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11.5. Activity Distribution
Table of Contents
Uniform activity
In GATE, an activity distribution describes how radioactive decays are spatially distributed inside a source volume. For a uniform activity distribution, every point inside the chosen volume has the same activity density, usually expressed in Bq per unit volume. If the total activity is $A$ and the volume is $V$, the activity density is $a = A / V$. Conceptually, the probability that a decay occurs in a small volume element $dV$ is proportional to $dV$ itself.
In practice, you do not specify $a$ directly. Instead, you define a geometric shape and tell GATE to sample source positions uniformly inside it, then set the total activity or the number of primaries. Examples include a uniform point distribution inside a box, a cylinder, or a sphere. For medical imaging and dosimetry, uniform sources are often used for basic tests, scanner calibration, or to approximate phantoms that are filled with a homogeneous solution of a radionuclide.
For example, you might define a uniform activity distribution in a spherical phantom that represents a water-filled test object. GATE will then randomly choose decay positions within the sphere, each location being equally likely. Because the distribution is uniform, the expected number of decays per unit volume is the same everywhere inside the sphere.
Uniform activity has important implications for image quality and dosimetry studies. The resulting images or dose maps should ideally be uniform, apart from noise and edge effects. Deviations from uniformity in reconstructed images can be used to study scanner performance or reconstruction artifacts. Similarly, in dosimetry, a uniform activity inside a simple phantom is often used to validate dose calculation methods, since the expected dose distribution is smooth and symmetric.
When using uniform activity in GATE, it is important to carefully align the source volume with your geometry. If your radioactive source is defined as uniform in a box, but the box extends outside the intended phantom, you will simulate decays in air or other unwanted regions. Likewise, if the box does not fully cover the region you want to activity-fill, part of the phantom will remain without activity. Visualization tools help you check that the uniform activity volume truly matches the physical volume you intend to simulate.
In time dependent simulations, uniform activity means that, at any given time, the spatial pattern of activity is still constant inside the chosen region, while the global activity can decay according to the radionuclide half life. The spatial probability distribution is uniform, but the absolute rate of events changes with time.
In a uniform activity distribution, the probability density of decay positions is constant within the source volume and zero outside it. Small geometry mistakes can introduce unintended non uniform regions, so always verify that the defined source volume matches the desired physical region.
Localized activity
Localized activity refers to activity that is concentrated in a relatively small spatial region, rather than being spread throughout a larger volume. This can represent hot spots in a phantom, tumors in a patient, or specific organs that take up a radiopharmaceutical. In GATE, you model localized activity by choosing a small source volume or by using a more complex distribution that strongly favors certain positions over others.
The simplest approach is to define a compact geometric source volume at the location of interest. For example, you might place a small spherical source inside a larger water phantom to study how a tumor with high uptake appears in PET or SPECT images. Inside that small sphere, the activity distribution may still be uniform, but since the sphere is much smaller than the entire phantom, the overall activity pattern is localized.
Localized activity changes both imaging and dosimetric behavior compared with a uniform fill. In imaging simulations, a small hot region produces a high intensity area in the reconstructed image, which is useful for evaluating spatial resolution, partial volume effects, and quantification accuracy. In dosimetry simulations, localized activity leads to high dose gradients near the source, especially for short range emissions, and lower doses further away. This is important when you study organ doses or tumor to normal tissue dose ratios.
In more advanced cases, localized activity distributions are not described by simple shapes. Instead, they come from images, such as PET or SPECT activity maps, or from mathematical functions that describe how uptake changes with position. These topics are covered in more detail under voxelized geometries and internal dosimetry. Here, the key idea is that localized activity means the probability for a decay to occur is higher in some regions and lower or zero in others.
When specifying localized sources in GATE, positioning is critical. Small shifts in the source position can significantly alter measured response, especially for high resolution detectors or steep dose gradients. You should always verify the location of the source relative to detectors, phantoms, and any shielding you have defined. Visualization and inspection of output such as energy deposition maps can help confirm that the activity is where you expect it to be.
Localized activity can create very high local dose and steep gradients. To capture these accurately, use a sufficiently fine spatial resolution in actors that record dose or energy deposition, and always check that the small source region is placed correctly inside the geometry.
Multiple sources
Many practical simulations require more than a single activity distribution. Multiple sources let you superimpose different activity patterns, radionuclides, or emission characteristics within the same geometry. In GATE, you define several sources, each with its own geometry, activity or number of particles, and sometimes different particle or decay properties.
Multiple sources can represent several localized hot spots within a phantom, or a combination of a uniform background and embedded hot regions. For example, in SPECT you might simulate a uniform liver uptake plus one or more focal lesions with higher activity. In PET you can place multiple point or spherical sources at different positions to study detection efficiency as a function of location or to test how reconstruction handles multiple objects.
Each source can also correspond to a different radionuclide. This is important when simulating multi tracer imaging or radionuclide therapy combined with diagnostic imaging. Different radionuclides have different energy spectra and half lives, so defining them as separate sources allows GATE to handle their physics and time dependence correctly. When you combine them, the total activity at any point in space is the sum of contributions from all active sources.
Handling multiple sources introduces some practical considerations. You should decide how to allocate total activity among them, according to your experimental or clinical scenario. The rate of simulated events from each source is proportional to its assigned activity. If you want a strong hot spot over a lower background, you would assign a higher activity to the localized source and a lower activity density to the uniform background source.
It is also important to track which detected events come from which source, particularly when you analyze output data. GATE can store identifiers such as a source ID or event ID that allow you to filter results later. This is very useful when you want to separate contributions from background, lesions, or different radionuclides in the analysis phase.
Another frequent use of multiple sources is to approximate complex spatial distributions with a combination of simple ones. For instance, instead of building a detailed image based activity map, you might approximate an organ uptake by several overlapping spherical sources, each with a chosen activity. This approach is sometimes sufficient for basic sensitivity studies or for teaching purposes, and it is easier to set up than a full image based model.
When you simulate multiple sources that are active over time, you must consider possible time dependence, such as different start times or half lives. GATE can account for radioactive decay and acquisition duration, but you need to define consistent parameters so that the temporal behavior of each source matches your scenario.
With multiple sources, always keep track of:
- The activity assigned to each source.
- The spatial extent and position of each source volume.
- Any identifiers that let you separate their contributions in the output.
Inconsistent activity definitions or overlapping source regions can lead to incorrect overall activity distributions and misleading simulation results.
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