KAHIBARO
26.3. PET Detector Geometry
Table of Contents
Cylindrical scanners
In PET, the detector system is usually arranged around the patient in a cylindrical shape. This cylindrical scanner geometry surrounds the field of view so that annihilation photons can be detected from many angles at once. In GATE, you typically build such a scanner by combining the concepts of world volume, detector ring, and repeated detector modules, but the technical details of ring construction are covered in another chapter. Here the focus is on what defines a PET cylindrical geometry and how these choices affect your simulations.
A cylindrical PET scanner is characterized mainly by its ring radius, axial length, and the number of detector elements around and along the ring. The ring radius is the distance from the scanner axis to the center of the detector crystals. It controls the size of the field of view and has an impact on sensitivity and spatial resolution. A smaller radius increases geometric efficiency, because a larger fraction of emitted photons intersect the detector, but at the same time it increases the effect of parallax error, which can blur the reconstructed image, especially for events that interact at different depths inside the crystal.
The axial length of the scanner is the length of the detector cylinder along the patient axis. A longer axial field of view covers more anatomy in a single bed position and collects more coincidences per unit activity and time. In GATE, this is usually implemented by repeating detector modules or blocks in the axial direction. Short scanners, which have only one or a few rings of detectors, are useful for small animal imaging or for focused brain scanners. Long scanners, such as total body PET systems, can have axial lengths of tens of centimeters to more than a meter and require careful planning of geometry repetition to keep simulations efficient.
Another key parameter is the number of detector positions around the ring. If you imagine cutting the cylinder like a pizza, each slice corresponds to one detector block or a group of crystals. The angular sampling is determined by how many such positions exist. In simulation, you typically define a single module and then repeat it using angular repetition around the axis. The angular pitch is the angle between successive modules, for example $360^\circ / 64$ for 64 equally spaced modules. More angular positions give better sampling of the lines of response, which can improve reconstructed image quality, but also increase the number of channels and the complexity of the simulation.
The physical cylinder of detectors is not a continuous wall of scintillator, but a collection of discrete crystals organized in blocks. There are usually small gaps between blocks for mechanical support, light guides, and electronics. When you design a cylindrical scanner in GATE, you must decide whether to model these gaps explicitly. Including realistic gaps and support structures can improve the realism of sensitivity and resolution, but it also increases the complexity of the geometry and the computation time. For many educational or proof of concept simulations, it is acceptable to approximate the ring with closely packed detectors and ignore small support structures.
Cylindrical PET scanners can be single layer or multi layer in radius. In a single layer, there is only one ring of crystals in the radial direction. In a multi layer design, there are two or more layers of crystals at different radii. This can improve sensitivity and depth of interaction estimation, because a photon that penetrates the first layer can interact in the second layer. In GATE, you model such systems by adding multiple concentric rings of detector volumes, each with its own position and possibly its own material or thickness. The logic of assigning different detector IDs to each layer belongs to the digitizer and identification chapters, so here it is enough to remember that the geometry must be built so that these layers are clearly separated and non overlapping.
An important geometric consideration is depth of interaction. Even if you model only a single layer of crystals, the finite thickness of each crystal means the actual interaction can occur at any depth. When photons arrive at an angle, this depth uncertainty can lead to parallax errors, where events are mispositioned in reconstruction. You can partially control this in simulation by choosing crystal thickness and ring radius that match a particular scanner design. Some advanced systems use phoswich detectors or dual layer crystals to measure depth of interaction. In GATE, this corresponds to stacking two different scintillator layers radially inside each detector element, which must be carefully aligned inside the cylindrical arrangement.
Finally, for cylindrical scanners you must consider how the patient or phantom is placed relative to the scanner. In most PET simulations, the scanner axis is taken as the $z$ axis and the patient lies along this axis. The center of the field of view is usually at the origin. In a cylindrical geometry, it is important to verify with visualization that the phantom is correctly centered and does not intersect the detector ring or lie too far from the center, which would reduce sensitivity and distort the angular coverage.
