KAHIBARO
25.4. Respiratory Motion
Table of Contents
Moving anatomy
In many realistic medical simulations the patient anatomy does not stay still. The chest and upper abdomen move as the patient breathes, and this motion can significantly affect imaging data and delivered dose. In GATE you can represent this respiratory motion by moving volumes or voxel-based patient geometries in a time-dependent way during the simulation.
At the simplest level, moving anatomy in GATE means that one or more volumes change their position and possibly orientation as a function of time. For example, you can move a simple lung phantom, a tumor region inside the lung, or an entire voxelized CT patient. In time-dependent simulations the geometry is not static over the whole run. Instead, GATE updates the geometry at discrete time points according to a motion description that you define.
When you work with respiratory motion it is useful to distinguish between two situations. In imaging-oriented simulations, you mostly care about how motion blurs or distorts the measured data, such as PET or SPECT projections acquired over several breathing cycles. In dosimetry or radiotherapy simulations, you care about how the moving anatomy changes the spatial distribution of dose, for example when a lung tumor moves through a narrow high-dose region.
In GATE the technical mechanism for moving anatomy is to attach a time-dependent transform to the relevant volume. The transform can be a translation, a rotation, or a combination of both. For a simple analytical phantom, this may mean translating an organ volume along the superior–inferior direction following a breathing curve. For a voxelized CT patient, it can mean translating or deforming the CT image volume as a whole according to a respiratory model.
For absolute beginners, it is helpful to start with a very simple case, for example a single volume that moves up and down along one axis, and a static detector that records how this motion changes the detected signal. Once this basic idea is clear, you can extend it to more realistic patient geometries and more complex motion.
Whenever you move anatomy in a time-dependent simulation, it is crucial to relate the simulation time to the breathing phase. You define an overall acquisition duration, for example several seconds, and the respiratory cycle repeats with a chosen period inside that duration. Each event in the Monte Carlo simulation is then associated with a particular time within that cycle, which determines the instantaneous anatomical configuration that particles will see.
In respiratory-motion simulations you must ensure that time, breathing phase, and geometry motion are all consistent. A mismatch between the defined acquisition time, the breathing period, and the motion transform will lead to unrealistic motion patterns and incorrect results.
Motion models
A motion model describes how anatomy moves as a function of time during the respiratory cycle. In GATE, you can implement motion models in several ways, from simple analytical formulas to more advanced models based on measured patient data or precomputed image sets.
The simplest and most common motion model for the chest region is a periodic translation model. In this case the displacement of a volume along a chosen axis is given by a simple periodic function of time, often a sinusoid. For example, if you want to move a tumor volume along the superior–inferior axis with amplitude $A$ and respiratory period $T$, you can use a displacement function
$$
\Delta z(t) = A \sin\left(2\pi \frac{t}{T}\right)
$$
where $t$ is the simulation time. This model assumes perfectly regular breathing and purely one-dimensional motion. In GATE you implement this by updating the translation component of the volume transform at each motion step using this equation.
You can also use piecewise linear or more general periodic functions instead of a pure sinusoid. For instance, you can model longer exhalation phases and shorter inhalation phases by defining asymmetric functions of time that better reflect physiological breathing. The key idea remains the same: for each simulation time $t$ you compute a displacement and assign that displacement to the volume transform.
In some applications, especially with voxelized patients, motion models are derived from external data. One option is to use 4D imaging, for example a 4D CT dataset that contains several respiratory phases acquired at different points in the breathing cycle. Each phase represents a static snapshot of the anatomy. In a motion model based on 4D images you can either use discrete phase simulations or interpolate between phases.
A discrete phase approach divides the breathing cycle into a small number of distinct phases, such as end-inhale, mid-inhale, end-exhale. You then run separate simulations for each phase using the corresponding image volume, and combine the results afterward with phase weightings that reflect the fraction of breathing time spent in each phase. This method is straightforward conceptually and requires no continuous motion within a single simulation, but it leads to multiple separate runs and post-processing.
A continuous approach, closer to real motion, uses time-dependent transforms that map a reference image to intermediate configurations. In this case, you can use deformation fields or parameterized motion fields derived from image registration between 4D CT phases. In GATE this corresponds to updating the patient geometry with a transform that encodes both translation and deformation over time. For beginners, handling full deformation fields can be complex, so it is usually better to start with rigid or simple nonrigid translations of volumes.
Besides purely geometric models, some motion models incorporate correlation with external signals such as a respiratory belt or marker. In such a model, a recorded breathing trace $s(t)$ is used to drive motion. You then define a relationship between $s(t)$ and displacement, for example
$$
\Delta z(t) = f(s(t))
$$
where $f$ maps the respiratory signal amplitude to anatomical displacement. In GATE, this sort of model is implemented by reading the time series data and updating the transform of the volumes at times that match the trace.
When choosing a motion model, you should always match the complexity of the model to the goal of the simulation. For basic teaching examples and quick studies of motion blur, a single-axis sinusoidal model is usually sufficient. For quantitative patient-specific studies, especially for radiotherapy, you will often need models derived from patient data such as 4D CT or motion tracking.
Finally, it is essential to ensure that the temporal sampling of the motion model in GATE is fine enough to represent the breathing pattern correctly. If the time steps between geometry updates are too large compared to the breathing period, fast motion may be poorly sampled. On the other hand, overly small time steps can make the simulation unnecessarily slow. A reasonable choice is to use several tens of motion steps per breathing cycle so that the geometry changes smoothly from one configuration to the next.
Always verify that your motion model produces realistic displacements for the breathing period and amplitude you intend. Visualize the moving geometry and check that the maximum displacement, the timing of inhalation and exhalation, and the range of motion match physiological expectations or your reference data.
Views: 12