![\"Proton](\"https:\/\/rtmedical.com.br\/wp-content\/uploads\/2026\/06\/proton-range.jpg\")
This article discusses the physical foundations, available commercial implementations, and validation evidence that guide the choice between PB and MC, with an emphasis on situations where the differences are clinically relevant. The text is aimed at medical physicists, dosimetrists and radiation oncologists directly involved in the commissioning and approval of treatment plans.<\/p>\n
In this Article<\/h2>\n\n- 1. Why range uncertainty dominates proton therapy<\/a><\/li>\n
- 2. How Pencil Beam models proton transport<\/a><\/li>\n
- 3. What Monte Carlo adds<\/a><\/li>\n
- 4. Nuclear interactions, halo and out-of-field dose<\/a><\/li>\n
- 5. Lung, bone, cavities and implants<\/a><\/li>\n
- 6. PBS, respiratory motion and interplay effect<\/a><\/li>\n
- 7. Robustness, commissioning and clinical decision<\/a><\/li>\n
- 8. FAQ<\/a><\/li>\n
- 9. References<\/a><\/li>\n<\/ul>\n<\/div>\n
Why range uncertainty dominates proton therapy<\/h2>\n
The range of a proton beam in tissue is determined by the ratio between the initial kinetic energy and the braking power of the medium. Clinically, this range is calculated from the Hounsfield units (HU) of the planning CT, converted into relative braking power (RSP) through calibration curves. This conversion introduces a systematic uncertainty whose magnitude varies depending on the calibration method and tissue composition \u2014 detailed values \u200b\u200band sources are discussed by Paganetti (2012)<\/a>, who places this contribution among the largest sources of uncertainty in clinical proton therapy.<\/p>\nIn addition to the HU\u2192RSP calibration, the following contribute to range uncertainty: interfraction positioning variations, anatomical deformation, metal artifacts in the CT and the limitations of the calculation algorithms themselves in reproducing real transport in heterogeneous media. The practical result is that additional margins (“range margins”) are applied distally to ensure tumor coverage, often at the expense of exposing critical structures posterior to the target.<\/p>\n
The dose calculation algorithm is one of the few sources of uncertainty that the medical physicist can reduce without relying on technological improvements external to the department. The difference between the dose predicted by PB and MC can, in complex geometries, be comparable to or greater than the range margins used clinically. Therefore, understanding when this difference is clinically significant is a fundamental skill in working with proton TPS.<\/p>\n
How Pencil Beam models proton transport<\/h2>\n
The Pencil Beam formalism in proton therapy derives from the Fermi-Eyges model for the transport of charged particles in approximately homogeneous media. The dose of an elementary beam is decomposed into components: the deposition along the central axis (determined by depth and accumulated braking power), the lateral scattering by multiple Coulomb interactions with atomic nuclei, and the heterogeneity corrections calculated by ray tracing in water-equivalent tissue layers.<\/p>\n
In clinical implementation, the PB represents the beam as a superposition of individual beamlets, each with a parameterized lateral Gaussian profile. TPS converts HU into RSP pixel by pixel along rays traced from the source, accumulates braking power and estimates the range of each pencil. Lateral inhomogeneities \u2014 density variations perpendicular to the beam axis \u2014 are treated approximately, generally by expanding the Gaussian kernel or by dividing the fluence into sub-pencils. This approximation is reasonable in nearly homogeneous media, but fails when there are abrupt density interfaces such as lung\/chest wall or air cavities immediately adjacent to the target.<\/p>\n
Commissioning a PB algorithm requires measurements of axis-integrated dose (IDD) and lateral scattering profiles in water dummy, in addition to validation in controlled heterogeneity geometries. The central limitation of PB is not the calculation time \u2014 on the order of seconds to minutes, which makes iterative optimization viable \u2014 but the structural inability to rigorously simulate transport in the presence of large lateral density gradients and inelastic nuclear interactions.<\/p>\n
What Monte Carlo adds<\/h2>\n
The Monte Carlo method simulates the transport of each proton individually, sampling physical processes \u2014 elastic Coulomb scattering, continuous and discrete energy losses, elastic and inelastic nuclear interactions \u2014 from tabulated cross sections. The result is a stochastic dose distribution that converges to the physically consistent solution as the number of simulated histories increases. Accuracy is limited in practice by uncertainties in the cross sections themselves and nuclear fragmentation models, not by the sampling methodology itself.<\/p>\n
