Synopsis

Keywords: Electromagnetic Tissue Properties, White Matter

The magnetic source separation method can estimate contributions of diamagnetic myelin and paramagnetic iron in the white matter using solely gradient-echo data in white matter. This study determined the relationship between negative susceptibility (χ-) and fractional anisotropy as a myelin-sensitive biomarker and compared with the conventional susceptibility (χ) in young healthy volunteers. There was a significant negative correlation between the χ- and FA. In contrast, the conventional χ has a weaker correlation to the FA than the χ- result. However, the χ- in white matter represented the non-monotonic fiber orientation dependence on the B0 field.

Introduction

Magnetic source separation method was recently developed using solely gradient-echo data to estimate the positive (χ+) and negative (χ-) magnetic susceptibility sources as an advanced quantitative susceptibility mapping (QSM) algorithm^{1, 2}. We compared the relationships between fractional anisotropy (FA) evaluated by diffusion tensor imaging (DTI) and χ+, χ-, and conventional χ from single-orientation acquisition, and investigated the fiber orientation dependences in R2* and χ- with respect to the B0 field due to the susceptibility anisotropy effect in the white matter in healthy volunteers.

Materials and methods

1. Closed-form solution of magnetic source separation
The R2* signal decay rate represents the summation of R2 and R2’ signal decay rates. The R2* can be approximated by χ+, χ-, and relaxomatric constant α assuming spatial invariant from gradient echo data alone using a first-order approximation expressed by the below equation³.
$$R_2^*(r)=R_2^,(r)+R_{2}(r)\approx\alpha(\chi^{+}(r)-\chi^{-}(r)) $$
The minimization problem can estimate the χ+ and χ- maps using the above approximation of R2* and the relationship between the tissue local field and the two susceptibility maps.
$$argmin_{\chi^{+},\chi^{-}}\parallel R_2^*-\alpha(\chi^{+}-\chi^{-})\parallel_2^2+\parallel f_{local}-D(\chi^{+}+\chi^{-})\parallel _2^2+\lambda\parallel WG\chi^{+}\parallel_1+\lambda\parallel WG\chi^{-}\parallel_1$$
where α is 1.98 × 137 Hz/ppm, f is tissue local field, λ is L1-regularization parameter, G are gradient operators in x, y, and z directions, W is data-weighting mask generated from second deviation of local field, and D is dipole kernel. This minimization problem adopted the alternative direction method of multipliers formalism and introduced additional variables z_1,2 and s_1,2.
$$argmin_{\chi^{+},\chi^{-},z_1, z_2}\parallel R_2^*-\alpha(\chi^{+}-\chi^{-})\parallel_2^2+\parallel f_{local}-D(\chi^{+}+\chi^{-})\parallel _2^2+\lambda\parallel Wz_1\parallel_1$$
$$+\lambda\parallel Wz_2\parallel_1+\frac{\mu}{2}\parallel G\chi^{+}-z_1+s_1\parallel_2^2+\frac{\mu}{2}\parallel G\chi^{-}-z_2+s_2\parallel_2^2$$
This extended minimization problem was solved by iterative calculation by splitting into the four subproblems for χ+, χ-, z₁, and z₂ with updating s₁ and s₂ to minimize L1-norm via L2-minimization and soft-thresholding with an additional parameter μ = 100λ.

2. MR acquisition and imaging processing
We enrolled 17 healthy volunteers (mean age: 28 ± 5,) on a 3.0 T MRI (Ingenia 3T; Philips Medical Systems International). They were acquired multiple spoiled gradient echo (mSPGR), DTI, and magnetization-prepared rapid acquisition with a gradient echo sequence (MPRAGE) for the spatial normalization. The scan parameters for mSPGR with bipolar readout were as follows: field of view, 192 × 192 × 148 mm³; acquisition voxel size, 1 × 1 × 1 mm³; the number of TE values, 17; TE1, 1.9 ms; ΔTE, 1.9 ms; TR, 35 ms; and flip angle, 15. The multiple-phase images that underwent eddy current correction due to bipolar readout⁴ were performed Laplacian-based phase unwrapping⁵ and background field removal by a variable-kernel sophisticated harmonic artifact reduction for the phase-data algorithm⁶ at each TE. Weighted averaging was performed on the local fields of each TE based on the R2* map estimated from the magnitude images⁷. Then, the χ+, χ-, and conventional susceptibility and R2* maps were reconstructed. To estimate the FA and main fiber orientation with respect to the B0 field, DTI with the 15-diffusion gradient axis was acquired by the following parameter: field of view, 192 × 192 × 148 mm³; acquisition voxel size, 2 × 2 × 2 mm³; TE, 84 ms; and acceleration factor, 2.0. The spatial distortion and eddy current corrections to the DTI were performed by FUGUE using a field map and eddy_correct function⁸ on FSL.

3. Imaging analysis
The χ+, χ-, conventional χ, R2*, FA, and fiber orientation maps were performed co-registration and spatial normalization without spatial smoothing using MPRAGE on SPM12. To determine the relationships among FA and χ+, χ-, and conventional susceptibility using bivariate correlation analyses, we measured the mean values in the spatially normalized FA and susceptibility maps in all regions mapped in the JHU-WM atlas⁹. Moreover, to investigate the main fiber orientation dependences of R2* and χ-, the pixel values in all white matter regions were binned for main fiber orientation with 3° intervals.

Results and Discussion

The χ+ and χ- maps were successfully reconstructed by the closed-form solution of magnetic source separation (Figure1). There was a significant negative correlation between the χ- and FA, while the χ+ was not agreed with the FA (Figure2a and b). Moreover, the conventional χ has a weaker correlation to the FA than the χ- result (Figure2c). The diamagnetic myelin and paramagnetic iron can contribute to the whiter matter susceptibility estimated by conventional χ. The χ- map estimated by the susceptibility separation method might be a more myelin-sensitive biomarker than the conventional χ map. The binned R2* values were increased with increasing fiber orientation in the white matter regions mapped in the JHU-WM atlas. This result was consistent with the linear combination model of cos2θ and cos4θ functions¹⁰ (Figure 3b). However, the binned χ- values represented the non-monotonic fiber orientation dependence on the B0 field (Figure 3a). This nonlinearity might be caused by the susceptibility anisotropy effect and echo-time dependence on the tissue local field¹¹, which can affect the estimated susceptibility value. Although the χ- was sensitive to the myelin, similar to the FA, the χ- evaluation in the white matter needs to consider the fiber orientation dependence on the B0 field.

Conclusion

The χ- map might be a more myelin-sensitive biomarker than the conventional χ map. The χ- estimated from a single-orientation acquisition in white matter represented the non-monotonic fiber orientation dependence on the B0 field.

Acknowledgements

No acknowledgement found.