In this work, stray radiation was defined as the undesirable radiation produced from interactions between the proton beam and the components in the treatment unit or the patient. Secondary neutrons emanating from the treatment unit (or ‘external neutrons’) and within the patient (or ‘internal neutrons’) have been shown to be the primary contributor to absorbed dose from stray radiation (Agosteo et al 1998 (link), Fontenot et al 2008 (link), Zheng et al 2008 (link)). E, HT and Dv were calculated separately for both external and internal neutrons. However, because the MCNPX code does not directly differentiate between the absorbed dose from external versus internal radiation, the following method was used to separate the absorbed dose from each of these two components.
To isolate the absorbed dose from external neutrons, Dv,ext, the Monte Carlo system was configured to track neutrons and protons throughout the entire geometry (mode n h; imp:h, n > 0). However, all proton trajectories were terminated immediately upstream of the patient by a proton stopping plane (imp:h = 0), modeled as very thin slab of air. Thus, in simulations with the stopping plane, only external neutrons were incident upon the patient. A type 3 mesh tally (keyword ‘total’) was used to calculate energy deposition in each anatomic voxel of the patient, and Dv,ext was calculated according to the methods described in section 2.3.
Isolating the contribution to absorbed dose from internal neutrons, Dv,int, required a slightly more complex procedure. The additional complexity was necessary because MCNPX tallies did not discriminate between therapeutic (primary) protons and protons that were liberated from inelastic nuclear reactions. First, the absorbed dose from primary protons was calculated by tracking only protons (and not neutrons) throughout the geometry (mode n h; imp:h > 0; imp:n = 0). In this case, secondary neutrons were generated, but their trajectories were immediately terminated at their points of origin. Absorbed dose was calculated in each voxel for primary protons, Dv[p1], using a type 1 mesh tally (keyword ‘pedep’). Second, a simulation was performed in which protons were tracked throughout the model but neutrons were tracked only within the patient (i.e. external neutrons were not allowed to contribute to absorbed dose). This model was identical to the previous one except that the secondary neutrons were tracked within the voxelized anatomy (imp:n > 0 in the phantom). Absorbed dose was calculated in each voxel separately for protons, Dv[p2], and neutrons, Dv[n], using type 1 rectangular mesh tallies (card ‘rmesh’, keyword ‘pedep’). In the MCNPX code, the type 1 mesh tally included energy deposition only from particles that were explicitly specified on the RMESH card (e.g. ‘rmesh21:n pedep’ for neutrons). Thus, the tally excluded the proportion of energy that was deposited by other particles that were being transported, where the list of particles transported was specified on the ‘mode’ card, for example recoil protons (Pelowitz 2005 ). Therefore, the absorbed dose from recoil protons that originated from interactions with internal neutrons was added to Dv[n] using the methods described by Taddei et al (2008) (link), which was based on the assumption that the ratio of neutron dose to secondary proton dose is constant throughout the body. An average of Dv [p2]/Dv [n] for all voxels outside the treatment field, A, was calculated, including contributions from all treatment fields. This average value was then used to estimate the contribution to absorbed dose from secondary protons for each voxel inside the treatment field, and this contribution was added to the absorbed dose from internal neutrons for that voxel,
Dv,int was calculated in terms of mGy from internal neutrons per therapeutic Gy according to the methods described in section 2.3.
Because of computer memory constraints, photons, alpha particles and other secondary particles were not tracked, and their energy was deposited locally at their points of origin. This was not a limitation of the study because in proton therapy equivalent dose from stray radiation is predominated by neutrons (Agosteo et al 1998 (link), Fontenot et al 2008 (link), Zheng et al 2008 (link)).
To isolate the absorbed dose from external neutrons, Dv,ext, the Monte Carlo system was configured to track neutrons and protons throughout the entire geometry (mode n h; imp:h, n > 0). However, all proton trajectories were terminated immediately upstream of the patient by a proton stopping plane (imp:h = 0), modeled as very thin slab of air. Thus, in simulations with the stopping plane, only external neutrons were incident upon the patient. A type 3 mesh tally (keyword ‘total’) was used to calculate energy deposition in each anatomic voxel of the patient, and Dv,ext was calculated according to the methods described in section 2.3.
Isolating the contribution to absorbed dose from internal neutrons, Dv,int, required a slightly more complex procedure. The additional complexity was necessary because MCNPX tallies did not discriminate between therapeutic (primary) protons and protons that were liberated from inelastic nuclear reactions. First, the absorbed dose from primary protons was calculated by tracking only protons (and not neutrons) throughout the geometry (mode n h; imp:h > 0; imp:n = 0). In this case, secondary neutrons were generated, but their trajectories were immediately terminated at their points of origin. Absorbed dose was calculated in each voxel for primary protons, Dv[p1], using a type 1 mesh tally (keyword ‘pedep’). Second, a simulation was performed in which protons were tracked throughout the model but neutrons were tracked only within the patient (i.e. external neutrons were not allowed to contribute to absorbed dose). This model was identical to the previous one except that the secondary neutrons were tracked within the voxelized anatomy (imp:n > 0 in the phantom). Absorbed dose was calculated in each voxel separately for protons, Dv[p2], and neutrons, Dv[n], using type 1 rectangular mesh tallies (card ‘rmesh’, keyword ‘pedep’). In the MCNPX code, the type 1 mesh tally included energy deposition only from particles that were explicitly specified on the RMESH card (e.g. ‘rmesh21:n pedep’ for neutrons). Thus, the tally excluded the proportion of energy that was deposited by other particles that were being transported, where the list of particles transported was specified on the ‘mode’ card, for example recoil protons (Pelowitz 2005 ). Therefore, the absorbed dose from recoil protons that originated from interactions with internal neutrons was added to Dv[n] using the methods described by Taddei et al (2008) (link), which was based on the assumption that the ratio of neutron dose to secondary proton dose is constant throughout the body. An average of Dv [p2]/Dv [n] for all voxels outside the treatment field, A, was calculated, including contributions from all treatment fields. This average value was then used to estimate the contribution to absorbed dose from secondary protons for each voxel inside the treatment field, and this contribution was added to the absorbed dose from internal neutrons for that voxel,
Dv,int was calculated in terms of mGy from internal neutrons per therapeutic Gy according to the methods described in section 2.3.
Because of computer memory constraints, photons, alpha particles and other secondary particles were not tracked, and their energy was deposited locally at their points of origin. This was not a limitation of the study because in proton therapy equivalent dose from stray radiation is predominated by neutrons (Agosteo et al 1998 (link), Fontenot et al 2008 (link), Zheng et al 2008 (link)).