Incident protons and lithium target parameters

In this study, the physical dynamics of target bombardment were simulated using a unidirectional parallel proton beam. A threshold energy of 1.88 MeV for the ⁷Li(p,n)⁷Be reaction was referenced from the Evaluated Nuclear Data File (ENDF) [29]. Figure 1(a) illustrates the average neutron energies resulting from various incident proton energies within the 2.0–4.0 MeV range. A clear trend was observed where the average neutron energy rose consistently with increasing proton energy, yet remained below 1.0 MeV for proton energies up to 4.0 MeV, the average energy of the produced neutrons did not exceed 1.0 MeV. Figure 1(b) shows the fast neutron flux after incident protons with different energies bombarded lithium targets with a 10 mA beam intensity. Additionally, Fig. 2 depicts the neutron spectra for incident proton energies ranging from 2.0 MeV to 4.0 MeV, showing that both the spectrum and total neutron flux increase with proton energy. However, excessively high neutron energies complicate their moderation to the epithermal range suitable for BNCT. Consequently, to maintain neutron energies within a manageable range for BNCT, this study restricted incident proton energies to 2.0–4.0 MeV and set the beam intensity at 10 mA.

Fig. 1Full-screen View

(a) Average neutron energy after bombardment of lithium target by protons with different energies; (b) Fast neutron flux values at different incident proton energies with 10 mA beam intensity

Fig. 2Full-screen View

(Color online) Neutron spectra under different incident proton energies

Notably, with an appropriate lithium target thickness, neutron yield increased as the incident proton energy rose from 2.0 MeV to 4.0 MeV. To optimize neutron production, simulations were conducted on bombarding a lithium target with protons at an incident energy of 4.0 MeV and a beam radius of 3 cm. The energy deposition in the lithium target by a 4.0 MeV proton beam is depicted in Fig. 3, where a notable Bragg Peak is observed at the end of the proton's trajectory. To prevent target blistering and enhance heat dissipation, the Bragg Peak’s position was strategically placed outside the target’s main body. The simulation showed that the Bragg Peak occurred at a lithium target thickness of approximately 450 μm for a 4.0 MeV proton beam. Consequently, to meet the objectives and ensure adequate neutron yields for protons up to 4.0 MeV, the lithium target was designed with a thickness of 500 μm and a radius of 8 cm for further calculations.

Fig. 3Full-screen View

Energy deposition in the lithium target with an incident proton energy of 4.0 MeV

