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The influence of B0 drift on the performance of the PLANET method and an algorithm for correction
Yulia Shcherbakova1, Cornelis A.T. van den Berg2, Chrit T.W. Moonen1, and Lambertus W. Bartels1

1Center for Image Sciences, Imaging Division, UMC Utrecht, Utrecht, Netherlands, 2Department of Radiotherapy, Imaging Devision, UMC Utrecht, Utrecht, Netherlands

### Synopsis

The PLANET method has been recently proposed to quantify the relaxation parameters T1 and T2, the banding free magnitude, the local off-resonance ∆f0, and the RF phase from RF phase-cycled balanced steady-state free precession (bSSFP) data. The PLANET model requires a static B0 field over the course of the acquisition. However, due to gradient activity, B0 drift can happen. In this work we present a study of the influence of B0 drift on the performance of the method and we propose a strategy for correction.

### Purpose

The PLANET method was introduced to simultaneously map T1 and T2, the banding free magnitude, the local off-resonance, and the RF phase using phase-cycled bSSFP data [1]. The method is based on linear least squares fitting of an ellipse to bSSFP data in the complex signal plane and subsequent analytical parameter estimation from the fitting results. The PLANET model requires a static B0 field over the course of PLANET acquisition. In practice, however, drift can occur. The purpose of this work was to investigate the influence of B0 drift on the performance of the PLANET method and to propose a strategy for correction.

### Methods

The complex phase-cycled bSSFP signal without drift can be represented as [2,3]:

$I = M_{eff}\frac{1-ae^{i(2πTRΔf_{0}+Δ\theta)}}{1-b\cos(2πTRΔf_{0}+Δ\theta)}e^{i(2πTEΔf_{0}+φ_{RF})}$ [1]

where Meff, a, b depend on T1, T2, TR, FA. ∆θ is the user-controlled RF phase increment, Δf0 is the local off-resonance, φRF is the combined RF transmit and receive phase.

With frequency drift modeled as Δf0 → Δf0 + Δfdrift(t), Eq. [1] becomes:

$I = M_{eff}\frac{1-ae^{i(2πTRΔf_{0}+Δ\theta+2πTRΔf_{drift})}}{1-b\cos(2πTRΔf_{0}+Δ\theta+2πTRΔf_{drift})}e^{i(2πTEΔf_{0}+φ_{RF})}e^{i2πTEΔf_{drift}}$ [2]

The first part of Eq.[2] multiplied by the first exponential represents the same elliptical equation as Eq.[1] with only an offset in the RF phase increment: Δθnew = Δθ +2πTRΔfdrift. This corresponds to a drift-dependent displacement of all data points along the ellipse, see Figure 1(b). The second exponential corresponds to an additional drift-dependent rotation of all data points around the origin, see Figure 1(c,d). Ignoring the presence of drift, fitting an ellipse to the ”drifted” data points leads to a different fit compared to the fit for the “non-drifted” case, see Figure (e). After performing PLANET post-processing, this would result in errors in the parameter estimates.

We propose a 3-step correction algorithm:

1. Calculation of the spatial time-dependent B0 drift during PLANET acquisition Δfdrift n (i,j)(t), where n – is the number of dynamic acquisition, t - is the time, corresponding to nth acquisition. Assuming temporally linear drift, the frequency drift over nth phase-cycled acquisition is estimated by:

$Δf_{drift,n} (i,j)(t)=n\frac{Δf_{total, drift}(i,j)}{N_{cycles}}$ (Hz), n = {1, ...Ncycles} [3]

where total drift over PLANET acquisition Δftotal drift (i,j) is calculated by subtracting two reference B0 maps acquired right before and after PLANET acquisition.

2. Correction of Meff, T1, T2 by multiplying the experimental complex data by e-i2πTEΔfdrift n (i,j)(t), the geometrical equivalent of which is the rotation of the “drifted” data points around the origin back to the “non-drifted” ellipse.

3. Correction of ∆f0 and φRF by defining Δθnew (i,j)(t) = Δθ(t)+2πTRΔfdrift (i,j)(t), which geometrically moves the “drifted” data points along the ellipse back to their “non-drifted” positions. Δθ(t)– is the user controlled RF phase increment.

