Evaluating the therapeutic potential and the suitability of neutron beams designed for clinical BNCT

: The standard of neutron beam quality for Boron Neutron Capture Therapy (BNCT) of deep-seated tumours is currently deﬁned by its physical characteristics in air: the epithermal neutron ﬂux, the ratio of thermal and epithermal neutron ﬂux, the fast neutron and photon dose contamination, and the beam collimation. Traditionally, the beam design consists in tailoring a Beam Shaping Assembly (BSA) able to deliver a neutron beam with the recommended values of these ﬁgures of merit (FOMs). This work investigated the possibility to produce an epithermal neutron beam able to guarantee the best clinical performance for deep-seated tumours, starting from a 5 MeV, 30 mA proton beam coupled to a beryllium target. Diﬀerent Beam Shaping Assemblies were designed using those physical FOMs which, however, were not enough to establish a clear ranking of the diﬀerent beams, nor to describe their clinical relevance. To go beyond this traditional approach, beams were then evaluated employing new criteria based on the dose distributions obtained in-phantom and on the calculation of the Uncomplicated Tumour Control Probability (UTCP). Such radiobiological FOM allows establishing the therapeutic potential of the beams. Moreover, we included the concept of suitability as a criterion to select the safest BSA design, calculating the in-patient out-of-beam dosimetry. The clinical relevance of the selected beam was ﬁnally tested in the treatment planning of a clinical case treated at the FiR 1 beam in Finland, where several patients have safely and successfully received BNCT in the last years. Despite the selected beam does not comply with all the standard physical recommendations, it shows a therapeutic potential comparable and even better than that of FiR 1. This conﬁrms that establishing the performance of a beam cannot rely only on its physical characteristics, but requires additional criteria able to predict the clinical outcome of a BNCT treatment. whole-body phantom to evaluate the dose delivered to peripheral organs. The information retrieved from these evaluations led to the selection of the best BSA conﬁguration. The candidate beam was ﬁnally used to simulate a treatment plan in a patient bearing head and neck tumour, one of the most promising targets in present BNCT clinical trials. The result of the radiobiological ﬁgure of merit in the treatment planning was compared with that of the original BNCT treatment. results of this of show that parameters to provide clear To predicting clinical outcome treatment, which is the relevant goal when designing a clinical facility. This work proposes a comprehensive method to adequately evaluate the therapeutic potential and the suitability of BNCT beams. Our approach adds to the standard evaluation of the in-air physical parameters, the calculation of suitable radiobiological FOMs and out-of-ﬁeld dose that directly account for the clinical performance and safety of these beams. An important discussion is now ongoing within the BNCT community on the necessity to establish common guidelines to evaluate BNCT beams. This is a non-trivial issue because the evaluation criteria strictly depend on the type of tumours that are addressed, i.e. shallow or deep-seated, and thus on the spectra that are preferable. Nevertheless, the biological eﬀects of the overall dose distributions in patient must be taken into account. For this reason, radiobiological ﬁgures of merit such as TCP, NTCP and UTCP, give a deeper insight into the clinical eﬀectiveness and outcome of the simulated treatment planning thus providing a robust criterion to predict the beam performance.

