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Four angle method for accurate and rapid clinical high-resolution whole-brain mapping of longitudinal relaxation time and proton density with B1 inhomogeneity correction
Abinand Rejimon1, Luis Cortina1, Richard G. Spencer1, and Mustapha Bouhrara1

1National Institute on Aging (NIA), National Institutes of Health (NIH), Baltimore, MD, United States

### Synopsis

Changes in longitudinal relaxation time (T1) and proton density (PD) are sensitive markers of microstructural damage associated with different neurological conditions including myelin degradation, axonal loss, inflammation, and edema. In this study, we propose an accurate and rapid approach to mapping T1 and PD with B1 inhomogeneity correction. This four angle method (FAM) is based on the use of four images acquired with different flip angles and short repetition times using the spoiled-gradient recalled-echo sequence available on all preclinical and clinical MRI machines. The accuracy and ease of implementation of the FAM renders it of great potential for clinical investigations.

### PURPOSE

To introduce an accurate approach for rapid high-resolution (HR) whole-brain mapping of longitudinal relaxation time, T1, and proton density, PD, with correction of B1 inhomogeneity.

### METHODS

The Four angle method (FAM) for T1 and PD mapping

The FAM is based on the use of four spoiled-gradient recalled-echo (SPGR) images acquired at different flip angles (FAs) and short repetition times (TRs). Two low-resolution images are used to map the B1 field using the recently-introduced steady-state double angle method (SS-DAM) described below. This B1 map is then used, as a known parameter, in conjunction with two additional HR SPGR images to map T1 and PD, voxel-wise, through a nonlinear least-squares fit of the magnitude of the SPGR signal given by: $$S_{SPGR-Mag}=|\frac{PD (1-exp(-TR⁄T_1 )) sin(B_1 α)}{1-exp(-TR⁄T_1 ) cos(B_1 α)}|$$.

The steady-state double angle method (SS-DAM) for B1 mapping

Similar to the double angle method (DAM) (1), the SS-DAM uses the signal intensity ratio of two SPGR images acquired with different FAs, but with very short TR. In brief, the SS-DAM exploits the linearity of the SPGR signal as a function of FA around 180o (2, 3). In this linear regime, the intensity ratio, $Q =S_{SPGR-Mag} (B_1 (180°-θ),TR)⁄S_{SPGR-Mag} (B_1 (180^°+θ),TR)$, of two SPGR images acquired with different FAs is independent of T1.

To calculate B1 voxel-wise, Q is computed for a large range of B1, assuming a reasonable but arbitrary value of T1 and for a specified value of θ, to create a look-up table of Q vs. B1. The experimental value of Q is determined from the acquired SPGR images. B1 is then estimated in each voxel using a linear interpolation based on the pre-defined look-up table.

Analysis

To evaluate the SS-DAM for B1 mapping, two 3D SPGR images were acquired from the brain of two healthy subjects (male, age 52, and female, age 72) at FAs of 120o or 240o (i.e. θ=60o). Experimental parameters were: TR=35ms, TE=5.1ms, field-of-view (FoV)=260mm x 260mm x 215mm, and acquisition voxel size=2mm x2mm x5mm reconstructed to 2mm x2mm x2mm. The total acquisition time (TAT) was ~3min. B1 maps derived from the SS-DAM were compared to those derived from the DAM (1). Experimental parameters for the DAM consisted of 3D SPGR images acquired at FAs of 120o or 240o with TR=8000ms, TE=6.2ms, EPI factor=11, FoV=260mm x 260mm x 215mm, and acquisition voxel size=4mm x4mm x5mm reconstructed to 2mm x2mm x2mm. The TAT was ~45min. Relative error (RE) maps, given by RE (%) = 100×|B1,SS-DAM - B1,SS-DAM|⁄B1,SS-DAM, and corresponding mean and standard deviation (SD) RE values were also calculated.

To evaluate FAM for T1 and PD mapping, four 3D SPGR images were acquired from the brains of three healthy males of ages 23, 38, and 53. Images were acquired with FA/TR/TE combinations of 120o/35ms/4.7ms and 240o/35ms/4.7ms for B1 mapping using the SS-DAM, and 4o/6.5ms/3ms and 16o/6.5ms/3ms for T1 and PD mapping using the FAM. Experimental parameters were: FoV = 200mm x 200ms x 180mm, voxel size=3.1mm x 3.1mm x 5mm for the images obtained with FAs of 120o and 240o, and voxel size=1.2mm x 1.2mm x 1.2mm for the images obtained with FAs of 4o and 16o. All images were reconstructed to 1mm3. The TAT was ~4min. To analyze the effect of B1 on T1 and PD determination, all derived T1 and PD maps were obtained with and without B1 correction. RE, given by RE (%) = 100×|PCorr - PUncorr|/PCorr, where PCorr and PUncorr are the corrected and uncorrected parameter maps, were also computed. All experiments were performed at 3T after written consent was obtained from each participant.

### RESULTS & DISCUSSION

Visual inspection, RE maps, and mean and SD RE values show that the B1 maps derived using the SS-DAM are quantitatively similar to those derived from the DAM (Fig. 1). We note that the small differences between these methods seen in cerebrospinal fluid and some peripheral regions are due, respectively, to the known T1 dependence of the DAM given the relatively short TR used and susceptibility artifacts resulting from the limited imaging resolution and EPI encoding used in the DAM.

FAM-derived T1 and PD maps with B1 correction exhibit substantially greater homogeneity across the brain as compared to those derived without B1 correction; this is readily seen in the RE maps, showing large differences in T1 and PD values in regions where B1≠1 (Fig. 2). These results demonstrate the necessity of B1 mapping for accurate determination of T1 and PD as well as the accuracy and potential applicability of the FAM.

### CONCLUSION

The FAM is straightforward to implement and permits accurate, rapid, and high-resolution T1 and PD mapping.

### Acknowledgements

The work was supported by the Intramural Research Program of the National Institute of Aging of the National Institutes of Health.

### References

1. Stollberger R, Wach P. Imaging of the active B1 field in vivo. Magnetic Resonance in Medicine. 1996;35:246-51.

2. Dowell NG, Tofts PS. Fast, accurate, and precise mapping of the RF field in vivo using the 180 degrees signal null. Magnetic Resonance in Medicine. 2007;58:622-30.

3. Rejimon AC, Lee DY, Bergeron CM, Zhuo Y, Qian W, Spencer RG, Bouhrara M. Rapid B1 field mapping at 3T using the 180 degrees signal null method with extended flip angle. Magnetic Resonance Imaging. 2018;53:173-179.

### Figures

Figure 1. DAM and SS-DAM SPGR images, and corresponding B1 and RE maps obtained from the brains of two participants. For each slice, mean and SD RE values are computed. Visual inspection of the weighted images shows a large spatial variation in overall signal intensity across the brain. This is quantitatively illustrated by the smooth variation seen in the B1 maps. Furthermore, and more importantly, visual inspection, RE maps, and mean and SD RE values show that the B1 maps derived using SS-DAM are very similar to those derived from the DAM.

Figure 2. Estimated B1, T1, and PD maps obtained from the brains of three participants using high-resolution SPGR images and the FAM. For each participant, results are shown for two slices with (corrected) and without (uncorrected) B1 correction. For each parameter, the relative error map (RE), calculated between corrected and uncorrected maps, and corresponding mean and standard deviation RE value are displayed. FAM-derived T1 and PD maps with B1 correction exhibit greater homogeneity across the brain as compared to those derived without B1 correction; this is readily seen in the RE maps, showing large differences in regions where B1≠1.

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