In this work, we use the next sub-volume method (NSM) to investigate the possibility of using the compartment-based (“on-lattice”) model to simulate water radiolysis.
Note: The following contents are extract from your paper. The entry will be online only after author check and submit it.
2. Simulation of DiffusionIn this test, we simulated the diffusion of solvated electrons (e−aq) in a 0.2 × 0.2 × 0.2 µm3 water cubic volume without chemical reactions taking place. In the compartment-based simulation, the water volume was split into a mesh of 213 voxels with a voxel size of () kept constant over time. The simulation started with 200 e−aq molecules placed randomly in the central voxel of the mesh. The diffusion coefficient of the solvated electron was set to , reflecting a temperature of 25 °C. The NSM algorithm is only used for diffusion. Figure 1 shows the comparison of spatial distributions of e−aq species at time 10 ns, 20 ns, 50 ns, and 100 ns obtained by the compartment-based and the particle-based SBS models. For the particle-based model, since the cubic volume is chosen large enough, we processed four different simulations with one single time step of 10 ns, 20 ns, 50 ns, and 100 ns . We obtained a general good agreement between the results obtained with the compartment-based and the particle-based simulations.
3. Simulation of a Simple Reaction-Diffusion System
|End time||1 ns||10 ns||100 ns||1 µs||10 µs||100 µs|
|Speedup factor||13||15.7||16.5||2.5 × 10||2||2.3 × 10||3||2.3 × 10||4|
4. Full Water Radiolysis Simulation
|1||H||•||+ e||−aq||+ H||2||O → OH||−||+ H||2||2.5|
|2||H||•||+||•||OH → H||2||O||1.55|
|3||H||•||+ H||•||→ H||2||0.503|
|4||H||2||O||2||+ e||−aq||→ OH||−||+||•||OH||1.1|
|5||H||3||O||+||+ e||−aq||→ H||•||+ H||2||O||2.11|
|6||H||3||O||+||+ OH||−||→ 2H||2||O||11.3|
|7||•||OH + e||−aq||→ OH||−||2.95|
|8||•||OH +||•||OH → H||2||O||2||0.55|
|9||e||−aq||+ e||−aq||+ 2H||2||O → 2OH||−||+ H||2||0.636|
5. Materials and MethodsThe main characteristic of our model is the combination of the SBS Brownian dynamics model already available in Geant4-DNA with the compartment-based model using the RDME (so-called “SBS-RDME model”) in water radiolysis simulations. Figure 6 illustrates the simulation scheme of this combination.
6. ConclusionsIn this work, we implemented, in Geant4-DNA, the compartment-based model combined with the SBS Brownian dynamics model already available in Geant4-DNA. We showed that the compartment-based model can reproduce the same species yield obtained by the particle-based SBS of Geant4-DNA but with 100 to 1000 times less computing time. Moreover, our new model can also extend the simulation timescale beyond the microsecond when the system has reached a steady-state. These advantages will allow us to study the production and evolution of reactive oxygen species generated under irradiation with different dose rate conditions, such as in FLASH and conventional radiotherapy. In this work, we only considered a radiation-induced species system in a cubic water volume. The approach could be applied for more complicated systems, such as complex geometries including biological materials. This may be technically more difficult since we need to handle the two different representations (compartment-based and particle-based) in one simulation. We plan to work on such an extension in the future.
- 1. Novakovskaya, Y.V. Theoretical estimation of the ionization potential of water in condensed phase. ii. superficial water layers. Prot. Met. 2007, 43, 22–33.
- 2. Gauduel, Y.; Pommeret, S.; Antonetti, A. Femtosecond spec- troscopy of ultrafast reactions in aqueous media. J. Phys. Condens. Matter 1990, 2, SA171.
- 3. Ogura, H.; Hamill, W.H. Positive hole migration in pulse-irradiated water and heavy water. J. Phys. Chem. 1973, 77, 2952–2954.
- 4. Mozumder, A.; Magee, J.L. The early events of radiation chemistry. Int. J. Radiat. Phys. Chem. 1975, 7, 83–93.
- 5. Clifford, P.; Green, N.J.B.; Pilling, M.J. Monte Carlo Simulation of diffusion and reaction in radiation-induced spurs. Comparison with analytic models. J. Phys. Chem. 1982, 86, 1322–1327.