The Italian National Institute of Nuclear Physics (INFN) designed and constructed an RFQ proton accelerator delivering a 5 MeV, 30 mA proton beam in Continuous Wave (CW) mode [13]. The neutron yield at the Be target is 10 14 s −1 with maximum neutron energy around 3.2 MeV [14]. This spectrum must be tailored for BNCT, acting on moderation and collimation.
The optimal neutron beam for BNCT of deep-seated tumours has a spectrum peaked between 1 and 10 keV [15][16][17], requiring a Beam Shaping Assembly (BSA) to decrease neutron energy and to collimate the beam to minimize out-of-beam dose. The BSA is a typical element of the BNCT equipment, both for accelerators and reactors, and its characteristics depend on the initial neutron energy distribution (i.e. on the type of target and on the projectile energy) in the accelerator case. Presently, there is an increasing research work designing BSAs for ab-BNCT [12,14,[18][19][20][21][22][23][24][25]. Hence, methods to compare and evaluate simulated beams are currently under discussion, introducing new simulation instruments, computational strategies and analysis criteria.
IAEA published the TecDoc-1223 in 2001 [26] describing the desired characteristics of the neutron beams for BNCT: values had been indicated for the minimum epithermal neutron flux, the minimum degree of collimation and the maximum gamma, thermal and fast neutron contamination in air (Table 1). Together with some in-phantom quantities [27], these FOMs until now have been the only guidelines to evaluate the suitability of neutron beams for BNCT. Presently, the idea is taking shape that a neutron beam should rather be evaluated using treatment planning calculations in real clinical cases for a reliable performance evaluation: beams that do not comply with the IAEA guidelines can still be effective for some tumours. Furthermore, a neutron beam for BNCT must also follow other important criteria: it must be safe for the whole body of the patient, and it must be tested for the radio-protection limitations according to the regulations in each country. In literature, few examples of more refined computational evaluations are available [28,29].

Beam parameter Recommended value
Epithermal Flux (φ epi ) > 10 9 cm −2 s −1 Table 1. IAEA recommendations on beam quality. The suffix epi refers to energy range between 0.5 eV and 10 keV.
In this work, beams obtained with different BSA configurations have been first evaluated according to the classic IAEA FOMs. For a more significant analysis, we then exploited a radiobiological figure of merit capable of classifying the beams according to their clinical performance. The same beams were then tested on a human whole-body phantom to evaluate the dose delivered to peripheral organs. The information retrieved from these evaluations led to the selection of the best BSA configuration. The candidate beam was finally used to simulate a treatment plan in a patient bearing head and neck tumour, one of the most promising targets in present BNCT clinical trials. The result of the radiobiological figure of merit in the treatment planning was compared with that of the original BNCT treatment.
The results of this set of evaluations show that free-beam, in-air parameters are unable to provide a clear ranking of the beams performance. To define the most adequate configuration other criteria are needed, more suitable for predicting the clinical outcome of a treatment, which is the relevant goal when designing a clinical facility.

Materials and Methods
Presently many reactor and accelerator-based neutron sources are available, all with characteristic neutron spectra, needing ad hoc BSA materials and geometrical configuration. For the INFN RFQ accelerator (5 MeV protons on Be target), the most performing moderating material has been proved to be aluminium fluoride (AlF3) [30], which is available only in powder. To obtain a mechanically stable BSA, a dedicated study was carried out in Pavia to densify powders of AlF3, added with LiF. An innovative sintering process has been devised and a dedicated machine has been designed and constructed, able to obtain, for the first time, aluminium fluoride elements with nearly 100% density, showing very good mechanical properties and resistance to radiation. AlF3 doped with LiF is used throughout this work as the bulk moderation unit, to control the epithermal neutron flux and to lower as much as possible the fast (> 10 keV) and thermal (< 0.5 eV) neutron contamination. For simplicity, we do not present all the tested BSA materials and geometrical configurations. Instead, only five set-ups are reported to show the use of a radiobiological FOM as a criterion to select the most performing BSA. Figure 1 shows the geometrical configurations used for this work. The geometrical set-up shown in Figure 1a has a reflector (black) that embeds the bulk moderating material (grey) which is subsequently embedded into shield 1, aimed at decreasing contamination. In the second set-up, Figure 1b, the bulk material embeds the target region, to guide neutrons with the desired energy towards the beam-port, while the reflecting material separates shield 2 from the bulk material. This buffer area prevents thermal neutrons from scattering in shield 2 back into the bulk material. At the same time, epithermal neutrons escaping from the bulk material are scattered back. This BSA has a larger shield 2, to further decrease beam contamination. Finally, the configuration shown in Figure 1c is a modification of 1b, aimed at increasing lateral neutron moderation and absorption. The cone shape of 1b was reduced by increasing the amount of moderating material. To mitigate the unavoidable loss of flux, the volume of reflecting material around the bulk moderator was increased. The shape of reflector, lateral shielding and bulk moderator were optimised to reach a satisfactory epithermal neutron flux at the beam-port. The BSA in Figure 1c was also intended to better collimate the neutron beam.

