KAHIBARO
15.1. Energy Deposition
Table of Contents
Energy deposited in matter
When ionizing radiation passes through matter, it transfers part or all of its kinetic energy to the material. This transferred energy is called energy deposition. In GATE, as in Geant4, this process is followed step by step: each time a particle moves through a small segment of its track, interactions can occur and a certain amount of energy is deposited in the surrounding medium.
At the microscopic level, energy deposition happens through many small physical processes such as ionization and excitation for charged particles, or photoelectric absorption and Compton scattering for photons. You do not configure these processes in detail in this chapter, since they are part of physics lists, but it is important to understand that each individual interaction contributes a small amount of deposited energy, denoted by $dE$.
In a Monte Carlo simulation like GATE, the track of each particle is divided into steps. For each step $i$ in a given volume, the simulation calculates a step length $\Delta s_i$ and an associated deposited energy $\Delta E_i$. Even if a particle leaves the volume, only the energy deposited inside that specific volume is accounted for in that volume. The total energy $E_{\text{dep}}$ deposited by a particle in one volume is the sum over all its steps in that volume,
$$
E_{\text{dep}} = \sum_{i=1}^{N_{\text{steps}}} \Delta E_i.
$$
Most actors that deal with energy in GATE do not track energy for single particles. Instead, they accumulate deposited energy over many events. If $N_{\text{events}}$ primary particles are simulated and the deposited energies from all events are added, the total energy deposited becomes
$$
E_{\text{tot}} = \sum_{j=1}^{N_{\text{events}}} E_{\text{dep},j}.
$$
For dose calculations, the absolute value of this total energy is less intuitive than the energy per unit mass, which defines absorbed dose and is covered in the next subchapter of the course. In this chapter, the focus is simply on how GATE represents and accumulates deposited energy.
In a typical GATE simulation, energy deposition can be recorded in different ways. A hit collection records individual interaction steps, often including the deposited energy for each hit. An energy deposition actor can sum energies over an entire volume or a set of volumes. These tools allow you to examine how energy is distributed spatially inside your geometry.
Because GATE is unit aware, you must specify energies with explicit units. For example,
$$
1\ \text{MeV} = 10^6\ \text{eV}.
$$
If you forget the unit or mix units, your deposited energies and any derived quantities will be incorrect.
To interpret deposited energy as a physical quantity, it is important to relate it to the material and mass of the region where the energy is deposited. Dense materials, such as bone or detector crystals, will typically show larger energy deposition per unit path length compared to less dense materials such as lung. This dependence is handled automatically by the physics models, but when you inspect simulation results you should always remember that both the energy of the particles and the properties of the material influence how much energy is deposited.
Because Monte Carlo simulations use random sampling, the total deposited energy will fluctuate from one simulation run to another, especially if the number of primary particles is small. As you increase the number of events, these random fluctuations decrease, and the energy deposition results become more stable and more representative of the physical expectation.
Finally, keep in mind that in GATE you can restrict energy deposition scoring to selected regions of your geometry. This is useful when you want to focus on, for example, a tumor region, a detector element, or a specific organ in a patient model. In practice, you attach energy deposition or dose actors to the volume of interest and let them accumulate the energy deposited there during the simulation.
In GATE, energy deposition in a volume is obtained by summing all step-wise deposited energies $\Delta E_i$ of all particles inside that volume:
$$
E_{\text{dep}} = \sum_{i} \Delta E_i.
$$
Always specify energies with explicit units, such as 1 * MeV in Python, to avoid incorrect deposited energy values.
Voxel energy deposition
For many medical physics applications, energy deposition must be known not just in an entire organ or detector block, but with fine spatial detail inside a three-dimensional region. GATE handles this by dividing space into small volume elements, called voxels. Each voxel is a small rectangular box with its own material and mass. Voxel energy deposition is the process of accumulating the deposited energy separately in each voxel.