MC codes widely used in research include TOPAS<\/a> (based on Geant4), GATE, FLUKA and FRED. Commercial engines also exist, but availability, implemented physics, regulatory purpose, and licensed modality change between products and versions. GPUMCD, originally described for coupled transport of photons and electrons, should not be used as a synonym for Monte Carlo for protons.<\/p>\nA relevant distinction is the output quantity. D_m and D_w depend on system definition and implementation, and cannot be automatically assigned just because a motor is PB or MC. Comparisons between algorithms must record the dose convention, the biological model when applicable and the way TPS converts stopping power and materials.<\/p>\n
An alternative approach to stochastic methods is deterministic solvers of the transport equation. In photons, Acuros XB is a commercial example. For protons, names, availability, and maturity change rapidly; Therefore, the article does not assume the universal absence or presence of a commercial solver and requires consultation of the documentation of the evaluated version.<\/p>\n
Nuclear interactions, halo and out-of-field dose<\/h2>\n
When a proton collides with an atomic nucleus inelastically, secondary fragments are emitted \u2014 low-energy protons, neutrons, alpha particles and heavier fragments. These products deposit doses in regions beyond the geometric field and outside the beam axis, constituting the so-called nuclear dose halo<\/strong>. Its amplitude is small in relation to the Bragg peak, but it can be dosimetrically relevant in low tolerance structures located close to the field \u2014 a particularly important scenario in pediatric and head and neck treatments.<\/p>\nPB, in most commercial implementations, does not explicitly model inelastic nuclear interactions. MC, on the contrary, simulates them directly, which improves dose prediction outside the field and at the edges of the target. The Proton Therapy Physics Review (Newhauser & Zhang, 2015)<\/a> locates nuclear interactions among the key determinants of differences between algorithms in clinically relevant geometries.<\/p>\nThe nuclear dose halo also affects commissioning: measurement of the wide-field integral dose (large-field IDD) is necessary to capture the nuclear contribution, which is not detected by small-diameter ionization chambers. PB-based TPS often uses an empirically parameterized halo component, whose adjustment in commissioning is critical to minimize systematic errors in absolute dose.<\/p>\n
Table 1 \u2014 Comparison between Pencil Beam and Monte Carlo in clinical proton therapy<\/strong><\/p>\n\n\n\nCharacteristic<\/th>\n Pencil Beam (PB)<\/th>\n Monte Carlo (MC)<\/th>\n<\/tr>\n<\/thead>\n \n\nPhysical basis<\/td>\n Fermi-Eyges formalism + ray tracing<\/td>\n Particle-to-particle stochastic transport<\/td>\n<\/tr>\n \nLateral heterogeneities<\/td>\n Gaussian kernel approximation<\/td>\n Explicit modeling<\/td>\n<\/tr>\n \nInelastic nuclear interactions<\/td>\n Generally empirically parameterized<\/td>\n Simulated with tabulated cross sections<\/td>\n<\/tr>\n \nNuclear dose halo<\/td>\n Empirical or missing component<\/td>\n Physically calculated<\/td>\n<\/tr>\n \nDose magnitude<\/td>\n Depends on TPS and implementation<\/td>\n Depends on TPS and implementation<\/td>\n<\/tr>\n \nCalculation time<\/td>\n Generally smaller<\/td>\n Depends on hardware, statistics and implementation<\/td>\n<\/tr>\n \nNumerical uncertainty<\/td>\n Deterministic<\/td>\n Statistics; depends on number of stories<\/td>\n<\/tr>\n \nMain commissioning<\/td>\n IDD + side profiles in water<\/td>\n Same + heterogeneous phantoms<\/td>\n<\/tr>\n \nPredominant clinical use<\/td>\n Iterative optimization, simple sites<\/td>\n Verification and complex sites<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\nLung, bone, cavities and implants<\/h2>\n
The limitations of PB they become more pronounced in extreme heterogeneities, and the choice of algorithm must consider the anatomical site:<\/p>\n
