Dose Calculation Algorithm Comparison

Clinical treatment planning relies on algorithms that vary dramatically in how they model radiation transport through heterogeneous tissue. This comparison is based on published literature including AAPM TG-65, TG-186, and peer-reviewed studies benchmarking algorithms against Monte Carlo.

Depth-Dose Profile Comparison (6 MV)

3×3 (SBRT)20×20
FPB
AAA
CCC
Acuros XB
MC Reference

Lateral Profile at Depth

1 cm25 cm
FPB
AAA
CCC
Acuros XB

Pencil Beam Convolution / Finite Pencil Beam (PBC/FPB)

Physical Model

The photon beam is decomposed into infinitely narrow pencil beams. Each deposits dose along its central axis using a pre-computed depth-dose kernel derived from MC in water. Lateral spread is modeled by a Gaussian function. Heterogeneity is corrected solely via 1D equivalent path length (EPL) — density-scaling the central-axis depth only. Lateral photon scatter and electron transport are not recalculated in the transverse plane.

D(x,y,z) = ∑∑ K_PB(z_eff) ⊗ G(x,y,σ) × Φ(x',y') z_eff = ∫ ρ(z') dz' [EPL correction only]

The algorithm assumes lateral electronic equilibrium everywhere — the fundamental assumption that breaks down in low-density or small-field conditions.

Key Failure Mechanism in Lung

In low-density lung (~0.3 g/cm³), secondary electrons scatter ~3× farther laterally. For fields narrower than the electron range, lateral electronic disequilibrium occurs: dose at the field center is reduced relative to water because fewer electrons arrive from the surrounding low-density medium. FPB ignores this, overestimating by 5–15% for SBRT fields, scaling with energy (worse at 18 MV than 6 MV).

Accuracy vs. Monte Carlo

ScenarioRatingDeviation
Homogeneous tissueGood< 2%
Lung, large field (≥10×10)Moderate3–8% over
Lung SBRT (small field)Poor10–20% over
Air cavities (H&N)Poor>20% over
Bone interfaceModerate3–5%
Small fields <3×3 cm²Poor5–10%
Metal implantsPoor10–20% under
AAPM TG-65 and current practice guidelines classify PBC/FPB as unacceptable for thoracic SBRT and other highly heterogeneous sites. Convolution/superposition or LBTE algorithms are required.

Clinical Use

  • 3D-CRT in homogeneous regions (brain, prostate, pelvis)
  • Breast tangents with minimal lung involvement

Avoid for: lung SBRT, H&N with air cavities, small-field SRS, metal implants

Physical Phenomena Handled

  • Assumes full lateral electronic equilibrium — breaks down for fields smaller than electron range in medium
  • 1D EPL heterogeneity correction ignores lateral density variations; errors scale with transverse density gradients
  • Gaussian lateral spread derived from water; not re-scaled for local medium density
  • Cannot model dose buildup/rebuild at tissue–air interfaces
  • No secondary electron transport beyond implicit scatter term

Anisotropic Analytical Algorithm (AAA) — Varian Eclipse

Physical Model

AAA is a convolution/superposition algorithm. The beam is decomposed into multiple sub-sources representing primary photons, extra-focal photons, and electron contamination. Monte Carlo–derived energy deposition kernels are convolved with the energy fluence field and then scaled anisotropically using density along multiple ray directions (hence "anisotropic").

D(r) = ∫ Ψ(r') × K(r−r', ρ_eff(r,r')) dV' K scaled independently in each azimuthal direction

Critically, the kernels themselves are still derived in water and density-scaled — not recomputed in the actual medium. Lateral electron transport uses a density-scaled Gaussian approximation, not rigorous transport.

Key Limitation in Air Cavities

In air gaps (larynx, sinuses, oral cavity), AAA still significantly overestimates dose. A study of H&N VMAT plans found AAA RMSE inside air cavity profiles of up to 96.5% versus measurement, compared to ~10.3% for Acuros XB. When PTV air content exceeds ~5%, AAA D95% is roughly equivalent to the Acuros D100% excluding air — a clinically meaningful difference in plan interpretation.

