KAHIBARO
6.4. Cylindrical Geometry
Table of Contents
Tubes
Cylindrical geometry in GATE is built mainly from tube volumes. A tube is a hollow or solid cylinder described by a length along the $z$ axis and inner and outer radii in the $x$–$y$ plane. In Geant4 and GATE this shape corresponds to the G4Tubs solid, which is the basic building block for cylindrical components such as collimators, shielding, and detector housings.
A tube is defined by three main geometric parameters: the half length, the inner radius, and the outer radius. The half length is half of the full cylinder length along $z$. The inner radius defines the radius of an empty central hole. If the inner radius is set to zero, the volume becomes a solid cylinder. The outer radius defines the external size of the cylinder. In GATE Python scripts you specify these parameters together with the associated material, parent volume, and placement.
Tubes always have their axis aligned with the local $z$ axis of their parent volume. If you need a cylinder oriented differently in space, you keep the tube definition the same but apply a rotation when you place the volume. This separation between shape definition and orientation is important for complex detectors, where a single tube model is placed many times with different positions and rotations.
In medical applications, tube volumes are natural representations of objects that are physically cylindrical. Scatter shields around gamma cameras, collimator bodies, cylindrical housings for photodetectors, and many mechanical supports are conveniently modeled as tubes. As you start building more involved systems, tubes become the natural partner to boxes to cover most simple shapes.
When defining tube parameters, it is important that the inner radius is strictly smaller than the outer radius. If you accidentally swap them, or set the inner radius equal to the outer radius, the geometry becomes invalid. You should also keep the tube dimensions consistent with your world volume size so that tubes are fully contained within their parent volumes. Geometry visualization is particularly helpful here for confirming that the cylindrical shapes appear as expected and that they do not extend outside their parents.
GATE also supports partial tubes by specifying an angular span, which results in cylindrical sectors instead of full circles. While the detailed configuration belongs to more advanced geometry topics, you should be aware that cylindrical sectors are often used to build partial rings, collimator sectors, or support structures that do not cover a full $360^\circ$.
For Monte Carlo simulations, the cylindrical symmetry of tube volumes can be useful when you compare against analytical models. Many analytical attenuation and dose calculations assume infinite or long cylinders, and a tube in GATE provides a close numerical representation that you can use for validation of simple scenarios before moving to more complex geometries.
Detector rings
Detector rings are a key cylindrical structure in medical imaging, particularly in PET and some CT designs. Conceptually, a detector ring is a set of identical detector elements, such as crystals or modules, arranged evenly around a circle of given radius. In GATE, this circular arrangement is typically built using repeated placements of small detector volumes around the axis, often relying on tube-like or ring-like parent volumes to help organize the geometry.
For beginners, it is useful to think of a detector ring as two separate parts. The first part is a cylindrical envelope, often a tube volume, that represents the overall mechanical region where detectors are mounted. The second part is the regular repetition of detector building blocks along the circumference of this envelope. The tube defines the approximate inner and outer radii and axial length of the ring, while the repeated detectors define where radiation is actually detected.
The main geometric parameters you control for a detector ring are its inner radius, outer radius or effective detector radius, axial length, and the number of detectors around the circle. The inner radius is essentially the distance from the center to the front face of the detectors. The axial length sets the field of view in the direction parallel to the patient body, while the number of detectors defines the angular sampling. All of these parameters must be chosen so that the detectors fit inside the world and do not intersect each other or other components.
The angular position of each detector element is usually determined by dividing the full circle into equal sectors. If you have $N$ detectors around the ring, the angular separation between them is
$$
\Delta \phi = \frac{2\pi}{N}.
$$
You can use this angle to compute the position of each detector center in Cartesian coordinates with
$$
x = R \cos \phi, \quad y = R \sin \phi,
$$
where $R$ is the chosen detector radius and $\phi$ takes values $0, \Delta \phi, 2 \Delta \phi, \dots$. In GATE you usually do not write these formulas explicitly for every detector, because higher level repetition tools handle the placement for you, but it is important to understand the underlying geometry.