Crystal arrays
Inside the cylindrical PET scanner, the basic sensitive elements are scintillator crystals that convert gamma interactions into light. Instead of a single large crystal, modern PET detectors use arrays of many small crystals. In GATE, modeling these crystal arrays correctly is essential if you want realistic results for sensitivity, spatial resolution, and detector response.
A crystal array is usually a regular grid of identical crystals organized in one or two dimensions. For example, a common configuration is a block with 8 by 8 or 16 by 16 crystals, so 64 or 256 crystals per block. Each crystal has a width, height, and thickness. In simulation, the width and height correspond to the transverse size of the crystal element, and the thickness is typically along the radial or axial direction, depending on how the block is oriented in the scanner. The crystal material is a scintillator such as LYSO or BGO, defined in the materials chapters, and each crystal is a separate volume that can record energy deposits.
Within a block, crystals are separated by small gaps that may contain reflective material or light guides. You can represent these gaps explicitly as separate volumes or implicitly by leaving small spaces between crystals. If you choose to include explicit gaps, you must ensure there are no overlaps between neighboring crystals and the gap material. Overlaps can cause Geant4 geometry problems that lead to incorrect tracking. A common practice is to compute the pitch of the crystal grid as the crystal size plus a defined gap size, then place crystals using this pitch along the array axes.
In a cylindrical PET geometry, each crystal array block is then positioned at a specific angle around the ring and at a specific axial position. Inside each block, the local coordinate system defines crystal indices along two directions. One index usually corresponds to the tangential direction around the ring, and the other to the axial direction along the scanner. In more complex blocks where crystals are stacked radially, a third index may represent the radial layer. Although the management of these indices for detector identification is covered elsewhere, during geometry construction you must maintain a consistent order of repetition so that indices map correctly to positions.
The spatial resolution of the PET system is strongly influenced by the crystal size. Smaller crystals allow more precise localization of the interaction position, because the detected event is assigned to a smaller volume. For instance, 2 mm by 2 mm crystals will give better intrinsic spatial resolution than 4 mm by 4 mm crystals, at the cost of many more detector channels. In GATE, you explore this trade off by changing the crystal size and number of crystals in an array. Sensitivity and count rate capabilities are also affected, since smaller crystals can have more dead boundaries and might be more sensitive to misalignment.
Another important property is the crystal thickness along the direction of incoming photons. Thick crystals increase the probability that a 511 keV photon will interact in the detector, which improves sensitivity. However, very thick crystals can worsen depth of interaction uncertainty and lead to more parallax error. In simulation, if you increase the thickness in your crystal volume definition, you will see more detected events but also potentially broader point spread functions. The right thickness depends on the scanner design you want to emulate.
In some PET systems, crystal arrays are not perfectly rectangular. There can be tapered crystals or arrays that approximate a curved shape to better match the ring curvature. In GATE, you can approximate such curved arrays with standard boxes that are individually rotated or translated, or you can ignore the small geometric deviations and keep them as simple rectangular blocks. For most educational simulations, using simple rectangular arrays placed on a cylindrical radius is adequate and much easier to implement and debug.
Crystal arrays are also used to implement depth of interaction detection. In such designs, crystals are stacked in the radial direction so that each line of response can be associated with a measured layer of interaction. To simulate this, you model two or more crystal layers in each array, each as a separate grid of volumes. Their positions must be offset radially so that the inner and outer layers do not overlap. By attaching appropriate actors to these volumes, you can record how often events happen in each layer and study the depth of interaction performance.
Finally, to verify that a crystal array is built correctly, visualization is extremely helpful. After defining the array geometry, you should display it and examine a few detector blocks from different angles. Check that crystals are properly aligned, that gaps look reasonable, and that there is no visible overlap within the block or between neighboring blocks around the ring. A visually consistent crystal array is usually a good sign that your numerical spacing and repetition parameters are correct and that the PET detector geometry is ready for use in further simulations.
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