Lung:<\/strong> The reduced density of lung tissue amplifies lateral scattering and modifies the range. PB underestimates scatter at lung\/tumor interfaces and may incorrectly position the distal dose edge. Validation studies with MC document relevant local dose differences in fields crossing extensive lung regions, although the magnitude depends on the specific plane geometry.<\/p>\nCortical bone:<\/strong> High density increases braking power and concentrates spreading. PB underestimates scattering near bone\/soft tissue interfaces, resulting in local errors that may be relevant to adjacent critical structures such as the spinal cord, optic nerves, and chiasm.<\/p>\nAir cavities:<\/strong> Paranasal sinuses, nasopharynx, middle ear, and thoracic air spaces create abrupt density gradients. PB axial ray tracing may fail to capture the lateral scattering induced by these cavities, affecting the positioning of the Bragg peak and the target coverage estimate.<\/p>\nMetallic implants:<\/strong> Titanium prostheses, staples and stents introduce two simultaneous problems: metal artifacts in the CT that degrade the HU\u2192RSP conversion, and scattering\/absorption much higher than expected for soft tissue. MC explicitly simulates transport in high atomic number materials, but the accuracy is limited by the quality of the CT image. CT protocols with metal artifact reduction (MAR) algorithms must precede planning in any algorithm.<\/p>\nTable 2 \u2014 Heterogeneities, algorithmic limitations and potential clinical impact<\/strong><\/p>\n\n\n\nType of heterogeneity<\/th>\n Main limitation of PB<\/th>\n Advantage of MC<\/th>\n Potential clinical impact<\/th>\n<\/tr>\n<\/thead>\n \n\nLung (low density)<\/td>\n Underestimated lateral scatter<\/td>\n Multi-interface explicit transport<\/td>\n GTV coverage; chest wall dose<\/td>\n<\/tr>\n \nCortical bone<\/td>\n Inaccurate dose-shadow interface<\/td>\n Accurate high-Z modeling<\/td>\n Spinal cord, optic nerves, chiasm<\/td>\n<\/tr>\n \nAir cavities<\/td>\n Bragg peak shift<\/td>\n Explicit density gradient<\/td>\n Targets in head and neck, base skull<\/td>\n<\/tr>\n \nMetallic implant<\/td>\n RSP with artifact; sub-simulated scattering<\/td>\n Direct high-Z physics<\/td>\n Coverage and dose distal to implant<\/td>\n<\/tr>\n \nMobile interface (rectal, vaginal)<\/td>\n Interfraction variation not captured by any<\/td>\n Does not correct mobility<\/td>\n Requires independent robustness analysis<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\nPBS, respiratory motion and interplay effect<\/h2>\n
O Pencil Beam Scanning (PBS) \u2014 the predominant beam delivery modality in the modern clinic \u2014 dynamically scans the field spot by spot. In thoracic and abdominal tumors, respiratory motion overlaps the scan, creating the interplay effect<\/strong>: the dose delivered to any voxel depends on the exact respiratory phase at the time each spot passes over that region. The result can be cold spots and hot spots that do not appear in the static calculation on the planning CT, even if the average dose over many fractions is close to what is intended.<\/p>\nThe interplay effect is not a limitation of dose algorithms per se \u2014 PB and MC calculate dose over static anatomy. The difference emerges when using MC in 4D-CT accumulated dose simulations: the greater precision of MC in each respiratory phase produces a more accurate accumulated estimate, especially when there is strong lung heterogeneity. Using PB in each phase of a 4D-CT and accumulating the dose propagates the individual PB errors to the accumulated estimate.<\/p>\n
Strategies to mitigate interplay include rescanning (multiple scans per field per fraction), respiratory gating, and active breath-hold irradiation. Robust planning must incorporate not only positioning and range uncertainties, but also the spectrum of dose distributions induced by motion, which demands repeated calculations \u2014 a scenario in which MC calculation time becomes a critical operational variable and justifies the investment in GPU acceleration.<\/p>\n
Robustness, commissioning and clinical decision<\/h2>\nRobustness analysis<\/h3>\n
In proton therapy, the robustness analysis evaluates how the plan behaves under systematic perturbations: positioning displacements in the three axes, range variations and interfraction anatomical changes. The result is an envelope of dose distributions\u2014not a single distribution\u2014that the clinician uses to decide whether minimum coverage and organ-at-risk restrictions are met across all plausible scenarios.<\/p>\n
The choice of algorithm directly influences the value and interpretation of this analysis. If the nominal calculation in PB underestimates doses in organs at risk in geometries with lateral heterogeneities, the robustness analysis based exclusively on PB may indicate acceptability where the MC would indicate insufficient margin. Therefore, recent guidelines converge to recommend verification by MC before approving plans in anatomically complex sites, even if the optimization is carried out in PB for reasons of calculation speed.<\/p>\n
Commissioning<\/h3>\n
