KAHIBARO
10.6. Source Activity
Table of Contents
Activity
In GATE, the activity of a source connects the physical radioactive strength of your source to how many particles are simulated. Activity $A$ describes how many decays happen per second. Its SI unit is the becquerel, with $1 \,\text{Bq} = 1$ decay per second. In medical applications, you will more often use kBq, MBq, or GBq.
When you configure a source in GATE, you typically specify its activity together with a total acquisition or simulation time. GATE then uses these values to decide how many decays to simulate. The core physical relation is
The link between activity, time, and number of decays is
$$ N = A \times T $$
where
$N$ is the expected number of decays,
$A$ is the activity,
$T$ is the acquisition time.
You should always pay attention to units when setting the activity and time. For example, if you want to simulate a $10 \,\text{MBq}$ source for $60 \,\text{s}$, you are describing an expected number of decays
$$ N = 10 \times 10^6 \,\text{s}^{-1} \times 60 \,\text{s} = 6 \times 10^8 \,\text{decays}. $$
You will almost never simulate all of these decays, because that would be computationally expensive. Instead, you choose a smaller number of simulated events and interpret them statistically as representing the full physical acquisition. The idea of scaling real activity to a manageable number of simulated events is essential in Monte Carlo simulation.
GATE allows different ways to control how activity is used. You can set a constant activity over the entire acquisition, or you can define a time dependent activity profile, for example to mimic radioactive decay or changes in injected activity. In this chapter, focus on the static case: a source with a fixed activity during a fixed acquisition time.
It is also important to understand that in a radioactive source, activity refers to decays, not directly to emitted particles. A single decay may produce one, two, or more emitted particles depending on the radionuclide and decay scheme. GATE uses the physics of the radionuclide to convert decays into individual particles.
Number of particles
In GATE, the basic unit of simulation is an event. For a radioactive source, an event usually corresponds to a single nuclear decay. Each decay produces zero, one, or several particles that are then transported. When you think about how many particles will appear in your simulation, you must distinguish between the number of decays and the number of emitted particles.
If an event represents one decay, then the expected number of decays $N$ during a time $T$ with activity $A$ is
$$ N = A \times T. $$
The number of emitted particles depends on the decay scheme. For example, a positron emitter may create a positron, which in turn annihilates and produces two 511 keV gammas. In this case, one decay can produce multiple tracked particles. GATE handles this automatically through its physics models, so you usually control only the number of decays or events.
There are two main ways you will see the number of particles controlled:
- By specifying an activity and simulation time. GATE computes the corresponding number of decays based on $N = A \times T$. Internally, it samples decay times over the acquisition interval and generates events accordingly.
- By specifying directly the number of primaries or events to simulate. Here you say how many particles, or how many decays, you want GATE to generate, regardless of any physical activity. You then interpret this number relative to the physical activity you want to model.
These two approaches can be combined conceptually. If you choose a certain number of simulated decays $N_{\text{sim}}$ to represent a real acquisition with expected decays $N_{\text{real}}$, then you can scale your results. For example, if $N_{\text{sim}}$ is one hundred times smaller than $N_{\text{real}}$, every simulated count statistically represents about 100 real counts. This scaling is used later when you analyze dose, count rates, or images.
When you set up a simulation, always keep this logical chain in mind:
- Decide the physical activity $A$.
- Decide the physical acquisition time $T$.
- Compute the expected number of decays $N = A \times T$.
- Decide how many decays $N_{\text{sim}}$ you can afford to simulate.
- Use the ratio $N_{\text{real}} / N_{\text{sim}}$ to scale your results if needed.
For absolute beginners, a practical workflow is to start from the number of events you want to simulate, for example $10^5$ or $10^6$ events, and then decide what combination of activity and time that should represent. This avoids extremely long simulations while still keeping a clear physical interpretation.
Simulation duration
The simulation duration, often called the acquisition time, defines how long the virtual experiment runs. Together with activity, it controls the expected number of decays in your model.
In a simple case with constant activity, the relation is again
$$ N = A \times T. $$
Here $T$ is the simulation duration. You choose $T$ based on the clinical or experimental scenario you want to reproduce. For instance, in PET you may have a 10 minute acquisition, so $T = 600 \,\text{s}$. In SPECT you may have multiple projections, each with its own acquisition time.
In GATE, the simulation duration is also used to define the time window over which source events are sampled. For a static source with constant activity, GATE will distribute event times uniformly over the interval from time zero to time $T$. These times then propagate to detector hits, singles, and coincidences, which allows time based analysis, such as coincidence timing or count rate calculations.
You must be careful to keep activity and duration consistent with the number of events you actually simulate. If you fix $T$ and $A$ to some realistic values but then simulate far fewer events than $N = A \times T$, your results will be statistically noisy, but still represent the chosen duration. If you instead keep $N$ fixed and change $T$, then you change the implied activity of the simulation.
You can think of three equivalent ways to specify your simulation:
- Fix $A$ and $T$, derive $N = A \times T$, and simulate $N$ decays.
- Fix $N$ and $T$, derive an implied activity $A = N/T$.
- Fix $A$ and $N$, derive an implied duration $T = N/A$.
GATE can operate with any of these combinations. For realistic medical physics simulations, it is usually most intuitive to fix $A$ and $T$ from the experimental setup, then select $N_{\text{sim}}$ as a fraction of $N$ that you can simulate in a reasonable time, and finally interpret results with the appropriate scaling.
The table below summarizes the relationships:
| Known quantities | Derived quantity | Formula |
|---|---|---|
| Activity $A$, time $T$ | Decays $N$ | $N = A \times T$ |
| Decays $N$, time $T$ | Activity $A$ | $A = N / T$ |
| Activity $A$, decays $N$ | Duration $T$ | $T = N / A$ |
Always check consistency between activity, number of simulated events, and simulation duration. Incorrect combinations can lead to unrealistic count rates or dose, even if the geometry and physics are correct.
In more advanced time dependent simulations, activity itself can change as a function of time, for example due to radioactive decay or moving sources. The same basic ideas apply, but $A$ becomes $A(t)$ and the total number of decays is obtained by integrating $A(t)$ over the acquisition interval. For now, keep the static case in mind and ensure you are comfortable with the simple relation between activity, number of particles, and simulation duration.
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