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.
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.
The algorithm assumes lateral electronic equilibrium everywhere — the fundamental assumption that breaks down in low-density or small-field conditions.
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).
| Scenario | Rating | Deviation |
|---|---|---|
| Homogeneous tissue | Good | < 2% |
| Lung, large field (≥10×10) | Moderate | 3–8% over |
| Lung SBRT (small field) | Poor | 10–20% over |
| Air cavities (H&N) | Poor | >20% over |
| Bone interface | Moderate | 3–5% |
| Small fields <3×3 cm² | Poor | 5–10% |
| Metal implants | Poor | 10–20% under |
Avoid for: lung SBRT, H&N with air cavities, small-field SRS, metal implants
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").
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.
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.
| Scenario | Rating | Deviation |
|---|---|---|
| Homogeneous tissue | Excellent | < 2% |
| Lung, large field | Good | 2–5% |
| Lung SBRT (small field) | Moderate | 5–12% vs Acuros |
| Air cavities (H&N) | Moderate | RMSE ~96% in cavity |
| Bone interface | Good | 2–3% |
| Small fields <3×3 | Moderate | 3–5% |
| Metal implants | Poor | >10% (mucosa overestimate) |
Caution: lung SBRT, H&N with significant air involvement, metal implants
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.
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 and AAA are physically equivalent in tier (both convolution/superposition with water-derived, density-scaled kernels), but differ in implementation:
| Scenario | Rating | Deviation |
|---|---|---|
| Homogeneous tissue | Excellent | < 2% |
| Lung, large field | Good | ~2–5% |
| Lung/tissue interface | Good | ~2.9–3.5% (vs MC) |
| Lung SBRT (small field) | Moderate | 4–10% |
| Air cavities | Moderate | Similar to AAA |
| Bone interface | Good | 2–4% |
| Small fields <3×3 | Moderate | 3–6% |
Caution: large air cavities, metal implants, very small SRS fields
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.
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.
Acuros XB (and Monte Carlo) can report dose in two modes:
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%).
| Scenario | Rating | Deviation |
|---|---|---|
| Homogeneous tissue | Excellent | < 1% |
| Lung SBRT (all fields) | Excellent | ±1–3% vs MC |
| Air cavities (H&N) | Very Good | RMSE ~10% in cavity |
| Bone interface | Excellent | < 2% |
| Small fields <3×3 | Excellent | < 2% |
| Metal implants (Ti) | Very Good | ~2–3% |
| Dental amalgam near mucosa | Good | < 7% (vs >10% for AAA) |
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.
| Physical Phenomenon | FPB | AAA | CCC | Acuros XB |
|---|---|---|---|---|
| 1D density scaling (EPL) | Yes | Partial | No (3D) | Exact |
| 3D anisotropic scatter redistribution | No | Yes | Yes | Yes |
| Lateral electron transport | No | Approximate | Approximate | Exact (LBTE) |
| Penumbra broadening in lung | No | Partial | Partial | Yes |
| Lateral electronic disequilibrium | No | Partial | Partial | Yes |
| Interface dose build-up/rebuild | No | Partial | Partial | Yes |
| Material composition (non-water σ) | No | No | No | Yes |
| Dose-to-medium reporting | No | No | No | Yes |
| Kernel type | Water PB kernel | Water kernel (anisotropic) | Water DSK (3D cone) | Material cross-sections |
| Relative computation speed | Fastest | Fast | Moderate | Moderate (deterministic) |
| Clinical Scenario | FPB | AAA | CCC | Acuros XB |
|---|---|---|---|---|
| Homogeneous tissue | <2% | <2% | <2% | <1% |
| Lung, large field (≥10×10) | 3–8% over | 2–5% | 2–5% | <2% |
| Lung SBRT (3×3–5×5 cm²) | 10–20% over | 5–12% | 4–10% | 1–3% |
| Air cavity profile (RMSE) | >50% | ~97% in cavity | Similar to AAA | ~10% |
| Bone interface | 3–5% | 2–3% | 2–4% | <2% |
| Metal hip prosthesis | 10–20% under | 5–12% error | 5–10% | 2–3% |
| Small field <3×3 | 5–10% | 3–5% | 3–6% | <2% |