Commissioning an MC algorithm in commercial TPS requires, in addition to standard IDD measurements and lateral profiles on water dummy, validation on heterogeneous phantoms that replicate clinically relevant geometries: low-density lung equivalent material, bone\/soft tissue interfaces, and air cavity inserts. The comparison between MC calculation and experimental measurement must satisfy gamma criteria (typically 2%\/2 mm or 3%\/3 mm depending on institutional protocol) at the fraction of points required by the center’s QA protocol.<\/p>\n
Commissioning PB algorithms, historically less demanding in terms of heterogeneous phantoms, can mask systematic errors that only emerge in specific geometries. Centers that have migrated from PB to MC often identify systematic differences in certain anatomies \u2014 which may require revision of range margin protocols and, in selected cases, replanning of patients undergoing treatment.<\/p>\n
Clinical decision<\/h3>\n
The choice between PB and MC does not need to be binary. A common and reasonable practice is to use PB for iterative optimization \u2014 for speed \u2014 and MC for checking the final plan. When MC is available as an optimization engine, its direct use eliminates the inconsistency between optimization and verification. The institutional decision must consider:<\/p>\n
\n- Availability of dedicated hardware (GPU for MC in clinical time)<\/li>\n
- Anatomical sites of the clinical portfolio (PBS in lung and skull base demands MC; simple fields in prostate with favorable geometry tolerate PB with lower risk)<\/li>\n
- Acceptable clinical flow time in the context of patient volume<\/li>\n
- Institutional and societal guideline requirements such as AAPM, ESTRO, and IAEA<\/li>\n<\/ul>\n
For dose-independent QA\u2014secondary system plan verification\u2014software such as FRED or MC-based platforms provide physics-equivalent verification, while secondary QA analytical tools for MC are still in development and clinical validation.<\/p>\n
FAQ<\/h2>\nDoes Monte Carlo always produce more accurate results than Pencil Beam?<\/h3>\n
MC is physically more complete, but its accuracy depends on the implemented cross sections, voxel resolution, and the number of simulated histories \u2014 which defines statistical uncertainty. In simple and homogeneous geometries, a well-commissioned PB and a well-implemented MC produce equivalent results. The differences become clinically relevant mainly in extreme heterogeneities, field edges and situations with significant nuclear interactions. “More accurate” should be understood as “less dependent on geometric approximations”, not as a guarantee of superiority in any scenario.<\/p>\n
Which TPS commercials offer clinical MC for protons?<\/h3>\n
There are commercial TPS with Monte Carlo calculation for protons, but availability and clinical scope depend on version, country and license. The responsible physicist must check the technical and regulatory documentation of the local system. TOPAS, GATE, and other research codes are valuable for validation, but their healthcare use cannot be inferred from software availability alone.<\/p>\n
How does “dose to medium” versus “dose to water” affect plan comparison?<\/h3>\n
In tissues with a composition close to water (muscle, solid tumor), Dm \u2248 Dw. In cortical bone and high-density materials, Dm may differ from Dw by values \u200b\u200bthat are not clinically negligible, as the mass braking power of these materials differs from that of water. Comparing a PB plane (implicit Dw) with an MC plane (Dm) without explaining the quantity can lead to an error in interpretation. The practical recommendation is to institutionally define which magnitude is adopted and maintain consistency between the planning algorithm and the dose limits of the organs at risk of the protocols in use.<\/p>\n
How should the interplay effect be addressed in commissioning and clinical planning?<\/h3>\n
The interplay effect cannot be verified by static measurements on a water dummy. Commissioning must include measurements on a moving mannequin (dynamic) or 4D-CT simulations with calculation of accumulated dose in controlled geometry. In clinical planning, the magnitude of interplay must be estimated for each patient with a tumor in a relevant motion location (lung, liver, pancreas). When the effect is clinically significant, strategies such as rescanning or gating must be incorporated into the treatment protocol, with explicit documentation in the approved plan and in the medical record.<\/p>\n
When is it recommended to use MC instead of PB for plan approval?<\/h3>\n
