig. 2). This issue has been empirically solved in several studies by fitting together N and α in Eq. 6, which resulted in tenfold lower radiosensitivity and unrealistic tumor cells number ranging from 0.4 [33] to 3.4 [4, 34]. In fact, using the tumor cell number corresponding to the mean tumor volume (36 ml) and a standard deviation of 30% around the in vivo HCC cell radiosensitivity between patients is sufficient to rightly predict the observed TCP shape (Fig. 2).

Note that the nonclonogenicity within a tumor does not change its TCP step shape. Indeed, the TCP of such tumor is obtained by the product of the P(0) (Eq. 6) corresponding to the different clonogenic subsets. This product can be translated into a summation in the exponent which does not change the step shape. The step shape smoothing is the result of compiling together responses of tumors having different radiosensitivities and different volumes in order to build the TCP.

As a result, the TCP assessment is not a true Bernoulli trial which should had required that for a specific EUD all studied tumors would have the same probability to be controlled. Even for a true Bernoulli trial, the methodology choice for accurate confidence estimation is still under debate [35] and is fully unknown in the clinical case described by Eq. 7. It is why we preferred to use the likelihood fwhm/2.35 as an estimator of the potential error.

It could appear amazing that using the mean tumor volume (36 ml) is sufficient to predict the TCP, while there is a tenfold factor between the observed tumor volumes (Table 1). This results from the exponential behavior of the cells surviving fraction: an additive of only 6 Gy to the EUD is sufficient to reduce the survival fraction by this tenfold factor.

We want also to emphasize that the radiosensitivity used in the EUD derivation and the one used in the TCP modeling are two different concepts. An apparent radiosensitivity α* has to be used in the EUD derivation in order to compensate the limited spatial resolution obtained for in vivo dose distribution. After obtaining the right EUD, it is obvious that the surviving tumor cells number is governed by the intrinsic tumor cells radiosensitivity α.

The purpose of the study was not to evaluate the efficiency of radioembolization, in which case it should have been suitable to use the recommended mRECIST method. The study purpose was to investigate the rightness of a EUD and of a response assessment methodology, i.e. PET uptake iso-contour based EUD together with metabolic PET response. The rightness of this choice is clearly supported by the fact that the methodology provided similar dose-TCP independently of the treatment devices (resin, glass or EBRT).

Also, note that the Poisson theory shows that TCP is governed by the number of surviving tumor cells. To this regard, metabolic response assessment is a more direct estimation of the number of surviving cells than anatomical image which cannot differentiate between surviving cells and dead cells not yet cleared by the immune system.

The optimal ΔTLM 95% threshold, and not 100%, used to obtain the best agreement results from different effects: errors in the TLM assessment resulting from breathing motion, inflammatory response, variation in other competing tissues metabolism; FU delay too short to allow all the tumor cells to die or in contrary FU delay sufficiently long enough to allow a repopulation of the tumor site by healthy liver tissue which also takes up 11C-acetate or 18F-FDG.

Therapeutic considerations

The similarity of the RE and EBRT TCPs consolidates that a EUD of 100 Gy is needed to efficiently control a tumor, i.e., TCP > 0.95. The sigmoid shape of the TCP curve enlightens the importance to reach at least a EUD of 100 Gy in each tumor and emphasize the necessity to optimize the treatment to reach this goal [3, 27, 28]. Note that the absorbed dose D needed to achieve this EUD can vary from 190 to 1800 Gy depending on the absorbed dose distribution heterogeneity (Additional file 1: Appendix A).

The observed RE TCP also explains why the EUD = 40 Gy threshold split the patient survival curves into 2 clear different groups [26]. Indeed, this threshold correspond to the EUD50. As a result, one group contains a majority of responding patients and the other one a majority of non-responding patients.

Limitations

This study has some limitations. First, analyses were performed in a limited number of patients and tumors compared to previous reported studies [4, 6, 12]. Only few tumors received low absorbed doses and demonstrated a poor metabolic response, limiting the accuracy of our radiobiological model for low doses. Second, the follow-up was 4 months at maximum but some tumors could respond later to radiations and hence the effects of radiations could be sometimes underestimated, justifying the choice of the threshold ΔTLM = 95% rather than 100% in the TCP derivation. EUD is based on a single alpha value and it is likely that the radiosensitivity may vary between HCC occurring within different clinical entities. Accordingly, this delayed response may explain why some tumors did not disclose complete metabolic response 4 months after therapy despite a very efficient EUD.

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