Accuracy vs. Monte Carlo

ScenarioRatingDeviation
Homogeneous tissueExcellent< 2%
Lung, large fieldGood2–5%
Lung SBRT (small field)Moderate5–12% vs Acuros
Air cavities (H&N)ModerateRMSE ~96% in cavity
Bone interfaceGood2–3%
Small fields <3×3Moderate3–5%
Metal implantsPoor>10% (mucosa overestimate)
Lung SBRT plans optimized with AAA may deliver measurably less dose to the target than intended when recalculated with Acuros XB or Monte Carlo. PTV D98% differences up to 12.3% have been reported for stage I NSCLC plans.

Clinical Use

  • IMRT/VMAT planning — widely commissioned
  • Lung (non-SBRT), head & neck, pelvis, prostate
  • Acceptable for most conventional fractionation in heterogeneous regions

Caution: lung SBRT, H&N with significant air involvement, metal implants

Collapsed Cone Convolution/Superposition (CCC) — Pinnacle / RayStation

Physical Model

CCC evaluates the full 3D convolution of the total energy release per unit mass (TERMA) with a polyenergetic dose-spread kernel (DSK) computed by MC in water. Rather than integrating over all solid angles (computationally prohibitive), it collapses the integral onto a finite set of discrete ray directions (cones), propagating energy release along each cone and accumulating dose contributions.

D(r) = ∫ T(r') × h(r−r', ρ) dV' Approximated by: D(r) ≈ ∑_cones T(r_n) × h_cone(|r−r_n|, ρ_n)

Like AAA, the DSK is water-derived and density-scaled — placing CCC in the same physical tier as AAA. Its advantage over AAA is efficient 3D scatter integration via the cone approximation. In RayStation, CCC is often benchmarked alongside Monte Carlo with good agreement for conventional sites.

CCC vs AAA — Key Differences

CCC and AAA are physically equivalent in tier (both convolution/superposition with water-derived, density-scaled kernels), but differ in implementation:

  • CCC: full 3D scatter captured via cone rays; computationally heavier but captures more scatter directions
  • AAA: anisotropic kernel scaling along multiple directions; faster, tuned to Varian linac source models
  • In practice, CCC and AAA perform comparably in benchmarks: both agree with MC to within ~2–5% in lung, both fail similarly in air cavities

Accuracy vs. Monte Carlo

ScenarioRatingDeviation
Homogeneous tissueExcellent< 2%
Lung, large fieldGood~2–5%
Lung/tissue interfaceGood~2.9–3.5% (vs MC)
Lung SBRT (small field)Moderate4–10%
Air cavitiesModerateSimilar to AAA
Bone interfaceGood2–4%
Small fields <3×3Moderate3–6%
A retrospective study of Halcyon lung VMAT plans found CCC in good agreement with Monte Carlo: PTV mean dose within ~0.1%, lung-tissue interface within ~3.5%. CCC is generally considered acceptable for lung SBRT when MC is unavailable, but Acuros XB or MC remain preferred.

Clinical Use

  • Full IMRT/VMAT planning in Pinnacle and RayStation
  • Acceptable for lung SBRT in many institutional protocols
  • H&N, pelvis, breast — well-validated

Caution: large air cavities, metal implants, very small SRS fields

Acuros XB — Linear Boltzmann Transport Equation Solver

Physical Model

Acuros XB deterministically solves the Linear Boltzmann Transport Equation (LBTE) on a voxel grid. This is the same governing equation as Monte Carlo, but solved numerically rather than stochastically. It explicitly transports both photon and electron angular flux through the actual material compositions of each voxel — not water-equivalent densities.

Ω·∇ψ(r,E,Ω) + σ_t(r,E) ψ = ∫∫ σ_s(r,E'→E,Ω'→Ω) ψ dE'dΩ' + Q ψ = angular particle flux; σ_t = total cross-section; σ_s = scattering

Cross-sections for photon interactions (Compton, photoelectric, pair production) and electron stopping power are looked up from material libraries for actual tissue compositions (muscle, adipose, lung, bone, air) — not water scaled by density.

