KAHIBARO
11.2. Medical Radionuclides
Table of Contents
F-18
Fluorine 18, written as $^{18}\text{F}$, is the workhorse radionuclide in clinical PET. It is a positron emitter with a physical half life of about 109.7 minutes. In GATE simulations, $^{18}\text{F}$ is most often used to model PET imaging with FDG or similar tracers.
From a simulation point of view, there are several key properties to remember. First, $^{18}\text{F}$ decays almost exclusively by positron emission. The endpoint positron energy is about 0.635 MeV, and the mean positron energy is significantly lower. This relatively low positron energy leads to a short positron range in tissue, which is important for spatial resolution in PET simulations. Second, each decay produces two 511 keV annihilation photons, which are the main signal detected by the PET scanner.
In GATE, you usually do not define the positron spectrum by hand. Instead, you select $^{18}\text{F}$ as a radionuclide in the source configuration, and let the radioactive decay physics handle the beta spectrum, positron transport, and annihilation. When you configure a PET source, you can choose between a simple annihilation photon source at 511 keV or a full $^{18}\text{F}$ decay source. The full decay is more realistic, because it includes the positron range and any extra radiation, but it is also more computationally expensive.
A common task is to convert clinical activity levels into simulation parameters. For example, if you simulate an FDG injection, you might specify an activity $A$ in MBq and a total acquisition time $T$. The total expected number of decays is then $N \approx A \, T$ if you ignore decay during the scan, or you use the full decay law otherwise.
For an $^{18}\text{F}$ source, the activity decays according to
$$A(t) = A_0 e^{-\lambda t}, \quad \lambda = \frac{\ln 2}{T_{1/2}}, \quad T_{1/2} \approx 109.7\ \text{min}.$$
Always specify the correct half life if you use time dependent activity in GATE.
When building PET simulations with $^{18}\text{F}$, you often generate activity distributions inside phantoms or voxelized patient images. In that case, each voxel contains a local $^{18}\text{F}$ activity density. GATE then samples decay positions according to this distribution, and the $^{18}\text{F}$ decay physics defines how many positrons and annihilation photons are produced and where they go.
C-11
Carbon 11, or $^{11}\text{C}$, is another positron emitter used in PET, especially in research tracers such as $^{11}\text{C}$-raclopride or $^{11}\text{C}$-PiB. Its key feature is a very short physical half life of about 20.3 minutes. This has important implications when you simulate time dependent activity or dynamic PET acquisitions.
Like $^{18}\text{F}$, $^{11}\text{C}$ decays predominantly by positron emission and produces two 511 keV annihilation photons. The positron endpoint energy is higher than for $^{18}\text{F}$, about 0.96 MeV, which means a somewhat longer positron range and a slightly worse intrinsic spatial resolution. In GATE, if you activate detailed positron transport, these differences can become visible in the spatial blurring of the reconstructed image.
Because of the short half life, $^{11}\text{C}$ activity changes significantly over minutes. If you simulate multi frame or dynamic studies with $^{11}\text{C}$, you should pay attention to how GATE handles time windows and source activity. When you configure a time dependent source, GATE can sample decays according to the exponential law, but you must provide consistent start times, end times, and initial activity.
For $^{11}\text{C}$, the decay constant is
$$\lambda = \frac{\ln 2}{T_{1/2}}, \quad T_{1/2} \approx 20.3\ \text{min}.$$
Over a 60 minute scan, the activity decreases by a factor of more than 7. You must account for this if you compare simulated count rates between early and late time frames.
In practice, when you choose between $^{11}\text{C}$ and $^{18}\text{F}$ in GATE, the configuration steps are similar. You select the nuclide name, define the spatial activity distribution, and let the radioactive decay physics handle the details. The main difference is in the time scale of the simulation, the count rates, and the effect of the higher positron energy on resolution.
Ga-68
Gallium 68, or $^{68}\text{Ga}$, is a positron emitter commonly used with generator based tracers such as $^{68}\text{Ga}$-DOTATATE or $^{68}\text{Ga}$-PSMA. It has a physical half life of about 67.7 minutes, which lies between $^{11}\text{C}$ and $^{18}\text{F}$. For GATE simulations, $^{68}\text{Ga}$ is important because it combines relatively high positron energy with additional gamma emissions.
The positron endpoint energy of $^{68}\text{Ga}$ is around 1.9 MeV, significantly higher than for $^{18}\text{F}$. This leads to a longer positron range in tissue and more image blurring at the fundamental physical level. If you simulate detailed PET resolution or small animal imaging with $^{68}\text{Ga}$, this effect can be relevant and should be included by using full decay and transport physics.
In addition to the positron decay, $^{68}\text{Ga}$ emits prompt gamma rays at characteristic energies. These photons can interact in the detector and contribute to scatter and random coincidences. If you use a simplified source that only emits 511 keV photons, you will miss these contributions. A full $^{68}\text{Ga}$ decay model in GATE automatically includes the prompt gammas and their impact on detector hits and coincidence data.
