With the increasing popularity of field strengths of 3T and above, there has been a growing appreciation for the need to correct for the dephasing effects of through-plane gradients in 2D gradient-echo acquisitions^[1], since susceptibility gradients (e.g., due to air-tissue interfaces) are more prominent at higher fields. A sinc-term correction is often employed for this purpose^[2-5], based on the assumption of “ideal” rectangular slice profiles. Our goal here was to measure the slice profiles generated by typical 2D gradient-echo sequences on a clinical scanner and to compare the effectiveness of the sinc-term correction for R₂* mapping with a correction based on experimentally measured slice profiles.

A Siemens cylindrical phantom (1900 mL; 3.75g NiSO₄×6H₂O + 5g NaCl per 1000g distilled H₂O) was scanned on a 1.5T Avanto MR system (Siemens Healthcare, Erlangen, Germany) with a 12-channel receive coil. The product multi-gradient-echo sequence (“gre”) was run with following parameters: FA=90°, TR=2 s, 12 unipolar gradient-echoes with TEs from 6 to 77.5 ms (BW=230 Hz/px), 2D acquisition with 15 axial slices with 4/2 mm slice thickness/gap and 2×2 mm² in-plane voxel size (matrix=128×128). To investigate the effect of through-plane gradients, shim settings were deliberately adjusted in order to induce z-direction gradients of BGz = 0, 50, 100 or 200 µT/m. To measure slice profiles (BGz=0 only), the “gre” pulse-sequence code was modified to have the readout (RO) gradient in the same direction as the slice-select (SS) gradient (see Fig. 1a). All parameters were as above, except for the number of slices and the voxel size, which were reduced to 1 and 0.5×0.5 mm², respectively (matrix=512×512; BW=570 Hz/px), with the increased resolution chosen here to provide a more fine-grained slice profile measurement.

For each voxel in a 50×50 mm² region of interest (ROI) in the center of the phantom (for the 2×2 mm² acquisitions described above), reference R₂* values were obtained from straight-line fits to $\ln{(S)}$ versus $\text{TE}$ for the BGz=0 data, where $S(\text{TE})$ is the signal magnitude at time $\text{TE}$, with monoexponential decay assumed. Through-plane gradients cause dephasing that modulates $S(\text{TE})$ with a multiplicative factor $F(\text{TE})$; for a rectangular slice profile, $F_{\text{RECT}}(\text{TE})=\text{sinc}(\frac{\gamma}{2}\ \text{BGz}\ \Delta z\ \text{TE})$, where $\gamma$ is the gyromagnetic ratio and $\Delta z$ is the nominal slice thickness^[2]. Given measured slice profiles (MSP), an alternative modulation function $F_{\text{MSP}}(\text{TE})$ was obtained via numerical integration, as described by Hernando et al^[1]. Corrected R₂* values were then obtained by dividing $S(\text{TE})$ by $F_{\text{RECT}}(\text{TE})$ prior to fitting^[2,3] (with care taken to avoid “divide-by-zero” issues) or alternatively by dividing by $F_{\text{MSP}}(\text{TE})$ instead.

Fig. 1 shows the result of the slice profile measurement on the cylindrical phantom—note the substantial departure from the “ideal” rectangular profile. For a central voxel in the 2×2 mm² data, Fig. 2 shows plots of signal magnitude $S$ versus $\text{TE}$ for BGz=0 (black curves), for which the decay is indeed monoexponential, and for BGz=200 µT/m (black dots). Multiplying the BGz=0 data by $F_{\text{RECT}}$ and $F_{\text{MSP}}$ results in the red and blue curves, respectively, with $F_{\text{MSP}}$ clearly providing a much better agreement with the BGz=200 µT/m data. Fig. 3 shows a comparison of the corrected R₂* values obtained from using $F_{\text{RECT}}$ versus $F_{\text{MSP}}$, with the latter in much closer agreement with the reference R₂* values (from the BGz=0 data) of $10.6 \pm 0.2$ s^-1 in the green ROI shown in Fig. 2a.Failure to adequately correct for the effect of through-plane gradients in 2D gradient-echo acquisitions could obscure the “intrinsic” R₂* near air-tissue susceptibility interfaces, compromising information about field perturbations and therefore tissue structure at microscopic-to-mesoscopic spatial scales^[2]. We have shown here that sinc-term corrections fare poorly compared to corrections based on measured slice profiles when using the Siemens product “gre” sequence, which uses Hanning-filtered sinc waveforms for RF excitation pulses. We acknowledge that this discrepancy may be reduced with the use of custom RF pulses (e.g., SLR pulses^[6]) that may provide slice profiles that are closer to rectangular, or with the use of thinner slices. We remark that the considerations herein do not apply to 3D gradient-echo acquisitions, for which the effect of “through-plane” gradients (i.e., in the 2^nd phase-encoding direction) is very different^[7,8].