1. Introduction
Uveal melanoma is a rare (two to eight cases per million in Europe) but aggressive disease. This tumor is the most common primary ocular tumor in adults and represents 83% of intraocular malignancies and around 60% of all non-skin melanomas. Uveal melanoma is mainly located in choroid (90%), although it could appear in ciliary body (6%) and iris (4%). It is an aggressive malignancy with high mortality rates (up to 90% at 15 years in posterior uveal melanoma) [
1]. Treatment options for uveal melanomas are resection, radiation therapy and enucleation. Classically, enucleation was the main treatment to achieve local control, although, currently, plaque brachytherapy is the most commonly used treatment for small and medium melanomas, with local control rates of 88–98% at five years [
2]. Results are equivalent to enucleation in terms of metastasis free survival and overall survival [
3], while having additional benefits, such as better cosmetic results and vision preservation in most of the cases.
Plaque brachytherapy for uveal melanoma is a personalized treatment depending on tumor size and intraocular localization. Several isotopes (I-125, Ru-106, Pd-103, Co-60) are used, with beta-emitting Ru/Rh-106 ophthalmic applicators [
4] being one of the preferred options to treat intraocular malignancies [
5]. Historically, dose calculations in ocular treatments with Ru applicators (manufactured only by Eckert and Ziegler BEBIG, GmbH, Berlin, Germany) used to be only based on water and limited to the central axis of the plaque. The latest recommendations on ocular plaque therapy [
6] emphasize the importance of a transition to model-based calculation algorithms [
7], which allow personalized treatment planning. However, accurate dosimetry in these treatments is hindered by a number of special features, such as the small dimensions and complex shapes of the applicators, made of non-water equivalent materials, and the short range of beta particles, which produce steep-gradient dose distributions. All these factors challenge dose determination by means of both experimental measurements and Monte Carlo (MC) simulations. The dosimetry problem is even more pronounced for the special case of the asymmetric plaques, which have a cutout, so-called notch, to prevent irradiation of critical structures such as the optic nerve, the macula, or the lens. These hurdles likely contribute to the lack of abundant literature on asymmetric Ru plaque dosimetry and to the reported disagreements between calculations and experimental measurements or between different articles.
To the best of our knowledge, only three works [
8,
9,
10] included some experimental results for asymmetric Ru plaques. All these works used in-house developed phantoms for the radiochromic film-based dosimetry. Taccini et al. [
8] and Trichter et al. [
10] presented dosimetric results in the form of isodose distributions and lateral profiles for the BEBIG asymmetric plaque models CIB and CIA, respectively, without comparing to other published data or calculations. Heileman et al. [
9] performed film measurements of the asymmetric COB plaque dose, showing important discrepancies with respect to simulations with the MC code MCNP6, especially in the cut-out region.
Solc et al. [
11] were one of the first to present MC results for an asymmetric applicator. They used MCNPX [
12] to simulate the COB applicator and compared their results with both central axis (CAX) reference data provided by the manufacturer and off-axis surface point dose values specified on the calibration certificates. They reported large discrepancies for the off-axis surface points that were attributed to a lack of uniformity in the activity distribution across the active layer.
The most complete dosimetric dataset of Ru ophthalmic applicators was published by Hermida et al. [
13], who used penEasy+PENELOPE [
14,
15] MC codes to simulate a set of different applicators, including the asymmetric types CIA and CIB. Their results were compared with the manufacturer’s reference data and other previously published results, obtained either from experimental measurements or MC simulations. They found good agreement for all plaques compared to manufacturer CAX reference data, but with large discrepancies with respect to the Taccini et al. [
8] dose plane for the CIB plaque.
Of note, most of these published works only present partial dosimetric results for a single type of notched plaque, and all the works that present MC simulations using asymmetric plaques obtain great discrepancies compared to experimental data.
We recently published a paper [
16] that presents
EyeMC, an MC calculation system for ophthalmic brachytherapy treatments, either with COMS plaques loaded with I-125 seeds or with Ru applicators. In that work, we validated the MC models of the Ru plaques against data from the work by Hermida-López et al. [
13] and the manufacturer’s reference data for the CAX using the penEasy+PENELOPE MC codes. While we found a general good agreement with Hermida’s database, there were significant differences in the lateral dose profiles for asymmetric Ru plaques. We also benchmarked our results against Plaque Simulator [
17,
18], the only tool commercially available for personalized ophthalmic brachytherapy treatments, obtaining similar deviations for asymmetric-type plaques as well.
In this work, we attempted to bridge the observed discrepancies by developing more accurate and detailed geometries for MC simulations. We used graphical mathematical tools to determine new values for the geometric parameters, which were then used to modify the geometry of the MC models of the asymmetric Ru plaques presented in our previous work [
16]. These new models were benchmarked using experimental dosimetric data from (i) radiochromic film measurements, (ii) data provided by the manufacturer in the calibration certificates, and (iii) experimental results published in some of the works cited above. We expect the conclusions presented in this work will help to improve ophthalmic treatments with Ru plaques as a consequence of a more accurate determination of dose delivered to the tumor and to the critical structures in each patient.
4. Discussion
The use of three independent sources of experimental data to validate our results strengthens the thesis of this work. Nonetheless, our aim was not to propose a new definite value set for the geometric parameters but rather to point out the need to improve the geometric models used to simulate asymmetric plaques. In order to facilitate comparison with our results, we have included
Table S1 as Supplementary Material containing lateral profiles at different depths for each plaque type extracted from the MC calculations with the modified geometry.
