KAHIBARO
36.4. Dose Maps
Table of Contents
Voxel dose
In internal dosimetry with GATE you usually score dose on a three dimensional grid that covers the patient or phantom. Each small box in this grid is a voxel. A dose map is simply the spatial distribution of absorbed dose, $D(\vec{r})$, stored voxel by voxel.
To create a voxel dose map, a dose actor is attached to a volume that has been discretized into voxels, for example a water phantom, a stylized computational phantom, or a patient CT based geometry. Each time a particle deposits energy in a voxel, the actor accumulates that energy and divides by the voxel mass. The resulting quantity is the absorbed dose in that voxel.
The basic relation between deposited energy and dose in one voxel is
$$
D_i = \frac{E_{\text{dep},i}}{m_i},
$$
where $D_i$ is the dose in voxel $i$, $E_{\text{dep},i}$ is the total energy deposited in that voxel and $m_i$ is its mass. The voxel mass is given by
$$
m_i = \rho_i \, V_i,
$$
with $\rho_i$ the material density in voxel $i$ and $V_i$ the voxel volume.
In a voxel dose map each voxel dose is computed as
$$D_i = \frac{E_{\text{dep},i}}{\rho_i V_i}.$$
Make sure densities and voxel dimensions are correct, otherwise all doses will be wrong.
In internal dosimetry, voxel size and material assignment have a strong impact on the quality of the dose map. Smaller voxels represent anatomical detail and heterogeneous activity distributions more accurately, but they increase memory usage and statistical noise. Larger voxels reduce noise and file size, but they smear out steep gradients, for example near organ boundaries or around small high activity lesions.
GATE dose actors usually provide, in the same output, the 3D arrays of dose values and of statistical uncertainty per voxel. Uncertainty is often given as a relative standard deviation for each voxel that has received some dose. Good practice in internal dosimetry is to check both the dose values and their uncertainties: voxels with very high uncertainty can be misleading if interpreted without care. For absolute beginners it is enough to remember that increasing the number of simulated histories will reduce this uncertainty everywhere, but at the cost of longer simulation time.
Voxelized geometries based on CT or nuclear medicine images require a consistent mapping between image voxels and simulation voxels. When the same grid is used for both geometry and dose scoring, the 3D dose map can be directly co registered with the patient anatomy or with activity images. This makes it possible to inspect dose distributions in axial, coronal and sagittal planes, and to extract profiles across structures of interest.
A voxel dose map also serves as the basis for deriving more global quantities. Summing dose over a region gives organ averaged dose, and deriving histograms from the voxel dose values yields dose volume histograms. These higher level metrics are important in radionuclide therapy planning and evaluation, but they are always built from the fundamental voxel by voxel dose information produced by GATE.
Organ dose
While voxel dose gives local information, internal dosimetry is usually reported in terms of average dose to entire organs or specific regions, such as target tumors and critical normal tissues. Organ dose is obtained by combining voxel dose maps with a segmentation of the anatomy into labeled regions.
Conceptually, if an organ occupies a set of voxels $\{i\}$, the mass weighted mean dose to that organ is
$$
\bar{D}_{\text{organ}} = \frac{\sum_{i \in \text{organ}} D_i \, m_i}{\sum_{i \in \text{organ}} m_i}
= \frac{\sum_{i \in \text{organ}} E_{\text{dep},i}}{\sum_{i \in \text{organ}} m_i}.
$$
This definition uses the same physics as the voxel dose computation, but aggregates over all voxels that belong to the organ. The organ mass is the sum of the masses of its voxels. If the organ is homogeneous, this average dose reflects very well the macroscopic absorbed dose that is relevant for many biological and clinical endpoints.
Average organ dose is a mass weighted quantity:
$$\bar{D}_{\text{organ}} = \dfrac{\sum D_i m_i}{\sum m_i}.$$
Never compute organ dose by simply averaging voxel doses without accounting for different voxel masses.
To obtain organ dose from a GATE simulation, you need three ingredients. First, a voxel dose map that covers the anatomy. Second, a label map or structure definition that tells you which voxels belong to each organ. Third, a way to combine these two pieces of information, typically using external analysis tools such as Python or ROOT. GATE itself focuses on producing accurate dose per voxel. The grouping by organ is usually performed after the simulation, using the organ masks that come from CT segmentation, RT structure sets, or pre defined phantom labels.
In radionuclide therapy, organ dose is often compared between different candidate treatment plans or activity distributions. Critical organs such as kidneys, liver, or red marrow have tolerance limits. The organ averaged dose derived from the voxel map is used to check whether a planned administered activity will keep all organ doses within acceptable ranges. This is also where the uncertainty on each voxel dose plays a role, since it propagates into an uncertainty on mean organ dose.
Organ dose can also be described using dose volume information, in particular dose volume histograms. These histograms are built by grouping the voxel doses belonging to an organ into bins and plotting the cumulative volume that receives at least a given dose. From a GATE voxel dose map, you can construct such histograms by selecting all voxels for one organ, reading their dose values, and then computing the corresponding distribution. The resulting curves provide a more detailed view than a single average dose, for instance allowing detection of hot spots inside an organ.
Finally, when interpreting organ dose from internal dosimetry simulations, always keep in mind how realistic the input activity distribution and the anatomical model are. The physics scoring of dose in GATE is consistent with the Monte Carlo transport, but the clinical relevance of organ dose values depends on how accurately the simulated activity represents the real patient and on the assumptions used in image to activity conversion.
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