Gaetan Duchene^{1}, Frank Peeters^{1}, Jorge Abarca-Quinones^{1}, and Thierry Duprez^{1}

Recently, Double Diffusion Encoding (DDE) has been proposed for quantification of pore size distributions in a voxel or a Region Of Interest. Although the technique has been validated on animals with experimental MR systems, its translation to human scanners is challenging, mainly because of the limited gradient strength available on clinical systems. In this work, we present a validation of DDE on a clinical scanner on a biological phantom (asparagus). Furthermore, we restricted the acquisition time to 16 minutes which remains acceptable in clinical conditions.

We implemented a DDE sequence (double spin echo with single
shot EPI read out of the second echo) on an Achieva 3T scanner (Philips, Best,
The Netherlands). The two gradient pairs had identical diffusion time and zero
mixing time. Six white asparagus stems were placed in a wrist antenna (4
Channels) with their axis aligned with the z-direction (Feet-Head). Five axial
slices (thickness 4 mm) were imaged with 2mm*2mm in plane resolution
(acquisition) and 1.35mm for reconstruction. Diffusion parameters were: 6
equidistant q-values from 0 to 40mm^{-1} by stepping the gradient
pulses (duration δ=12.6ms) from 0 to 80mT/m and diffusion time ∆=60ms. Five
equidistant angles θ between the two gradient pairs were used, ranging from 0
to 180° in the xy-image plane (first pair was along the y-direction). Other
parameters were: TE=162ms, TR=4654ms, SENSE factor=2, NSA=8 leading to a scan time=16min.
An extra standard DTI sequence with 32 gradient directions and b=800s/mm^{2}
with the same resolution as DDE was performed in order to locate the fibers of
the pro-epidermis.
The signal attenuation E_{V} of a voxel ($$$\frac{S(q,\theta)}{S(q=0)}$$$)
is :

$$E_V(q,\theta)=\sum_{i=1}^N f_i.E(q,\theta,a_i) \qquad[1]$$

where N is the number of sampled pore sizes, E is the
attenuation for a cylindrical pore of radius a_{i} and f_{i }is
its volume-weighted contribution. The relative probability is then P_{i}=
f_{i}/a_{i}^{2} and the PSD is given^{3} by the
ensemble of P_{i} normalized to 1. E was calculated numerically with
the MCF method^{4 }and we used N=20. A parametric estimation was performed assuming a
log-normal distribution (2 parameters: µ and σ). Note that a gaussian
contribution was added in eq. [1] but was always found to be negligible in our
work. For validation, light microscopy was performed wherefrom PSD estimations where
obtained using ImageJ software (National Institutes of Health, USA).
Pore
sizes can also be obtained from DDE using only one q-value and two angles (0
and 180°) and thus with reduced scan time. The mean radius of gyration <r^{2}>
is then estimated through^{1,5} :

$$<r^2>=(3/2)\frac{E_V(q,180°)-E_V(q,0)}{q^2} \qquad [2]$$

For a cylinder, <r^{2}>=a^{2}/2. We compared the
results of both methods.

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