BSA material and geometrical composition
Five different beams based on these three geometrical structures were selected. Table 2 describes the material composition and geometrical set-up of these BSAs. shielding material (shield 1), the black region is the reflector, the striped area represents a second shielding material (shield 2) and the grey area is the bulk moderating material. The central white box is the position of the target, neutrons are moderated and transported horizontally from the white box towards the beam port on the right. Lateral dimensions are 160 cm by 160 cm, for the horizontal extension refer to Table 2. The neutron source is located inside the white rectangle at the centre of the BSA and the proton beam is perpendicular to the direction of the neutron beam.  Table 2. Materials and design of some tested BSA setup. The last column refers to the BSA designs shown in Figure 1

Evaluation of physical in-air parameters
The described beams were tested against the Figures

Evaluation of the therapeutic potential of beams by a radiobiological FOM
To introduce a criterion predicting the treatment outcome, we tested the beams in a phantom representing a human neck bearing a tumour. Head and neck (H&N) cancer is presently the principal target of clinical BNCT: promising clinical results have been obtained with reactors and BNCT trials for these tumours are ongoing at ab-BNCT facilities in Japan [1,5]. The phantom is a cylinder (radius of 10 cm and height of 24 cm) of mucosa, which is the tissue at risk in H&N BNCT treatments. A 2 cm radius sphere centred 3 cm from the phantom equator surface represents the tumour. Boron concentration was assumed to be the standard in Finland treatments: 15 ppm in blood, which results in 30 ppm in mucosa and 52.5 ppm in tumour [32].  reproducing the average distance of patients from the beam port in clinical experience [33]. The dose was calculated with the photon iso-effective model [34]. To assess the therapeutic potential, we calculated the Uncomplicated Tumour Control Probability (UTCP) [33], defined as the probability to control the tumour without complication in the relevant healthy tissue, in this case, mucosa. UTCP is the product of the tumour Control Probability (TCP) and the complementary of Normal Tissue Complication Probability (1-NTCP). The closer this FOM is to 1, the highest is the probability to control the tumour without normal tissue complications. This criterion was used for the first time by Provenzano et al. [33] for the comparison of different clinical facilities, and it is proposed here as a criterion to select adequate beams among different candidates. UTCP was computed using TCP model for inhomogeneous dose distribution [33] and NTCP model that can predict mucositis of grade 3 or higher (≥G3) after head and neck cancer radiotherapy with photons and BNCT [34]. With this model, it is possible to calculate the treatment time that maximizes UTCP.

Evaluation of the beams suitability by out-of-beam dosimetry
Besides the therapeutic potential, it is critical to select the safest beam for the patient, i.e. the one delivering the lowest dose to the organs outside the irradiation field. To study this property, the beams were tested using the anthropomorphic phantom MIRD [35,36]. Equivalent dose was calculated with the prescription of ICRP report 116 [37]: weight for photon dose is 1, for boron component is 20 and neutron dose has been weighted according to the function of energy described in the ICRP report 116. To compare the out-of-beam dose values with those found in literature, biologically weighted dose was also obtained by multiplying the different components by RBE/CBE shown in Table 3. These doses were computed with MCNP6 using F4 tally type combined with kerma factors.  Boron concentration was assumed to be 15 ppm in all the normal tissues except for the skin and kidneys, set to absorb 22.5 ppm [41] and 75 ppm, respectively. Kidneys are known to uptake a higher boron concentration than other tissues due to excretion of BPA via the urinary system: pharmacokinetics studies performed in animals and humans using fluorinated BPA and PET imaging have been analysed [42,43]. The combination of therapeutic potential and suitability assessment allowed the ranking of the candidate beams, resulting in a clear selection of the best BSA design.

