Mu Lin^{1}, Qiuping Ding^{1}, Xu Yan^{2}, Thorsten Feiweier^{3}, Hongjian He^{1}, and Jianhui Zhong^{4}

Myelin water is abundant in white matter but myelin signal is often ignored in diffusion models due to its short T2. There is however substantial water exchange between myelin and non-myelin water within typical diffusion times. Using Monte Carlo simulation and in-vivo measurement, we demonstrate that this water exchange might result in an echo-time (TE) dependence of DTI-derived parameters. As myelin water exchange increases with the thickness of myelin sheath, the TE dependence can be used to assess the degree of myelination.

A biophysical
model including myelin compartment and allowing inter-compartment exchange was
built to simulate the diffusion process in myelinated axons (Fig. 1). The simulation
of random walk and synthesis of diffusion signal were performed with Monte
Carlo method as described in a previous simulation work.^{2} The
DTI-derived parameters – fractional anisotropy (FA), mean diffusivity (MD),
axial diffusivty (DA) and radial diffusivity (DR) - were repeatedly calculated at
a set of TEs. The effects of water exchange and different g-ratios (0.6 - 1)
were investigated. Other simulation parameters are shown in Table 1.

In order to validate the TE dependence in vivo, two male and three female subjects (aged 23-29 years) were examined on a 3T system (MAGNETOM Prisma, Siemens Healthcare, Erlangen, Germany). Each subject was examined with a prototype single-shot PGSE-EPI sequence and the pulse parameters (TE, Δ, δ and b-value) were identical to those used in the simulations. Three white-matter structures (genu, body and splenium of corpus callosum) were outlined for statistical analysis.

Results

^{} As
shown in Fig. 2a, if the lifetime of intra-axonal water was infinite (no water
exchange), all DTI-derived parameters had no correlation with TE. As shown in
Fig. 2b, if water exchange was allowed, FA and DA had positive correlation with
TE while DR had negative correlation with TE.

The TE-correlation coefficients and p-value from simulated DTI-derived parameters at different g-ratios are shown in Fig. 3. When the g-ratio was smaller than 0.75 (well myelinated), FA and DA had positive correlation and DR had negative correlation with TE. When the g-ratio reached 0.8, only DR had correlation with TE. When g-ratio was larger than 0.85 (demyelinated), all the DTI-derived parameters had no correlation with TE.

As
the in-vivo brain data shows (Fig. 4), in the body of corpus callosum, FA and
DA had positive correlation and DR had negative correlation with TE at two
b-values (Fig. 4a). In the genu, except DA at b = 2000 mm^{2}/s, the other TE
dependences were similar to the body (Fig. 4b). In the splenium, only DR had
negative correlation with TE (Fig. 4c).

Using Monte Carlo simulations, we demonstrate that, in
myelinated axon, the exchange between myelin and intra/extra-axonal water can
introduce a dependence of DTI-derived parameters on TE (Fig. 2). This result is
consistent with a previous study on rhesus monkeys ^{3} and our in-vivo
human results (Fig. 4). With increasing g-ratio, the correlation of DTI-derived
parameters with TE is reduced (Fig. 3). The TE-dependence can be classified
into three cases. Case I: FA, DA and DR all have correlation with TE. This
indicates well myelinated axon (g-ratio < 0.75). Case II: DR and FA have
correlation or only DR has correlation with TE. This indicates moderately myelinated
axons. Case III: No parameter has correlation with TE. This indicates
demyelinated axons (g-ratio>0.85).

By applying our theory to
in-vivo data, we found the genu and body of corpus callosum belong to Case I
while the splenium of corpus callosum belongs to Case II, which implies that
the splenium is less myelinated than the genu and body. This observation is
consistent with a previous study by N. Stikov et al. showing that the g-ratio
is higher in the splenium than in the genu and body of macaque corpus callosum.^{4}
Compared
with the conventional g-ratio imaging that combines diffusion sensitized
imaging (NODDI) and myelin sensitized imaging (magnetization transfer or
multicomponent T2 relaxometry), our method reduces the complexity in
acquisition and calculation and is thus more practical for clinical
applications.

1. Dula AN, Gochberg DF, Valentine HL, Valentine WM, Does MD. Multiexponential T2, magnetization transfer, and quantitative histology in white matter tracts of rat spinal cord. Magnetic Resonance in Medicine Official Journal of the Society of Magnetic Resonance in Medicine 2010;63:902-9.

2. Lin M, He H, Schifitto G, Zhong J. Simulation of changes in diffusion related to different pathologies at cellular level after traumatic brain injury. Magnetic Resonance in Medicine 2015;41:130-131.

3. Wen Q, Yu CS, Fan Z, Xiang YD, Jiang H, Yu XY, Li KC. Effects of echo time on diffusion quantification of brain white matter at 1.5T and 3.0T. Magnetic Resonance in Medicine 2009;61:755-760.

4. Stikov N, Campbell JSW, Stroh T, Lavelée M, Frey S, Novek J, Nuara S, Ho MK, Bedell BJ, Dougherty RF. In vivo histology of the myelin g-ratio with magnetic resonance imaging. Neuroimage 2015;118:1050-4.

Fig. 1. The
myelinated axon model. Axons are contained in a periodic
array of hexagonal columns. Each axon is surrounded by permeable myelin sheath.
The 3D model divides tissue into three compartments: Intra-axonal compartment,
myelin compartment and extra-axonal compartment.

Fig. 3. The correlation
coefficients between DTI-derived parameters and TE as functions of g-ratio (**a**) and the corresponding p-value as
functions of g-ratio (**b**). The dashed
lines represent the p-value of 0.05.

Table 1. The simulation parameters.