KAHIBARO
Particle Fluence
Table of Contents
Particle distributions
Particle fluence in GATE describes how particles are distributed as they pass through or intersect a region of space. Instead of focusing on energy deposition or dose, fluence counts how many particles cross a surface or are present in a volume and how this number varies with position, direction, or energy. For beginners it is helpful to keep in mind that fluence is about “how many particles go where,” not “how much energy they leave behind.”
In GATE, particle fluence is measured with a dedicated actor that you attach to one or more volumes in your geometry. Conceptually, you decide which region of space you want to monitor, for example a plane in front of a detector or a surface inside a phantom, and the fluence actor records information for every simulated particle that passes through or interacts in that region. Because this is an actor, you configure it in the same way as other actors, using the simulation object, selecting a volume, and choosing what should be scored.
There are several closely related ideas behind particle distributions. The most basic is spatial distribution, which tells you how fluence varies from point to point. In practice, you divide the region of interest into pixels for surfaces or voxels for volumes and count how many particles enter each element. Over many simulated events this builds up a map of where the particle field is strong and where it is weak. You can use this to check uniformity of a beam, to locate alignment problems in a scanner, or to understand shielding effects.
A second aspect is angular distribution. Even if the fluence is spatially uniform, the directions of the particles may not be. For example, an ideal broad beam might have all particles moving in nearly the same direction, while scattered particles in a phantom arrive from many angles. In GATE, fluence actors can often record directional information for each recorded particle so that you can later create angular histograms, for instance distributions in polar angle and azimuthal angle. This helps you separate primary, forward-going particles from wide-angle scattered particles.
Energy distribution is another important facet of particle fluence. Instead of simply counting each particle equally, you can bin particles by their kinetic energy when they pass through the scoring region. The result is an energy spectrum associated with a given spatial region. For example, you might observe a narrow peak around a nominal beam energy for unscattered photons or protons, and a broad low-energy tail from scattered particles. When configured appropriately, the fluence actor will write out per-particle energy information so that you can analyze these spectra with external tools.
Because GATE is a Monte Carlo toolkit, all these distributions come with statistical uncertainties. The number of particles counted in each bin follows counting statistics, and bins with few counts are less reliable. If you need smoother, more precise fluence distributions then you must run more histories, that is simulate more primary particles or longer acquisition times, until the statistical noise is acceptable for your purpose.
In many applications, particle fluence is an intermediate quantity that links the incident radiation field to other quantities of interest. For example, in imaging, the fluence at the front of a detector helps you understand detector count rates and saturation. In dosimetry, the particle fluence inside a region, combined with cross section information, can be used to estimate energy deposition and dose. GATE does not automatically convert fluence into dose within the fluence actor itself, but having accurate spatial, directional, and energy distributions is a crucial prerequisite for such calculations.
To work effectively with particle distributions, you typically decide up front what needs to be recorded. If the goal is a 2D fluence profile across a detector, you might configure the actor to score fluence on a plane with modest spatial resolution and record position and energy. If, instead, you want a 3D picture of fluence in a phantom, you might define a voxel grid in a volume and record positions and particle types. Recording too much detailed information can increase file sizes and slow down analysis, so it is useful to limit the scored attributes to what you actually need.
Finally, fluence distributions are often interpreted alongside other actor outputs. For example, you may compare a fluence map at the entrance of a water phantom with a dose map inside the phantom to understand how the entrance field translates into an internal dose distribution. Although different actors perform these measurements, consistent use of geometry and units makes it possible to line up the results and interpret them together.
In GATE, particle fluence describes how many particles pass through or are present in a region, as a function of position, direction, or energy. It is a distribution of particle counts, not a measure of energy deposition or absorbed dose.
Fluence maps
A fluence map is a spatial representation of particle fluence in a chosen region, typically arranged as a 2D or 3D grid of bins. Each bin contains the number of particles that have crossed that small element of area or volume during the simulation. In its simplest form a fluence map is like an image where pixel intensity encodes how many particles have passed through that location. This visual form makes it much easier to understand complex particle fields than by looking at individual particle records.
