This paper describes a method for 4D imaging, which is used to study respiratory organ motion, a key problem in various treatments. Whilst the commonly used imaging methods rely on simplified breathing patterns to acquire one breathing cycle, the proposed method was developed to study irregularities in organ motion during free breathing over tens of minutes. The method does not assume a constant breathing depth or even strict periodicity and does not depend on an external respiratory signal. Time-resolved 3D image sequences were reconstructed by retrospective stacking of dynamic 2D images using internal image-based sorting. The generic method is demonstrated for the liver and for the lung. Quantitative evaluations of the volume consistency show the advantages over one-dimensional measurements for image sorting. Dense deformation fields describing the respiratory motion were estimated from the reconstructed volumes using non-rigid 3D registration. All obtained motion fields showed variations in the range of minutes such as drifts and deformations, which changed both the exhalation position of the liver and the breathing pattern. The obtained motion data are used in proton therapy planning to evaluate dose delivery methodologies with respect to their motion sensitivity. Besides this application, the new possibilities of studying respiratory motion are valuable for other applications such as the evaluation of gating techniques with respect to residual motion.

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This article shows the limitations of respiratory gating due to intrafraction deformations of the right liver lobe. The variability of organ shape and motion over tens of minutes was taken into account for this evaluation, which closes the gap between short-term analysis of a few regular cycles, as it is possible with 4DCT, and long-term analysis of interfraction motion. Time resolved MR volumes (4D MR sequences) were reconstructed for 12 volunteers and subsequent non-rigid registration provided estimates of the 3D trajectories of points within the liver over time. The full motion during free breathing and its distribution over the liver were quantified and respiratory gating was simulated to determine the gating accuracy for different gating signals, duty cycles, and different intervals between patient setup and treatment. Gating effectively compensated for the respiratory motion within short sequences (3 min), but deformations, mainly in the anterior inferior part (Couinaud segments IVb and V), led to systematic deviations from the setup position of more than 5 mm in 7 of 12 subjects after 20 min. We conclude that measurements over a few breathing cycles should not be used as a proof of accurate reproducibility of motion, not even within the same fraction, if it is longer than a few minutes. Although the diaphragm shows the largest magnitude of motion, it should not be used to assess the gating accuracy over the entire liver because the reproducibility is typically much more limited in inferior parts. Simple gating signals, such as the trajectory of skin motion, can detect the exhalation phase, but do not allow for an absolute localization of the complete liver over longer periods because the drift of these signals does not necessarily correlate with the internal drift.

This paper presents a statistical model of the liver deformation that occurs in addition to the quasi-periodic respiratory motion. Having an elastic but still compact model of this variability is an important step towards reliable targeting in radiation therapy. To build this model, the deformation of the liver at exhalation was determined for 12 volunteers over roughly one hour using 4DMRI and subsequent non-rigid registration. The correspondence between subjects was established based on mechanically relevant landmarks on the liver surface. Leave-one-out experiments were performed to evaluate the accuracy in predicting the liver deformation from partial information, such as a point tracked by ultrasound imaging. Already predictions from a single point strongly reduced the localisation errors, whilst the method is robust with respect to the exact choice of the measured predictor.

Respiratory organ motion is a key problem in proton therapy and in many other treatments. This paper presents a novel retrospective gating method for 4D (dynamic 3D) MR imaging during free breathing to capture the full variability of respiratory organ deformation. In contrast to other imaging methods, a constant breathing depth or even strict periodicity are not assumed. 3D images of moving organs can be reconstructed for complete respiratory cycles by retrospective stacking of dynamic 2D images using internal image-based gating. Additional noise reduction by combining multiple images significantly increases the signalto-noise ratio. The resulting image quality is comparable to breath-hold acquisitions. Although the method was developed for proton therapy planning, the new possibilities to study respiratory motion are valuable to improve other treatments and to assess gating techniques, which rely on stronger assumptions about the breathing pattern.