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6.5. Spherical Geometry
Table of Contents
Spheres
Spherical geometry in GATE is used whenever you need an object with radial symmetry, for example small calibration phantoms, point-like detectors, or simplified organs. In Geant4 and therefore in GATE, a sphere is defined by a center position, an inner and outer radius, and optional angular ranges in polar and azimuthal directions. For most medical-physics simulations, you will work with full solid spheres that have only an outer radius and cover all angles.
A basic solid sphere has inner radius $R_{\text{in}} = 0$ and outer radius $R_{\text{out}} > 0$. The meaningful physical size of the object is given entirely by $R_{\text{out}}$. The radius is always given in GATE units, such as mm or cm, and you must be consistent with the units used elsewhere in your simulation. The sphere is placed inside a parent volume, typically the world, by specifying its center position $(x, y, z)$ in the coordinate system of that parent.
In practice you configure a spherical volume in GATE by choosing a logical name, assigning a material that represents what the sphere is made of, and setting the outer radius. The sphere then behaves like any other volume. It can contain other nested volumes, for example a small detector at its center, and it can be used as a scoring region for actors such as energy deposition or dose. When you think about how particles pass through a sphere, remember that the distance from the center to any point on the surface is exactly the radius, which makes analytical checks simpler than for more complex shapes.
The angular parameters that Geant4 allows for spheres are mainly useful if you want a spherical segment instead of a full sphere. In such a case, you restrict the polar angle $\theta$ and azimuthal angle $\phi$ ranges that define which part of the full sphere is included. For beginners and for most medical imaging and dosimetry tasks, you can safely begin with full spheres that span all angles and revisit partial spheres only if you need more specialized geometries.
Spherical geometry is often chosen because it minimizes directional bias. Any straight line through the center cuts the sphere into equal halves, and the path length from the surface to the center is exactly the radius. This symmetry makes spheres useful as simple test objects when you are checking that your simulation behaves correctly. For example, if you place a uniform source inside a homogeneous spherical phantom, you expect symmetric activity or dose patterns around the center, which can help you detect geometry or physics configuration errors.
When you work with spheres in combination with other shapes, it is important to pay attention to possible overlaps. A spherical volume that is too large can intersect with boxes or cylinders unintentionally, which can cause Geant4 warnings or incorrect particle tracking. Visualization tools in GATE are particularly useful to confirm that your spheres are positioned correctly and do not overlap with neighboring volumes.
Spherical sources
Spherical sources use the same geometric idea as spherical volumes, but now you are defining where particles are born instead of where matter is present. In GATE, a spherical source means that primary particles are sampled within or on a sphere according to some spatial distribution that you choose. This is different from a point source, where all particles originate from a single position, and different from a box or cylindrical source, which do not have radial symmetry.
The simplest spherical source is a source that is uniform inside a full sphere of radius $R$. Uniform means that each small volume element inside the sphere has the same probability of containing an emission. Physically, this represents a small approximately spherical region filled with a radionuclide, or a simplified model of a spherical organ where the activity is assumed to be homogeneous. When the spatial sampling is uniform by volume, most emissions occur near the outer region of the sphere, simply because the outer shells contain more volume than the central region.
You can also define a source that is restricted to the spherical surface instead of the entire volume. In that case, particle origins lie at radius $R$ from the center, but not inside the sphere. This is similar to an isotropic shell of activity around a region, and is useful as an idealized model of surface contamination or a thin radioactive layer. Whether you choose a volumetric or surface spherical source depends on the physical situation you want to represent.
Spherical sources are especially helpful when you want isotropic irradiation of another object. If you place a spherical surface source around a detector or phantom and configure the emission direction to point inward, you can approximate uniform irradiation from all directions. This is a convenient way to test detector performance or to study how dose distributes in a region that is surrounded by a radioactive environment.
The geometry and the source definition must agree. If you create a spherical activity distribution intended to sit inside a spherical volume of material, make sure that the source radius does not exceed the radius of the containing volume. It is often useful to define the same center coordinates for both the spherical volume and its associated spherical source, so that your activity distribution is correctly embedded in the material. Visualization of source positions can help you verify that particles start inside the region you expect.
For time dependent or multi region simulations, you may use several spherical sources with different radii and positions to represent clusters of activity, for example several small lesions in a patient or multiple spherical calibration sources in a water phantom. Each spherical source is configured independently, with its own radius, position, and activity. By doing this systematically, you can model quite complex spatial activity distributions while still using simple spherical shapes.
Finally, spherical sources are valuable for validation. Because the geometry and emission pattern are symmetric, the resulting fluence or dose patterns often have analytic expectations that you can compare with. This is particularly true if you consider regions at a fixed distance from the center of a spherical source. Using such symmetric configurations helps you gain confidence that your more complex simulations, where analytical solutions are not available, are correctly configured.
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