KAHIBARO
25.5. Scanner Rotation
Table of Contents
SPECT rotation
In SPECT, scanner rotation is essential because the gamma camera measures only a 2D projection from one angle at a time. To reconstruct a 3D (or at least tomographic) distribution of activity, you must acquire projections from many angles around the patient or phantom. In GATE, this rotation is modeled explicitly as a time dependent motion of the detector head.
A typical SPECT system has one or more detector heads that rotate around the patient along a circular orbit. In a simple GATE setup, you define a static world and patient geometry, then make the gamma camera head a volume that rotates around the patient over the course of the simulation time. The source activity may be constant during the rotation, which is common for SPECT acquisitions that last several minutes.
The key ingredients are the rotation center, the rotation axis, the angular range, the number of projections, and the acquisition time per angle. In practice, you choose a center that corresponds to the patient or phantom center, for example at the origin. You place the detector head at one initial angle, often at 0 degrees on a circle of given radius, and then define a motion that rotates this volume around the chosen axis.
In GATE, time dependent motion is described by attaching a motion model to a volume. For rotation, you specify the rotation axis, usually the $z$ axis for a standard transaxial orbit, and a function that gives the rotation angle as a function of simulation time. For a full 360 degree SPECT acquisition with constant angular speed, the angular position $\theta(t)$ can be written as a simple linear function of time:
$$
\theta(t) = \theta_0 + \omega t
$$
where $\theta_0$ is the initial angle and $\omega$ is the angular speed in radians per second, selected so that the detector completes the desired angular range in the total acquisition time. For example, to scan 360 degrees in $T$ seconds, you choose $\omega = 2\pi / T$.
The rotation angle must be defined consistently with the simulation time, and the total acquisition time must match the product of the number of projections and the time per projection to avoid inconsistent motion or incomplete coverage.
For SPECT, it is common to think in terms of discrete projection angles. You might want $N$ projections equally spaced over 360 degrees. The angular step is then
$$
\Delta \theta = \frac{360^\circ}{N}.
$$
If you want to simulate step and shoot acquisition, where the camera moves to a particular angle, acquires counts, then moves to the next angle, you can approximate this by splitting the full acquisition into multiple shorter simulations, each with the detector fixed at a given angle, and then combining the resulting projection images afterward. Alternatively, for continuous rotation, you keep the camera moving during the entire simulation, and use an actor in each detector head or in the digitizer to bin detected photons in time intervals that correspond to different angular positions.
A practical way to connect rotation and projection data is to decide, for each projection $k$, a time interval $[t_k, t_{k+1}]$ that corresponds to that angle range. You then configure an actor to store separate images or histograms for each time interval, which act as different projection images. For example, with a total acquisition time $T$ and $N$ equally spaced projections in continuous rotation, each projection covers a time interval of
$$
\Delta t = \frac{T}{N}.
$$
You map projection index $k$ to time $t_k = k \Delta t$. During post processing, you relate each time bin to the corresponding detector angle using the rotation formula.
In SPECT, the mechanical geometry of the rotation must also be consistent with the collimator and the field of view. When you rotate the detector head, the attached collimator, crystal, and shielding should move as a rigid structure. In GATE, you typically achieve this by making the detector head a logical parent volume that contains all these components, and by applying a single rotation motion to that parent. This ensures that the collimator holes always point toward the center of rotation in the same way as in a real gamma camera.
It is important to make sure the rotation axis passes through the intended center of the camera orbit. If the center is offset relative to the patient, your projections may be asymmetric or physically unrealistic compared to the real system. Before running a long simulation, you should visualize the geometry, enable the motion, and inspect the rotated positions of the detector at a few time points. This helps you catch mistakes such as rotating around the wrong axis or using an incorrect radius.
Always check that the detector trajectory does not intersect the patient or phantom geometry during rotation. Intersections can cause invalid geometries, overlapping volumes, or nonphysical behavior.
Finally, the choice between step and shoot and continuous rotation affects the noise properties of your projection data. In a step and shoot model, each projection is acquired with a fixed detector angle, so all counts in a projection come from exactly the same geometry. In continuous rotation, the detector angle changes during counting, which may blur the effective angle if you use long time bins. When modeling a specific clinical system, you should choose the rotation model and time binning that best approximates the real acquisition protocol.