Treatment Planning simulation
The selected beam was finally used to simulate a BNCT treatment plan. The chosen clinical case is a Head and Neck cancer patient (squamous cell carcinoma) treated with BPA-mediated BNCT in Finland [32]. The performance of the selected beam is compared with that of FiR 1 in the real treatment. MultiCell was used as the Treatment Planning System, to obtain the voxelized patient model shown in Figure 3a (segmented image) and in Figure 3b (3D representation), to set the two fractions treatment configuration and to produce the input for dose calculation by MCNP [45,46]. Figure Table 4 shows the results of the calculation of physical FOMs for each beam ( Table 2 and Figure 1), compared to the recommended values. BSA #1 and BSA #4 ensure a lower gamma contamination while keeping a high neutron flux. This is mainly due to the use of heavy water and graphite, in shield 2 region, instead of materials containing hydrogen. BSA #2 is the one with the lowest fast neutron dose contamination, while BSA #3 is the one with the lowest gamma dose contamination. These beams show lower fast neutron dose contamination compared to BSA #1 and BSA #4, the main reason being that the shielding material contains hydrogen, which scatters low energy neutrons back into the beam. As a result, the epithermal neutron flux increases, but the epithermal energy spectrum is shifted towards energies lower than 1 keV. BSA #5 is characterised by higher collimation (it is the only one complying with IAEA recommendation for this parameter) at the expense of lower epithermal neutron flux and the highest fast neutron dose contamination. Table 4 shows how difficult it can be to evaluate a beam based on fixed values of physical properties. None of the tested beams is clearly optimal compared to the IAEA values. However, they may still be useful for patient treatment. To assess the suitability for clinical use, the beams were tested using the UTCP.   Table 4. IAEA FOM calculated for the BSAs listed in Table 2. The reported results have a relative error lower than 2%.

Out-of-beam dosimetry
The anthropomorphic male MIRD phantom, as shown in Figure 4 was positioned in a representative irradiation position for H&N cancer treatment. For all beams, the biological weighted dose in Gy_Eq has been calculated in all the organs of the phantom. Figure 5 shows that BSA #5 delivers doses significantly lower to the organs outside the irradiation field. In this respect, it is thus preferable.
This result together with the therapeutic potential is a clear demonstration that BSA #5 is clinically the most performing beam. Table 6 shows the dosimetry of this BSA on the organs of MIRD phantom. The values refer to the dose absorbed by a patient in a treatment time as calculated to maximise the UTCP: 24.5 minutes. The Table   reports also the absorbed dose (Gy) separating the radiation components, and the weighted dose (Sv), calculated following the prescription of ICRP report 116 [48].

Characteristics of the selected beam
The BSA delivering BSA #5 is showed in detail in Figure 6. The neutron spectrum averaged over the beam-port area (6 cm radius circle) peaks around the desired energy of 10 keV. The flux decreases sharply when averaged over a circular ring going from 6 cm radius to 12 cm radius, the out-of-beam area (Figure 7). Figure 8 shows spectrum and flux behavior in-beam and out-of-beam. In Figure 8a, the logarithmic spectrum averaged over circular sectors of radii between 1 and 11 cm, demonstrates that the spectral distribution is maintained below 6 cm (in-beam). Out of beam, the flux decreases with the radius, and the proportion of the spectrum components changes. Figure 8b shows the distribution of the different spectral components as a function of the radius. Flux variation is within 20% inside the beam-port, and it sharply decreases out of beam. The thermal, epithermal and fast neutron components change at increasing radial distance. This is due to the different material composition of  Table 6.

