BSA design

In this work, we specify that the set direction is along the proton beam direction. Fig. 1 shows a cross section view of the target system and side view of some backup coins.

Fig. 1Full-screen View

(Color online) Cross section of the Coin-structured beam shaping assembly and side view of some backup coins. 1: bellows, 2: lithium target, 3: moderator coins, 4: thermal neutron filter and gamma-ray filter coins, 5: collimator coins and beam port, 6: side reflector, 7: back reflector coins, 8: back reflector. The black wireframe in the corner shows modern and ancient Chinese coins.

The target, which contained a lithium layer and copper substrate with cooling water, is connected to a section of bellows which allowed the target to move back and forth in the direction of the proton beam. Based on the conclusions obtained from a previous work ^[38], a lithium layer with a thickness of 150 μm was used and the corresponding neutron yield was 1.40×10¹² n/mC under the condition of 2.8 MeV incident protons. The neutron spectrum was recorded and set as the initial source term for subsequent neutron transportation in the BSA to reduce the calculation time.

Along the beam, a cylindrical moderator made of magnesium fluoride was placed behind the target. As discussed in previous studies ^{[19, 39-41]}, Magnesium fluoride is the preferred moderator material for our proton beam and target scheme. We designed the moderator as six coins, each with a diameter of 50 cm and thicknesses of 2 cm for one coin, 4 cm for four coins, and 20 cm for one coin. Unlike dividing the moderator into two or more layers with fixed thicknesses and installing them as the moderator ^{[16, 27, 42-44]}, designing the moderator as multiple coins with different thicknesses facilitates flexible combinations to adjust the neutron energy spectrum. In this work, the density of magnesium fluoride is 2.8 g/cm³ unless otherwise specified. Taking into account several factors such as the density influence on neutronic properties ^[38], processing difficulty, cost and potential density inhomogeneity, a density of 2.8 g/cm³ is a conservative but reasonable assumption, although higher-density magnesium fluoride blocks may be processed.

There are three kinds of reflectors are to reflect neutrons back to the moderator to reduce neutron leakage and increase the neutron flux at the port. First, the moderator was encased in lead of a thickness of 15 cm as the side reflector, and the length of this lead cylinder that also named moderating tunnel is 40 cm. A hollow cylindrical back reflector was arranged in front of tunnel to wrap the bellows as the back reflector. During operation, the position of the port remained unchanged. To ensure the largest possible neutron flux at the port, after embedding the appropriate moderator coins in the tunnel and pressing them tightly to cling to the filter, the target was moved close to the moderator by telescoping the bellows. Then space in the tunnel was filled with backup lead rings, also known as back reflector coins.

Behind the moderator were thermal neutron and gamma-ray filters used to reduce doses harmful to patients. The thickness and material of these filters can also be changed by backup filter coins according to requirements. We calculated and compared the effect and influence of LiF, Cd, Bi, and Pb as filters and selected materials according to the actual situation of the equipment.

Next the collimator was made of PE mixed with natural LiF at a 60% mass fraction. A series of collimators with apertures ranging from 10 cm to 20 cm, called collimator coins, were designed to meet different needs. In order to mitigate the detrimental effects of neutron leakage, a two-stage step design was employed which incorporated a filter and collimator whose diameters were 55 cm and 60 cm respectively (enlarged part of Fig. 1).

Since our design requires disassembly and replacement of the moderator coins, especially during the commissioning phase of the equipment, the neutron induced radioactivity of different candidate materials for each component mentioned above was considered while selecting the appropriate materials. This was to reduce the risk of exposure to irradiation that may occur during the change process (Table 1).

Epithermal neutron beam

The five recommended parameters for epithermal neutron beams are given in IAEA-TECDOC-1223 ^[7], and the details are listed in Table 2. Considering the discussions of different upper limit of the epithermal neutron, we performed comparative calculations for 0.5 eV to 10 keV and 0.5 eV to 40 keV, as listed in Table 2. Considering that the energy of the generated neutrons from the Li(p,n) reaction with a 2.8 MeV proton is within 1.1 MeV, the fast neutron contamination calculation we refer to the literature ^[40] and it is defined by $D_{\text{f}}/{\varnothing }_{\text{epi}}=\underset{\text{epi THR}.}{\overset{1.1\text{ MeV}}{{\displaystyle \int }}}\varnothing \left(E\right)\cdot K\left(E\right)\text{d}E/\underset{0.5\text{ eV}}{\overset{\text{epi THR}.}{{\displaystyle \int }}}\varnothing \left(E\right)\text{d}E$ (1)

Here, Φ and K denote the neutron flux at the port and the ICRU-63^[45] neutron kerma coefficient [Gy cm²] for soft tissue. In such a case, the contamination should be less than 1.0 × 10^-12 Gy cm². Similarly, gamma-ray contamination is gamma-ray heat divided by the epithermal neutron flux.

