KAHIBARO
15.2. Absorbed Dose
Table of Contents
Energy per unit mass
In GATE, as in medical physics in general, absorbed dose is defined from a very simple physical idea. When ionizing radiation passes through matter, it deposits energy in that matter. Absorbed dose quantifies how much energy is deposited, relative to how much material received it.
Formally, the absorbed dose $D$ in a small amount of material is defined as
$$
D = \frac{\mathrm{d}E}{\mathrm{d}m},
$$
where $\mathrm{d}E$ is the mean energy deposited by ionizing radiation in the mass element $\mathrm{d}m$.
This means that dose is an energy per unit mass quantity. The numerator is an energy, usually expressed in joules, and the denominator is a mass, usually expressed in kilograms. The unit of dose is therefore joules per kilogram.
In a simulation, you rarely work with infinitesimal elements, but the same concept applies to finite volumes. Suppose a small voxel in a phantom has mass $m_{\text{voxel}}$ and receives a total energy deposition $E_{\text{dep}}$ from all particles during the simulation. The average dose to that voxel is
$$
D_{\text{voxel}} = \frac{E_{\text{dep}}}{m_{\text{voxel}}}.
$$
The energy deposition $E_{\text{dep}}$ is obtained from GATE by summing all local energy deposits in that voxel. The voxel mass is determined by its physical volume and the material density assigned to it, so
$$
m_{\text{voxel}} = \rho_{\text{material}} \, V_{\text{voxel}}.
$$
The same definition applies at the organ level. If you know the total energy deposited in an organ volume and the mass of that organ, the mean organ dose is the energy deposited divided by that mass.
In Monte Carlo simulations, absorbed dose is always an average quantity, because each simulation history is a random realization of many possible interaction chains. When you run more primary events, the estimates for $E_{\text{dep}}$ and $D$ converge and the statistical uncertainty decreases. However, the definition as energy per unit mass does not change with statistics.
You should also be aware that dose is fundamentally a local quantity. GATE dose actors typically compute dose in a spatial grid, so different regions can receive very different doses, even within the same material. High dose gradients near interfaces, beams, or sources are common in both imaging and therapy simulations.
Key definition:
Absorbed dose $D$ at a point is the mean energy deposited $\mathrm{d}E$ by ionizing radiation in a small mass element $\mathrm{d}m$ around that point,
$$D = \dfrac{\mathrm{d}E}{\mathrm{d}m}.$$
Its unit is joule per kilogram.
Gray
The special unit used for absorbed dose is the gray. By definition,
$$
1 \,\text{gray} = 1 \,\text{Gy} = 1 \,\frac{\text{joule}}{\text{kilogram}} = 1 \,\frac{\text{J}}{\text{kg}}.
$$
The gray is a large unit. Typical values span a wide range depending on the application:
| Application context | Typical dose scale |
|---|---|
| Background radiation | $\mu\text{Gy}$ to mGy per year |
| Diagnostic CT scan | A few mGy to tens of mGy |
| Nuclear medicine diagnostics | mGy range |
| External beam radiotherapy fraction | Around 1 Gy to 3 Gy per fraction |
| Full radiotherapy course | A few tens of Gy |
Because of this range, you often use metric prefixes for dose:
| Symbol | Name | Relation to gray |
|---|---|---|
| mGy | milligray | $1 \,\text{mGy} = 10^{-3} \,\text{Gy}$ |
| μGy | microgray | $1 \,\mu\text{Gy} = 10^{-6} \,\text{Gy}$ |
| kGy | kilogray | $1 \,\text{kGy} = 10^{3} \,\text{Gy}$ |
In GATE, dose actors report absorbed dose values in gray by default. Internally, energy depositions are handled in electronvolts, but these are converted to joules, then divided by mass in kilograms to produce values in gray. You do not have to perform this unit conversion manually when you use the built-in dose scoring tools, provided you use GATE units correctly in your geometry and materials.
When you look at dose maps, you will typically see voxel dose values in Gy or mGy. To convert between total energy deposition and dose in a given volume, you can use the relationships
$$
D \,[\text{Gy}] = \frac{E_{\text{dep}} \,[\text{J}]}{m \,[\text{kg}]},
$$
and, if your simulation provides energy in MeV,
$$
E_{\text{dep}} \,[\text{J}] = E_{\text{dep}} \,[\text{MeV}] \times 1.602 \times 10^{-13} \,\frac{\text{J}}{\text{MeV}}.
$$
Combining both gives the practical expression
$$
D \,[\text{Gy}] = \frac{E_{\text{dep}} \,[\text{MeV}] \times 1.602 \times 10^{-13}}{m \,[\text{kg}]}.
$$
This is useful when you want to verify a dose actor result by hand, or when you compute dose from energy deposition data that you have exported.
Remember that absorbed dose, measured in gray, describes the physical energy deposited per unit mass. It does not include biological effect weighting. Quantities such as equivalent dose and effective dose, which use the sievert as their unit, introduce additional weighting factors and belong to radiological protection, not to basic absorbed dose scoring. In GATE, you primarily work with the gray, since it is directly tied to the Monte Carlo transport of particles and the energy they leave in matter.
Important relationship:
1 gray is defined as 1 joule of deposited energy per kilogram of material,
$$1 \,\text{Gy} = 1 \,\frac{\text{J}}{\text{kg}}.$$
In GATE dose actors, reported dose values are in gray by default.
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