Technical Note: Monte Carlo Study of the Mechanism of Proton-Boron Fusion Therapy

Abstract

Goal:

Proton beam therapy has been found to have enhanced biological effectiveness in targets that contain the boron isotope ¹¹B, with the alpha particles resulting from the p + ¹¹B → 3α reaction being hypothesized as the mechanism; in this study, we aimed to elucidate the causes of the enhanced biological effectiveness of proton-boron fusion therapy by performing a detailed Monte Carlo study of the p + ¹¹B → 3α reaction in a phantom geometry.

Methods:

We utilized the Geant4 toolkit to create Monte Carlo particle physics simulations. These simulations consisted of a proton beam with a range 30 mm, creating a Spread-Out Bragg Peak with a modulation width of 10 mm, directed into a water phantom containing a region of boron material. Energy deposition, particle energy, and particle fluence were scored along the path of the beam and grouped by particle species. The scoring was performed using a series of cylindrical volumes with a radius of 2.5 mm and depth of 0.1 mm, constructed such that the depth was parallel to the proton beam. Root was then used to perform the data analysis.

Results:

Our simulations showed that the dose delivered by alpha particles produced by p + ¹¹B → 3α was several orders of magnitude lower than the dose delivered directly by protons, even when the boron uptake region was comprised entirely of natural boron or pure ¹¹B.

Conclusions:

Our findings do not support the theory that an alpha particle-based mechanism is responsible for the enhanced biological effectiveness of proton-boron fusion therapy. We conclude that any enhanced biological effect seen in experimental studies was not caused by fusion reactions between protons and ¹¹B nuclei. However, it is necessary to reproduce the past experiments that indicated significant dose enhancement.

Introduction

Proton-boron fusion therapy (PBFT) is a hypothesized proton therapy modality in which protons are fused with ¹¹B,^1–5 a stable isotope that comprises about 80% of natural boron. This fusion reaction creates an excited state ¹²C nucleus, which decays into an alpha particle and a ⁸Be nucleus, which further decay into two alpha particles (p + ¹¹B → 3α). This fusion reaction releases 8.7 MeV of energy, which is carried by the three resultant alpha particles, typically giving them a range of less than 30 μm.¹

Boron compounds, such as sodium borocaptate, have been developed to selectively deliver boron to tumors. Thus, the alpha particles that would be generated by the proton-boron fusion reaction would predominantly deposit their energy in tumor cells. Because low-energy alpha particles can induce more complex clusters of DNA damage than can protons, they have, in theory, a higher likelihood of causing irreparable damage to cells. Thus, a treatment modality that provides location-specific enhancement of the alpha particle dose could be more effective than traditional proton therapy.

Previous studies of PBFT have had varying results. The most notable work is that by Cirrone et al.,¹ who presented evidence of the enhanced biological effectiveness of PBFT in in vitro studies. Specifically, they reported a dose-modifying factor of 1.46 ± 0.12 at 10% cell survival, meaning that the dose delivered to boron-enriched tumors has effects that are equivalent to an approximately 1.46 times higher dose. Previous Monte Carlo studies demonstrated evidence of a significant dose increase.^2–4 However, there is significant dispute about this paper’s findings.⁵ Mazzone et al.⁵ suggested that the effects seen by Cirrone et al.¹ were more likely due to a biochemical effect, as the p + ¹¹B → 3α reaction is unlikely to contribute a significant number of alpha particles. Mazzone et al.’s⁵ study utilized Monte Carlo simulations that supported this claim.

The mechanism, magnitude, and clinical feasibility of PBFT warrant further exploration. If the p + ¹¹B → 3α reaction results in significant dose enhancement, PBFT would represent a treatment modality that could selectively increase the biological effectiveness of proton beams in the target volume. Such a selective increase in biological effectiveness could reduce the dose that must be delivered to the patient to achieve adequate tumor cell killing. Thus, PBFT could provide effective tumor cell killing, with less severe complications in normal tissue.

To determine the role of nuclear physics-based mechanisms in PBFT, we performed a detailed Monte Carlo study of the p + ¹¹B → 3α reaction in a phantom geometry.

Materials and Methods

Monte Carlo simulations were performed using the Geat4 toolkit.⁶ The QGSP_BIC_AllHP physics list was used because it uses the binary cascade de-excitation model, standard electromagnetic physics option 4, and a high-precision data-driven model for low-energy protons, neutrons, deuterium, tritium, ³He, and alpha particles. Both the binary cascade and standard electromagnetic physics option 4 have been evaluated to provide the best agreement between simulation and measurements of proton therapy,⁷ and the high-precision model provides additional accuracy for the low-energy (<10 MeV) hadrons described previously.

The simulations consisted of a proton beam that delivered an SOBP with a 10-mm modulation in a 20 × 20 × 20 cm³ water phantom. The scoring region consisted of 400 cylindrical slices with a radius of 2.5 mm and depth of 0.1 mm. In simulations that required the use of a substance other than pure water, the material for slices from a depth of 20 mm to 30 mm was altered, while the rest of the scoring region was kept as pure water. This approach was used to simulate a boron uptake region (BUR), as would be seen in any in vitro studies. To investigate the feasibility of using the p + ¹¹B → 3α reaction to contribute a significant alpha particle dose, we performed simulations with a BUR of pure ¹¹B, as well as pure natural boron, and compared them to those of pure water. We used pure boron targets because simulations using 80-ppm concentrations of ¹¹B, as used by Cirrone et al.¹, did not result in any significant differences in initial simulations.

