KAHIBARO
5.5. Radioactivity Units
Table of Contents
`Bq`
In GATE, all radioactive source strengths are expressed in activity units that are consistent with the SI system. The fundamental activity unit is the becquerel, written in code and configuration files as Bq. Activity measures how many nuclear decays happen per unit time. By definition, an activity of 1 becquerel means that, on average, there is one nuclear decay every second:
$$1 \,\text{Bq} = 1 \,\text{decay per second}$$
In medical physics, you rarely simulate a source as weak as 1 Bq, but this unit is the base from which larger units are built. In a GATE simulation, when you define the activity of a source, you typically write something like:
source.activity = 1e6 * Bq
Here, Bq is the unit imported from GATE or Geant4 units. The numeric factor in front is in pure SI, so 1e6 * Bq means a source activity of one million decays per second.
You can think of the activity as the rate at which primary particles are generated by the radioactive decay process. Internally, GATE uses this activity together with the simulated time interval to decide how many decays occur during your run. This means that if you double the activity, with the same simulated acquisition time, you will approximately double the total number of emitted particles.
The fact that 1 Bq is a very small activity is important conceptually. Clinical imaging and therapy typically use activities millions or billions of times larger, so it is convenient to use prefixes that group many becquerels into a single, more readable number. Before introducing those, it is useful to remember that activity is a rate, not a total count. If you run your simulation for a simulated time $\Delta t$, and your source activity is $A$, the expected number of decays $N$ is approximately:
$$N = A \cdot \Delta t$$
For example, a source with $A = 1000 \,\text{Bq}$ simulated over $\Delta t = 10 \,\text{s}$ will produce on average $N = 10{,}000$ decays.
Key rule: In GATE, always specify source strengths using activity units like Bq, kBq, or MBq. Never confuse activity (decays per second) with the number of simulated events, which is configured separately.
`kBq`
Clinical and preclinical simulations often require activities much higher than a few becquerels. The kilobecquerel, written as kBq, is one thousand becquerels:
$$1 \,\text{kBq} = 10^3 \,\text{Bq}$$
and therefore
$$A \,\text{kBq} = A \cdot 10^3 \,\text{Bq}$$
for any activity value $A$.
In GATE configuration, you typically write:
source.activity = 500 * kBqThis means the source has an activity of $500 \times 10^3 = 5 \times 10^5$ Bq, so on average half a million decays per second.
The use of kBq is common for small laboratory sources, calibration sources, or low-activity preclinical imaging studies. In practice, your choice of prefix does not change the physics at all, it only affects readability and helps you avoid mistakes when entering large or very small numbers. For instance, the two following lines are equivalent:
source.activity = 2e5 * Bq
source.activity = 200 * kBqThe second version is easier to read and compare with activity values reported in literature, which are often given in kBq or MBq.
When planning a simulation, it can be helpful to connect activity in kBq to the total number of decays over a typical acquisition time. For example, for a 10-minute (600 second) acquisition with a 250 kBq source, the expected number of decays is:
$$N = 250 \,\text{kBq} \times 600 \,\text{s} = 250 \times 10^3 \,\text{Bq} \times 600 \,\text{s} = 1.5 \times 10^8 \text{ decays}$$
If you actually simulate 1.5 × 10^8 events, the run may be long. In practice, you often simulate a smaller number of decays and then scale your results, a topic that is treated in more detail in later chapters on dose and statistical analysis. What matters here is to understand that kBq is simply a scaled version of Bq, and you can move between them by powers of ten.
A compact way to remember the relationship is summarized here:
| Unit | Definition | Meaning |
|---|---|---|
| Bq | $1$ decay per second | Base unit |
| kBq | $10^3$ Bq | 1,000 decays per second |
Important conversion:
$$1 \,\text{kBq} = 1000 \,\text{Bq}$$
Always check that your code uses the correct power of ten when converting between Bq and kBq.
`MBq`
In nuclear medicine imaging, the most common activity unit is the megabecquerel, written as MBq in both clinical reports and GATE simulations. One megabecquerel is one million becquerels:
$$1 \,\text{MBq} = 10^6 \,\text{Bq}$$
so in general
$$A \,\text{MBq} = A \cdot 10^6 \,\text{Bq}$$
Activities administered to patients for PET and SPECT studies are typically in the range of a few to several hundred MBq. In GATE scripts, you specify these activities using the MBq unit, for example:
source.activity = 370 * MBqThis line represents a source with $370 \times 10^6$ decays per second, which is a realistic value for a clinical PET injection at scanner start. A similar activity for SPECT might be written as:
source.activity = 740 * MBq
The advantage of MBq is that it keeps numbers in a human friendly range. Without the prefix, the same examples would require you to write very large numbers:
source.activity = 3.7e8 * Bq # 370 MBq
source.activity = 7.4e8 * Bq # 740 MBq
Using MBq makes your simulation configuration easier to read and reduces the risk of accidentally adding or removing zeros.
In time-dependent simulations, the combination of MBq and acquisition duration gives quick insight into the total number of decays. For instance, if you simulate a 20 minute (1200 second) PET acquisition of a 200 MBq source, the expected number of decays is:
$$N = 200 \,\text{MBq} \times 1200 \,\text{s} = 200 \times 10^6 \times 1200 = 2.4 \times 10^{11} \text{ decays}$$
Simulating this exact number of events is typically not feasible. Instead, you choose a manageable number of primary events in the simulation, say $10^7$ or $10^8$, and later scale the results by the ratio between the simulated decays and the physical decays. This is one reason why using the correct units in your activity definition is crucial, since any factor-of-ten error in MBq will propagate directly into your scaled doses or expected count rates.
To connect all three frequently used activity units, it is useful to remember:
| Unit | Relation to Bq | Relation to kBq |
|---|---|---|
| Bq | $1$ Bq | $10^{-3}$ kBq |
| kBq | $10^3$ Bq | $1$ kBq |
| MBq | $10^6$ Bq | $10^3$ kBq |
In GATE, Bq, kBq, and MBq are predefined constants. You should never attempt to define your own activity units. Instead, always import the provided units and multiply by the numerical activity that you want.
For example, a source activity line in GATE might be:
source.activity = 50 * MBqor, if you wish to express the same value in kBq:
source.activity = 50000 * kBqBoth are equivalent, but the MBq version is usually preferred in clinical contexts.
Key relations for activity units:
$$1 \,\text{kBq} = 10^3 \,\text{Bq}$$
$$1 \,\text{MBq} = 10^6 \,\text{Bq} = 10^3 \,\text{kBq}$$
When configuring radioactive sources in GATE, always double check that you have chosen the correct prefix (Bq, kBq, MBq) to match your intended clinical or experimental activity.
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