Background Phase Correction for Quantitative Phase-Contrast MRI
Rizwan Ahmad1, Ning Jin2, and Orlando P Simonetti3

1Electrical and Computer Engineering, The Ohio State University, Columbus, OH, United States, 2Siemens Healthcare, Columbus, OH, United States, 3Radiology and Internal Medicine, The Ohio State University, Columbus, OH, United States

### Synopsis

Virtually every phase-contrast MRI (PC-MRI) measurement is contaminated with background phase (BP) from eddy currents and concomitant gradient terms. A widely reported method to correct BP relies on a polynomial fitting of the static pixels within regions of static tissue. This method requires sufficient static tissue in close proximity to the region of interest—a requirement that cannot be met for imaging of the heart or great vessels. In this work, we propose a BP correction method that leverages information from multiple slices collected under identical conditions but with different table positions.

### Purpose

The credibility of phase-contrast MRI (PC-MRI) as a quantitative diagnostic tool is challenged by the inaccuracies introduced by background phase (BP). In this work, we propose a new data collection and processing method—called multi-slice acquisition and processing (mSAP) —that can provide an accurate estimation of BP.

### Methods

Theory: In addition to the slice of interest (SOI), we propose to collect data from at least one extra slice in the same imaging orientation and using the same gradient waveforms but with different table position. The extra slice aims to image a large cross section of a static tissue (e.g., the liver) and thus uses the patient as its own static calibration phantom. The information from the additional slices, called “helper” slices (HS), is leveraged by jointly fitting the phase maps from SOI and HS using weighted least squares with a 5th order polynomial [1]. To guard against overfitting, we further impose $\ell_1$ regularization to the polynomial regression.

Phantom imaging: A pulsatile flow pump was connected to a flexible pipe that was bent into a u-shape such that two sections of the pipe were aligned in parallel inside the magnet. To mimic static tissue, a total of 9 water bottles of various sizes were placed around the pipe. Ten parallel slices were imaged, each at the isocenter of the magnet by changing the table position. The distance between adjacent slices was fixed at 20 mm. The phase maps from those ten slices are shown in Figure 1. The imaging parameters were: 3T scanner (Magnetom Trio, Siemens), 400x400 mm2 FOV, 256x256 matrix, 2.4/4.8 ms TE/TR, rate 2 parallel acceleration, 6 mm slice thickness, 100 cm/s VENC, and GRE with ECG retrospective triggering. One of the ten slices was designated as the SOI because the pipes in this slice were in close proximity to the static fluid bottles; this allowed us to use the traditional method [2] with a 5th order polynomial to obtain a stable estimate of EC-BP. The EC-BP estimated using this method was treated as the ground truth. To fabricate the absence of static tissue in the SOI, the signal from the static fluid in close proximity to the pipes was disregarded, i.e., pixels near the two pipe cross-sections were not included in the fitting process. We refer to this handicapped version as SOI* (Figure 2). SOI* was also fitted with the traditional method but only with a 1st order polynomial; higher order fitting of SOI* (not shown) yielded worse results.

In vivo imaging: A dataset was collected from a healthy volunteer on a 3T scanner. Two distinct, nonparallel slices were imaged to measure flow in the main pulmonary artery (Qp) and in the ascending aorta (Qs). In addition to these two SOI, four HS were collected, one on either side of each SOI, by the moving the table. After applying the Maxwell correction, the residual background phase was corrected using the traditional single slice correction with a 2nd order polynomial fitting and using mSAP where SOI and HS were jointly fitted with a 5th order polynomial.

### Results

For the phantom data, the traditional background correction generated inaccurate flow quantification in SOI* (Figure 3). All HS slices, when included individually, improved the flow quantification in SOI*, which affirms the key assumption made for mSAP: all slices collected under the same gradient waveforms but with different table positions have the same (or very similar) background phase. For the in vivo dataset, the uncorrected Qp/Qs value was 0.90, which improved to 0.92 when traditional correction method was used. For mSAP, each SOI was jointly processed with each of the two corresponding helper slices, resulting in two different correction maps for each SOI. The resulting Qp/Qs values for these four combination resided within the range of 0.99 to 1.03. Figure 4 provides an example of the fitting results when one of the SOI was jointly processed with one of the helper slices.

### Conclusions

The traditional single slice processing is susceptible to errors due to the lack of static tissue in close proximity to the region of interest. mSAP circumvents this problem by leveraging information from slices with abundant static tissue. Our preliminary data from a pulsatile phantom and a healthy volunteer suggests that EC-BP phase in HS is consistent with the EC-BP in SOI, an underlying assumption of mSAP.

### Acknowledgements

This work was supported in part by the National Institutes of Health (NIH) under Grant NIHR01HL102450

### References

[1] ET Tan et al. JCMR 2014 P349. [2] PG Walker et al. JMRI 1993;3(3):521–30.

### Figures

Figure 1: Time-averaged phase maps from 10 different slices. The arrows point to the two cross sections of the pipe with flow. The display range is $\pm$5% of the VENC. One slice is designated as SOI (top row, second from the left); other nine slices are designated as HS.

Figure 2: Enlarged view of SOI shown in Figure 1. Left: time-averaged magnitude image, middle: time-averaged phase image (SOI), right: time-averaged phase image with the area that was excluded from the fitting displayed in white (SOI*).

Figure 3: Stroke volume (mL) in the two legs of the pipe (+ve for in-flow and -ve for return-flow). SOI indicates ground truth, SOI* indicates when the static signal proximal to the pipes was removed, SOI* + HSn indicates when the data from SOI* and HSn was jointly processed.

Figure 4: (a) Slice of interest (SOI) and one of the helper slices (HS). (b) The correction map generated by jointly processing SOI and HS using regularized, weighted least squares. (c) The SOI and HS after EC-BP correction. The display range is ±5% of the VENC value.

Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)
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