BSA model for Monte Carlo simulation

A beam shaping assembly (BSA) is designed to transform the fast neutrons produced by proton bombardment into an epithermal neutron beam suitable for BNCT applications. Figure 4 presents a sectional view of a BSA, with the proton beam directed positively along the X-axis. The BSA consists of a cylindrical structure that includes a moderator, reflector, thermal neutron absorption layer, gamma-ray shielding layer, and collimator. The reflector surrounds the moderator and the proton beam channel, reflecting neutrons back into the moderator to enhance the epithermal neutron flux at the BSA outlet. Suitable reflector materials are those with high elastic scattering and low absorption cross-sections in the epithermal neutron energy range. During neutron moderation, thermal neutrons and gamma-rays. Hence, the thermal neutron absorption layer and gamma shielding layer are designed to protect healthy tissues from damage. A collimator shapes and directs the therapeutic neutron beam, minimizing neutron scattering outside the treatment area by absorbing the off-target emissions. The BSA’s design features include an 8 cm radius lithium target with a 500 μm thickness, surrounded by a 0.5 cm aluminum-wrapped moderator with a 15 cm radius located behind the target. Following the moderator, 0.5 cm lithium fluoride (LiF) thermal neutron absorption layer and a 0.5 cm bismuth gamma-ray shielding layer are sequentially positioned. LiF was chosen for its high thermal neutron absorption capability, and bismuth for its effective gamma-ray shielding. Surrounding the moderator radially were two types of reflectors made from lead and Teflon, chosen for their favourable scattering and absorption properties in the epithermal neutron energy range, with radii set at 15 cm and 5 cm, respectively. The collimator, composed of lithiated polyethylene with a 7% lithium-6 content, utilized Hydrogen-1’s low atomic mass to efficiently slow down neutrons for absorption by lithium-6. The therapeutic neutron beam’s exit to the bismuth gamma-ray shielding layer was set at a distance of 8 cm (L1), with the beam outlet also measuring 8 cm in diameter. The moderator is the core component of the entire BSA design. Its primary role is to reduce the energy of fast neutrons into the epithermal neutron energy range through the scattering effect. Many contributions to the design of moderators based on ⁷Li (p, n)⁷Be reactions have been made [30–32]. Generally, a good moderator needs a higher scattering cross-section in the fast neutron energy region and a lower absorption cross-section in the epithermal neutron energy region [33]. For neutrons generated from the ⁷Li(p,n)⁷Be reaction, fluorine-19 and magnesium-24 have complementary scattering resonance peaks in the desired energy region, which is beneficial for moderating. The scattering cross-sections of fluorine-19 and magnesium-24 are shown in Fig. 5. Moreover, MgF₂ has a low cost, stable properties, and no long-life radionuclides after irradiation. Thus, MgF₂ was employed as the moderator in this research, and its thickness (L2) was optimized for a series of incident proton energies from 2.0 MeV to 4.0 MeV in the subsequent simulations. Table 1 lists the materials used for all of the BSA facility components, along with their densities.

Fig. 4Full-screen View

(Color online) Sectional view of BSA

Fig. 5Full-screen View

(Color online) Scattering cross-sections of fluorine-19 and magnesium-24

Search for optimum incident proton energy

In general, the neutron flux is an important parameter of a neutron radiation field, especially the flux of epithermal neutrons, which plays a primary role in the BNCT procedure [34]. Therefore, the proportion and absolute flux of epithermal neutrons determine the quality of the therapeutic neutron beam. The International Atomic Energy Agency (IAEA) has provided recommended values for therapeutic neutron beams in TECDOC-1223, including values for the absolute flux of epithermal neutrons (Φ_epi), the fast neutron component of a therapeutic neutron beam (D_fast/Φ_epi), gamma-ray component of a therapeutic neutron beam (D_γ/Φ_epi), ratio of the epithermal neutron flux to thermal neutron flux (Φ_epi/Φ_th), and ratio of the neutron current to total neutron flux (J/Φ) [35]. Although the ratio of the epithermal neutron flux to total neutron flux is not clearly listed in these recommended values, this parameter (Φ_epi/Φ_total) is non-ignorable and significant. It is worth mentioning that this parameter has also been used as a standard for evaluating the quality of therapeutic neutron beams in recent research [36]. Therefore, this standard was also adopted as a main indicator of whether the therapeutic neutron beam reached the optimal moderating state under the conditions of different incident proton energies in this work.

Figure 6 (a) shows the ratio of the epithermal neutron flux to total neutron flux with an MgF₂ moderator for seven typical incident proton energy values. The trend for the change in the ratio of the epithermal neutron flux to total neutron flux with the thickness of the moderator was first to increase to a peak and then decrease for all of the incident proton energy values. Obviously, excessive moderation would reduce the quality of the therapeutic neutron beam as a result of unexpected neutron scattering and absorption effects. As the energy of the incident proton increased, the thickness of the moderator needed to reach the optimal moderating state also continuously increased. This was consistent with the previously described conclusion that the difficulty of moderation increases with the incident proton energy. In Fig. 6 (a), the peaks for the ratio of epithermal neutrons to total neutrons have been marked with colored arrows, and the details are listed in Table 2. Moreover, other neutron beam quality parameters for these incident proton energy values at their optimal moderating states and the recommended values from IAEA are also presented in Table 3. As can be seen from Table 3, all seven incident proton energies could basically meet the values recommended by IAEA for the therapeutic neutron beam parameters from the BSA exit at their optimal moderating states, except for the ratio of epithermal neutrons to thermal neutrons when the incident proton energy was greater than 3.0 MeV, and the situation where the absolute flux of epithermal neutrons was insufficient when the incident proton energy was less than 2.3 MeV.

