Respiratory motion reduces cardiac and abdominal diagnostic magnetic resonance (MR) image quality significantly. It remains one of the major challenges for diagnostic MR imaging as well as for many image-guided surgical interventions and treatments in the region of thorax and abdomen. Most respiratory-navigation strategies treat respiratory motion as one-dimensional, limiting robustness and accuracy of navigation in cases of irregular respiration, or pronounced hysteresis. Some MR-signal-based navigation schemes can provide multiple respiratory directions, but interfere with the MR measurement [1,2]. Thus, there is a need for continuous multidimensional characterization of respiratory motion. Recently, a novel Pilot Tone (PT) navigator was proposed by one of the authors [3]. We investigate if the method can provide two-dimensional respiratory information.

As in [3], a commercial signal generator produced a small amplitude PT with a fixed frequency outside the frequency band of the MR signal, but inside the received frequency band. The PT was transmitted into the magnet bore by a non-resonant pick-up coil taped to the outer cover, close to the funnel of the magnet bore. The modulation of the PT received by the local MR coils was processed to characterize respiratory motion.

To generate ground truth for the respiratory motion, we recorded sagittal image streams of the right liver dome using standard fluoroscopic sequences (GRE, 513-1000 images, frame rate: 4-5 images/s, TE: 1-2 ms, TR: 4 ms, posterior spine array + anterior body array). Measurements on 6 volunteers were performed on MAGNETOM Skyra (3T) and MAGNETOM Aera (1.5T) (Siemens Healthcare, Erlangen, Germany). For every received line and channel, we extracted one PT amplitude value using a prototype image reconstruction program as described in [3].

Offline processing was performed in MATLAB (MathWorks, Natick, MA, USA).

Optimal channel combination coefficients $$$\boldsymbol{w}$$$ for PT navigators were determined by comparison to image-based ground truth in a separate calibration phase (see Figure 1) as follows: Incoming PT amplitudes were first Hann low-pass filtered (cutoff 0.1-0.5 Hz), yielding the navigator matrix $$$\boldsymbol{P}$$$. Optimal weights $$$\boldsymbol{w}$$$ were found by solving the least-square optimization problem

$$\boldsymbol{w}(\boldsymbol{g}) = \underset{\boldsymbol{\boldsymbol{w}}}{\operatorname{argmin}} ||\boldsymbol{P}\cdot\boldsymbol{w} - \boldsymbol{g}||^2_2 = \boldsymbol{P}^\dagger\cdot\boldsymbol{g}$$

where $$$\boldsymbol{P}^\dagger$$$ is the Moore-Penrose pseudo-inverse of $$$\boldsymbol{P}$$$.

Respiratory ground truth signals $$$\boldsymbol{g}_{SI}$$$ and $$$\boldsymbol{g}_{AP}$$$ were generated from deformation vector fields generated by elastic registration of the calibration images to a key frame by averaging one vector component over manually selected ROIs: the superior-inferior (SI) component $$$\boldsymbol{g}_{SI}$$$ from a region centered around the liver dome, and an additional anterior-posterior (AP) component $$$\boldsymbol{g}_{AP}$$$ from a region centered on the sternum (see Figure 2).

The resulting weights $$$\boldsymbol{w}_{SI}$$$ and $$$\boldsymbol{w}_{AP}$$$ were applied in subsequent measurements to generate PT navigators (right side of Figure 1).

We evaluated the quality of the resulting PT navigators $$$\boldsymbol{g}_{SI}$$$ and $$$\boldsymbol{g}_{AP}$$$ by sorting the calibration images according to the PT navigator values into bins. In the last step, the mean structural similarity index (SSIM [4]) of all images in a given bin is calculated.

Volunteer experiments included model experiments with instructed regular breathing patterns and experiments featuring complex free-breathing patterns.

Over all experiments, PT navigators derived with weights from a separate calibration measurement showed excellent correlation with the ground truth in those directions (for $$$\boldsymbol{g}_{SI}$$$: 0.90 $$$\pm$$$0.13; for $$$\boldsymbol{g}_{AP}$$$: 0.82 $$$\pm$$$0.21).

Figure 3 shows PT navigators for instructed interleaved abdominal and chest breathing: The two respiration modes can be clearly distinguished using $$$\boldsymbol{g}_{SI}$$$ and $$$\boldsymbol{g}_{AP}$$$.

Figure 4 shows PT navigators for a case of irregular free-breathing.

The result of binning and averaging the images according to the PT navigators is shown for the free-breathing example of Figure 4 in Figure 5: The top left image shows the average over all bins, the top column the average over all $$$\boldsymbol{g}_{SI}$$$ bins, the leftmost column the average over all $$$\boldsymbol{g}_{AP}$$$ bins, all other images are binned according to both navigators. Binning in two dimensions improves image sharpness especially for extreme positions of the diaphragm, as also indicated by higher SSIM values.

Our results demonstrate that PT navigation can provide two-dimensional characterization of regular and irregular respiratory motion without interfering with the MR measurement and should thus be considered as an promising alternative to established navigation methods.