There is no universal rule applicable to all systems. Strong lateral heterogeneities, implants, cavities and high gradient regions are reasons to require more rigorous analysis and, when available, comparison with a more complete transport engine. The policy must be based on risk, intended use of TPS and local commissioning.<\/p>\n
References<\/h2>\n\n- Paganetti H. Range uncertainties in proton therapy and the role of Monte Carlo simulations. Phys Med Biol.<\/em> 2012;57(11):R99\u2013R117.<\/a><\/li>\n
- Perl J, Shin J, Sch\u00fcmann J, Faddegon B, Paganetti H. TOPAS: An innovative proton Monte Carlo platform for research and clinical applications. Med Phys.<\/em> 2012;39(11):6818\u20136837.<\/a><\/li>\n
- Newhauser WD, Zhang R. The physics of proton therapy. Phys Med Biol.<\/em> 2015;60(8):R155\u2013R209.<\/a><\/li>\n
- IAEA Technical Reports Series No. 398. Absorbed Dose Determination in External Beam Radiotherapy. Vienna: IAEA; 2000.<\/li>\n
- AAPM Task Group Report 224. Comprehensive Proton Therapy Machine Quality Assurance. Med Phys. 2019.<\/li>\n<\/ul>\n
Why range uncertainty dominates proton therapy<\/h2>\n
The range of a proton beam in tissue is determined by the ratio between the initial kinetic energy and the braking power of the medium. Clinically, this range is calculated from the Hounsfield units (HU) of the planning CT, converted into relative braking power (RSP) through calibration curves. This conversion introduces a systematic uncertainty whose magnitude varies depending on the calibration method and tissue composition \u2014 detailed values \u200b\u200band sources are discussed by Paganetti (2012)<\/a>, who places this contribution among the largest sources of uncertainty in clinical proton therapy.<\/p>\n In addition to the HU\u2192RSP calibration, the following contribute to range uncertainty: interfraction positioning variations, anatomical deformation, metal artifacts in the CT and the limitations of the calculation algorithms themselves in reproducing real transport in heterogeneous media. The practical result is that additional margins (“range margins”) are applied distally to ensure tumor coverage, often at the expense of exposing critical structures posterior to the target.<\/p>\n The dose calculation algorithm is one of the few sources of uncertainty that the medical physicist can reduce without relying on technological improvements external to the department. The difference between the dose predicted by PB and MC can, in complex geometries, be comparable to or greater than the range margins used clinically. Therefore, understanding when this difference is clinically significant is a fundamental skill in working with proton TPS.<\/p>\n The Pencil Beam formalism in proton therapy derives from the Fermi-Eyges model for the transport of charged particles in approximately homogeneous media. The dose of an elementary beam is decomposed into components: the deposition along the central axis (determined by depth and accumulated braking power), the lateral scattering by multiple Coulomb interactions with atomic nuclei, and the heterogeneity corrections calculated by ray tracing in water-equivalent tissue layers.<\/p>\n In clinical implementation, the PB represents the beam as a superposition of individual beamlets, each with a parameterized lateral Gaussian profile. TPS converts HU into RSP pixel by pixel along rays traced from the source, accumulates braking power and estimates the range of each pencil. Lateral inhomogeneities \u2014 density variations perpendicular to the beam axis \u2014 are treated approximately, generally by expanding the Gaussian kernel or by dividing the fluence into sub-pencils. This approximation is reasonable in nearly homogeneous media, but fails when there are abrupt density interfaces such as lung\/chest wall or air cavities immediately adjacent to the target.<\/p>\n Commissioning a PB algorithm requires measurements of axis-integrated dose (IDD) and lateral scattering profiles in water dummy, in addition to validation in controlled heterogeneity geometries. The central limitation of PB is not the calculation time \u2014 on the order of seconds to minutes, which makes iterative optimization viable \u2014 but the structural inability to rigorously simulate transport in the presence of large lateral density gradients and inelastic nuclear interactions.<\/p>\n The Monte Carlo method simulates the transport of each proton individually, sampling physical processes \u2014 elastic Coulomb scattering, continuous and discrete energy losses, elastic and inelastic nuclear interactions \u2014 from tabulated cross sections. The result is a stochastic dose distribution that converges to the physically consistent solution as the number of simulated histories increases. Accuracy is limited in practice by uncertainties in the cross sections themselves and nuclear fragmentation models, not by the sampling methodology itself.