In GATE, you obtain fluence maps by configuring the fluence actor with a discretization that matches your physical problem. For a beam that irradiates a flat surface, it is natural to create a 2D map over a plane. You specify the plane’s size and the number of bins along each axis so that the actor implicitly defines a regular grid of pixels. During the simulation, each particle that is recorded by the actor is assigned to one of these pixels based on its position when it crosses the plane, and the corresponding count is incremented. The result is a matrix of counts that you can write to an output file and display as an image.
For volumetric analysis you can set up a 3D fluence map within a selected volume, for instance inside a phantom or around a detector. Here the actor divides the volume into voxels and accumulates counts in each. Volumetric fluence maps are useful when you want to see how a field evolves as it penetrates matter, such as a beam passing through layers of tissue or shielding. The map then shows not just entrance fluence but how the spatial distribution changes deeper inside the object.
Different visualization approaches can highlight different aspects of a fluence map. Displaying raw counts reveals absolute differences, but in many cases it is informative to normalize by the total number of simulated primaries or by the area or volume of each bin. This gives a normalized fluence per primary that is independent of the number of events you ran. If the simulation parameters are known, such normalized maps can even be converted into physical units of fluence, typically expressed as particles per unit area.
Table 1 illustrates the conceptual structure of a simple 2D fluence map for a square plane discretized into pixels.
| Pixel index (i, j) | Physical position (x, y) | Counts in pixel | Normalized fluence |
|---|---|---|---|
| (0, 0) | lower left corner | $N_{00}$ | $N_{00} / N_\text{prim}$ |
| (i, j) | inside the field | $N_{ij}$ | $N_{ij} / N_\text{prim}$ |
| (N\_x-1, N\_y-1) | upper right corner | $N_{N_x-1,N_y-1}$ | $N_{N_x-1,N_y-1} / N_\text{prim}$ |
Here $N_\text{prim}$ is the total number of primary particles simulated. By working with normalized values, you can more easily compare maps from simulations with different numbers of events or different acquisition times.
Fluence maps also carry implicit statistical information. Each bin has a count $N_{ij}$ that is subject to statistical fluctuations. If you interpret the counting process as Poisson, then the standard deviation in a bin is approximately $\sqrt{N_{ij}}$. This means that bins with low counts have high relative uncertainty. When analyzing fluence maps, you often smooth images or average symmetrically equivalent regions to reduce noise and reveal underlying structure. However, any postprocessing should respect the discrete nature of the data and the binning you chose in GATE.
You can build more specialized fluence maps by adding selection criteria through actor filters. For instance, you may want a fluence map of only primary photons, excluding scattered photons. In that case you configure the actor to record only particles that meet certain conditions, such as particle type, energy range, or interaction history. The resulting map then represents a restricted subset of the fluence, which can be compared with a map of all photons to understand the contribution of scatter or secondary particles.
In imaging applications, fluence maps at different planes or angles provide a powerful way to verify scanner geometry and acquisition settings. For a PET or SPECT camera, a fluence map just in front of the detector can reveal whether the collimator or shielding blocks parts of the field as expected. Regions with unexpectedly low fluence might point to mispositioned components. Similarly, fluence maps behind a collimator show the pattern of transmitted photons that the crystal should detect, which is useful during system design and troubleshooting.
In therapy simulations, entrance fluence maps at the surface of a phantom or patient model allow you to check the shape and intensity profile of therapeutic beams before analyzing dose. For example, the flat region and penumbra of a photon beam can be inspected visually as a 2D fluence map at a reference plane. Later, fluence maps at several depths can be compared with dose maps to see how the beam evolves and deposits energy.
Once GATE has written fluence map data, you usually analyze it with external tools, such as Python or ROOT. You can read the binned counts into arrays, plot them as images with color scales, compute profiles along selected lines, or integrate over regions of interest. These operations make fluence maps a bridge between raw Monte Carlo particle transport and practical performance metrics, such as field uniformity, beam alignment, and effective irradiated area.
A fluence map is a binned spatial representation of particle fluence, where each pixel or voxel stores the number of particles recorded in that small region. Choosing appropriate binning, normalizing by the number of primaries, and considering counting statistics are essential for meaningful interpretation.
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