BEBIG reported the absolute dose measurement of the central point with ±20% (2σ) uncertainty until 2019 and ±11% since 2020, but no uncertainties are given for the relative dose rates measured at the surface points. The statistical variability (standard deviation reported in
Table 4) from different calibration certificates can be considered as an estimation of the uncertainty (1σ) combining both the uncertainty of the measurement and the inhomogeneities in the distribution of the radioactive isotope across the active layer. According to Zaragoza et al. [
31], the latter can reach values up to 25%. It is worth noting that, as pointed out by Hansen et al. [
32], BEBIG does not subtract Cerenkov contributions during Ru plaque measurements, which has been found to be dependent on the dose rate reaching the optical fiber and the orientation of the scintillator detector [
33]. As the surface dose rate values reported in the certificate are values relative to the central point, they are only affected by relative differences of the Cerenkov signal between different measurement points. Eichmann et al. [
33] observed an increasing Cerenkov ratio in the scintillator positions beyond the active surface of the plaque in the experimental setup for surface dose measurements, which is the case for the points in the fourth circle according to the notation adopted in this work. Using the results of Eichmann et al., we estimated the Cerenkov correction for the point (C4, 0°) of the CIB plaque (see
Figure 2). However, the difference between the uncorrected value of 5.2% and the corrected value of 4.9% seems not significant considering our estimated uncertainty of 0.7%, obtained from combining the uncertainties reported in
Table 4 for the C4 points of the CIB plaque.
In order to find the cause of the isodose disagreement between film measurements and MC calculations in the low-dose region, some simulations were carried out, including the Ru/Rh-106 gamma spectrum, obtaining results similar to those of Hermida-López et al. [
34], who reported an insignificant contribution of the gamma spectrum for clinical depths (below 10 cm). Besides gamma contribution, there are at least two other factors that may have a significant impact on the isodose distributions: (a) The measurement depth as to film measurements and (b) the inactive rim size parameter as to MC simulations. For the former, we determined the distance from the film to the central point of the plaque’s inner face from the heights, measured with a caliper, of the different elements conforming to the experimental setup: The plaque, the mold, and the Solid Water structure. This procedure yielded an estimated uncertainty of the film to plaque distances of 1 mm, which is a relatively high value considering the small dimensions of the experimental setup and the steep dose gradients of the Ru applicators. For the latter, no information regarding the uncertainty of the size of the inactive rim was available. We determined its optimal value for each plaque type by minimizing the differences between the MC calculations and the reference data at the points close to the edge of the plaque. However, this method does not necessarily approach the actual inactive rim size. As shown, variations of tenths of millimeters produce appreciable differences in the isodose distributions. Therefore, it seems reasonable to assume that the combined uncertainty of the measurement depth and the inactive rim size explain the differences observed in the low-dose region of the dose planes represented in
Figure 8.
The normalization adopted in
Figure 6 consisted in estimating the central relative dose value from dose plane by Taccini et al. [
8] and assigning this value to the corresponding point of our MC generated dose planes. Results from Taccini et al. [
8] lacked a clear normalization procedure to represent the isodose lines for the CIB plaque. In the figure where they presented a depth dose curve measured for a CCA plaque, the data was normalized to a CAX point at 2 mm depth. Applying this normalization to the CIB plaque calculations, as Hermida-López et al. did in their work [
13], produces a relative dose value in the center of the dose plane around 60%, while the corresponding value in the figure by Taccini is between the values of 20% and 30%. Hermida-López et al. [
13] attributed the large differences in the dose planes to the possibility that Taccini’s dose plane corresponded to another applicator such as the COB. In this work we assumed that the plaque type reported by Taccini et al. [
8] was correct, but they used a different normalization.
Clinical cases show how much variations in the geometry of plaques can affect the estimated dose to critical structures. In general, calculations using the modified geometry resulted in higher doses to the structures close to the notch. Of note, in the resimulation of the clinical cases with the modified plaque geometries, the plaque position coordinates on the eye were not changed. However, the positioning of the plaque on the eye is often determined by adjusting the notch to the critical organ that is to be preserved. Thus, if the notch depth parameter is changed, it would affect the plaque position coordinates.
The fact that Plaque Simulator results for the clinical cases are closer to the MC calculations using the modified geometries might suggest that the geometric models implemented in the planning system differ from the geometric information provided in the applicator user manual. Indeed, when exchanging the pictures of the plaques in
Figure 5 by the plaque diagrams from the Plaque Simulator, it is observed that the superimposed circles corresponding to the modified parameter values are better adjusted, although not completely, to the plaques diagram. An example of this for the COC plaque is shown in
Figure 10.
5. Conclusions
Personalized eye dosimetry is required for an optimal treatment planning able to deliver the prescription dose to the tumor and OAR sparing. Given the mentioned problems associated with the experimental measurements of Ru ocular plaques, MC techniques remain the best alternative tool for providing a dosimetric characterization precise enough for personalized ocular brachytherapy. However, an essential condition to build good MC models is having a precise characterization of the radiation source geometry. Our results indicate that the geometric parameterization of the asymmetric Ru plaques proposed by the manufacturer is adequate for modeling the geometry of the cutout region, but the geometric parameter values provided for each plaque type do not necessarily fit properly to their real shape. Therefore, its implementation in MC models may lead to wrong results. The graphical method described in this work allowed us to find new values for the geometric parameters that fit better to the real geometry. MC simulations of the notched plaques using these modified geometries produced results agreeing better with the experimental data published in the literature, the surface dose point measurements reported in the plaques calibration certificates, and radiochromic film dose measurements performed for this work.
Finally, we have shown that variations on the values of the geometric parameters may have an important effect on the estimated dose to critical structures in real ocular plaque treatments. A good geometric characterization of the asymmetric applicators is thus essential for accurate positioning and dosimetry in this kind of personalized treatment.