A 20 cm cubic block filled with soft tissue (ICRU four component) was used a phantom to evaluate the absorbed dose and therapeutic potential of the different neutron beams. The concentration of ¹⁰B in normal tissues and tumors was set as 18 ppm and 65 ppm, respectively. The relative biological effectiveness (RBE) of nitrogen, hydrogen, and gamma-rays were assumed to be 3.2, 3.2, and 1.0, respectively. The compound biological effectiveness (CBE) for tumor and normal tissues was assumed to be 3.8 and 1.35, respectively. The total dose was calculated using Eq. (2) as follows: $D=CB{E}_{\text{B}}{D}_{\text{B}}+RB{E}_{\text{N}}{D}_{\text{N}}+RB{E}_{\text{H}}{D}_{\text{H}}+RB{E}_{\gamma }{D}_{\gamma }$ (2) where D_B, D_N, D_H, D_γ are the four absorbed doses in BNCT, namely the boron, thermal, fast neutron and gamma-ray doses respectively.

The irradiation time, also called the treatment time (TT), was determined by setting the point dose limit on the normal tissue to 12.5 Gy ^[15]. According to that the sufficient dose for killing a tumor is at least 30 Gy, the maximum depth in the tumor that can be reached by 30 Gy within the irradiation time is the treatment depth (TD) ^[14]. And the depth where could reach 15 Gy within the irradiation time means that treatment can be completed with two irradiations from different directions. Section 3.2 discusses the detailed effects of parameters such as moderator thickness and density, the ratio of boron concentration in tumor and normal tissue (T/N) and beam power of accelerator on the dose rate and TD.

Relatively low energy neutron beam

In order to adapt the epithermal neutron beam to superficial tumor treatment, we can place the thermal neutron moderator inside the BSA, that is, use a combination of a more efficient material and magnesium fluoride as the moderator. This is in addition to the measures that could be adopted, such as a bolus adhering to the skin and dose distribution shifter at the port. We compared heavy water, BeO, and PE. We chose PE as a further moderator after calculations and comparisons, and considering cost and other factors. Multiple PE disks, each with a thickness of 2 cm and diameter identical to that of the magnesium fluoride disks, served as moderator coins for the tunable BSA alongside the MgF₂ disks. The effects of the PE placement and thickness on the outgoing neutron beam are discussed. Compared to its non-disassemblable counterparts, this tunable BSA facilitates the utilization of both epithermal and thermal neutron moderators, as well as the removal of the thermal neutron filter at the port in favor of a thicker gamma filter, leading to a higher thermal neutron flux. To evaluate the treatment effect of relatively low energy neutron beams, the RBE, TT, and TD doses were also calculated.

Multi-size apertures

The moderator can be adjusted, to adapt it for treating tumors at different depths. By adjusting the diameter of the port, the treatment requirements for tumors of different sizes can be met. Although an adjustable aperture design is common in BSA, we mainly focus on the points directly related to this coin-structured tunable BSA design, such as the impact of using the same collimator port on the neutron beam after changing the moderator and adaptation of the moderator after selecting the port with a certain diameter.

