In-vivo characterization of grey matter microstructure at 3T from the transverse component of the MRI signal

Antoine Lutti^{1}

The effect of magnetic material
(e.g. iron, myelin) on the MRI signal of water can be described by the AW theory^{4,5}:

$$S=S_{0}e^{-\triangle\omega^{2}\tau^{2}(\exp(\frac{-t}{\tau})-1+\frac{t}{\tau})}$$

In equation 1, Δω_{0}^{2} is the mean square frequency
fluctuation of water molecules diffusing in the spatially inhomogeneous
magnetic field created by the magnetic material and may be expected to correlate with the
local density in magnetic material within the tissue. τ is the decay constant of the frequency
auto-correlation function. It arises from molecular diffusion in the inhomogeneous field and
yields estimates of topological distances within the tissue. Note that equation
1 relies on the assumption of Gaussian distributed changes in frequency and on
an exponential dependence of the frequency auto-correlation. Equation 1 establishes
a relationship between the dynamics of the water displacement (τ) and the distribution of
frequencies due to the magnetic material (Δω_{0}^{2}). In the fast-motion limit (Δω_{0}^{2}τ^{2}<<1) equation 1 reduces to^{5}:

$$S=S_{0}e^{-\frac{t}{T_{2}}}$$

with T_{2}^{-1}= Δω_{0}^{2}τ. The standard exponential form of the transverse magnetization decay is recovered and the effects of Δω_{0}^{2} and τ on the decay cannot be distinguished.

Data was acquired on one subject
on a 3T Siemens Prisma MRI scanner (Erlangen, Germany) using a 64ch head-neck
coil and a custom-made 3D FLASH acquisition. The image resolution was 1mm^{3}
and the matrix size was 222x192x176 along the phase, read and partition directions.
The repetition time (TR) was 80ms and the RF excitation flip angle was 10^{o}.
32 images were acquired using a bipolar readout with echo times (TE)
ranging from 2.2ms to 74.12ms in steps of 2.32ms. Parallel imaging
(acceleration factor 2, GRAPPA image reconstruction) and Partial Fourier
(factor 6/8) were used along the phase and partition directions respectively.
The acquisition time was 21min49s. Data was prospectively corrected for subject motion using
a prospective motion camera system^{6 }(Kineticor,
HI, USA).

The
acquired data were fit to equation 1 using in-house code written in Matlab (Mathworks, Sherborn, MA, USA). Region-specific estimates of the parameter fits
were extracted using the anatomical labelling (AAL) atlas^{7} and compared with
histological measures of iron concentration^{8,9}.

1. Bauer W.R., Ziener C.H., Jakob P.M., Physical Review A, 2005

2. Jensen J.H., Chandra R., Magnetic Resonance in Medicine, 2000

3. Sukstanskii A.L., Yablonskiy D.A., Journal of Magnetic Resonance, 2003

4. Anderson, P.W. and Weiss P.R. Rev. Mod. Phys. 25, 1953.

5. Callaghan P.T. Principles of Nuclear Magnetic Resonance Microscopy, Oxford University Press, 1991.

6. Zaitsev, M., Dold, C., Sakas, G., Hennig, J., and Speck, O. Neuroimage 2006

7. Tzourio-Mazoyer N, Landeau B, Papathanassiou D, Crivello F, Etard O, Delcroix N, Mazoyer B, Joliot M. NeuroImage 2002.

8. Hallgren B., Sourander P., J Neurochem, 1958

9. Uddin M.N., Lebel, R.M., Wilman, A.H., Magnetic Resonance Imaging, 2015.

10. Zhang H., Schneider T., Wheeler-Kingshott C.A., Alexander D.C., Neuroimage 2012

Map
of the parameter R_{2}* from the standard mono-exponential model of
transverse relaxation (a) and set of parameter estimates obtained from the
Anderson-Weiss (AW) theory (b). The AW theory allows the characterization of
the microstructural tissue properties that contribute to the signal decay.

Distributions of the estimates of the parameters
τ (a) and Δω_{0}^{2} (b) provided by the Anderson-Weiss theory in sub-cortical
regions and cortical grey matter.

Linear
correlation between the Δω_{0}^{2} parameter
estimates and histological measures of iron concentration showing excellent correlation supporting the fact that Δω_{0}^{2} could act as a surrogate marker for iron concentration in vivo.

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

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