Steven T. Whitaker^{1}, Gopal Nataraj^{2}, Mingjie Gao^{1}, Jon-Fredrik Nielsen^{3}, and Jeffrey A. Fessler^{1}

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.

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.

The STFR pulse sequence^{3} 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}

[1] A. Mackay, K. Whittall, J. Adler, D. Li, D. Paty, and D. Graeb. In vivo visualization of myelin water in brain by magnetic resonance. Mag. Res. Med., 31(6):673–7, June 1994.

[2] G. Nataraj, J-F. Nielsen, M. Gao, J. A. Fessler. Fast, precise myelin water quantification using DESS MRI and kernel learning. arXiv:1809.08908v1 [physics.med-ph].

[3] J-F. Nielsen, D. Yoon, D. Noll. Small‐tip fast recovery imaging using non‐slice‐selective tailored tip‐up pulses and radiofrequency‐spoiling. Mag. Res. Med., 69(3):657-66, March 2013.

[4] K. Miller, S. Smith, P. Jezzard. Asymmetries of the balanced SSFP profile. Part II: white matter. Mag. Res. Med., 63(2):396-406, February 2010.

[5] G. Nataraj, J-F. Nielsen, and J. A. Fessler. Optimizing MR scan design for model-based T1, T2 estimation from steady-state sequences. IEEE Trans. Med. Imag., 36(2):467–77, February 2017.

[6] D. L. Collins, A. P. Zijdenbos, V. Kollokian, J. G. Sled, N. J. Kabani, C. J. Holmes, and A. C. Evans. Design and construction of a realistic digital brain phantom. IEEE Trans. Med. Imag., 17(3):463–8, June 1998.

[7] G. Nataraj, J-F. Nielsen, C. D. Scott, and J. A. Fessler. Dictionary-free MRI PERK: Parameter estimation via regression with kernels. IEEE Trans. Med. Imag., 37(9):2103–14, September 2018.

Table 1: Optimized STFR scan parameters for the 9 scans. $$$\alpha$$$ and $$$\beta$$$ were limited to 15 degrees. The optimization was done over a range of unknown parameter values: $$$f_\mathrm{f}$$$ ranged from 0.03-0.31, $$$T_{1,\mathrm{f}}$$$ from 320 to 480 ms, $$$T_{1,\mathrm{s}}$$$ from 800 to 1000 ms, $$$T_{2,\mathrm{f}}$$$ from 16-24 ms, $$$T_{2,\mathrm{s}}$$$ from 64-96 ms, and $$$\Delta\omega_\mathrm{f}$$$ from 5-35 Hz.

Figure 1: MWF estimates from simulated STFR scans compared to ground truth. The MWF estimates in white matter agree well with the true values.

Table 2: Sample statistics and RMSE of estimated MWF values, computed over 7742 white-matter-like voxels. MWF is slightly overestimated, but the estimates are very precise and have low RMSE. In particular, the RMSE here is better than the methods explored in ^{2} (cf. Table 2 in ^{2}).

Figure 2: MWF estimates from simulated STFR scans compared to ground truth when $$$\Delta\omega_\mathrm{f} = 0$$$. The MWF estimates in white matter no longer agree well with the true values.