Diffusion-weighted imaging with multiple diffusion time to assess water-exchange between restricted and hindered diffusion components in vivo

Yasuhiko Tachibana^{1,2}, Takayuki Obata^{1,2}, Hiroki Tsuchiya^{1}, Tokuhiko Omatsu^{1,2}, Riwa Kishimoto^{1,2}, Thorsten Feiweier^{3}, and Hiroshi Tsuji^{1}

Seven
healthy female volunteers were recruited for this study (20-33 years, mean 24).
Their brain MbMdT-DWIs were acquired by 3T MRI (MAGNETOM Skyra, Siemens
Healthcare, Erlangen, Germany) with a proto type sequence (Table 1). 11
b-values from 0 to 4000 sec/mm^{2} were selected, with two encoding
directions, respectively. The separation times of the gradients (Δ) were set at 43.4, 63.4, and 83.4 msec, while the diffusion gradient
duration (δ) was fixed at 25.0 msec. Regions-of-interest
(ROI) were designated manually at the corticospinal tract of the left internal
capsule (PLIC) and deep white matter of the left centrum semiovale (CS). A free-water
phantom and a phantom of pure restricted-diffusion (Capillary Plate (CP),
Hamamatsu Photonics, Japan) were scanned as well as references.

1. DT dependency was assessed by plotting the intra-ROI signal intensity (the mean of the two encoding directions) of the subjects.

2.
A diffusion model based on the Karger model was assessed
(Fig.1) [1-3].
The model consisted
of restricted and hindered diffusion components (RDC and HDC: their fractions
were *fr* and *fh*) with inter-compartment exchange. The measured signal at a certain
DT was expressed as the sum of the signal from RDC (*Cr(DT)*) and HDC (*Ch(DT)*) (Fig.2
Eq.1). RDC was defined as the compartment of which the diffusion-coefficient (*Dr*) was inversely proportional to DT. A
supplementary independent variable (*A*)
was set to define this diffusion (*A* =
*Dr*×DT)
[3]. HDC was defined as the compartment
with diffusion independent of DT. The diffusion-coefficient of HDC (*Dh*) was fixed at 0.0012 mm^{2}/sec
in this study. The inter-compartment exchange was defined by the exchange time
from RDC to HDC (*tr*) and that from
HDC to RDC (*th*) (Fig.2 Eq.2). The
independent variables *A*, *fr*, and *tr* were calculated (Fig.2 Eq.3,4). The variables between PLIC and
CS were statistically compared (Wilcoxon signed-rank test; P<0.05 was
considered significant).

1. Strong DT dependency nearly linear with the b-value was found in CP, while no DT dependency was found in free water (Fig.3, upper row). In PLIC and CS, DT dependency was found at high b-values. Signal-intensity was elevated or it was slightly decreased when DT was increased from Δ=43.4 to 63.4 msec, and was then decreased by increasing DT further from Δ=63.4 to 83.4 msec (Fig.3, lower row).

2.
The observed signal intensities were fit well by the signal-change-curve
obtained from the calculated parameters of the proposed model (Fig. 2). The
medians of *fr* and *tr* in PLIC were larger than those in CS,
with significant differences. Statistical difference was not found in *A* (Table 2).

1.
The model of mixed RDC and HDC was reasonable in the DTs
applied in this study, because a DT relation was found in high b-values, but
not in low b-values *in vivo*. Furthermore,
the fact that the signal was first elevated (or slightly decreased) and then
decreased as DT increased may prove the existence of inter-compartment water exchange,
because if the compartments were independent, the difference between different
DTs should have increased monotonically (as adding the signal of CP and free
water).

2.
The significantly larger *fr*
in PLIC than CS may suggest larger intra-axonal space, and the small difference
in *A* may suggest a relatively
consistent axon diameter by the analogy of the assessment of corticospinal
tract by q-space imaging [4]. The significant
difference found in *tr* (larger in
PLIC) may possibly reflect myelin density. However, the results do not provide
sufficient evidence to prove these hypotheses at this moment. Further study
with larger numbers of MPG encoding directions, as well as longer diffusion
time (requiring larger gradient strength to maintain TE) may support our
results. A study of myelin-water fraction may also help. On the other hand, another previous *in vitro* study that assessed water exchange in
aquaporin-4-expressing and -non-expressing cells reported the exchange times
from intra- to extra-cellular space as 43.1 msec and 100.7 msec, respectively [5]. The range included *tr* of PLIC and CS in this study, which
may somewhat support the appropriateness of our results, as RDC may mostly belong
to intracellular water.

This work was partially supported by grants from the Ministry of Education, Culture, Sports, and Science.

The authors appreciate H. Kamata for her general assistance, and K. Murata for his technical advice.

1. Lee JH, Springer CS, Jr. (2003) Effects of equilibrium exchange on diffusion-weighted NMR signals: the diffusigraphic "shutter-speed". Magn Reson Med 49: 450-458.

2. Kärger J, Pfeifer H, Heink W (1988) Principles and applications of self-diffusion measurements by nuclear magnetic resonance. Advances in Magnetic Resonance 12: 1-89.

3. Lam WW, Jbabdi S, Miller KL (2014) A model for extra-axonal diffusion spectra with frequency-dependent restriction. Magn Reson Med.

4. Kamiya K, Hori M, Miyajima M, Nakajima M, Suzuki Y, et al. (2014) Axon diameter and intra-axonal volume fraction of the corticospinal tract in idiopathic normal pressure hydrocephalus measured by q-space imaging. PLoS One 9: e103842.

5. Ibata K, Takimoto S, Morisaku T, Miyawaki A, Yasui M (2011) Analysis of aquaporin-mediated diffusional water permeability by coherent anti-stokes Raman scattering microscopy. Biophys J 101: 2277-2283.

Figure 1: Schema of the model of
restricted and hindered diffusion components (RDC and HDC) with
inter-compartment exchange

Figure 2: Calculation of the
independent parameters of the model

Diffusion time and b-value
dependent signal change of the phantoms and human brain.
The stars and the dotted lines
indicate the observed signal intensities and the signal-change-curve obtained
from the calculated diffusion parameters, respectively. The model fits the observed
data well.

Table 1: Major
parameters of multiple b-value with multiple diffusion-time diffusion-weighted
imaging (MbMdT-DWI) sequence

Table 2: Calculated diffusion
parameters and the results of statistical comparisons

Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)

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