Fig. 6Full-screen View

(Color online) (a) Variation of ratio of epithermal neutron flux to total neutron flux with the thickness of the moderator for seven typical incident proton energies; (b) Optimal moderator thicknesses for incident proton energies from 2.0 MeV to 4.0 MeV

As an evaluation criterion, it was determined that the neutron beam had reached the optimal moderating state when the proportion of epithermal neutrons reached its highest value. We used these data points at the optimal moderating states and the curve fit by the optimal thicknesses of the moderator for incident proton energies from 2.0 MeV to 4.0 MeV, as presented in Fig. 6(b). At this point, we could obtain all of the moderator thicknesses where the optimal moderating state was reached with incident proton energies from 2.0 MeV to 4.0 MeV. Under the condition of the optimal moderating state, the ratios of the epithermal neutron flux to total neutron flux of protons with incident energy values ranging from 2.0 MeV to 4.0 MeV in 0.1 MeV steps are presented in Fig. 7. On the whole, the proportion of epithermal neutrons at the optimal moderating state tended to decrease with an increase in the incident proton energy. However, the difference between the maximum and minimum values for the ratio of the epithermal neutron flux to total neutron flux did not exceed 5%, which showed that there were only slight differences. It is important to highlight that the ratio of epithermal neutron flux to total neutron flux is critical for assessing the effectiveness of therapeutic neutron beams for therapeutic use, particularly as this ratio approaches critical values. To identify the most effective proton energy for neutron production, we also examined the absolute flux of epithermal neutrons at the BSA outlet across the same range of incident proton energies, under optimal conditions. In the context of BNCT, managing the heat produced in neutron generation targets is crucial. The use of lithium in the (p, n) reaction poses challenges due to its low melting point, which is a limitation for accelerator-based neutron sources. Thus, the efficiency of epithermal neutron production per unit of proton energy is a more suitable metric for evaluating the quality of the therapeutic neutron beam, as shown in Fig. 8.

Fig. 7Full-screen View

Ratios of epithermal neutron flux to total neutron flux at optimal moderating states

Fig. 8Full-screen View

Absolute flux of epithermal neutrons generated by protons per unit of energy at the optimal moderating state

As depicted in Fig. 8, there exists a favorable range for the absolute epithermal neutron flux per unit of energy when the incident proton energy falls between 2.5 MeV and 2.9 MeV. Beyond an incident proton energy of 2.9 MeV, there is a noticeable decline in the absolute epithermal neutron yield per unit of energy. The most appealing finding is the peak value, which reaches 1.66 × 10⁸/cm²·s at an incident proton energy of 2.7 MeV. For the sake of comparison, the absolute epithermal neutron flux per unit of energy at 2.7 MeV incident proton energy is 3.7 times greater than that at 2.0 MeV. Furthermore, the difference in the ratios of epithermal neutron flux to total neutron flux between 2.0 MeV and 2.7 MeV incident proton energies is less than 1.4%. Consequently, an incident proton energy of 2.7 MeV is deemed the most advantageous choice.