<\/p>\n MC codes widely used in research include TOPAS<\/a> (based on Geant4), GATE, FLUKA and FRED. Commercial engines also exist, but availability, implemented physics, regulatory purpose, and licensed modality change between products and versions. GPUMCD, originally described for coupled transport of photons and electrons, should not be used as a synonym for Monte Carlo for protons.<\/p>\n A relevant distinction is the output quantity. D_m and D_w depend on system definition and implementation, and cannot be automatically assigned just because a motor is PB or MC. Comparisons between algorithms must record the dose convention, the biological model when applicable and the way TPS converts stopping power and materials.<\/p>\n An alternative approach to stochastic methods is deterministic solvers of the transport equation. In photons, Acuros XB is a commercial example. For protons, names, availability, and maturity change rapidly; Therefore, the article does not assume the universal absence or presence of a commercial solver and requires consultation of the documentation of the evaluated version.<\/p>\n When a proton collides with an atomic nucleus inelastically, secondary fragments are emitted \u2014 low-energy protons, neutrons, alpha particles and heavier fragments. These products deposit doses in regions beyond the geometric field and outside the beam axis, constituting the so-called nuclear dose halo<\/strong>. Its amplitude is small in relation to the Bragg peak, but it can be dosimetrically relevant in low tolerance structures located close to the field \u2014 a particularly important scenario in pediatric and head and neck treatments.<\/p>\n PB, in most commercial implementations, does not explicitly model inelastic nuclear interactions. MC, on the contrary, simulates them directly, which improves dose prediction outside the field and at the edges of the target. The Proton Therapy Physics Review (Newhauser & Zhang, 2015)<\/a> locates nuclear interactions among the key determinants of differences between algorithms in clinically relevant geometries.<\/p>\n The nuclear dose halo also affects commissioning: measurement of the wide-field integral dose (large-field IDD) is necessary to capture the nuclear contribution, which is not detected by small-diameter ionization chambers. PB-based TPS often uses an empirically parameterized halo component, whose adjustment in commissioning is critical to minimize systematic errors in absolute dose.<\/p>\n Table 1 \u2014 Comparison between Pencil Beam and Monte Carlo in clinical proton therapy<\/strong><\/p>\n The limitations of PB they become more pronounced in extreme heterogeneities, and the choice of algorithm must consider the anatomical site:<\/p>\n Lung:<\/strong> The reduced density of lung tissue amplifies lateral scattering and modifies the range. PB underestimates scatter at lung\/tumor interfaces and may incorrectly position the distal dose edge. Validation studies with MC document relevant local dose differences in fields crossing extensive lung regions, although the magnitude depends on the specific plane geometry.<\/p>\n Cortical bone:<\/strong> High density increases braking power and concentrates spreading. PB underestimates scattering near bone\/soft tissue interfaces, resulting in local errors that may be relevant to adjacent critical structures such as the spinal cord, optic nerves, and chiasm.<\/p>\n Air cavities:<\/strong> Paranasal sinuses, nasopharynx, middle ear, and thoracic air spaces create abrupt density gradients. PB axial ray tracing may fail to capture the lateral scattering induced by these cavities, affecting the positioning of the Bragg peak and the target coverage estimate.<\/p>\n Metallic implants:<\/strong> Titanium prostheses, staples and stents introduce two simultaneous problems: metal artifacts in the CT that degrade the HU\u2192RSP conversion, and scattering\/absorption much higher than expected for soft tissue. MC explicitly simulates transport in high atomic number materials, but the accuracy is limited by the quality of the CT image. CT protocols with metal artifact reduction (MAR) algorithms must precede planning in any algorithm.<\/p>\n Table 2 \u2014 Heterogeneities, algorithmic limitations and potential clinical impact<\/strong><\/p>\n O Pencil Beam Scanning (PBS) \u2014 the predominant beam delivery modality in the modern clinic \u2014 dynamically scans the field spot by spot. In thoracic and abdominal tumors, respiratory motion overlaps the scan, creating the interplay effect<\/strong>: the dose delivered to any voxel depends on the exact respiratory phase at the time each spot passes over that region. The result can be cold spots and hot spots that do not appear in the static calculation on the planning CT, even if the average dose over many fractions is close to what is intended.