Reducing bias due to B0 inhomogeneity in abdominal T2* mapping
Pippa Storey1 and Dmitry S. Novikov1

1Radiology Department, New York University School of Medicine, New York, NY, United States

### Synopsis

T2* measurements in the abdomen are often corrupted by macroscopic magnetic susceptibility effects from air in the lung and bowel. We show that sensitivity to linear B0 variations can be eliminated by tailoring the 2D slice profile appropriately and truncating the echo train where the phase difference between adjacent voxels within or across slices exceeds $\pi/2$. This improves T2* accuracy without the need for post hoc corrections. When compared with a conventional approach, the proposed technique demonstrates reduced sensitivity to B0 inhomogeneity in the liver caused by magnetic susceptibility differences in the lung.

### Introduction

T2* mapping is frequently performed in the abdomen for iron quantification and blood oxygen level dependent (BOLD) imaging. However, accuracy can be compromised by macroscopic susceptibility effects due to air in the lung and bowel. These produce magnetic field gradients over entire voxels, which translate into phase gradients that increase with echo time. Fortuitously, the image intensity is largely insensitive to such gradients in the phase- and frequency-encoding directions up to a threshold determined by the Nyquist limit [1]. For 2D acquisitions, however, it remains sensitive to background gradients in the through-slice direction. We show that, by tailoring the slice profile appropriately, the signal attenuation due to through-slice gradients can be eliminated up to a certain threshold, which corresponds to a phase difference of $\pi/2$ across the slice. By truncating the echo train where this threshold is exceeded, T2* accuracy can be improved without the need for post hoc corrections.

### Theory

A background magnetic field gradient $\mathbf{G}$ across the tissue gives rise to a linearly varying phase $\phi(\mathbf{r})=\gamma\mathbf{G}.\mathbf{r}\,\text{TE}$. In the Fourier-encoded directions, this simply displaces the signal in k-space. The image intensity is largely unaffected up to the TE value at which the echo approaches the edge of the sampling range [1]. This corresponds to a phase difference of $\pi$ across the voxel. In the through-slice direction, however, the signal is attenuated as a function of TE according to $F\left(\text{TE}\right)=\mathscr{M}\left(\gamma G_z \text{TE}\right)$ where $\mathscr{M}$ is the Fourier transform of the slice profile $M_{\perp}(z)$, and $G_z$ is the through-slice component of the background gradient. Furthermore, in the small flip angle approximation, the slice profile is, in turn, the Fourier transform of the pulse waveform. Hence, by choosing a pulse waveform with a broad plateau about its center, such as the Tukey function shown in Figure 1, the signal attenuation due to background gradients can be eliminated up to a certain TE value, which corresponds to phase difference of $\pi/2$ across the slice.

### Methods

Phantom and human studies were performed at 3T (Siemens Prisma) using a 2D multiple gradient echo sequence. Comparisons were made between the standard pulse (a windowed sinc with time-bandwidth product of 2) and the proposed Tukey pulse. Three adjacent slices were imaged in interleaved fashion so that the phase difference across the central slice could be quantified. Data from a standard doped phantom were acquired once with a good $B_0$ shim and once with a gradient offset in the through-slice direction. Liver imaging was performed in 4 healthy volunteers after achieving the best possible shim across a thick shim volume. Since there was no way to determine the ‘true’ T2* in vivo, data were acquired once using a typical clinical slice thickness of 6mm and once using a thinner slice (4.25mm). The thinner slice produced lower signal but was less sensitive to background gradients. For data obtained using the standard pulse, T2* was calculated for each voxel by truncating the echo train where the signal fell below twice the noise level. For data collected with the Tukey pulse, the echo train was truncated at the TE value for which the phase difference between adjacent voxels within the slice or across neighboring slices exceeded $\pi/2$.

### Results

With good shimming, the signal in the phantom decayed monoexponentially, and was almost identical between the Tukey pulse and the standard pulse (Figure 2). With a through-slice gradient offset, the signal obtained using the standard pulse exhibited a more rapid, nonexponential decay, while the signal from the Tukey pulse was unaffected up to the threshold TE value. The resulting maps of R2* (=1/T2*) showed R2* elevation in the presence of the gradient offset using the standard pulse. This bias was eliminated using the Tukey pulse (Figure 3). Liver R2* maps obtained using the standard pulse exhibited elevated R2* near the chest wall, due to susceptibility effects from the lung (Figure 4). The degree of elevation depended on slice thickness. With the Tukey pulse, less R2* bias was observed, and there was minimal dependence on slice thickness.

### Discussion

We have demonstrated that the sensitivity of T2* measurements to linear $B_0$ variations can be eliminated by using a Tukey-shaped RF pulse and truncating the echo train where the phase difference across the voxel in any direction exceeds $\pi/2$. Three adjacent slices were acquired to determine the phase difference across the central slice. Alternatively, the truncation point could be determined from the decay curve itself. The technique improves T2* accuracy without the need for post hoc corrections. However, it does not mitigate problems due to higher order $B_0$ variations.

### Acknowledgements

NIH grant: P41 EB017183

### References

[1] Proc. ISMRM 2014; 0442

### Figures

Figure 1: The signal attenuation due to linear B0 variations (right) is the Fourier transform of the slice profile (center), which, in the small flip angle approximation, is in turn the Fourier transform of the pulse waveform (left). Choosing a Tukey pulse eliminates signal attenuation due to background gradients up to a threshold TE.

Figure 2: Signal decay on a semilogarithmic scale from an ROI in the phantom. With good shimming, the signal decays monoexponentially. In the presence of a through-slice gradient offset, the signal obtained using the standard pulse decays nonexponentially and more rapidly, while the signal acquired with the Tukey pulse is unaffected up to a threshold TE.

Figure 3: R2* maps from the phantom using the standard RF pulse (left) and the Tukey pulse (right), with good shimming (top) and a through-slice gradient offset (bottom). R2* is increased in the presence of a background gradient using the standard pulse, but not using the Tukey pulse.

Figure 4: Liver R2* maps obtained using the standard RF pulse (left) and the Tukey pulse (right), with a 6mm slice (top) and a 4.25mm slice (bottom). Elevated R2* is observed near the chest wall using the standard pulse, due to susceptibility effects from the lung. Less bias occurs with the Tukey pulse.

Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)
2954