Vanessa Wiggermann^{1,2,3}, Irene M Vavasour^{3,4}, Enedino Hernandez-Torres^{2,3}, Gunther Helms^{5}, Alexander L MacKay^{1,3,4}, and Alexander Rauscher^{1,2,3,4}

^{1}Physics and Astronomy, University of British Columbia, Vancouver, BC, Canada, ^{2}Pediatrics, University of British Columbia, Vancouver, BC, Canada, ^{3}UBC MRI Research Centre, University of British Columbia, Vancouver, BC, Canada, ^{4}Radiology, University of British Columbia, Vancouver, BC, Canada, ^{5}Lund University, Lund, Sweden

### Synopsis

The
ability to determine the myelin water fraction (MWF) in
vivo is
essential to assessments of neurodevelopmental myelination and
myelin damage in neurodegenerative diseases.
The analysis of multi-exponential T2 decay data relies on the non-negative-least-squares (NNLS) fitting, which may be sensitive to the chosen fitting parameters. We performed simulations to explore the outcomes of NNLS under different parameter selection. The lowest allowed T2 was found to have the largest effect on correctly estimating the T2 of different water pools as well as the MWF. Lower refocusing FAs led to further underestimation of the MWF.

###

**Introduction**

The
ability to determine the myelin water fraction (MWF) in
vivo

^{1} is
essential to assessments of neurodevelopmental myelination and
myelin damage in neurodegenerative diseases. Multi-echo
spin-echo imaging has
been shown to correlate with optical density measurements of myelin
lipids

^{2,3}.
However, as
MW imaging has been extended to 48-echoes,
applied at higher magnetic fields

^{3}
and investigated post-mortem
during fixation

^{4}, selection
of post-processing parameters
for the non-negative least squares fitting (NNLS) needs
to be revisited. We
used simulations to
explore the outcomes of NNLS fitting for
different parameter
selections in a given water environment
at 3T and drew parallels
to

*in vivo*
data.

###

**Methods**

Independent
decay data were computed by multi-echo spin-echo simulations of the
magnetization of 256x256 spins in with given T

_{1} and
T

_{2}-properties, taken from literature to mimic white matter
values

^{5,6}. Various resonance frequencies were assigned to the
different water compartments

^{7}, after computing the local magnetic
environment from tissue magnetic susceptibilities. All T

_{1}'s,
T

_{2}'s and resonance frequencies were assigned to each spin
by random sampling from a Gaussian distribution. Finally, Gaussian
noise was added to the images. The voxel and its properties are shown
in

**Figure 1**. The MWF, i.e. the amount of MW relative to all
water within a voxel, was 21%. Decay data were computed assuming a
signal-to-noise ratio of 300, imperfect refocusing flip angles
(FA=30,150,170,180º) and
MWT

_{2}-times (5,10,15,20 ms) using a 32-echo sequence with
TE/ΔTE/TR=10/10/1000ms.
Decay
curves were analyzed by fitting the measured decay curve with decay
curves estimated by the extended-phase-graph algorithm to estimate FA
in the presence of stimulated echoes

^{8,9}, while minimizing χ2
with respect to FA. Regularized NNLS was employed with varying
numbers of T

_{2}-components (nT

_{2}) to fit the decay
curves. The estimated parameters, i.e. the FA, the geometric mean T

_{2}
of the intra/extracellular water (GMT2 IEW), GMT2
of the MW and the MWF were computed under varying nT

_{2}s
(20,32,40,80,120) and different T

_{2}-ranges for which the
shortest T

_{2} was varied (T

_{2,1}=5-15ms,
T

_{2,end}=2s).

###

**Results**

The
FA estimation was independent of nT

_{2}. The computed FAs
differed from the true FAs by 2.46±1.49,
3.00±0.51, 1.99±0.58 and
2.36±0.51 for 130,150,170,180º,
respectively.

**Figure 2**
shows the
estimated
GMT

_{2}
IEW values. As FA
decreaed,
the GMT

_{2}
IEW moved
further away from the reference: 69.70±0.71ms (180º),
69.74±0.62ms (170º),
68.85±1.08ms (150º),
67.93±1.38ms (130º).
For MWT

_{2}
values, lower
refocusing FAs resulted
in greater deviations from the true GMT

_{2}
IEW. This was explored in more detail in

**Figure
3**, by comparing the
computed T

_{2}-distributions. For all
FAs,
the GMT

_{2}
of MW and IEW were well determined when T

_{2,1}
was
less than T

_{2}
of MW.
When T

_{2}
MW was
shorter than the first allowed T

_{2},
the MW peak was
incompletely described and the estimated MWT

_{2}
depended
on the value of T

_{2,1}.
However, the GMT

_{2}
IEW was
accurately estimated.
Finally, we compared the estimated MWF, with respect to FA, nT

_{2}'s
and T

_{2,1} (

**Figure
4**).
Again, MWFs were well estimated if T

_{2,1}
was less than MWT

_{2}.
Note that once the MW peak was
fully captured, further shortening of T

_{2,1}
did
not change the MWF. With decreasing FA, the MWF was underestimated.
When assessing the impact of
changed analysis
parameters on in vivo
data acquired at 3T with the imaging parameters matching
the simulation parameters
(Figure 5),
we noted visually an
improvement in the assessed MWF when lowering T

_{2,1}
from 14 to 12ms. Both GMT

_{2}
IEW and MWF were
in line with the observations of the simulation, with stronger
effects observed for
single voxels. FAs in the regions-of-interest were 151.7,164.3,154.3º
in the internal capsule, white matter and globus pallidus,
respectively.

###

**Discussion**

Although
the true FAs were
well captured by the extended-phase-graph algorithm, MWF may be
under-estimated,
even when
the MWT

_{2}
was
within the T

_{2}-range.
The GMT

_{2}
of IEW and MW shortened
slightly at lower
FAs if T

_{2,1}<MW
T

_{2},
but MWT

_{2}
estimation failed
if T

_{2,1}
was
chosen too long. FAs
at 3T are generally
greater than 150,
but regions of low FA as
well as further T

_{2}-shortening
at
higer magnetic field strength, or due to fixation, will
be problematic for estimating MWF correctly.

* In vivo* data showed good
correspondence with the simulations. Single-voxel data were affected by the choice of parameters, but averages
within regions containing multiple voxels provided stable estimates.

###

**Conclusions**

The
MWF was robustly estimated with respect to many parameters.
Successfully measuring the MWF however depends on the actual MWT

_{2},
which is unknown, and the chosen T

_{2}-range, relative to the
MWT

_{2}. By lowering the T

_{2}-range, the MW signal is better
captured. Further work should investigate how underestimations of the
MWF at lower, known FAs can be recovered.

### Acknowledgements

No acknowledgement found.### References

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