<\/p>\n The interplay effect is not a limitation of dose algorithms per se \u2014 PB and MC calculate dose over static anatomy. The difference emerges when using MC in 4D-CT accumulated dose simulations: the greater precision of MC in each respiratory phase produces a more accurate accumulated estimate, especially when there is strong lung heterogeneity. Using PB in each phase of a 4D-CT and accumulating the dose propagates the individual PB errors to the accumulated estimate.<\/p>\n Strategies to mitigate interplay include rescanning (multiple scans per field per fraction), respiratory gating, and active breath-hold irradiation. Robust planning must incorporate not only positioning and range uncertainties, but also the spectrum of dose distributions induced by motion, which demands repeated calculations \u2014 a scenario in which MC calculation time becomes a critical operational variable and justifies the investment in GPU acceleration.<\/p>\n In proton therapy, the robustness analysis evaluates how the plan behaves under systematic perturbations: positioning displacements in the three axes, range variations and interfraction anatomical changes. The result is an envelope of dose distributions\u2014not a single distribution\u2014that the clinician uses to decide whether minimum coverage and organ-at-risk restrictions are met across all plausible scenarios.<\/p>\n The choice of algorithm directly influences the value and interpretation of this analysis. If the nominal calculation in PB underestimates doses in organs at risk in geometries with lateral heterogeneities, the robustness analysis based exclusively on PB may indicate acceptability where the MC would indicate insufficient margin. Therefore, recent guidelines converge to recommend verification by MC before approving plans in anatomically complex sites, even if the optimization is carried out in PB for reasons of calculation speed.<\/p>\n Commissioning an MC algorithm in commercial TPS requires, in addition to standard IDD measurements and lateral profiles on water dummy, validation on heterogeneous phantoms that replicate clinically relevant geometries: low-density lung equivalent material, bone\/soft tissue interfaces, and air cavity inserts. The comparison between MC calculation and experimental measurement must satisfy gamma criteria (typically 2%\/2 mm or 3%\/3 mm depending on institutional protocol) at the fraction of points required by the center’s QA protocol.<\/p>\n Commissioning PB algorithms, historically less demanding in terms of heterogeneous phantoms, can mask systematic errors that only emerge in specific geometries. Centers that have migrated from PB to MC often identify systematic differences in certain anatomies \u2014 which may require revision of range margin protocols and, in selected cases, replanning of patients undergoing treatment.<\/p>\n The choice between PB and MC does not need to be binary. A common and reasonable practice is to use PB for iterative optimization \u2014 for speed \u2014 and MC for checking the final plan. When MC is available as an optimization engine, its direct use eliminates the inconsistency between optimization and verification. The institutional decision must consider:<\/p>\n For dose-independent QA\u2014secondary system plan verification\u2014software such as FRED or MC-based platforms provide physics-equivalent verification, while secondary QA analytical tools for MC are still in development and clinical validation.<\/p>\n MC is physically more complete, but its accuracy depends on the implemented cross sections, voxel resolution, and the number of simulated histories \u2014 which defines statistical uncertainty. In simple and homogeneous geometries, a well-commissioned PB and a well-implemented MC produce equivalent results. The differences become clinically relevant mainly in extreme heterogeneities, field edges and situations with significant nuclear interactions. “More accurate” should be understood as “less dependent on geometric approximations”, not as a guarantee of superiority in any scenario.<\/p>\n There are commercial TPS with Monte Carlo calculation for protons, but availability and clinical scope depend on version, country and license. The responsible physicist must check the technical and regulatory documentation of the local system. TOPAS, GATE, and other research codes are valuable for validation, but their healthcare use cannot be inferred from software availability alone.