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7.3. Ring Geometry
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PET detector rings
Ring geometry is a central idea in many medical imaging simulations, especially PET, where detector crystals surround the patient in a cylindrical arrangement. In GATE, you rarely place each crystal one by one. Instead, you define a smaller detector unit, then repeat it around a circle. This chapter focuses on how to think about and configure that circular repetition, not on general PET physics or digitization, which are covered elsewhere.
Conceptually, a PET detector ring is a set of identical detector elements arranged on a circle of radius $R$ in the transverse plane. If you have $N$ identical elements, the angle between neighboring elements is usually
$$
\Delta \phi = \frac{360^\circ}{N}.
$$
You can describe each element by its angular index $i$ and its placement angle
$$
\phi_i = i \,\Delta \phi \quad \text{for } i = 0, 1, \dots, N-1.
$$
In a simulation, this angular placement is not something you compute manually for every detector. You tell GATE how many copies you want, what the ring radius is, and along which axis the repetition should occur. GATE and its Geant4 engine then calculate the positions and orientations for you.
In most PET scanners, the ring lies in the $x$-$y$ plane and the scanner axis is the $z$ axis. In that case, the center of the $i$th detector module can be thought of as
$$
x_i = R \cos\phi_i, \quad
y_i = R \sin\phi_i, \quad
z_i = z_0,
$$
where $z_0$ is the axial position for that ring. The detector face is rotated so that it points toward the center, which means its local axis normal to the crystal face is aligned with the vector from the origin to $(x_i, y_i, z_0)$.
In GATE you achieve this circular arrangement by defining a logical volume that represents the detector block or crystal, setting a mother volume that will contain the ring, and then specifying that this volume is to be repeated by rotation around an axis. You give the number of copies, the angular span to cover, and the ring radius. For a full ring, the angular span is $360^\circ$. For partial-ring systems, such as some brain PET or hybrid scanners, you use a smaller angular span and GATE will distribute the modules evenly over that range.
It is useful to keep a clear distinction between the ring radius and the detector dimensions. The ring radius is measured from the scanner center to the center of each module, not to its inner or outer face. If you change the crystal thickness or add shielding, you typically keep the ring radius fixed and adjust the module geometry so that the active detector region still sits at the desired distance from the center. This consistency is important when you compare different scanner designs.
When simulating multiple rings along the axial direction, you can think of each axial ring as a repetition of the basic module in $z$. Often you first create one ring in the transverse plane using angular repetition, then stack that ring along the $z$ axis using another level of repetition. This hierarchical approach matches the physical structure of many scanners, where crystals form modules, modules form rings, and rings form the full PET scanner.
Repeated modules
Repeated modules are the key tool for building realistic ring geometries efficiently. Instead of describing every detector crystal placement manually, you define a module volume once, then tell GATE how to replicate it. These repetitions can be along a line, in a 2D grid, or around a circle. For ring geometry, the angular repetition is the most relevant.
At the lowest level, you often start with a single crystal, for example a rectangular prism of LYSO. Several crystals in a grid form a detector block, and this block becomes the unit you repeat around the ring. By separating the problem into these levels, you only have to adjust one block definition when you change dimensions or materials, and all repeated modules update automatically.
In a ring, repeated modules are arranged by specifying the repetition pattern about an axis. You define the module once, then provide parameters such as the number of copies, the rotation axis, the angular step or total angular range, and the radial distance from the center. GATE uses Geant4’s parameterised or replicated placements internally, so it can manage many copies without storing completely separate geometry for each one. This is especially important when you have thousands of crystals.
You can also combine repetitions in different directions. For instance, you might repeat a crystal in a 2D grid inside a block, then repeat the block itself around the ring, and finally repeat the whole ring along the scanner axis. This three-level repetition gives you a complete cylindrical volume made of many small crystals, while you still control everything through a small number of parameters. Because the repetition parameters are numerical, they are easy to change from Python configuration variables, which is helpful for scanner optimization studies.
A common practical concern with repetitions is detector identification. Since many modules are created from the same base volume, you need a systematic way to assign IDs that reflect their position in the hierarchy. GATE provides structured volume IDs that encode indices such as ring number, block number, and crystal indices inside a block. These IDs can be used later by digitizers and analysis code to group events by ring or by detector element. When you design your repetition structure, it is useful to think ahead about how you will interpret these IDs.
Repeated modules also help you avoid geometry errors. Because the placement is generated algorithmically, the modules are placed exactly on the circle with consistent spacing and rotation. This reduces the chance of accidental overlaps or gaps that might occur if you tried to position everything by hand. Even so, it is good practice to use visualization to inspect the ring and confirm that modules are not intersecting and that they point towards the scanner center.
Finally, repeated modules are valuable for performance. Using repetition means the geometry description is compact, which simplifies memory use and can speed up the navigation of particles through the geometry. When you start building more complex ring-based systems, such as multi-ring PET or combined PET/CT systems, this efficient, parameterized approach to ring geometry becomes essential for managing complexity and maintaining simulation performance.
In ring geometry, always define a small detector module once and use repeated placements to build the full ring. Never try to place each detector manually, because this is error-prone and makes your simulation difficult to maintain and extend.
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