Dushyant Kumar^{1}, Hari Hariharan^{1}, Jens Fiehler^{2}, Susanne Siemonsen^{2}, Jan Sedlacik^{2}, and Ravinder Reddy^{1}

**Problem:** The clinical
utility of myelin water fraction (MWF) mapping based on multi-echo-spin-echo
(MESE) T2-relaxometry is prohibitively slow (~90-120 minutes for acquisition matrix
128x128x50; TR 3s). MWF-values from T2-prep based approach and mcDESPOT (Multicomponent-driven-equilibrium-single-pulse-observation-of-T1-and-T2)
matches poorly with MESE based quantification.

**Methods: **We compare GRASE (Gradient-and-Spin-Echo)
based MWF quantifications against those from MESE and compare our algorithm
against current state of the art. 3D non-selective GRASE, MESE were optimized. Implemented
post-processing method utilizes spatial correlations in 3D local neighborhoods to
improve noise stability, while simultaneously accounting for stimulated echo
contributions.

**Results &
Conclusions:**
Results demonstrate good consistency
between both sequences.

The clinical utility of
myelin water fraction (MWF) mapping based multi-echo-spin-echo (MESE) T2-relaxometry
is impeded due to prohibitively slow scan time, needing ~60-90 minutes for
whole brain coverage (matrix 128x128x50; TR 3 sec). There are alternative clinical
feasible methods to measure MWF-maps, such as T2-prep based approach and
mcDESPOT (Multicomponent-driven-equilibrium-single-pulse-observation-of-T1-and-T2),
though they do not show good correspondence with MESE based MWF-quantification^{1-5}. The purpose of this study is to
evaluate the effect of filling up outer k-space using gradient echoes on
MWF-quantification in GRASE (gradient and spin echo) based quantifications.
ROI-averaged
MWF-values extracted using 3D non-selective GRASE have been shown to correspond
very well with corresponding values from 3D non-selective MESE^{6};
those voxelwise match appear less consistent.

We have recently proposed an
expectation-maximization (EM) based algorithm (submitted in another abstract;
also refer to Fig 1 for flow chart), which utilizes the local spatial
correlation in 3 dimensional neighborhood to improve noise stability of underlying
T2-distributions. In this abstract, we compare the performance of our EM based
algorithm against that proposed by Prasloski et al.^{7}. We demonstrate
better consistency with MESE-based quantification in WM-tracts.

For
a known flip angle error (FAE), the T2-decay can be written as the linear
function of underlying T2 distributions (x)^{8}: y_{EPG}
= A_{EPG}x + ε, with
A_{EPG}(i,j) = intensity at echo time-point TE(i) due to unit water fraction at T2 value T2(j) . The
single voxel parameters x, y, ε can
be stacked as multi voxel column vectors $$$\overline{x}, \overline{y}, \overline{\epsilon}$$$
and the corresponding multi voxel equivalent
can be written as: $$$\overline{y} = A_{MV}\overline{x}+\overline{\epsilon}$$$
.
Here, A_{MV} is the block
diagonal matrix, constructed with voxelwise-A_{EPG} along its block. It
was previously shown^{8} that by simultaneous implementation of
conventional and spatial regularization, a more noise robust reconstruction of
MWF-map is possible:

$$\widehat{x} = arg min_x {||A_{MV}\overline{x}- \overline{y} ||}^2+M_T{||\overline{x}||}^2+\mu_s{||D_s \overline{x}||}^2$$

**Data:** QT2R
data was acquired from 2 healthy volunteers using CPMG based non-selective MESE
and GRASE sequences (3T Philips-Ingenia) with: axial FOV 230x190 mm, voxel
resolution 2 x 2 x 3.5 mm3, receiver bandwidth 355 kHz, 12 slices,
TR 2000 ms, 32 echoes, SENSE-factor: inplane = 2 & Slice-encoding = 2; echo
spacing 6 ms; Average 2. Additionally, EPI-factor of 3 was used for GRASE
sequence. It took ~14 and ~42 minutes to acquire MESE and GRASE data with
limited coverage. Average of 2 was essential for the FID correction.

**Algorithm:** The flow-chart is shown in Fig 1.
As an initialization step, first the joint estimation of μT-map
and flip angle error map (or equivalently B1-error) is performed using extended
L-curve approach. Following this, we iteratively improve over T2-distribution
map (M-step) and refine over flip angle error until the convergence of solutions (T2 distributions). In practice, the convergence is achieved with in fourth iteration.

This project was partly supported by the National Institute of Biomedical Imaging and Bioengineering of the National Institutes of Health (Grant Number P41-EB015893) and the National Institute of Neurological Disorders and Stroke (Award Number R01NS087516).

All authors would like to thank Dr. Hendrik Kooijman, Philips Healthcare, Hamburg, Germany for providing valuable support and guidance regarding the optimization of sequence. We would also like to thank Prof. Stephen Becker, Applied Mathematics, University of Colorado at Boulder, USA for sharing his L-BFGS-B code. We would also like to thank Mr. Mohamad Nawab Alam, Dept. of Electric Engineering, Indian Institute of Technology, Roorkee, India for help in develop genetic algorithm for minimizing expression in E-step, though it was not used in here as we were able to get better performance from “lsqnonlin” solver.

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