CT rotation
In CT, scanner rotation is used to measure x ray attenuation from many angles around the patient. A simple CT simulation in GATE involves an x ray source and a detector array that rotate together around the patient as a rigid gantry. The patient or phantom remains fixed at the center of rotation while the source detector pair moves around it.
The essential difference with SPECT is that in CT you are mainly interested in transmission measurements rather than emission, and you typically consider projections as sets of line integrals from source to each detector pixel. In simulation, you create a geometry where the x ray source and detector array are placed at opposite sides of the phantom, with a certain source to isocenter and source to detector distance. You then define a rotation around the isocenter so that the entire gantry rotates during the scan.
As with SPECT, SPECT like motion models are used, but for CT it is more natural to tie the rotation directly to discrete projection angles used in reconstruction. For a single rotation CT scan with $N$ projection angles evenly spaced over 360 degrees, you define
$$
\Delta \theta = \frac{360^\circ}{N}
$$
and projections at angles
$$
\theta_k = \theta_0 + k \Delta \theta
$$
for $k = 0, 1, \dots, N-1$. In a step and shoot CT simulation, each projection can be modeled by a separate simulation where the gantry is static at angle $\theta_k$ and a certain number of photons are emitted. This approach is easy to implement and aligns well with analytical reconstruction algorithms that treat each angle separately.
In continuous rotation CT, similar to helical or spiral CT, the gantry rotates while the source emits continuously and the detector measures continuously. To model this, you specify a rotation function for the gantry as in SPECT, but often with additional motion in the patient table direction for helical scans. At the simplest level, you treat the gantry rotation as
$$
\theta(t) = \theta_0 + \omega t
$$
with the same meaning as in SPECT, and you collect detected photons into time bins corresponding to desired projection angles. For a helical scan, you also define a translation of the patient or table along the $z$ axis that is linear in time. The pitch is determined by how much the table moves per gantry rotation, but that detailed modeling usually belongs in more advanced CT specific chapters.
For CT, the source and detector must remain exactly opposed during rotation. Any inconsistency in their relative position or rotation center leads to incorrect path lengths and therefore unphysical attenuation measurements.
To keep the source and detector aligned in GATE, you typically define a parent volume for the gantry that contains both the source and detector array volumes. You then apply a rotation motion only to this gantry volume. As the parent rotates around the central axis, both the source and detector move together, and their relative geometry remains constant. The world and the patient remain static.
A typical CT rotation is about the $z$ axis for an axial scan. You set the rotation center at the isocenter, usually at the origin. You then place the source at a given radius on one side, for example at $(R, 0, 0)$, and the detector arc or flat panel at the opposite side, for example near $(-R, 0, 0)$, possibly with an offset to adjust magnification. The rotation axis vector is then $\hat{z}$, and the rotation follows standard cylindrical geometry.
The relationship between gantry speed, tube output, and projection statistics is important for simulation planning. If you assume a constant source rate and a uniform rotation, then the number of photons per projection is proportional to the time assigned to that projection. For a full rotation of duration $T$ and $N$ equal time projections, each projection time is $\Delta t = T/N$. This defines how many primary particles you need to simulate to achieve a desired statistical precision in each projection.
For CT, motion and rotation also interact with the dose delivered to the phantom. As the gantry rotates, the same anatomical region may pass through the beam multiple times, depending on collimation and pitch. If you are interested in patient dose, you must ensure that the rotation model and source intensity reflect the clinical protocol, for example by assigning a realistic tube current time product (mAs) per rotation and per projection. While dose modeling details belong elsewhere, the rotation geometry is the basis for any correct CT dose simulation.
It is useful to visualize a few gantry positions to verify the rotation. In particular, you should check angles at 0, 90, 180, and 270 degrees to confirm that the source and detector positions correspond to the intended mechanical design. This step helps detect errors such as wrong rotation direction, wrong axis, or offset centers. If the rotation axis is not coincident with the patient center, or if the source to detector distance changes unintentionally during motion, you may introduce artifacts in attenuation data.
Before running long CT simulations, always validate that the rotating gantry does not intersect or overlap with the patient support, couch, or other static structures, and confirm that the field of view fully covers the region of interest at all angles.
Overall, scanner rotation in CT simulations in GATE is modeled as a controlled time dependent rigid body motion of the gantry, with the main goals of reproducing realistic projection geometry and matching the acquisition protocol used in reconstruction and dose calculations.
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