Introduction

The transverse relaxation rate parameter R₂* represents the rate of free-induction-decay (FID) in the absence of macroscopic magnetic field (B₀) gradients. It is composed of reversible (R₂’) and irreversible (R₂) contributions as R₂*=R₂+R₂’. R₂’ is of particular interest as it characterizes susceptibility-induced voxel signal modulations, for example, in the presence of deoxygenated hemoglobin in brain microvasculature1 or iron deposits in deep gray matter (GM) structures². Currently practiced R₂’ measurement methods³ build on a spin-echo sequence configuration to eliminate the R₂ effect, and hence require impractically long scan time for volumetric 3D R₂’ mapping. Furthermore, large susceptibility gradients around air/tissue interfaces result in signal distortions with increasing echo times (TE), thus making it challenging to achieve accurate R₂’ estimation in deep GM regions. Here, we propose an alternating, 3D z-shimmed, unbalanced steady-state-free-precession (SSFP) technique for rapid and B₀-corrected R₂’ mapping in the human brain.

Methods

Sequence configuration: Figure 1a shows a timing diagram of the proposed pulse sequence. SSFP-FID and SSFP-ECHO modules are alternating along the entire echo train, while producing a plurality of gradient-recalled echo signals within each time-of-repetition (TR). The temporal evolution of these two sets of signals can be expressed in terms of rate constants, R₂* (=R₂+R₂’) and R₂** (=R₂-R₂’), for SSFP-FID and SSFP-ECHO, respectively (Fig. 1b). It is noted that this scheme is essentially analogous to the GESFIDE method⁴, but runs in a steady-state regime, thereby allowing rapid encoding of the relaxation information. Second, a radial stack-of-stars k-space sampling scheme (Fig. 1c) is employed so as to make the method relatively immune to physiologic motions⁵ that manifest as ghosting artifacts in Cartesian sampling. Finally, z-shim gradients and corresponding rewinders are alternately inserted along the z-axis (Fig. 1a) as in Han et al.⁶, making every even echo z-shimmed and thereby able to capture signals in regions with large B₀ gradients (g_z). The polarity of the z-shim gradients in SSFP-ECHO is reversed relative to that in SSFP-FID to account for the phase-reversal effect of the SSFP-ECHO signal mechanism. Figure 2 represents a simplified extended phase diagram for the present pulse sequence.
Data processing: Figure 3 illustrates a three-step data processing scheme consisting of image reconstruction, B₀ correction, and model fitting. K-space data were Fourier-transformed along the through-plane direction, followed by 2D gridding reconstruction for individual slices. Subsequently, a g_z map, obtained using the phase images from both SSFP-FID and SSFP-ECHO, was used to estimate the voxel-spread-function (VSF) along the z-direction. Briefly, the VSF method⁷ approximates a B₀ inhomogeneity induced voxel signal modulation as convolution of a signal-leakage function (VSF) with ideal signals in the neighboring voxels, leading to the correction of such effect. It has previously been shown that incorporating z-shimmed signals in the VSF method improves the accuracy of R₂* estimation in regions with large g_z values⁶. Finally, mono-exponential fitting of the B₀-corrected signals was performed voxel-by-voxel to yield R₂* and R₂** from SSFP-FID and SSFP-ECHO multi-echo data, leading to R₂ = (R₂*+R₂**)/2 and R₂’ = (R₂*-R₂**)/2 maps.
In vivo experiments: Experiments were performed at 3 T (Siemens Prisma) in two healthy subjects. A 32-channel head coil was used for signal reception. Imaging parameters were: TR = 32 ms, echo-spacing = 1.5 ms, number of echoes = 19, number of radial views = 160; FOV = 240 x 240 x 120 mm³, image matrix size = 160 x 160 x 40, voxel size = 1.5 x 1.5 x 3 mm³, slice oversampling factor = 25%, and scan time = 8.5 min. High-resolution T₁-weigthed images were additionally acquired for brain segmentation with SPM12 software⁸. Derived R₂ and R₂’ maps were overlaid onto the T₁-weighted images, while those in each voxel were averaged over segmented gray matter (GM) and white matter (WM) regions, respectively.

Results

Figure 3c shows the effectiveness of the present B₀ correction approach (z-shimming in combination with the VSF method). Without B₀ correction, both R₂* and R₂** are erroneously estimated in regions where the magnetic field varies rapidly (corresponding to high g_z in Fig. 3b), while with correction such errors are largely eliminated. Figure 4 shows R₂ and R₂’ maps in the three orthogonal planes, obtained in the two subjects (see Figure 4 for regional averages of the two parameters). Heavily T₂-weighted images (SSFP-ECHO at TE=2ms) are also provided as anatomical reference, particularly for deep GM structures in which, compared to cortical GM areas, both R₂ and R₂’ are substantially overestimated.

Discussion and Conclusions

The unbalanced SSFP-based approach makes it possible to achieve rapid 3D encoding of transverse relaxation parameters, while the VSF model with z-shim gradients allows estimation of those parameters in regions with strong B₀ inhomogeneity. While regional averages of R₂ (Fig. 4) agree well with literature values⁹, R2’ values are higher than those reported by Ni et al.’s³, which may be attributed to the large R₂’ values obtained in deep GM regions known to be rich in non-heme iron¹⁰, an issue that warrants further scrutiny with larger number of subjects and compartmentalized analysis. Upon further validation, the present method may serve as a tool for quantification of metabolic parameters as well as iron content covering much of the brain including regions suffering from large intrinsic gradients.

Acknowledgements

NIH grants R21EB022687 and UL1TR001878