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Impact of Magnetic Susceptibility Anisotropy at 3 T and 7 T on T2*-based Myelin Water Fraction Imaging

Eva Alonso Ortiz¹, Ives R. Levesque^1,2, and G. Bruce Pike³

¹McGill University, Montreal, QC, Canada, ²Research Institute, McGill University Health Centre, Montreal, QC, Canada, ³University of Calgary, Calgary, AB, Canada

Synopsis

In this work we estimated the impact of myelin’s magnetic susceptibility anisotropy on the Myelin Water Fraction (MWF) at 3T and 7T. We simulated realistic multicomponent T2* decay and then computed the MWF using three different fitting models. Our findings indicate that the effect of myelin’s magnetic susceptibility anisotropy does not need to be considered when computing the MWF at 3T. However, failure to do so at 7T can lead to a significant bias in the MWF.

Purpose

Myelin Water Fraction (MWF) mapping based on multi-gradient recalled echo (MGRE) imaging ^1-3 can be achieved though regularized non-negative least squares (rNNLS) fitting of a T2* distribution ³ or 3-component fitting ^{4, 5}, where the 3 components are assumed to be: myelin water (MW), extra-cellular water (EW) and axon water (AW). Recent work has indicated that a 3-component model with additional free parameters, corresponding to frequency offsets ($$$\delta f$$$) for the water components, may lead to improved multicomponent fitting ⁶ and more stable MWF estimates ⁷. The $$$\delta f$$$’s appear to depend on both B₀ and the orientation of white matter (WM) fiber bundles relative to B₀($$$\theta$$$). In this work, we assessed the impact of orientation-dependent $$$\delta f$$$’s on the MWF derived from multicomponent analysis of simulated T2* data at 3T and 7T.

Methods

Multicomponent T2* decay was simulated for WM at 3T and 7T. T2* components were generated for MW (12%), EW (38%), and AW (50%), with relaxation times at 3T equal to: 10 ms, 48 ms, and 64 ms ⁷, respectively. At 7T, the relaxation times were correspondingly set to 6 ms, 30 ms, and 40 ms ⁸. Another simulation was performed in which the EW and AW T2* values were switched. Additional component fractions (MWF = 5% and 20%) were simulated to reflect a range of myelin density from low myelination to densely myelinated. The frequency offsets for each of the three components were calculated using the Hollow Cylinder Fiber Model (HCFM) ⁹, for five $$$\theta$$$’s ranging from 0 to $$$\pi/2$$$ in steps of $$$\pi/8$$$. Complex signals were generated for each orientation with 64 echoes, TE1 = 2.4 ms and echo spacing = 1.2 ms. Two-hundred realizations of Gaussian-distributed zero-mean noise were added on the real and imaginary components to produce SNR levels of 100 to 200, in steps of 20, in the magnitude data at TE1. The simulated signals were analyzed using three different methods:

1. MCMT2*: rNNLS multi-component fitting of a T2* distribution to the signal magnitude, with a 25 ms cutoff time for MW.

2. 3CMT2*: 3-component T2* fitting to the signal magnitude:

$$ s=A_{MW}e^{-t(1/T^*_{2,MW})}+A_{EW}e^{-t(1/T^*_{2,EW})}+A_{AW}e^{-t(1/T^*_{2,AW})} $$

3. 3CCT2*: 3-component T2* fitting with $$$\delta f$$$ terms to the complex T2* signals:

$$ s=A_{MW}e^{-t(1/T^*_{2,MW}+i2\pi \delta f_{MW})}+A_{EW}e^{-t(1/T^*_{2,EW})}+A_{AW}e^{-t(1/T^*_{2,AW}+i2\pi\delta f_{AW})} $$

The HCFM model predicts $$$\delta f_{EW}$$$ = 0, therefore it was assumed to be zero. The MWF (defined as the ratio of MW to total water) and fit residuals obtained using the three different methods were compared and the stability of the fits with respect to SNR was evaluated.

