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Analysis of Coil Combination for bSSFP Elliptical Signal Model
Nicholas McKibben1, Grayson Tarbox2, Michael Mendoza1, and Neal K. Bangerter3

1Electrical and Computer Engineering, Brigham Young University, Provo, UT, United States, 2Brigham Young University, Provo, UT, United States, 3Imperial College London, London, United Kingdom

### Synopsis

The elliptical model method for removing residual banding in balanced steady state free precession images requires accurate phase information to operate. Most datasets have separate data for each coil channel with different sensitivity, requiring combination either before or after processing using the elliptical model to eliminate differences in coil sensitivity. We demonstrate that the order in which these steps are taken matters, requiring coil combination after processing with the elliptical model depending on the method.

### Introduction

In steady state free precession (SSFP) MRI there a variety of applications which require the combination of multiple phase-cycled images. These applications include band reduction (e.g. using sum of squares (SOS) or the elliptical signal model (ESM)),1,2 intrinsic parameter estimation (e.g. T1, T2 estimations),3 extrinsic parameter estimation (e.g. B0, B1 field map estimations)4 and water fat separation.5 Many of these techniques are nonlinear functions of multiple SSFP phase-cycle image acquisitions. In datasets with multiple coil channels, the information from each channel may be combined using a variety of methods, either prior to performing other estimates or after those estimates have been performed. Due to the nonlinear nature of these functions, it is unclear if the order of coil combination and algorithm evaluation have a significant impact on the quality of the output. In many cases, this order of operations can affect the magnitude and phase of the results of the algorithm. For algorithms that are highly phase sensitive, such as the ESM, the incorrect order of operations can cause the algorithm to produce low-quality results. In this work, we present a numerical analysis of coil combinations of bSSFP for the specific application of SSFP band reduction using the ESM.

### Methods

Simulated phantom data was generated for four phase cycled images. Coil sensitivity profiles were then estimated for a simulated birdcage coil to generate datasets with 4, 8, 16, and 32 different coil sensitivities. A band-free image was generated by solving the ESM either before or after combing coils. Three different coil combination methods were compared: SOS, an Inati adaptive method,6 and a Walsh iterative method.7 A truth image was produced by generating a band free image using the ESM with 20 simulated phase cycles but without adding any coil sensitivities. Mean square error and percent ripple1 was then compared between resulting images and the truth image at SNR levels of infinity, 50, 20, 10, 5, and 1.

Real phantom data was acquired on a Siemens TIM Trio 3T scanner with the Siemens Head Matrix coil. Images were acquired using a bSSFP sequence with RF phase increments of 0°, 45°, 90°, 135°, 180°, 225°, 270° and 315° of single 5 mm slices with a FOV of 260 x 130 mm, matrix size of 512x256, flip angle of 90°, and 16 averages. Reconstructions were then performed using the ESM to generate band-reduced images and then combining coil channels using the same three methods, or by combining coil channels and then using the ESM to generate band-reduced images. Percent ripple, defined as $100 x (S_{max}-S_{min})/S_{mean}$, was used to quantify residual banding and the metric to judge the impact of the order in which coil combination takes place.

### Results and Conclusions

Numerical results show a trend that solving the ESM coil by coil before coil combining results in less error than combining the coils then solving the ESM. Figure 1 shows examples using a Walsh iterative method and an Inati iterative method for combining the coils. Figure 2 summarizes the numerical trends in MSE at various SNR values. Figure 3 shows the percent ripple for the numerical simulations. It is clear that while other combinations are roughly equivalent for the simulation, combing coils using the Inati method and then solving the ESM is highly undesirable. Results in the actual phantom mirrored the results in the numerical phantom, with residual banding in images where ESM was applied first and then coils combined using the Inati method proving slightly better than the Walsh method, though both nearly indistinguishable. Notably, solution to ESM followed by coil combination produced ripple levels of about 3.89% using both the Walsh and Inati methods, but Inati produces significantly more ripple and other artifacts if applied to the set of coils images before application to ESM.

### Discussion

Our results demonstrate that careful consideration should be taken when designing an image processing pipeline when combining coils. The ESM tends to be sensitive to low-quality phase estimation, therefore each set phase-cycled coil images should be fed to ESM-based algorithms before coil combination is achieved using either the Walsh or Inati methods. More research is needed to determine the factors that lead to the deterioration of image quality when using the Inati iterative method. Other coil combination methods could also prove to be useful in reducing computation load when coil combination before ESM algorithm evaluation is necessary.

### Acknowledgements

We would like to thank Bradley Bolster from Siemens for his support of the BYU MRI Research Facility.

### References

1. Bangerter, Neal K., et al. "Analysis of multiple‐acquisition SSFP." Magnetic Resonance in Medicine, 51.5 (2004): 1038-1047.
2. Xiang, Qing‐San, and Michael N. Hoff. "Banding artifact removal for bSSFP imaging with an elliptical signal model." Magnetic Resonance in Medicine 71.3 (2014): 927-933.
3. Shcherbakova, Yulia, et al. "PLANET: An ellipse fitting approach for simultaneous T1 and T2 mapping using phase‐cycled balanced steady‐state free precession." Magnetic resonance in medicine 79.2 (2018): 711-722.
4. Taylor, Meredith, et al. "MRI Field Mapping using bSSFP Elliptical Signal model." Proceedings of ISMRM 25th Joint Annual Meeting (2017).
5. Glover, Gary H. "Multipoint Dixon technique for water and fat proton and susceptibility imaging." Journal of Magnetic Resonance Imaging 1.5 (1991): 521-530.
6. Inati, S. J., M. S. Hansen, and P. Kellman. "A solution to the phase problem in adaptive coil combination." ISMRM proceeding; 20–26 april; Salt Lake City, Utah, USA 2672 (2013).
7. Walsh, David O., Arthur F. Gmitro, and Michael W. Marcellin. "Adaptive reconstruction of phased array MR imagery." Magnetic Resonance in Medicine 43.5 (2000): 682-690.

### Figures

(a) shows the ESM then Walsh coil combination applied. (b) shows the ESM then Inati coil combination applied. (c) shows the Walsh method applied then ESM. (d) shows the Inati method applied then ESM. All figures have the center slice plotted in red above the image to show the ripple and artifact profiles.

MSE results for numerical simulations at given SNR values. The overall trend shows that error is reduced by using the Walsh method and combing coils after the ESM as been solved.

Percent ripple shown for numerical simulations at various SNR values.

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)
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