Dose-to-Medium (Dm) vs. Dose-to-Water (Dw)

Acuros XB (and Monte Carlo) can report dose in two modes:

  • Dm — energy deposited per gram of the actual medium. Bone: ~2–4% lower than Dw (bone stops electrons differently than water). More physically correct for radiobiological effect on bone mineral.
  • Dw — converts flux to dose as if the medium were water. Equivalent to AAA/CCC reporting. Preferred operationally because published dose-response data (NTCP/TCP models) were built on Dw-equivalent quantities.

AAPM TG-186 recommends Dm for dose prescription and outcomes analysis where material compositions are well characterized. In soft tissue, Dm ≈ Dw (difference <1%). Significant only for bone (2–4%) and lung (1–2%).

Accuracy vs. Monte Carlo

ScenarioRatingDeviation
Homogeneous tissueExcellent< 1%
Lung SBRT (all fields)Excellent±1–3% vs MC
Air cavities (H&N)Very GoodRMSE ~10% in cavity
Bone interfaceExcellent< 2%
Small fields <3×3Excellent< 2%
Metal implants (Ti)Very Good~2–3%
Dental amalgam near mucosaGood< 7% (vs >10% for AAA)
In lung SBRT benchmarks against XVMC Monte Carlo, Acuros XB achieves all dosimetric parameters within ±3.0–3.5%. In contrast, AAA shows PTV D98% differences of up to 12.3% and D95% up to 10% higher than MC. Acuros XB air cavity RMSE (~10.3%) is ~9× better than AAA (~96.5%) inside H&N air profiles.

Clinical Use

  • Lung SBRT/SABR — preferred algorithm
  • H&N with significant air cavity involvement
  • Spine SBRT near metal implants
  • Intracranial SRS small-field plans
  • Any case requiring highest heterogeneity accuracy

Why Acuros XB Is Near-MC in Accuracy

The fundamental distinction: while FPB/AAA/CCC all use water kernels scaled by density, Acuros uses actual material cross-sections. This means electron stopping power, scatter kernel shape, and photon interaction probability are all computed for the true tissue composition — not approximated from water. Lateral electronic disequilibrium is naturally captured because electron transport is solved explicitly, not assumed at equilibrium. The deterministic solver trades Monte Carlo's statistical noise for a small numerical grid-resolution error, achieving comparable accuracy at clinically practical calculation times.

Algorithm Overview — Hierarchy & Feature Comparison

Accuracy for heterogeneous media (least → most accurate)
FPB / PBC
<
AAA
CCC
<
Acuros XB
Monte Carlo

Physical Phenomena Handled

Physical Phenomenon FPB AAA CCC Acuros XB
1D density scaling (EPL)YesPartialNo (3D)Exact
3D anisotropic scatter redistributionNoYesYesYes
Lateral electron transportNoApproximateApproximateExact (LBTE)
Penumbra broadening in lungNoPartialPartialYes
Lateral electronic disequilibriumNoPartialPartialYes
Interface dose build-up/rebuildNoPartialPartialYes
Material composition (non-water σ)NoNoNoYes
Dose-to-medium reportingNoNoNoYes
Kernel typeWater PB kernelWater kernel (anisotropic)Water DSK (3D cone)Material cross-sections
Relative computation speedFastestFastModerateModerate (deterministic)

Quantitative Accuracy Summary (vs. Monte Carlo)

Clinical Scenario FPB AAA CCC Acuros XB
Homogeneous tissue <2%<2%<2%<1%
Lung, large field (≥10×10) 3–8% over2–5%2–5%<2%
Lung SBRT (3×3–5×5 cm²) 10–20% over5–12%4–10%1–3%
Air cavity profile (RMSE) >50%~97% in cavitySimilar to AAA~10%
Bone interface 3–5%2–3%2–4%<2%
Metal hip prosthesis 10–20% under5–12% error5–10%2–3%
Small field <3×3 5–10%3–5%3–6%<2%
Sources: AAPM TG-65 (heterogeneity corrections), TG-186 (advanced algorithms); Ojala et al. (lung SBRT MC benchmark); Ong et al. (AAA vs Acuros XB lung VMAT); Fogliata et al. (small field Acuros); Abo-Madyan et al. (H&N air cavity); PMC5875463, PMC3723919, PMC10547402, PMC5711096.