In a GATE configuration, you choose $^{68}\text{Ga}$ as the radionuclide and specify the activity and spatial distribution. Depending on your physics list, the radioactive decay module will take care of beta spectra and gamma lines. If you are interested in quantifying scatter fractions or randoms in $^{68}\text{Ga}$ PET imaging, it is important to verify that the selected physics list includes radioactive decay and atomic deexcitation processes.
For $^{68}\text{Ga}$ PET simulations, using a simple 511 keV photon source underestimates scatter and randoms, because it neglects prompt gamma emissions. Use full $^{68}\text{Ga}$ decay if you study image quality, scatter fraction, or quantitative accuracy.
Tc-99m
Technetium 99m, written $^{99\text{m}}\text{Tc}$, is the principal radionuclide in SPECT imaging. It is a pure gamma emitter for practical purposes, with a dominant photon energy of about 140 keV and a half life of about 6.02 hours. In contrast to PET radionuclides, $^{99\text{m}}\text{Tc}$ does not produce positrons, so there are no annihilation photons.
For GATE simulations of gamma cameras or SPECT systems, $^{99\text{m}}\text{Tc}$ is typically the default choice. The 140 keV photons interact strongly in collimators, scintillation crystals, and shielding, which means that collimator design and attenuation play a major role. When you configure a $^{99\text{m}}\text{Tc}$ source in GATE, you usually define a spatial activity distribution that matches a phantom or patient organ distribution, and then let each decay produce a 140 keV photon.
Depending on the chosen decay model, $^{99\text{m}}\text{Tc}$ can emit photons at several energies, but 140 keV dominates SPECT imaging. In your simulation, you will often set an energy window around this photopeak, for example 20 percent wide, to select mostly photoelectric interactions in the crystal and reduce scatter. To evaluate energy resolution and scatter performance, you must simulate the full photon transport through the collimator and into the crystal.
The half life of 6 hours is long enough that, for typical acquisition times of a few minutes, activity can be considered almost constant. This simplifies many SPECT simulations, because you can often ignore time dependent decay within a single projection view. For multi hour or dynamic studies, you should still use the exponential decay law to adjust activity over time.
In SPECT simulations with $^{99\text{m}}\text{Tc}$, the key photon energy is
$$E_\gamma \approx 140\ \text{keV}, \quad T_{1/2} \approx 6.02\ \text{h}.$$
Always set your energy window and detector energy resolution relative to this 140 keV photopeak.
When you validate a GATE model of a gamma camera, you often compare simulated $^{99\text{m}}\text{Tc}$ energy spectra, spatial resolution, and sensitivity with experimental measurements. Accurate collimator geometry, material definitions, and gamma physics are crucial in this context.
I-131
Iodine 131, or $^{131}\text{I}$, is a beta minus and gamma emitter widely used in radionuclide therapy, for example thyroid ablation, and sometimes in diagnostic imaging. It has a relatively long half life of about 8.02 days. From a GATE perspective, $^{131}\text{I}$ is particularly important for internal dosimetry and for simulations that combine therapy and imaging.
The beta minus emissions of $^{131}\text{I}$ have mean energies of a few hundred keV and maximum energies around 0.6 to 0.8 MeV, depending on the decay branch. These electrons deposit energy locally and are the main contributors to absorbed dose in targeted tissues. At the same time, $^{131}\text{I}$ emits gamma photons, with a prominent line at about 364 keV and several others. These gammas can be imaged with gamma cameras, but they also contribute to dose in surrounding organs.
In GATE, when you configure an $^{131}\text{I}$ source for dosimetry, it is important to include both beta and gamma emissions. A full radioactive decay model ensures that electrons and photons are generated with the correct energy spectrum and branching ratios. You can then score energy deposition and dose in voxelized phantoms or organ regions. If you limit the simulation to photons only, you will underestimate local dose in the source region.
Because $^{131}\text{I}$ has a long half life, internal dose builds up over days. In many Monte Carlo studies, you separate space and time. You simulate the energy deposited per decay, and then you use analytical formulas or external calculations to integrate over the full time activity curve. In more detailed dynamic simulations, you might change the activity distribution over time, for example to represent biological clearance from organs.
For dosimetry with $^{131}\text{I}$, the total absorbed dose $D$ is often computed from the energy deposited per decay and the total number of decays:
$$D = \frac{E_{\text{dep, per decay}} \times \tilde{N}}{m}, \quad \tilde{N} = \int_0^\infty A(t)\, dt.$$
Here $m$ is the mass of the target region, and $A(t)$ follows the combined physical and biological decay.
In SPECT imaging with $^{131}\text{I}$, the higher gamma energy around 364 keV affects collimator design and penetration. If you use GATE to simulate $^{131}\text{I}$ imaging, you must ensure that the collimator material and thickness are appropriate for this higher energy, and that your physics list correctly models gamma interactions at several hundred keV.
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