Verification of optimal incident proton energy using Snyder head phantom

To verify the therapeutic effect of the optimal incident proton energy of 2.7 MeV, a universal standard Snyder head phantom was used for dose analysis. The elemental composition of the Snyder head phantom was based on the ICRU 46 report, with the values listed in Table 4 [37]. In addition, the geometric dimensions of the Snyder head phantom are described in Eq. (2) [38]. $\begin{array}{l}\text{ Brain: }{\left(\frac{\text{x}}{\text{6}}\right)}^{\text{2}}\text{+}{\left(\frac{\text{y}}{\text{9}}\right)}^{\text{2}}\text{+}{\left(\frac{\text{z-1}}{\text{6}\text{.5}}\right)}^{\text{2}}\text{=1}\\ \text{ Skull: }{\left(\frac{\text{x}}{\text{6}\text{.8}}\right)}^{\text{2}}\text{+}{\left(\frac{\text{y}}{\text{9}\text{.8}}\right)}^{\text{2}}\text{+}{\left(\frac{\text{z}}{\text{8}\text{.3}}\right)}^{\text{2}}\text{=1}\\ \text{Skin: }{\left(\frac{\text{x}}{\text{7}\text{.3}}\right)}^{\text{2}}\text{+}{\left(\frac{\text{y}}{\text{10}\text{.3}}\right)}^{\text{2}}\text{+}{\left(\frac{\text{z}}{\text{8}\text{.8}}\right)}^{\text{2}}\text{=1}\end{array}$ (2)

Several figures of merit (FOMs) were computed to serve as benchmarks for assessing the quality of the therapeutic neutron beam. The key FOMs are described as follows. The advantage depth (AD) is defined as the depth at which the dose within a tumor equals the maximum dose in normal tissues. This parameter reflects the penetration capability of the therapeutic neutron beam. The treatable depth (TD) represents the depth at which the tumor dose equals twice the maximum dose in normal tissues. The therapeutic ratio (TR) is a valuable metric used to characterize the ratio of the peak dose in a tumor to the peak dose in normal tissues. This metric effectively reflects the specific efficacy of therapeutic neutron beams in eradicating tumors under identical irradiation conditions. The advantage depth dose rate (ADDR) denotes the maximum dose rate delivered to normal tissues. The treatment time (TT) could be estimated as the time to reach the maximum allowable equivalent dose (D_Eq) of 12.5 Gy in normal tissues [39].

During the BNCT procedure, there were four types of dose contributions. The boron dose (D_B) was the component that dominated the dose contribution and was generated by high LET particles released through the ¹⁰B(n,α)⁷Li reaction between the neutrons and boron-10 compound. The thermal neutron dose (D_th) was attributed to the ¹⁴N(n,p)¹⁴C reaction between the thermal neutrons and nitrogen-14 nuclei, which released 0.66 MeV of energy. The fast neutron dose (D_fast) was produced by the elastic scattering of fast neutrons and recoil protons through the ¹H(n,n)p reaction. There were two channels for gamma-ray dose (D_γ) generation. One was the result of the gamma-rays existing in the therapeutic neutron beam at the outlet of the BSA. The other was from the hydrogen capture effect between the neutrons and hydrogen-1 nuclei through the ¹H(n,γ)²H reaction [40].

The calculation of the dose distribution in the Snyder phantom was divided into the following two steps. First, the therapeutic neutron beam at the exit of the BSA was defined as the source pattern of the phantom irradiation. The F4 tally card and DE/DF card with the kinetic energy released in material (KERMA) factor were used to calculate the absorbed dose in each cell of the phantom. Then, the absorbed dose of each component was weighted and summed using equation (3) to obtain the equivalent biological dose [41]. $D_{\text{Eq}}\text{=CBE factor}\times D_{\text{B}}\text{+}{\omega }_{\text{th}}\times D_{\text{th}}\text{+}{\omega }_{\text{fast}}\times D_{\text{fast}}\text{+}{\omega }_{\text{γ}}\times D_{\text{γ}}$ (3)

The compound biological effectiveness (CBE) factor is characterized by values of 1.3 in normal tissues and 3.8 in tumors. Furthermore, the relative biological effect (RBE) factors, ω_th, ω_fast, and ω_γ, serve as weighting factors for thermal neutrons, fast neutrons, and gamma-rays, respectively. These factors were assigned values of 3.2, 3.2, and 1.0, respectively, in the dose calculation [42]. It was assumed that boron-10 compound concentrations were 10 ppm in normal tissues and 35 ppm in tumors.