For each simulation run, 10⁶ protons were transported through the water phantom containing the scoring region and BUR. The incident proton energies were selected using a table with predetermined probabilities for each energy to produce a flat SOBP. The energies of the protons ranged from 47.1 MeV to 59.1 MeV, giving the SOBP a range of 30 mm in water and a modulation width of 10 mm. These beam characteristics were used as the basis for the placement of the BUR at a depth of 20 mm. When using 10⁶ primary protons, the statistical uncertainty of the mean dose in the results was less than 0.3% in regions with doses higher than 10% of the maximum dose.

For each run, several quantities were scored and separated out for various particles and ions. The three quantities that were scored for each scoring volume were energy deposition, volume population, and volume fluence. For volume population and volume fluence, the energy of each particle that was registered as a hit for those detectors was also scored. Energy deposition scoring was performed in total and for protons, neutrons, alpha particles, gamma rays, ⁷Li, ⁹Be, and ¹¹B. These energy deposition data were then used to calculate the total and proton dose delivered to water. The conversion from energy deposition to dose to water was performed by summing the energy deposited in each volume, converting to the units of Joules, dividing by the mass of each volume, multiplying by the stopping power ratio to water of the material, and normalizing to the number of primary particles. The stopping power ratios were obtained by dividing the energy depositions at the water-BUR interface by the volume of the cell and the number of primary particles and then dividing the result by each scoring volume’s width and material density to obtain the material stopping power. These stopping powers for B_nat and ¹¹B were then used to calculate a stopping power ratio to water. The scoring of the volume population was performed for ¹²C to investigate any possible spikes in carbon production as a result of the p + ¹¹B → 3α reaction. Fluence was scored for protons and alpha particles to investigate any increases in alpha particles traversing a particular slice, as evidence of an increase in the p + ¹¹B → 3α reaction.

To extract the simulation data, we used Geant4’s built-in g4analysis class, which automatically handles the thread safety and merging of data into one file when running a multi-threaded simulation. However, the g4analysis class only supports automatic merging for Root file outputs; thus, all data analyses produced by the simulation were performed using Root.

All simulations were run on a personal computer with an Intel i7-9750H CPU that has 6 physical cores and 12 logical cores, all of which were utilized in running these simulations. The utilization of this hardware to run the simulations resulted in a runtime of 1246 seconds in pure water, 1456 seconds with a natural boron BUR, and 1490 seconds for pure ¹¹B BUR.

Results

Figure 1 shows the integral depth dose to water for each cylindrical scoring volume with a 2.5-mm radius and 0.1-mm thickness when the proton beam was applied to a water phantom with BURs of natural boron and ¹¹B, compared to that of a pure water phantom. The total dose delivered in the BUR was very similar to that of the pure water phantom. Figure 2 shows that the difference between the total dose to water in the BUR and pure water was nearly 1%, with the total dose in the boron being higher. This difference in dose was greater than the statistical uncertainty of the data set and was thus significant.

Figure 1:

Depth-dose profile for water, B_nat, and ¹¹B.

Figure 2:

Peak region of the depth-dose curve shown in Figure 1.

Figure 3 shows that there was a notable increase in the dose delivered by alpha particles when the proton beam traversed the interface between water and a pure boron target. At the water-boron interface, the dose delivered by alpha particles was approximately 2–3 times higher than that delivered by alpha particles at the same depth in pure water. Figure 3 also shows that the dose delivered by alpha particles in the BUR accounted for less than 1% of the total dose delivered.

Figure 3:

Depth-dose profile of alpha particles in BURs of water, B_nat, and ¹¹B

Discussion

The data produced by these simulations demonstrate that a nuclear physics-based mechanism is not responsible for the effectiveness of PBFT. Even when irradiating regions that were composed entirely of boron, there was a minimal increase in alpha particle production and the resultant dose. Figures 1 and 2 show that there was only an increase in the total dose delivered to water of approximately 1%, which was greater than the statistical uncertainty of the data. However, the increase in the dose to water was not large enough to provide any significant biological effect. Figure 3 shows that the dose due to alpha particles was smaller, by more than two orders of magnitude, than the total dose, as it contributes <1% of the total dose. Thus, the relative biological effectiveness of the alpha particles produced in the BUR would have to be 5–6 orders of magnitude greater than the value of 1.1 used for protons to achieve the same biological effect as when the protons are considered in isolation. In addition to being orders of magnitude lower than the total dose, the alpha particle dose was the same order of magnitude when measured at the entrance of the water phantom and at the peak alpha particle dose in the BUR; thus, the increase seen is not significant enough to support the increase in biological effectiveness shown in previous studies.¹ Although it is not shown in the figures, the particle fluence and population scores showed no evidence of an increase in alpha particle contributions, which is in agreement with the dose to water data.

It should be noted that all of the data presented were derived from simulations that were performed under conditions that were significantly more favorable than those of in vitro experiments that demonstrated enhanced biological effectiveness.¹ The BURs simulated in this work were composed entirely of natural boron or the ¹¹B isotope, which allowed for a considerable increase in the p + ¹¹B → 3α reaction and thus a considerable increase in the resultant alpha particle dose. When scaling the dose contributed by alpha particles based on a boron concentration which is achievable in living cells, such as the 80 parts per million used in other studies¹, the increase in dose due to alpha particles is lowered to 0.00008%. Thus, the relative biological effectiveness required to achieve results similar to previous studies¹ would be on the 10⁵ or 10⁶ order of magnitude. Because of this, it is even less likely that the concentrations of boron that are achievable in tumor cells would cause an increase in the alpha particle dose large enough to result in enhanced biological effectiveness.

Conclusions

On the basis of the previously stated data and analysis, the nuclear physics mechanism proposed for the enhanced biological effectiveness of PBFT seen in in vitro studies was not substantiated.⁷ Thus, further exploration of the effect of PBFT on cell survival is needed to ensure the reproducibility of previous in vitro studies and explore the possibilities of alternate mechanisms.