Residual radioactivity induced in the BSA

Taking the scenario of shutting down after running at full accelerated beam power of 56 kW for 2 hours as an example, the photon dose rate at the treatment position due to the residual radioactivity induced in each component of BSA is shown in Fig. 2. It can be seen that the neutron-induced radioactivity of cadmium is the highest among the alternative materials for each component. After 2 hours of irradiation, the information of dominant radioisotopes generated by the Cd filter, such as ¹¹⁵Cd, ¹¹⁷Cd, and ^117mIn, are listed in Table 1. The entire Cd filter that with a thickness of 0.2 cm has a radioactivity level of up to 3.7 × 10¹⁰ Bq, with a gamma dose rate of 2.4 × 10⁴ µSv/h at the treatment position at end of irradiation. Replacing the Cd coin with 0.3 mm LiF coin can significantly reduce the induced radioactivity to negligible level without affecting the parameters of the outgoing neutron beam, especially the ratio between thermal and epithermal neutrons. With the exception of Cd, the induced radioactivity of other components within the acceptance after cooling for 4 hours. However, it should be noted that LiF generates ³H with a half-life of 12.4 years after neutron irradiation, requiring proper handling of thermal neutron filters made of lithium fluoride and collimators containing lithium fluoride after decommissioning. But condensing that tritium could be also produced in the target by the ⁶Li(n, t)⁴He reaction, the management of the tritium is necessary for such a facility ^[46]. Bi generates ²¹⁰Bi after neutron irradiation, which has a half-life of approximately 5 days. Pb and Magnesium fluoride primarily generate ²⁰⁹Pb and ²⁴Na, respectively, both of which have a half-life of less than 1 day. As for the gamma filter, lead and bismuth exhibit little difference in neutron performance and activation, but lead is easier to obtain. Therefore, we used LiF and Pb for the thermal neutron and gamma filters, respectively.

Fig. 2Full-screen View

(Color online) The photon dose rate of the BSA components at the treatment position due to the neutron induced radioactivity.

Epithermal neutron beam parameters

The results of the neutron beam using magnesium fluoride as a moderator with a density of 2.8 g/cm³ and a beam port with a diameter of 10 cm and different thicknesses are shown in Table 2. We compared the results obtained using 10 keV and 40 keV as the upper limit of the epithermal energy. For all the cases, the epithermal neutron flux is greater than 1×10⁹ cm^-2s^-1 under full beam power of 56 kW. When the thickness of the Magnesium fluoride moderator is less than 24 cm, an upper limit of 40 keV increases the epithermal neutron flux by 20% or more compared with that obtained 10 keV. When the thickness of the magnesium fluoride moderator is between 24 cm and 32 cm, the rate of increase is between 20% and 10%. When the thickness of the magnesium fluoride moderator is greater than 32 cm, this increase rate is less than 10%. This is because a thicker moderator moderated neutrons more completely, resulting in fewer neutrons with energies between 10 keV and 40 keV. During operation, when a thinner moderator (less than 32 cm) is used, the different upper limits of the epithermal energy have a significant impact on the epithermal neutron flux. This, in turn, obviously affects the treatment time, and hence needs to be carefully considered. The minimum accelerated beam power required refers to the power at which the epithermal neutron flux reaches 1×10⁹ cm^-2s^-1. When the upper limit of the epithermal neutrons increases or the thickness of the moderator decreases, the minimum required beam power correspondingly decreases. The spectrums corresponding to partially different thicknesses of magnesium fluoride, ranging from 20 cm to 36 cm, are shown in Fig. 3. Their respective peak energy values are 16, 9.2, 4.5, 2.3, and 1.0 keV. This indicates that the average energy of the epithermal neutron beam can be conveniently regulated by adjusting the moderator coins.

Fig. 3Full-screen View

(Color online) Neutron spectra corresponding to different thicknesses of Magnesium fluoride or Magnesium fluoride with PE ranging from 20 cm to 36 cm.

For the forward beam direction, the ratio of the neutron current to the flux (c/f, J_n/Ф_n) increases with the thickness of the moderator, which indicates an increase in the fraction of neutrons moving in the forward beam direction. Table 2 shows that when magnesium fluoride with a thickness range of 26–36 cm is used as a moderator, the c/f range is 0.7000 ± 0.004, which meets the requirements. The gamma contamination and ratio of the thermal neutron flux to the epithermal neutron flux always meets the requirements within the calculation range and are not discussed further.

Adopting different divisions of the epithermal range not only has an intuitive impact on the epithermal neutron flux but also affects the fast neutron contamination that defined in Eq. (1). In comparison, a broader epithermal range results in a fast neutron contamination level that is approximately 50% of that observed with a narrower range. As per the guidelines set forth by the International Atomic Energy Agency (IAEA), the fast neutron contamination exerts a direct influence on the minimum thickness of the moderator required. However, in this design, apart from considering the beam parameters, we determined the optimal thickness of the moderator through the TD that discussed below.