Conceptually, the volume of interest is divided into a regular 3D grid along the $x$, $y$, and $z$ directions. If the number of voxels in each direction is $N_x$, $N_y$, and $N_z$, their physical dimensions are
$$
\Delta x = \frac{L_x}{N_x}, \quad
\Delta y = \frac{L_y}{N_y}, \quad
\Delta z = \frac{L_z}{N_z},
$$
where $L_x$, $L_y$, and $L_z$ are the physical lengths of the grid in each direction. The volume of one voxel is then
$$
V_{\text{voxel}} = \Delta x \, \Delta y \, \Delta z.
$$
During the simulation, every time a particle takes a step, GATE determines in which voxel that step occurs and adds the step-wise deposited energy $\Delta E_i$ to the corresponding voxel bin. If a step crosses multiple voxels, the simulation splits the step into substeps so that the energy is attributed correctly to each voxel.
You can think of voxel energy deposition as filling a 3D image, where each pixel in 2D becomes a voxel in 3D, and the value stored in each voxel is the total deposited energy for that small region. In practice, GATE often writes this information to an image file format such as MHD or NIfTI, which you can later analyze or visualize with external tools.
The following table summarizes the typical relationship between grid parameters and energy deposition per voxel:
| Quantity | Symbol | Description |
|---|---|---|
| Number of voxels in $x$ | $N_x$ | Grid size along $x$ |
| Number of voxels in $y$ | $N_y$ | Grid size along $y$ |
| Number of voxels in $z$ | $N_z$ | Grid size along $z$ |
| Voxel dimensions | $\Delta x, \Delta y, \Delta z$ | Physical size of each voxel |
| Voxel volume | $V_{\text{voxel}}$ | $\Delta x \Delta y \Delta z$ |
| Deposited energy in voxel | $E_{\text{voxel}}$ | Sum of all $\Delta E_i$ in that voxel |
In a voxelized phantom derived from a CT image, each voxel may have a different material and density. This affects how much energy particles deposit in different regions even if the incident radiation field is uniform. For example, a photon beam that traverses bone, lung, and soft tissue will produce a nonuniform pattern of voxel energy deposition due to differences in attenuation and scattering.
In GATE, voxel energy deposition is usually obtained with an image-type actor such as a dose actor or an energy deposition actor configured with a 3D grid. Even if you are interested mainly in absorbed dose, the first step is always voxel energy deposition. The dose for each voxel is then calculated from that energy using the voxel mass, which depends on the material and density assigned to the voxel.
It is essential to choose an appropriate voxel size. If voxels are too large, fine details in the energy deposition pattern will be blurred. If voxels are too small, the number of particles per voxel may be low, which increases statistical noise, and the simulation may become slow or memory intensive. In practice, voxel size is often chosen to match or be similar to the resolution of the underlying CT or phantom data.
Statistical uncertainty is particularly important for voxel energy deposition. Because each voxel covers a small volume, only a fraction of the simulated particles will interact in that voxel. As a result, voxel values can fluctuate significantly if the number of events is not high enough. To reduce these fluctuations, you can increase the number of primary particles, use variance reduction techniques when appropriate, or focus scoring only on regions of interest.
When you analyze voxel energy deposition, you often compute line profiles and region averages. A line profile extracts the voxel values along a straight line, for example along the central axis of a beam. A region average computes the mean deposited energy in a selected volume, such as a tumor or an organ at risk. These operations do not change the underlying scoring, they only process the 3D grid values after the simulation.
In a medical context, voxel energy deposition is the fundamental quantity from which absorbed dose distributions are derived. For each voxel $k$, with deposited energy $E_k$ and mass $m_k$, the absorbed dose $D_k$ is
$$
D_k = \frac{E_k}{m_k},
$$
expressed in gray when $E_k$ is in joules and $m_k$ in kilograms. This relationship, and the interpretation of dose, is developed further in the next chapter of the course. Here it is sufficient to remember that accurate voxel energy deposition is the necessary first step for any voxel-based dose calculation.
For a voxel grid, GATE accumulates deposited energy per voxel:
$$
E_k = \sum_{i \in k} \Delta E_i,
$$
where the sum runs over all steps $i$ that occur inside voxel $k$. Correct voxel dimensions and material definitions are essential, because they determine both the spatial resolution and the mass used later to convert $E_k$ to dose.
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