Detector rings often consist of several layers or axial stacks of rings. In that case, you create several repeated structures, each at a different $z$ position. This approach is typical for long PET scanners, where many rings are combined to increase axial coverage. Cylindrical symmetry then applies both around the axis and along it, and a careful choice of ring spacing and axial offsets is required to match a real scanner design.
When building detector rings, you must pay attention to geometry overlaps. Since detectors are placed close to each other around the circle, a slight error in radius, crystal width, or number of elements can create overlaps between neighboring crystals or between crystals and the ring envelope. Overlaps can cause simulation errors or incorrect particle tracking. Geometry checking and visualization are important tools to confirm that your ring is valid.
Detector rings defined with cylindrical geometry provide a convenient environment for other simulation components such as sources and phantoms. For example, you can place a point or cylindrical source at the center of the ring, or insert a cylindrical phantom that fills the inner radius. Understanding how the ring dimensions relate to the available interior space helps you design realistic test setups for sensitivity, resolution, and scatter studies.
Detector rings also influence how you define detector identifiers. Because the geometry is circular, you often assign an angular index to each detector, in addition to any radial or axial indexes. This indexing is important later, when you analyze singles, coincidences, or reconstructed images, since it connects each detected event to its physical position on the ring.
Phantoms
Phantoms are objects placed in the simulation to represent patients, organs, or test objects used to characterize imaging or therapy systems. Cylindrical phantoms, in particular, are extremely common because many standardized test objects have circular cross sections and because cylindrical symmetry simplifies interpretation of results. In GATE, you represent these phantoms naturally with tube volumes.
A cylindrical phantom is typically defined as a solid tube with inner radius set to zero, an outer radius matching the desired phantom radius, and a length representing the extent along the scanner axis. The material assigned to this tube determines how particles interact within the phantom. For imaging studies you may use water or soft tissue equivalent material, while for dosimetry and beam studies you may also consider bone or lung substitutes in cylindrical segments or inserts.
Cylindrical phantoms are often placed at the center of detector rings. The phantom axis aligns with the ring axis, and its radius is chosen to fit comfortably inside the inner radius of the detectors. This central positioning takes advantage of the symmetry of both the phantom and the detector system, and provides uniform coverage by the detector elements. It also facilitates comparisons with analytical models of attenuation or dose distribution in cylinders.
Within a cylindrical phantom you can include more detailed internal structures using additional volumes. For example, small cylindrical inserts of different materials can be embedded to test contrast in CT or SPECT, or to measure spatial resolution in PET. Each insert is itself usually defined as a small tube with a chosen radius and length, placed at a specific offset from the phantom center. Careful choice of insert radii and positions is necessary to avoid overlaps and to ensure that the inserts remain fully inside the main phantom volume.
Analytical descriptions of attenuation and dose in cylindrical phantoms are often used as reference checks. For a uniform cylindrical phantom irradiated by a simple source geometry, you may compare the simulated fluence or dose along a diameter or along the axis to formulas describing exponential attenuation or radial dose profiles. This comparison is easier when the geometry is cylindrical, since the symmetry reduces the dimensionality of the problem, making it possible to validate your physics and material settings before tackling more complex patient-specific geometries.
Cylindrical phantoms are also useful as intermediate test objects between very simple slabs and complex voxelized patients. They are straightforward to visualize, easy to parameterize, and their geometry can be described completely with a few numbers: radius, length, and material. This simplicity makes them ideal first targets when validating new sources, physics lists, or dose scoring configurations in GATE.
In practice, you often combine cylindrical phantoms with cylindrical detectors and sources. For example, a typical PET test setup might consist of a water-filled cylindrical phantom at the center of a detector ring, with a uniform or line source inside the phantom. A CT test setup might use a cylindrical phantom with embedded rods of different densities, again placed at the isocenter of a rotating x ray source and detector ring. By mastering cylindrical geometry for phantoms, you gain a flexible tool for designing a wide range of validation and benchmarking simulations in medical physics.
Cylindrical geometry in GATE is defined by a small set of critical parameters: inner radius, outer radius, and half length for tubes, plus the number of repeated elements and angular spacing for detector rings. Always ensure that inner radius is less than outer radius, that repeated detectors do not overlap, and that cylindrical phantoms fit entirely within the detector ring and world volume.
Views: 13