Synopsis

Myelin water fraction (MWF) is a good biomarker for myelin content. Traditional methods for acquiring MWF maps require long scan times. Recent work has estimated MWF from faster steady-state scans. In this work, we propose to acquire MWF maps from an optimized set of small-tip fast recovery (STFR) scans that can exploit resonance frequency differences between myelin water and the slow-relaxing water compartment.

Introduction

Myelin water fraction (MWF), the proportion of MR signal in a given voxel that originates in water bound within the myelin sheath, is a specific biomarker for myelin content. Such a biomarker is desirable for tracking the onset and progression of demyelinating diseases such as multiple sclerosis. A common way to estimate MWF is from a multi-echo spin echo (MESE) pulse sequence, which is time-consuming.¹ Recent work has estimated MWF from fast steady-state sequences.² In this abstract, we propose estimating MWF from an optimized set of small-tip fast recovery (STFR) scans that can exploit resonance frequency differences between myelin water and the slow-relaxing water compartment. Simulation results illustrate how well STFR scans can estimate MWF.

Methods

The STFR pulse sequence³ consists of a tip-down RF pulse, signal readout, a tip-up RF pulse, and a spoiler gradient. The transverse signal generated by a single STFR scan at a particular voxel (for a single compartment) is

$$M_T\left(M_0,T_1,T_2,\Delta\omega,\kappa,T_{\mathrm{free}},T_{\mathrm{g}},\alpha,\beta,\phi\right) = \frac{M_0 \sin\left(\kappa\cdot\alpha\right)\left[e^{-T_{\mathrm{g}}/T_1}\left(1-e^{-T_{\mathrm{free}}/T_1}\right)\cos\left(\kappa\cdot\beta\right)+\left(1-e^{-T_{\mathrm{g}}/T_1}\right)\right]}{1-e^{-T_{\mathrm{g}}/T_1}e^{-T_{\mathrm{free}}/T_2}\sin\left(\kappa\cdot\alpha\right)\sin\left(\kappa\cdot\beta\right)\cos\left(\Delta\omega\cdot T_{\mathrm{free}}-\phi\right)-e^{-T_{\mathrm{g}}/T_1}e^{-T_{\mathrm{free}}/T_1}\cos\left(\kappa\cdot\alpha\right)\cos\left(\kappa\cdot\beta\right)},$$

where $M_0$ is proton density, $T_1$ is the spin-lattice relaxation time constant, $T_2$ is the spin-spin relaxation time constant, $\Delta\omega$ is off-resonance frequency, $\kappa$ is a flip angle scaling factor (to account for imperfect transmit fields), $T_{\mathrm{free}}$ is the time between the tip-down and tip-up pulses, $T_{\mathrm{g}}$ is the duration of the spoiler gradient, $\alpha$ is the prescribed tip-down flip angle, $\beta$ is the prescribed tip-up flip angle, and $\phi$ is the phase of the tip-up pulse. Note that $M_0$, $T_1$, $T_2$, $\Delta\omega$, and $\kappa$ vary from voxel to voxel, whereas $T_{\mathrm{free}}$, $T_{\mathrm{g}}$, $\alpha$, $\beta$, and $\phi$ are scan parameters that are prescribed over the whole imaging volume.

We consider two non-exchanging intra-voxel water compartments: a fast-relaxing compartment with relaxation time constants $T_{1,\mathrm{f}}$ and $T_{2,\mathrm{f}}$, and a slow-relaxing compartment with relaxation time constants $T_{1,\mathrm{s}}$ and $T_{2,\mathrm{s}}$. We assume the fast-relaxing compartment experiences an additional off-resonance shift $\Delta\omega_\mathrm{f}$.⁴ The signal from a given voxel is a weighted sum of the signal that arises from the fast-relaxing and slow-relaxing compartments, where the weights are $f_\mathrm{f}$ and $1 - f_\mathrm{f}$, respectively, and $f_\mathrm{f}$ denotes the fraction of the signal arising from the fast-relaxing compartment. We estimate the MWF $f_\mathrm{f}$ for each voxel from multiple STFR scans.

We optimized a set of 9 STFR scans to maximize the precision of estimates of $f_\mathrm{f}$. We minimized the expected Cramer-Rao Bound (CRB) of estimates of $f_\mathrm{f}$.⁵ We fixed $T_{\mathrm{free}}$ to 8.0 ms and $T_{\mathrm{g}}$ to 1.5 ms and optimized $\alpha$, $\beta$, and $\phi$. For $\Delta\omega$ and $\kappa$ we used separately acquired B0 and B1 maps, respectively. Table 1 lists the optimized scan parameters.

Using the optimized scan parameters, we simulated the 9 STFR scans using a slice of the BrainWeb phantom.⁶ For white matter, we assigned $M_0 = 0.77$, $f_\mathrm{f} = 0.15$, $T_{1,\mathrm{f}} = T_{1,\mathrm{s}} = 832$ ms, $T_{2,\mathrm{f}} = 20$ ms, $T_{2,\mathrm{s}} = 80$ ms, and $\Delta\omega_\mathrm{f} = 17$ Hz; and for gray matter, we assigned $M_0 = 0.86$, $f_\mathrm{f} = 0.03$, $T_{1,\mathrm{f}} = T_{1,\mathrm{s}} = 1331$ ms, $T_{2,\mathrm{f}} = 20$ ms, $T_{2,\mathrm{s}} = 80$ ms, and $\Delta\omega_\mathrm{f} = 0$.² We generated $\kappa$ to vary from 0.8 to 1.2 (i.e., 20% flip angle variation), and $\Delta\omega$ to vary from -20 to 20 Hz. We added complex Gaussian noise to produce images with SNR ranging from 89-244 in white matter and 64-236 in gray matter, where SNR is defined as $\mathrm{SNR}\left(\mathbf{y},\boldsymbol{\epsilon}\right) \triangleq \frac{\|\mathbf{y}\|_2}{\|\boldsymbol{\epsilon}\|_2}$, where $\mathbf{y}$ is the noiseless data within a region of interest (ROI), and $\boldsymbol{\epsilon}$ is the noise added to the ROI. We estimated $f_\mathrm{f}$ from the STFR images using kernel machine learning.⁷

Results

Discussion and Conclusion

Acknowledgements

References

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