To test the correction algorithm, MRI experiments on a phantom (bottle filled with aqueous solution of MnCl2·4H2O) and in the brain of healthy volunteer were performed on a clinical 1.5T MR scanner (Philips Ingenia, Best, The Netherlands). A 16-channel head receive coil was used. Sequence parameter settings for 3D bSSFP: FOV 160x160x159 mm3 (phantom), 220x220x100 mm3 (the brain) , voxel size 1.1x1.1x3 mm3 (phantom), 0.98x0.98x4 mm3 (brain), TR 10 ms, FA 30˚, 10 phase cycles with Δθ = π/5. Reference B0 maps were calculated using a dual echo approach. Reference B1 maps were acquired for FA correction. Reference T1 and T2 maps were calculated using 2D MIXED method [4].

### Results

Figure 2 shows parameter maps of the phantom before and after drift correction. The average drift of 10 Hz was observed over 14-min PLANET acquisition. T1 values were overestimated by 4-5% compared to the reference values and the corrected T1 values are in agreement with the reference values with an accuracy of 1%. T2 values were underestimated by 10% compared to the reference values and after correction they are in agreement with the reference values with an accuracy of 2%. The estimated B0 map after correction is similar to the reference B0 acquired right before PLANET acquisition, which proves that the drift correction algorithm performs correctly. An average drift of 9 Hz was observed over 11-min PLANET acquisition in the brain. The estimated quantitative parameter maps before and after drift correction are shown in Figure 3. The reference T1 and T2 maps are shown for comparison. After drift correction, T1 values increased by around 1-2%, T2 values increased by around 5-7%. The corrected B0 map is approaching the reference B0 map acquired right before the PLANET acquisition, as expected.

### Discussion and conclusion

We have demonstrated that PLANET method is sensitive to B0 drift. Here we proposed a strategy for correction and experimentally demonstrated the effect of B0 drift and the performance of the correction. The implemented linear drift correction algorithm successfully improved the quantitative parameter estimation.

### Acknowledgements

This research was supported by The Netherlands Foundation for Scientific Research Institutes (NWO) , Domain Applied and Engineering Sciences; grant 12813.

### References

(1) Shcherbakova et.al. Magn. Reson. Med. 00 (2017); (2) Xiang et.al. Magn. Reson. Med. 71 (2014); (3) Lauzon et.al. Concepts Magn.Reson. 34A (2009); (4) In den Kleef JJ et. al. Magn. Reson. Med. 5 (1987)

### Figures

FIGURE 1. Schematic representation of the influence of B0 drift on the data points in the complex signal plane: a) the ellipse without drift; b) time dependent displacement of the data points along the ellipse due to B0 drift. The “non drifted” data points are blue, the displaced data points are red; c) time dependent rotation of the data points around the origin. The rotated data points are green; d) the ellipse without drift (blue) and the “drifted” ellipse (green); e) the vertical conic forms of the ellipse without drift (blue) and the “drifted” ellipse (green).

FIGURE 2. Experimental results obtained in the phantom: a) B0 drift over 14-min PLANET acquisition; b) Estimated T1, T2, ∆f0, φRF maps; c) T1, T2, ∆f0, φRF maps after drift correction; d) The reference T1, T2, and ∆f0 maps; e) T1 and T2 profiles along the selected lines on estimated, corrected and reference T1 and T2 maps; f) The magnitude image with white vertical and horizontal lines in the middle of the slice used for T1 and T2 profiles; g) The reference T1 and T2 values, the average calculated T1 and T2 values before and after drift correction for one slice of the phantom.

FIGURE 3. Experimental results obtained in the brain: a) The reference B0 maps before (1) and after (2) PLANET acquisition and the corresponding drift map (1-2) ; b) Banding free magnitude image, the reference T1 and T2 maps; c) T1, T2, Δf0, and φRF maps before drift correction; d) T1, T2, Δf0, and φRF maps after drift correction; e) Relative errors ε (in percent) in T1 and T2 values compared to the corrected value.

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