The dose rate distributions along the depth and total dose of the neutron beams at different thicknesses of the moderator in a soft tissue phantom are presented in Fig. 4(a) and Table 3. At each corresponding neutron beam and the treatment time of different moderator thickness, the accumulated dose distribution in the tumor varies with the depth, as shown in Fig. 4(b). When the thickness of the moderator is relatively thin (e.g., 20 cm), the treatment depth is shallow (approximately 4.8 cm). Within the scope of this discussion, as the thickness of the moderator increases, the treatment depth gradually increases until it reaches a constant depth of 5.6 cm when the thickness is greater than 28 cm. This is because when the moderator is thin, the fast neutron flux is high, and the fast neutron dose is relatively high among the four doses of BNCT, limiting the treatment depth. Table 3 presents the fast neutron dose converted to photon equivalent, the total dose on the skin, and their respective ratio. As the thickness of the moderator increases from 20 cm to 36 cm, the proportion of the fast neutron dose decreases gradually from 71% to 28%, and the total dose at the skin surface decreases distinctly at each corresponding treatment time. For example, when the thickness of the moderator is increased from 28 cm to 36 cm, the dose at the skin surface is reduced by 18% from 10.29 Gy to 8.39 Gy. This is consistent with the findings of Seki R., et al. (2017) [22].

Fig. 4Full-screen View

(Color online) Therapy parameters of neutron beams at different thicknesses of  the moderator in a soft tissue phantom: (a) dose rate distributions along the depth; (b) total dose distributions along the depth.

The results presented in Fig. 4 also demonstrate that the 15 Gy isodose curve attains its maximum value of approximately 7.6 cm at a moderator thickness of 28 cm. It is worth noting that in Ref. [14], the C-BENS treatment beam delivers 30 Gy and 15 Gy at depths of 5.5 cm and 8 cm, respectively, when the T/N was approximately 3.5. Although the spectrum of the epithermal neutron beam designed in this study differ from that of C-BENS, it achieved a similar TD. Nonetheless, if the boron concentrations in the tumor and normal tissue is assumed to be 65 ppm and 6.5 ppm, respectively, and the CBE remains constant, the TD obtained for the magnesium fluoride moderator with a thickness of 28 cm can be increased to 6.4 cm. Moreover, a change in T/N can affect CBE ^[47], implying that the actual treatment depth can be augmented further. Hence, compared with fine-tuning the neutron spectrum of Li(p,n) by adjusting the moderator, enhancing the T/N ratio is indisputably more crucial.

According to a previous study ^[38], increasing the density of magnesium fluoride from 2.8 g/cm3 to 3.15 g/cm3 requires a reduction of approximately 3 cm in the moderator thickness to maintain the same level of fast neutron contamination. However, as described previously, the effect on the TD can be ignored within the thickness range of 28–36 cm of magnesium fluoride. This implies that the same therapeutic effect can be achieved by either increasing the density of magnesium fluoride to 3.15 g/cm³ or increasing the thickness of magnesium fluoride with a density of 2.8 g/cm³ by 3 cm. In both cases, the resultant therapeutic effect of the neutron beam remained unchanged. For instance, using magnesium fluoride with a thickness of 26 cm as the moderator, an increase in density from 2.8 g/cm³ to 3.15 g/cm³ increases the treatment depth from 5.5 cm to 5.6 cm, reducing the maximum dose to the skin by 12% (1.3 Gy) during the corresponding treatment time. This effect is almost equivalent to adding 3 cm of magnesium fluoride with a density of 2.8 g/cm³ to the moderator thickness to increase it from 26 cm to 29 cm, as shown in Table 2. Based on previous work, it can be concluded that using magnesium fluoride with a density of 2.8 g/cm³ as the moderator is sufficient and meets the requirements for the application. Increasing the density to 3.15 g/cm³ would result in significant manufacturing difficulties and costs without providing any notable advantages on the treatment depth.

At last, utilizing a thin moderator allows the accelerator to operate at a lower beam power to attain the required epithermal neutron flux. Since there is a proportional reduction in neutrons in each energy region after lowering the power, the shape of neutron spectrum remains unaltered, and the treatment parameters remains constant except for an inverse change in treatment time. Table 3 validates the effect of the accelerator operating at full accelerated beam power and reduced power with a 26 cm magnesium fluoride moderator on dosimetric parameters.