Figure 7 and Fig. 8 illustrate that the highest epithermal neutron to total neutron ratio in the optimal moderating state was achieved with an incident proton energy of 2.0 MeV. However, the absolute epithermal neutron flux remained suboptimal. To determine whether the ratio of epithermal neutrons to total neutrons or the absolute flux of epithermal neutrons was the key parameter determining the therapeutic efficiency of BNCT, an incident proton energy of 2.0 MeV was employed as one of the validation cases. In addition, incident proton energies of 2.3 MeV and 3.0 MeV after interpolation were also considered. These verification cases with incident proton energies of 2.0 MeV, 2.3 MeV, and 3.0 MeV were compared with the case using 2.7 MeV. Figure 9(a) presents the spectra of therapeutic neutron beams at the outlet of the BSA for incident proton energies of 2.0 MeV, 2.3 MeV, and 2.7 MeV after optimal moderation. Furthermore, Fig. 9(b) displays the dose distributions of these therapeutic neutron beams in the Snyder head phantom, with corresponding FOMs provided in Table 5.

Fig. 9Full-screen View

(Color online) (a) Spectra of therapeutic neutron beams with incident proton energies of 2.0 MeV, 2.3 MeV, 2.7 MeV, and 3.0 MeV at their optimal moderating states; (b) Dose distributions in the Snyder head phantom

It is evident that the values of AD, TD, and TR with incident proton energies of 2.0 MeV, 2.3 MeV, 2.7 MeV, and 3.0 MeV exhibit remarkable proximity due to the similarity of their spectra in the epithermal neutron energy region. Nevertheless, with an incident proton energy of 2.7 MeV, TT was 40.9 min, which amounts to an 81% reduction compared to the TT with an incident proton energy of 2.0 MeV. In the context of BNCT procedures, it is imperative for the TT to be within an acceptable range. Therefore, based on this observation, it can be concluded that the absolute epithermal neutron flux plays a pivotal role in enhancing the therapeutic effectiveness of BNCT treatment, provided that the proportion of epithermal neutrons in the total neutron population does not exhibit a significant difference. The TT with an incident proton energy of 2.3 MeV was 73.7 min, which was between the values with 2.0 MeV and 2.7 MeV. As for the incident proton energy of 3.0 MeV, TT only decreased by 3.5% compared to that with 2.7 MeV. However, a higher incident proton energy made the heat dissipation of the target and neutron moderating process more difficult Furthermore, it is noteworthy that the absolute epithermal neutron flux per unit of energy for incident protons at 3.0 MeV was lower than that for 2.7 MeV. As a result, the incident proton energy of 2.7 MeV was deemed to be the optimal choice for AB-BNCT, primarily relying on the ⁷Li(p,n)⁷Be reaction.

Figures 10 (a) and (b) illustrate the distribution and relative proportions of four distinct types of dose contributions within tumors, as observed in the Snyder head phantom at an incident proton energy of 2.7 MeV. Notably, the boron dose emerged as the predominant component among the dose types. This boron dose peaked at a depth of 2.4 cm within the phantom, showcasing an initial increase up to this point followed by a gradual decline as the depth further increased beyond this point. In the shallower regions, closer to the skin, the fast neutron dose was more pronounced, but its significance and proportion dwindled with increasing depth. The thermal neutron dose maintained a steady contribution of approximately 2% across all depths within the phantom. In contrast, the gamma-ray dose, which was the second-largest contributor after the boron dose, showed a marked increase in its proportion for tumor depths exceeding 4 cm, highlighting its growing significance with depth.

Fig. 10Full-screen View

(Color online) (a) Four types of dose contributions in tumors using Snyder head phantom at an incident proton energy of 2.7 MeV; (b) Dose proportions at each depth of tumor in the Snyder head phantom at an incident proton energy of 2.7 MeV