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

^{1}Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI, United States, ^{2}Medical Physics, Memorial Sloan Kettering Cancer Center, New York, NY, United States, ^{3}Biomedical Engineering, University of Michigan, Ann Arbor, MI, United States

Myelin water fraction (MWF) estimates are desirable for tracking the progression of demyelinating diseases such as multiple sclerosis. To address the long scan times of conventional MWF imaging methods, faster steady-state scans have been studied recently. One such steady-state scan is small-tip fast recovery (STFR). This work compares STFR-based MWF estimates using a two-compartment tissue model without exchange to those obtained using a three-compartment tissue model with exchange. Using a three-compartment model with exchange results in MWF estimates that are closer to traditional multi-echo spin echo (MESE) estimates.

We first compared the two tissue models in simulation. We simulated STFR and MESE scans for typical white matter and gray matter tissue parameters using the three-compartment model with exchange. These simulations were computed by numerically solving the Bloch-McConnell equation. For the STFR scans, we used scan parameters that were optimized to minimize the Cramer-Rao Lower Bound (CRLB) of unbiased estimates of MWF

After simulating the scans, we estimated MWF from the STFR scans using a kernel-based estimation method (PERK).

We next compared the two tissue models in vivo. We acquired STFR and MESE scans of a healthy volunteer using the same scan parameters as in simulation. We also acquired a pair of Bloch-Siegert (BS) scans for separate B1+ estimation (used in the STFR-based MWF estimation). The scans were 3D acquisitions with matrix size 200 $$$\times$$$ 200 $$$\times$$$ 9 and isotropic 1.1 mm resolution. The STFR and BS scans combined took 7 min 14 s, and the MESE scan took 36 min 11 s. As in simulation, we estimated MWF from the STFR scans using PERK; in one case PERK was trained using the two-compartment model without exchange, and in the other case PERK was trained using the three-compartment model with exchange. We also estimated MWF from the MESE data using NNLS.

Figure 3 and Table 2 summarize in vivo results. Again, the STFR-based MWF estimates when training with the two-compartment model are higher than those obtained when training with the three-compartment model. These latter estimates are closer to the MESE-based MWF estimates. The MESE MWF map appears noisier than those shown in other works, which is likely due to the lower SNR of our data due to differences in voxel size. To match the STFR resolution, we acquired MESE with 1.1 mm isotropic voxels, whereas often MESE data is collected with slice thickness of 5 mm and 1.6 mm or greater in the phase encode direction.

We focused on a three-compartment tissue model in this work, where we combined intra- and extra-cellular water pools into a single, non-myelin water compartment. One could separate these into two compartments, resulting in a four-compartment model. Further work is needed to determine whether the additional model complexity leads to significantly better MWF estimates.

We thank Dr. Navid Seraji-Bozorgzad for discussions of in vivo results.

This work was supported by NIH R21 AG061839.

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Figure 1: Illustration of the two-compartment and three-compartment tissue models. The subscripts "f", "s", and "m" represent, respectively, myelin water, non-myelin water, and macromolecules. In both cases, we model the additional off-resonance experienced by the myelin water compartment.^{18} Other myelin water imaging works typically ignore this additional off-resonance parameter.

Figure 2: MWF maps from simulated test data for a three-compartment tissue model with exchange. STFR2-PERK shows MWF estimation using PERK trained with the two-compartment non-exchanging STFR model. STFR3-PERK shows MWF estimation using PERK trained with the three-compartment exchanging STFR model. MESE-NNLS shows MWF estimation using MESE and regularized NNLS. Using the three-compartment model results in more accurate MWF estimates than the two-compartment model. Table 2 reports numerical results. The anatomy for this simulated data is from BrainWeb.^{19}

Table 1: Numerical results associated with Figure 1. The reported time refers to the entire estimation, combining the time to estimate MWF in white matter voxels and gray matter voxels; it also includes training time for the methods that use PERK. The best value in each column is highlighted. Using the three-compartment model results in more accurate MWF estimates than using the two-compartment model. Furthermore, STFR3-PERK is the most accurate of the three methods compared here.

Figure 3: MWF maps from in vivo MESE data and STFR data. STFR2-PERK shows MWF estimation using PERK with the two-compartment non-exchanging STFR model. STFR3-PERK shows MWF estimation using PERK with the three-compartment exchanging STFR model. MESE-NNLS shows MWF estimation using MESE and regularized NNLS. Using the three-compartment model results in MWF estimates that are closer to MESE-NNLS values than using the two-compartment model. Table 3 shows numerical results for several manually selected regions of interest.

Table 2: *Left*: White matter (WM) and gray matter (GM) regions of interest (ROIs). The underlying image is from a standard MP-RAGE acquisition, acquired in the same scan session and registered to the other scans. *Right*: Sample means $$$\pm$$$ standard deviations of MWF estimates for four WM ROIs and one GM ROI for the MWF maps in Figure 3. The two-compartment STFR2-PERK MWF estimates differ significantly from the MESE-NNLS estimates,whereas,for each WM ROI,the STFR3-PERK MWF estimates match the MESE-NNLS estimates to within one standard deviation.