In summary, adjusting the moderator thickness within a certain range will not influence the treatment depth, but increasing the thickness can significantly decrease the dose at the skin surface. Achieving an increase in the treatment depth by using a magnesium fluoride moderator with the highest density can be done by increasing the thickness of the moderator. Furthermore, under the condition where all other factors remain unchanged, the beam power change does not affect the treatment depth. Based on the analysis presented above, along with the literatures ^{[7, 17-22, 39]} discussing the upper limit of the epithermal energy range, we contend that neutrons of several keV offer greater treatment depth and reduced harmful dose to shallow normal tissue. Nevertheless, the elimination of high-energy neutrons inevitably results in a reduction of the neutron flux at the optimal energy level, consequently leading to longer treatment times and potential issues such as position misalignment. Given the current status of neutron source and boron drug development, employing epithermal neutrons slightly above 10 keV becomes unavoidable and necessary.

Relatively low energy neutron beam parameters

An example of 24 cm moderator thickness is shown by the three red curves in Fig. 3. When the moderators consisted of 24 cm of magnesium fluoride (a), 4 cm of PE with 20 cm of magnesium fluoride (b), and 20 cm of magnesium fluoride with 4 cm of PE (c), the proportion of high-energy neutrons was progressively lower. Calculations demonstrated that under the three conditions (a), (b), and (c), the proportions of thermal neutrons to the total neutron flux were 2.46%, 24.15%, and 40.50%, respectively. The results indicate that replacing some of the magnesium fluoride with PE coins when using moderators of the same thickness can reduce the average energy of the original epithermal neutron beam. Additionally, placing PE behind magnesium fluoride has a more significant effect on energy reduction. This is due to the fact that the ¹H(n,elastic) cross-section of epithermal neutrons is larger compared to that of fast neutrons ⁴⁸. Furthermore, the c/f of the neutron beam under these three conditions are 0.695, 0.734, and 0.760, respectively, indicating that the introduction of the PE plate can increase c/f. Consequently, the collimators and exit ports designed for epithermal neutron beams continue to satisfy the requirement.

Furthermore, the dose rate distribution of the outing neutron beam in the soft tissue phantom with depth was studied and the results showed in Fig. 5. When 22 cm of magnesium fluoride is used as the moderator, and the thermal neutron filter is removed and replaced with the same thickness of lead, the position of the dose rate peak moves from a depth of 2.20 cm to 1.95 cm, and the peak value increases by 6%. Both of those change benefits the treatment of shallow tumors. When the moderator is changed to a 20 cm magnesium fluoride coin and a 2 cm PE coin, the dose rate peak moves further to a depth of 0.85 cm. Increasing the thickness of PE to 4 cm and 6 cm moves the positions of the dose rate curve peaks to depths of 0.35 cm and 0.25 cm, respectively, while maintaining a constant thickness of magnesium fluoride constant as 20 cm. Calculations indicate that increasing the thickness of PE within 6 cm can accomplish tumor treatment within the dose tolerable by normal tissues (12.5 Gy), although the peak values of the thermal neutron flux and dose rate are reduced.

Fig. 5Full-screen View

(Color online) The dose rate distribution of the outing neutron beam of the different moderators and filters in the soft tissue phantom along the depth.

In summary, the use of magnesium fluoride and PE coins as moderators can further moderate the epithermal neutron beam and adjust the depth of the dose rate peak by changing the thickness of the PE. This method can ensure that the peak falls at the target irradiation depth while reducing the dose received by surrounding tissues under the premise of killing shallow tumors. Compared with the method of placing the PE plate at the port to change the depth of the dose peak, this design can also reduce the gamma dose caused by H(n,γ) to some extent.

Multi-size apertures influence on beams

Table 2 illustrates that minor adjustments in the thickness of magnesium fluoride within a specific range have negligible effects on c/f, as exemplified by the 10 cm aperture. Therefore, although the moderator thickness is fine-tuned, the size of the collimator or the cone angle of the port need not be modified. Several collimators with aperture sizes between 10 and 20 cm were designed to conform to the parameters recommended by the International Atomic Energy Agency. The use of both magnesium fluoride and PE coins as moderators enhanced the c/f of the outgoing neutron beam compared to the use of magnesium fluoride alone, as mentioned in Sect. 3.4. Thus, the collimators initially designed for epithermal beams continue to remain functional. In addition, Ref. [17] suggests that the optimal neutron energy for treating deep-seated tumors partly depends on the size of the beam aperture. In contrast to other BNCT facilities, which can only adjust the aperture size, the tunable BSA enables modulation of the neutron energy spectrum by varying the thickness of the moderator after determining the beam aperture size that achieves the optimal therapeutic outcome.