KAHIBARO
36.1. Radioactive Sources in the Body
Table of Contents
Activity distributions
In internal dosimetry, the key idea is that radioactive sources are located inside the body, not outside it as in external beam therapy. This means that dose is delivered from within organs and tissues, often over long periods of time, and usually with nonuniform patterns of activity. GATE simulations for internal dosimetry must therefore start from a clear description of how the activity is distributed in space and time.
An activity distribution describes how the radioactivity $A$ is spread throughout the body, usually in units of Bq per voxel or Bq per organ at a particular reference time. In practice, you will often have two main ways to define this distribution in GATE. The first is a simple analytic description, such as a uniform activity in a spherical tumor or a set of discrete point or volume sources. The second is an image based description, for example a 3D SPECT or PET activity map registered to a patient CT. The analytic approach is useful for basic studies or phantoms, while the image based approach is essential for realistic patient specific dosimetry.
Even before you implement anything in GATE, you should decide which level of realism you need. If you want to study generic behavior, it is sufficient to define a homogeneous activity in a simplified organ or phantom. If you aim at patient specific dose estimates, you will need a voxelized activity map. In that case, activity is stored per voxel such as $A_{ijk}$ at voxel indices $(i,j,k)$, together with a CT-based material map that defines which tissue is present at each voxel. GATE then uses this information to sample emission positions according to the local activity, so that regions with higher activity generate more decays.
For conceptual understanding, it helps to distinguish between source regions and target regions. A source region is where the radionuclide is located and where decays originate. A target region is where dose is scored. In internal dosimetry, source and target regions can be the same, for example a thyroid treated with I 131, or different, for example bone marrow dose from radionuclide in the blood. In GATE, this distinction is implemented by defining sources in the volumes that correspond to source regions, and dose actors in volumes that correspond to target regions. The same source distribution can then be used to score dose in several organs.
A practical challenge is the normalization of the simulated activity. GATE usually uses activity in Bq together with simulation time to determine how many decays to simulate. In internal dosimetry, the important quantity is often the total number of decays over a period of time. This is called the cumulated activity, usually written $\tilde{A}$, and it is the time integral of the activity. To connect a realistic patient measurement to a Monte Carlo simulation, you can choose a convenient reference time and activity at that time, run the simulation with a certain number of decays, and then rescale the resulting dose to match the desired cumulated activity. For example, you might simulate $N_{\text{sim}}$ decays of a radionuclide and obtain a dose per decay, then multiply this per decay dose by the total expected number of decays in the patient.
A common workflow for patient specific internal dosimetry with GATE is to start from a reconstructed SPECT or PET image that gives activity concentration in Bq per mL at some reference time. You then map this image onto a CT based geometry, convert each voxel to a material with a given density, and convert activity concentration to voxel activity by multiplying by voxel volume. The result is a 3D activity distribution that GATE can use directly. Although the detailed steps are covered in other chapters, at this stage the important point is that GATE is well suited for handling these nonuniform, patient derived distributions and for propagating them into realistic dose calculations.
In simple educational examples, you might instead assign a constant activity density to a volume, for instance a sphere representing a tumor. In that case, you define a total activity $A_0$ in the sphere, and assume that emission is homogeneous within its volume. This helps beginners understand basic relationships between activity, decay rate, and dose deposition without needing full imaging data. Regardless of the complexity, the core concept is the same: an activity distribution defines where and how often radioactive decays occur, and GATE uses that to drive the Monte Carlo tracking of emitted particles.
The activity distribution determines where decays occur and how often. In internal dosimetry, always treat it as a spatially and temporally varying source, not as a single number. Incorrect or inconsistent activity distributions lead directly to incorrect dose estimates.
Radionuclide decay
Once the activity distribution is defined, the next step in internal dosimetry is to understand how radionuclide decay controls the emission of radiation over time. Each radionuclide decays according to its own decay scheme and half life. For internal dosimetry, this means that the intensity of the source is not constant but decreases as a function of time, while at each decay a specific set of radiation types and energies is emitted.
The basic physical law of radioactive decay is that the activity $A(t)$ at time $t$ is related to the initial activity $A_0$ by the exponential law
$$
A(t) = A_0 e^{ - \lambda t },
$$
where $\lambda$ is the decay constant. The decay constant is related to the physical half life $T_{1/2}$ of the radionuclide by
$$
\lambda = \frac{\ln 2}{T_{1/2}}.
$$
Radioactive decay follows
$$A(t) = A_0 e^{ - \lambda t }, \quad \lambda = \frac{\ln 2}{T_{1/2}}.$$
This exponential law is fundamental for converting instantaneous activity into cumulated activity and for time dependent dose calculations.
Internal dosimetry often uses the concept of cumulated activity, written $\tilde{A}$, which is the time integral of the activity:
$$
\tilde{A} = \int_0^{\infty} A(t)\, dt.
$$
If you assume only physical decay and no biological clearance, then
$$
\tilde{A} = \frac{A_0}{\lambda} = \frac{A_0 T_{1/2}}{\ln 2}.
$$
In reality, there is usually both physical decay and biological elimination of the tracer from organs. This leads to an effective half life $T_{\text{eff}}$, which is shorter than the physical half life. The corresponding effective decay constant is $\lambda_{\text{eff}}$ and is defined by
$$
\frac{1}{T_{\text{eff}}} = \frac{1}{T_{\text{phys}}} + \frac{1}{T_{\text{bio}}}.
$$
The effective activity then decays approximately as
$$
A(t) \approx A_0 e^{ - \lambda_{\text{eff}} t }.
$$
In GATE simulations, you will usually not simulate the entire physical or effective decay period in real time, because that would be computationally expensive. Instead, you simulate a representative number of decays and then scale the dose results by the ratio of the realistic cumulated activity to the simulated activity. The exponential decay law is what allows you to compute this scaling factor correctly.
The other key feature of radionuclide decay for internal dosimetry is the decay scheme. Each radionuclide emits a characteristic combination of particles and photons, with specific energies and branching ratios. For example, a beta emitter may emit electrons that deposit energy locally, along with a spectrum of bremsstrahlung photons. A gamma emitter may produce photons that can travel long distances and deposit dose in organs that do not contain any activity. In GATE, these decay schemes are implemented using the Geant4 radioactive decay libraries. When you select a radionuclide as a source, GATE can sample all possible decay branches according to their physical probabilities and generate the corresponding particles.
From a dosimetric point of view, this means that the spatial pattern of energy deposition depends on both the decay scheme and the transport of secondary particles in tissue. Short range beta particles tend to dominate self dose in the source organ, while long range gamma photons can contribute to cross organ dose. If your clinical or research question is sensitive to one or the other, you should check that the chosen physics and decay configurations in GATE are suited to the radionuclides of interest.
In time dependent simulations, GATE can explicitly model the acquisition over a finite time interval. You can choose to represent the changing activity with time explicitly, for example by using multiple time intervals with different source strengths to approximate a non constant time activity curve. Alternatively, for purely dosimetric studies, you can assume that the time dependence is captured in the cumulated activity and use a static simulation with an appropriate scaling factor. The choice depends on whether you care about dynamic imaging effects or only about the final absorbed dose.
In all cases, the link between microscopic decay events and macroscopic dose is provided by integrating in time and summing in space. GATE performs the first part by simulating individual decays and tracking energy deposition. You then perform the second part in your analysis by converting energy deposition per simulated decay into dose per cumulated activity, and finally into physical dose in gray for the patient or phantom. Radionuclide decay, through its exponential time behavior and discrete decay scheme, is therefore the bridge between activity distributions and absorbed dose in internal dosimetry.
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