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

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 180^o (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 120^o or 240^o (i.e. θ=60^o). 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 120^o or 240^o 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×|B_1,SS-DAM - B_1,SS-DAM|⁄B_1,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 120^o/35ms/4.7ms and 240^o/35ms/4.7ms for B₁ mapping using the SS-DAM, and 4^o/6.5ms/3ms and 16^o/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 120^o and 240^o, and voxel size=1.2mm x 1.2mm x 1.2mm for the images obtained with FAs of 4^o and 16^o. 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×|P_Corr - P_Uncorr|/P_Corr, where P_Corr and P_Uncorr 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

Acknowledgements

References

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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.