Results

At 3T, both MCMT2* and 3CMT2* led to accurate MWF values, independent of $$$\theta$$$. When considering all simulations (200 repetitions x 5 angles = 1000 simulations) with SNR = 140 and true MWF = 12%, the mean MWF (± standard deviation (std)) was (11.8 ± 1.0)% and (11.7 ± 0.9)% for MCMT2* and 3CMT2*, respectively. 3CCT2* led to increased variability in the MWF ((12.5 ± 9.9)% across all 1000 simulations). At 7T, the accuracy of the MWF obtained from MCMT2* and 3CMT2* decreased for $$$\theta > \pi/4$$$: (14.7 ± 2.6)% for MCMT2* and (12.8 ± 1.5)% for 3CMT2* when $$$\theta = 0$$$, vs. (5.3 ± 0.5)% for MCMT2* and (20.5 ± 6.5)% for 3CMT2* when $$$\theta = \pi/2$$$. Although 3CCT2* increased the accuracy of the MWF when $$$\theta > \pi/4$$$: (11.6 ± 3.3)% (when $$$\theta = \pi/2$$$), this came at the expense of accuracy in the MWF when $$$\theta = 0$$$ (5.1 ± 2.7)% (Figure 1). These observations were consistent across the SNR range used, when EW and AW T2* values were switched, and for MWF = 5 and 20%. For $$$\theta = \pi/2$$$ (i.e. when the $$$\delta f$$$’s were largest), 3CCT2* led to minimal fit residuals at both 3T and 7T, despite the fact that at 3T 3CCT2* produced the least accurate fit parameters. When $$$\theta = 0$$$, MCMT2*, 3CMT2* and 3CCT2* all possessed comparable fit residuals (Figure 2).

Discussion and Conclusions

While the examination of fit residuals indicated that inclusion of $$$\delta f$$$ terms in the fitting model led to improved fits, our simulations showed that MWFs were not necessarily accurate. These results demonstrate that if only MWF maps are sought, and not additional information regarding $$$\delta f$$$ or $$$\theta$$$, MCMT2* or 3CMT2* are appropriate at 3T. This does not hold at 7T, where lack of $$$\delta f$$$’s in the fitting model can result in large errors in the MWFs. It is noteworthy that 7T MWF estimates when $$$\theta \leq \pi/4$$$ were more accurate if frequency offsets were not included in the fit (MCMT2* or 3CMT2*). In our simulations, 3CCT2* was mainly beneficial when $$$\theta > \pi/4$$$.

Acknowledgements

This study was supported by the Fonds de recherche du Québec – Nature et technologies (FRQNT), Graduate Scholarship to Eva Alonso Ortiz, the CREATE Medical Physics Research Training Network grant of the Natural Sciences and Engineering Research Council (NSERC, Grant number 432290), the Canadian Institutes for Health Research (CIHR, Funding Reference Number 43871), and the Natural Sciences and Engineering Research Council (NSERC Discovery, Grant number 170426).

References

1. Du, Y., et al., Fast multislice mapping of the myelin water fraction using multicompartment analysis of T2* decay at 3T: a preliminary postmortem study. Magnetic resonance in medicine, 2007. 58(5): p. 865-870.

2. Hwang, D., D.-H. Kim, and Y. Du, In vivo multi-slice mapping of myelin water content using T2* decay. NeuroImage, 2010. 52(1): p. 198-204.

3. Lenz, C., M. Klarhöfer, and K. Scheffler, Feasibility of in vivo myelin water imaging using 3D multigradient-echo pulse sequences. Magnetic resonance in medicine, 2012. 68(2): p. 523-528.

4. Andrews, T., et al., Testing the three-pool white matter model adapted for use with T2 relaxometry. Magnetic resonance in medicine, 2005. 54(2): p. 449-454.

5. Lancaster, J., et al., Three-pool model of white matter. Journal of magnetic resonance imaging : JMRI, 2003. 17(1): p. 1-10.

6. van Gelderen, P., et al., Nonexponential T(2) decay in white matter. Magn Reson Med, 2012. 67(1): p. 110-7.

7. Nam, Y., et al., Improved estimation of myelin water fraction using complex model fitting. Neuroimage, 2015. 116: p. 214-21.

8. Sati, P., et al., Micro-compartment specific T2* relaxation in the brain. Neuroimage, 2013. 77: p. 268-78.

9. Wharton, S. and R. Bowtell, Fiber orientation-dependent white matter contrast in gradient echo MRI. Proc Natl Acad Sci U S A, 2012. 109(45): p. 18559-64.

Figures

Figure 1: Mean (red) ± std (blue) MWF for a range of fiber orientations, using MCMT2*, 3CMT2*, and 3CCT2* at 3 T (left) and 7 T (right). The true MWF is shown in green. The 95% confidence interval for the mean is shown in pink.

Figure 2: Average residuals (over 200 iterations of noise) ± std for θ = 0 (top) and θ = π/2 (bottom) using MCMT2* (black), 3CMT2* (blue), and 3CCT2* (red), at 3 T (left) and 7 T (right). The MCMT2* data points (black) at 3 T for θ = π/2 (bottom left plot) overlap with the 3CMT2* data points (blue).

Proc. Intl. Soc. Mag. Reson. Med. 25 (2017)

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