Table 2 Details of the PHITS transport computations and data post-processing

Code and version

PHITS v3.24

[27]

Source description

s-type = 24. Particles are produced uniformly from each tetrahedron, which belong to the specified universe

[27]

Cross sections

PDL97 for photons

[33]

EGS5 for photons, electrons, and positrons

[34]

INCL for nucleons and light ions

[35]

Transport parameters

Secondary electrons were followed for photon simulations. Alpha particles were simulated down to 0.1 MeV/nucleon, while gammas, electrons, and positrons were simulated down to 1 keV

[27]

Variance reduction

No variance reduction techniques were utilized for this study

Statistical uncertainties and history numbers

For single-region liver model: 1 million photons, electrons, positrons, and alpha particles histories were simulated independently at each energy, relative errors in energy deposition tallies were below 1%

[27]

For dual-region liver model: 1 million photons, electrons, positrons, and alpha particles histories were simulated independently at each energy, relative errors in energy deposition tallies were below 1% except for 10 keV electrons and positrons and 0.5 MeV alpha particles in which 10 million particles histories were simulated to achieve relative errors in energy deposition tallies below 1%

Data and post-processing

Energy deposited (MeV/source) was tallied in the single-region liver model. Absorbed fractions were calculated by normalizing the results to the particle source energy. Energy deposited (MeV/source) was tallied in the LOBV region of the dual-region liver model. Absorbed fractions from the following source–target combinations: (LOBV  ← LOBV) and (LOBV  ← LIBV) were calculated by normalizing the results to the particle source energy at each target. The fraction of blood mass was used to weight-average the absorbed fractions and normalizing by the mass of the target region (LOBV) (See Eq. 11)

[27]