From Gy/history to Gy/mAs: Absolute Dose in Monte Carlo

Short answer: this conversion is obtained not by an absolute simulation, but by cross-calibrating to a single measurement made with a calibrated ion chamber. Below we work through why this is so, the formula, the setup, chamber choice and the reference documents, step by step.

Why is MC output "per history"?

The MC code starts one particle from your defined source (a "history"), tracks it and all secondaries through matter, divides the deposited energy by the mass in the scoring volume, and averages over all histories. The result is the absorbed dose per starting particle.⁴ The code does not know how many photons your tube emits per mAs, because that is a physical quantity depending on the tube's absolute output, anode angle, filtration and geometry — and it is not provided as simulation input.

A subtlety: when you use a phase-space source, DOSXYZnrc reports dose "per incident particle," but the real physical link is the number of starting electrons hitting the target that generated that phase space (N_incident in BEAMnrc). With particle recycling/splitting, "history" and "true starting particle" can be conflated — the single most common source of a wrong normalization.⁶ This is why it is safest to tie the normalization to a physically measurable quantity (air kerma).

Two approaches

In principle there are two routes to absolute dose:

• (a) Absolute (ab initio) simulation: compute, from first principles, the number of photons the tube produces per mAs and feed it into the simulation. This requires knowing the absolute x-ray yield; in practice it is very hard, error-prone and rarely done.
• (b) Cross-calibration to measurement: measure air kerma (per mAs) with a calibrated chamber in a known geometry; simulate the same geometry in MC; derive a normalization factor from the ratio. This is the standard approach in imaging MC dosimetry and the one adopted by AAPM TG-195.¹

Cross-calibration steps

1. Reference measurement. Place a calibrated ion chamber at a defined reference point (typically isocentre or a specified source-to-chamber distance, free-in-air) and measure the air kerma. Record the mAs of the same exposure. Apply the standard kV dosimetry corrections to the raw reading:²³

where M is the raw reading, N_K the chamber's air-kerma calibration coefficient (for the relevant beam quality), k_TP temperature–pressure, k_pol polarity, k_s recombination and k_Q the beam-quality correction. Divide by mAs: K_air/mAs [mGy/mAs].

2. Simulate the same geometry. Reproduce the measurement exactly in MC: same kVp, same total filtration, same source-point geometry. Score air kerma (or dose in a small air/water voxel) at the same reference volume → K_MC [Gy/history]. At kV energies charged-particle equilibrium (CPE) holds in air, so collision kerma ≈ dose; converting fluence to kerma uses mass energy-absorption coefficients (μ_en/ρ).¹⁰

3. Normalization factor. Take the ratio of the two quantities:

Physically, this factor answers "how many starting histories correspond to one mAs."

4. Apply. You can now convert every MC score made with the same beam to absolute dose:

So the "Gy/mAs" constant is not a single magic number, but a facility- and beam-specific normalization factor derived from measurement.

Chamber & beam quality

Chamber choice. At kV/diagnostic energies, use a chamber carrying an air-kerma calibration coefficient (N_K) for the relevant beam quality, traceable to a primary standard:²

• For a point measurement, a small vented chamber: general-purpose thimble/Farmer type (≈0.6 cc) or 0.125 cc; at very low energies (mammographic band) a thin-window "soft-X" chamber.
• For a CTDI-like integrated measurement, the 100 mm CT pencil chamber.

Critical point: the chamber calibration must be at a beam quality matching the HVL of the beam you measure. Otherwise N_K is applied at the wrong energy and the absolute dose is systematically off.

Beam quality (RQR). In kV dosimetry the standard beam qualities are defined by the RQR series of IEC 61267 and characterized by HVL.⁷ Getting your measurement and simulation to yield the same HVL is the most practical proof of spectral matching (see below).

The Monte Carlo side

A normalization factor is only meaningful if the simulation physics is right:

• Validate the spectrum. Generate the tube spectrum either with a full BEAMnrc tube model or a validated spectrum generator (e.g. spekpy/SpekCalc, TASMICS), then validate by comparing simulated HVL to measured HVL. If the spectrum is wrong, because μ_en/ρ is energy-dependent, both the measurement–simulation match and the dose are corrupted.¹
• Kerma or dose? Under CPE in air, collision kerma coincides with dose; a track-length kerma estimator in a small air volume gives a low-variance result. If you model the chamber explicitly, include wall/cavity perturbations; if not, scoring free-in-air air kerma and matching to measurement is cleanest.
• Phase-space counting. Read the number of starting particles (N_incident) in the BEAMnrc phase-space header correctly; if recycling/splitting was used, reflect the difference between "history" and "true starting particle" properly in the normalization.⁶
• Statistics. Report the statistical uncertainty of the dose in the reference voxel (typical target <1%); the uncertainty of CF depends directly on it.

CBCT-specific notes

For kV-CBCT (Elekta XVI, Varian OBI–like) the methodology is identical; only a few extra cares apply:⁸⁹

• The bow-tie filter and collimation strongly shape the beam; they must be modelled completely in the simulation, otherwise the axial dose profile — and thus the value at the normalization point — shifts.
• Rotational (gantry) exposure: do not confuse the mAs of a single projection with the total mAs of a full rotation; fix CF to a defined reference exposure (e.g. a single static projection or a full scan) and use it consistently.
• Downes et al. build an MC model of a kV-CBCT unit with exactly this logic — normalizing to measured dose — and apply it to patient dosimetry; it is a concrete example to follow.⁸

Uncertainty budget

The uncertainty in absolute dose is a combination of several components: the chamber's N_K calibration uncertainty (from the standards lab, typically 1.5–3%, k=2), the correction factors (k_TP, k_s, k_pol), mAs reproducibility, spectrum/HVL matching and MC statistics. Reporting these separately is required for the result to be scientifically defensible; TRS-457 treats these components in detail.²

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