Treatment Planning
The results of the treatment planning simulation for the optimum irradiation time and the corresponding data for FiR 1 are shown in Table 7. Even though BSA #5 only partially satisfies the recommendations of the IAEA FoMs, the maximum UTCP is higher than the one obtain with Fir 1 (a beam that complies with all recommendations).
For approximately the same NTCP, the TCP for BSA #5 is 0.56, for FiR 1 is 0.49, as shown in Figure 9. The higher TCP is a consequence of the higher minimum dose delivered to the tumour, as shown in Figure 10. In fact, BSA #5 has a higher fast component than FiR 1, thus it is more penetrating.

Discussion
In designing a clinical BNCT facility based on the accelerator built by INFN, the first step was to chose the BSA generating a beam suitable to treat deep-seated tumours. The free-beam in-air parameters proved to be a  descriptive tool which however did not allow a ranking of the candidate beams. We then introduced the concept of therapeutic potential, i.e. the capacity to treat a deep-seated tumour without damaging the tissue at risk. For this assessment, we evaluated the UTCP, a radiobiological FOM which condenses the 3D dose distribution into one value related to the clinical outcome. This FOM allowed a rating of the 5 candidates. UTCP is particularly interesting because it is a prediction of the clinical outcome of the irradiation. To select the safest beam for the clinical treatment, we calculated the dose delivered to the other organs of the patient. This figure describes the suitability of a BNCT neutron beam. It is not possible to define a threshold above which the dose absorbed in an organ is considered too high for the treatment, because the priority is the clinical outcome of the tumour irradiation. Hence, we selected the configuration ensuring the minimum out-of-beam absorbed dose. We then compared the results with those obtained in similar irradiation position with both a designed ab-BNCT beam and with a reactor beam used in BNCT clinical applications (JRR4, Japan) [28,49]. To this end, the components of absorbed dose were weighted using the RBE/CBE values and considering boron concentration listed in the cited documents. Figure 11 shows that the selected beam is comparable with the one designed by Herrera et al. [28], and delivers a dose to peripheral organs only slightly higher than the JRR4 beam.
Finally, we used the selected beam to compare its performance with the reference neutron facility FiR 1, in a clinical case that was successfully treated there. If clinical decision is in favour of selecting the treatment time that maximises the UTCP, the therapeutic potential of the selected beam -quantified by the maximum UTCP-is 15% higher than the one obtained for FiR 1. The real irradiation time of the H&N cancer patient treated with FiR 1 was 110 min, a value slightly higher than the one that maximises the UTCP. If we now simulate an irradiation time to equate the NTCP of the real treatment, the candidate beam achieves a TCP value 15% higher than the one obtained with FiR 1 in an irradiation time almost identical (i.e., a TCP value of 0.7 in 105 min for BSA #5 VS a TCP value of 0.6 in 110 min for FiR 1).

Conclusions
The results obtained in this work confirm that it is possible to produce a neutron beam for clinical BNCT from the INFN RFQ, which accelerates a 5 MeV, 30 mA proton beam on a Be target. The described optimisation allowed selecting an appropriate beam for clinical BNCT. The final beam satisfies only some of the IAEA recommendations.
However, it proved to ensure a comparable clinical performance to that of our reference beam FiR 1 for H&N treatment.
This work proposes a comprehensive method to adequately evaluate the therapeutic potential and the suitability of BNCT beams. Our approach adds to the standard evaluation of the in-air physical parameters, the calculation of suitable radiobiological FOMs and out-of-field dose that directly account for the clinical performance and safety of these beams. An important discussion is now ongoing within the BNCT community on the necessity to establish common guidelines to evaluate BNCT beams. This is a non-trivial issue because the evaluation criteria strictly depend on the type of tumours that are addressed, i.e. shallow or deep-seated, and thus on the spectra that are preferable. Nevertheless, the biological effects of the overall dose distributions in patient must be taken into account. For this reason, radiobiological figures of merit such as TCP, NTCP and UTCP, give a deeper insight into the clinical effectiveness and outcome of the simulated treatment planning thus providing a robust criterion to predict the beam performance.