Respiratory motion model based on the noise covariance matrix of a receive array

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Respiratory motion detection and correction are essential for successful imaging and image‐guided therapy of mobile organs such as MR‐guided external beam radiotherapy 1 or high‐intensity focused ultrasound 3. The respiratory motion–induced artifacts or treatment inaccuracies are often reduced using breath‐holds or gated/triggered imaging/treatment. These strategies are somewhat challenging, because they demand a reliable patient cooperation and/or prolong substantially the session time. Motion tracking is an alternative way for motion compensation without these drawbacks. Image‐based tracking systems are preferable, because the displacement of the target and its surrounding is visualized and, therefore, can be directly quantified. However, the motion information obtained from such systems is strongly limited by the update time and latency constraints imposed by the MR‐based tracking system. An alternative approach consists of estimating the target motion by means of modeling. In a first training step, a motion model establishes a relationship between the target motion and an easily and quickly recorded surrogate of the target motion. Subsequently, the surrogate of the target motion is used in conjunction with the motion model to estimate the current target position 4. A good review of approaches proposed for model‐based respiratory motion estimation can be found in 4.
For a reliable motion model, the surrogate signal must be consistent between the two steps of the imaging session (i.e., the training set for the model formation and the interventional procedure), and have sufficient temporal resolution to resolve the physiological motion. In the scope of respiratory motion, the use of external sensors such as respiratory bellows 5, nasal air flow prong, spirometer 6, or optical imaging using a shielded MR‐compatible optical camera 7 have been suggested. The advantage of these methods is their ability to provide surrogate motion information with high temporal resolution and their independence from the imaging system. However, because these methods do not directly observe the organ of interest, the relationship between the surrogate and the target position may become inaccurate in the case of variations of the breathing pattern. The use of alternative surrogates more closely related to the moving internal anatomy, extracted from MR 8 or ultrasound 9 signals, has also been investigated, to provide quantitative measurements of the target displacement or at least surrounding tissues.
Respiratory motion can also be detected with a radiofrequency coil/array by active impedance measurement 10 or by passive monitoring of the thermal noise variance 11. In 11, only diagonal elements of the receive array's noise covariance matrix (NCM) (i.e., variance) were used. In this paper, off‐diagonal elements are included (i.e., covariance) to increase spatial encoding power of the motion surrogate. An MR‐based 2D motion model is proposed that uses the full NCM to estimate the motion. In the training step of the model, the excellent soft‐tissue contrast in MR images is used to obtain accurate motion fields of the moving target and its surroundings. The motion surrogate exploits the sensitivity of the receiver array's thermal noise to the motion; NCM dynamics serve as surrogate signals for the proposed model. The NCM is sensitive to the volumetric motion, as motion modulates and/or causes actual displacement of the main noise sources (i.e., human tissues) for the receive array at the field strengths above 0.5 T. A key advantage is that it can be updated rapidly (3.6 ms) and is simultaneous, synchronous, and non‐interfering with MR data acquisition 11. Thus, the proposed model does not lead to the spatial/temporal tradeoffs in contrast to models that are updated by MR navigators. Use of the NCM to estimate rigid head motion has been shown recently 12.

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