Dan Wu^{1,2} and Jiangyang Zhang^{3}

Diffusion-time
(*t _{d}*) dependent
diffusion MRI is a promising tool to probe tissue microstructure. Although different
diffusion gradient waveforms (DGW) have been introduced to achieve
short and long

Monte Carlo simulations
were performed using Camino (http://camino.cs.ucl.ac.uk) with regular
grid cylinder substrates with radius of 1µm, 2.5µm, and 5µm,
varying permeabilities (*p*=0.0025-0.01),
and constant intra- and extra-cylinder space ratios (0.78). Pulsed gradient
spin-echo (PGSE), bipolar pulsed (BGP) gradient [12], and oscillating
gradient spin-echo (OGSE) [13] with different number of cycles were
composed with *t _{d}*
ranging from 4 to 50ms (Figure 1A). As the exact

*In
vivo *experiments: These
DGWs were implemented on an 11.7T Bruker scanner, and calibrated with a mineral
oil phantom. Neonatal C57BL/6J mice were scanned at 48hrs after unilateral hypoxic-ischemic
(HI) injury (*n*=5) or sham injury (*n*=6). Data were acquired with OGSE with *f*=50Hz (*t _{d}*≈5ms), BGP with

Figure 2 show the *t _{d}*–dependent
kurtosis curves simulated with BGP, PGSE, and OGSE (1-3 cycles) for cylinders
at radius of 1µm,
2.5µm, and 5µm and permeabilities of 0.0025 (low) and 0.01 (high).

1) *t _{d}*–dependence and microstructure:
With

2) DGW
and td dependency:
Choice of DGW does not alter the overall patterns of time-dependent kurtosis curves described above. Visually,
the *t _{d}*-dependency
of kurtosis was the strongest with PGSE encoding (most
sensitive to change of

3) DGW and
microstructure: We examined the DGW-dependency by
comparing the kurtosis measured by PGSE and BGP (*K _{PGSE}*
/

*In
vivo
*data from the mouse brains agreed with the simulation results, e.g., at
equivalent *t _{d}*’s,

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Figure 1: (A) Diffusion gradient waveforms (DGWs) used in this study, including
the pulsed gradient spin-echo (PGSE) , bipolar pulsed (BGP) gradient,
and oscillating gradient spin-echo (OGSE) encoding schemes. The approximated diffusion-time (*t*_{d}) is indicated in
each waveform. Normalized power spectra were calculated based on PGSE, BGP, and
OGSE gradients with different number of cycles (1-3) at *t*_{d} of 5ms (B) and 20ms (C). Signal
attenuation curves (log(*S*/*S*_{0})) were obtained from the
Monte Carlo simulations using PGSE, BGP, and OGSE gradients with different
number of cycles (1-3) at *t*_{d}
of 5ms (D) and 20ms (E).

Figure 2: Time-dependent kurtosis and the effect of DGW. Kurtosis was calculated
from the diffusion signals simulated using five DGWs (PGSE, BGP, and OGSE with
1-3 cycles) with *t*_{d}
ranging from 4 to 50ms, for different sizes of cylinders (radius of 1 µm, 2.5
µm, and 5 µm) at low permeability (*p*=0.0025,
A) and high permeability (*p*=0.01, B).
Simulations were performed in 10 voxels in each scenario, and means and
standard deviations of the kurtosis measurements were presented. Black arrows in the middle column indicate the peaks of kurtosis curves measured in 2.5µm cylinder with PGSE sequence.

Figure 3: (A) Kurtosis ratio
between PGSE and BGP (*K*_{PGSE} /*K*_{BGP}) and that between BGP
and OGSE (*K*_{BGP
}/*K*_{OGSE}) obtained
from diffusion signals simulated at different cylinder sizes (radius of 1µm,
2.5µm, and 5µm) and two permeability levels. (B)
Kurtosis maps obtained from neonatal mouse brains after hypoxic-ischemic (HI)
injury or sham injury using OGSE and BGP sequences at *t*_{d} of 5ms, and BGP and PGSE sequences at *t*_{d} of 7ms and 10ms. (C) Comparison of
kurtosis ratios measured in the ipsilateral and contralateral cortex of
HI-injured mice (*n*=5) and bilateral
cortex of the sham mice (*n*=6). **p*<0.5 and ***p*<0.01 by t-test.