- 6. Karamitros, M.; Luan, S.; Bernal, M.; Allison, J.; Baldacchino, G.; Davidkova, M.; Francis, Z.; Friedland, W.; Ivantchenko, V.; Mantero, A.; et al. Diffusion-controlled reactions modeling in Geant4-DNA. J. Comput. Phys. 2014, 274, 841–882.
- 7. Uehara, S.; Nikjoo, H. Monte Carlo Simulation of Water Radiolysis for Low-energy Charged Particles. J. Radiat. Res. 2006, 47, 69–81.
- 8. Clifford, P.; Green, N.J.B.; Oldfield, M.J.; Pilling, M.J.; Pimblot, S.M. Stochastic models of multi-species kinetics in radiation-induced spurs. J. Chem. Soc. Faraday Trans. 1986, 82, 2673–2689.
- 9. Frongillo, Y.; Goulet, T.; Fraser, M.; Cobut, V.; Patau, J.P.; Jay-Gerin, J.-P. Monte Carlo simulation of fast electron and proton tracks in liquid water—II. Nonhomogeneous chemistry. Radiat. Phys. Chem. 1998, 51, 245–254.
- 10. Erban, R.; Chapman, S. Stochastic modelling of reaction-diffusion processes: Algorithms for bimolecular reactions. Phys. Biol. 2009, 6, 046001.
- 11. Gillespie, D.T. Exact Stochastic Simulation of Coupled Chemical Reactions. J. Phys. Chem. 1977, 81, 2340–2361.
- 12. Gillespie, D.T.; Hellander, A.; Petzold, L.R. Perspective: Stochastic algorithms for chemical kinetics. J. Chem. Phys. 2013, 138, 170901.
- 13. Plante, I.; Devroye, L. Considerations for the independent reaction times and step-by-step methods for radiation chemistry simulations. Radiat. Phys. Chem. 2017, 139, 157–172.
- 14. Incerti, S.; Baldacchino, G.; Bernal, M.A.; Capra, R.; Champion, C.; Francis, Z.; Guèye, P.; Mantero, A.; Mascialino, B.; Moretto, P.; et al. The Geant4-DNA project. Int. J. Model. Simul. Sci. Comput. 2010, 1, 157–178.
- 15. Incerti, S.; Ivanchenko, A.; Karamitros, M.; Mantero, A.; Moretto, P.; Tran, H.N.; Mascialino, B.; Champion, C.; Ivanchenko, V.N.; Bernal, M.A.; et al. Comparison of Geant4 very low energy cross section models with experimental data in water. Med. Phys. 2010, 37, 4692–4708.
- 16. Bernal, M.A.; Bordage, M.; Brown, J.; Davídková, M.; Delage, E.; El Bitar, Z.; Enger, S.; Francis, Z.; Guatelli, S.; Ivanchenko, V.; et al. Track structure modeling in liquid water: A review of the Geant4-DNA very low energy extension of the Geant4 Monte Carlo simulation toolkit. Phys. Medica 2015, 31, 861–874.
- 17. Incerti, S.; Kyriakou, I.; Bernal, M.A.; Bordage, M.C.; Francis, Z.; Guatelli, S.; Ivanchenko, V.; Karamitros, M.; Lampe, N.; Lee, S.B.; et al. Geant4-DNA example applications for track structure simulations in liquid water: A report from the Geant4-DNA Project. Med. Phys. 2018, 45, e722–e739.
- 18. Agostinelli, S.; Allison, J.; Amako, K.; Apostolakis, J.; Araujo, H.; Arce, P.; Asai, M.; Axen, D.; Banerjee, S.; Barrand, G.; et al. Geant4—a simulation toolkit. Nucl. Instrum. Methods Phys. Res. Sect. A Accel. Spectrometers Detect. Assoc. Equip. 2003, 506, 250–303.
- 19. Allison, J.; Amako, K.; Apostolakis, J.; Araujo, H.; Dubois, P.A.; Asai, M.; Barrand, G.; Capra, R.; Chauvie, S.; Chytracek, R.; et al. Geant4 developments and applications. IEEE Trans. Nucl. Sci. 2006, 53, 270–278.
- 20. Allison, J.; Amako, K.; Apostolakis, J.; Arce, P.; Asai, M.; Aso, T.; Bagli, E.; Bagulya, A.; Banerjee, S.; Barrand, G.; et al. Recent developments in GEANT4. Nucl. Instrum. Methods Phys. Res. Sect. A Accel. Spectrometers Detect. Assoc. Equip. 2016, 835, 186–225.