<\/p>\n In tissues with a composition close to water (muscle, solid tumor), Dm \u2248 Dw. In cortical bone and high-density materials, Dm may differ from Dw by values \u200b\u200bthat are not clinically negligible, as the mass braking power of these materials differs from that of water. Comparing a PB plane (implicit Dw) with an MC plane (Dm) without explaining the quantity can lead to an error in interpretation. The practical recommendation is to institutionally define which magnitude is adopted and maintain consistency between the planning algorithm and the dose limits of the organs at risk of the protocols in use.<\/p>\n The interplay effect cannot be verified by static measurements on a water dummy. Commissioning must include measurements on a moving mannequin (dynamic) or 4D-CT simulations with calculation of accumulated dose in controlled geometry. In clinical planning, the magnitude of interplay must be estimated for each patient with a tumor in a relevant motion location (lung, liver, pancreas). When the effect is clinically significant, strategies such as rescanning or gating must be incorporated into the treatment protocol, with explicit documentation in the approved plan and in the medical record.<\/p>\n There is no universal rule applicable to all systems. Strong lateral heterogeneities, implants, cavities and high gradient regions are reasons to require more rigorous analysis and, when available, comparison with a more complete transport engine. The policy must be based on risk, intended use of TPS and local commissioning.<\/p>\nHow Pencil Beam models proton transport<\/h2>\n
What Monte Carlo adds<\/h2>\n
Nuclear interactions, halo and out-of-field dose<\/h2>\n
\n\n
\n \nCharacteristic<\/th>\n Pencil Beam (PB)<\/th>\n Monte Carlo (MC)<\/th>\n<\/tr>\n<\/thead>\n \n Physical basis<\/td>\n Fermi-Eyges formalism + ray tracing<\/td>\n Particle-to-particle stochastic transport<\/td>\n<\/tr>\n \n Lateral heterogeneities<\/td>\n Gaussian kernel approximation<\/td>\n Explicit modeling<\/td>\n<\/tr>\n \n Inelastic nuclear interactions<\/td>\n Generally empirically parameterized<\/td>\n Simulated with tabulated cross sections<\/td>\n<\/tr>\n \n Nuclear dose halo<\/td>\n Empirical or missing component<\/td>\n Physically calculated<\/td>\n<\/tr>\n \n Dose magnitude<\/td>\n Depends on TPS and implementation<\/td>\n Depends on TPS and implementation<\/td>\n<\/tr>\n \n Calculation time<\/td>\n Generally smaller<\/td>\n Depends on hardware, statistics and implementation<\/td>\n<\/tr>\n \n Numerical uncertainty<\/td>\n Deterministic<\/td>\n Statistics; depends on number of stories<\/td>\n<\/tr>\n \n Main commissioning<\/td>\n IDD + side profiles in water<\/td>\n Same + heterogeneous phantoms<\/td>\n<\/tr>\n \n Predominant clinical use<\/td>\n Iterative optimization, simple sites<\/td>\n Verification and complex sites<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n Lung, bone, cavities and implants<\/h2>\n
\n\n
\n \nType of heterogeneity<\/th>\n Main limitation of PB<\/th>\n Advantage of MC<\/th>\n Potential clinical impact<\/th>\n<\/tr>\n<\/thead>\n \n Lung (low density)<\/td>\n Underestimated lateral scatter<\/td>\n Multi-interface explicit transport<\/td>\n GTV coverage; chest wall dose<\/td>\n<\/tr>\n \n Cortical bone<\/td>\n Inaccurate dose-shadow interface<\/td>\n Accurate high-Z modeling<\/td>\n Spinal cord, optic nerves, chiasm<\/td>\n<\/tr>\n \n Air cavities<\/td>\n Bragg peak shift<\/td>\n Explicit density gradient<\/td>\n Targets in head and neck, base skull<\/td>\n<\/tr>\n \n Metallic implant<\/td>\n RSP with artifact; sub-simulated scattering<\/td>\n Direct high-Z physics<\/td>\n Coverage and dose distal to implant<\/td>\n<\/tr>\n \n Mobile interface (rectal, vaginal)<\/td>\n Interfraction variation not captured by any<\/td>\n Does not correct mobility<\/td>\n Requires independent robustness analysis<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n PBS, respiratory motion and interplay effect<\/h2>\n
Robustness, commissioning and clinical decision<\/h2>\n
Robustness analysis<\/h3>\n
Commissioning<\/h3>\n
Clinical decision<\/h3>\n
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FAQ<\/h2>\n
Does Monte Carlo always produce more accurate results than Pencil Beam?<\/h3>\n
Which TPS commercials offer clinical MC for protons?<\/h3>\n
How does “dose to medium” versus “dose to water” affect plan comparison?<\/h3>\n
How should the interplay effect be addressed in commissioning and clinical planning?<\/h3>\n
When is it recommended to use MC instead of PB for plan approval?<\/h3>\n
References<\/h2>\n
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