In-vivo characterization of grey matter microstructure at 3T from the transverse component of the MRI signal
Antoine Lutti1

1LREN, Dept. of Clinical Neurosciences, Centre Hospitalier Universitaire Vaudois, Lausanne, Switzerland

### Synopsis

The characterization of brain microstructure from MRI data requires the development of specific MRI tissue biomarkers and of advanced models linking microscopic tissue properties to MRI signals. We apply the Anderson-Weiss theory, which describes the transverse relaxation of the MRI signal as a function of tissue microstructure, on in-vivo MRI data acquired at 3T. In grey matter, parameter estimates show a strong correlation with histological measures of iron concentration. The time constants provided by the model yield realistic estimates of microscopic compartment size. These results offer a promising perspective for the histological assessment of brain tissue in-vivo using MRI.

### Purpose

To extract specific biomarkers of brain tissue microstructure in-vivo at 3T using an advanced model of the relaxation of the transverse component of the MRI signal.

### Introduction

The development of advanced models relating tissue microstructure to MRI signals is an essential step towards the characterization of brain tissue in-vivo from MRI data (in-vivo histology). In particular, the effects of myelinated fibers and iron-rich cells on the transverse component of the water magnetization open the way for the quantification of magnetic material in brain tissue. Most models require strong assumptions on the spatial distribution of such material within the tissue and lead to analytical expressions that have found limited use with in-vivo data1,2,3. On the contrary the Anderson-Weiss (AW) theory provides a compact expression while preserving the essence of the microstructural mechanisms that impact transverse relaxation4. Here we present preliminary data that illustrate the potential offered by the Anderson-Weiss theory for the in-vivo characterization of brain tissue from MRI data.

### Theory

The effect of magnetic material (e.g. iron, myelin) on the MRI signal of water can be described by the AW theory4,5:

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

In equation 1, Δω02 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 (Δω02). In the fast-motion limit (Δω02τ2<<1) equation 1 reduces to5:

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

with T2-1= Δω02τ. The standard exponential form of the transverse magnetization decay is recovered and the effects of Δω02 and τ on the decay cannot be distinguished.

### Methods

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 1mm3 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 10o. 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 system6 (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) atlas7 and compared with histological measures of iron concentration8,9.

### Results

Figure 1 shows a map of the parameter R2* from the standard mono-exponential model of transverse relaxation (a) and the set of parameter estimates obtained from equation 1 (b). The values of (Δω0τ)2 in grey matter indicates that separate estimates of Δω02 and τ can be obtained. The low values of (Δω0τ)2 in white matter (~<0.01) indicate a largely exponential behaviour, making the contributions of Δω02 and τ to the signal decay inseparable. Figure 2 shows histograms of τ and Δω02 values in cortical and sub-cortical grey matter. Taking D=1.7mm2s-1 for the water diffusion coefficient10, the observed range of τ values (~1-20ms) yield L~1.8-8.2 μm as the typical length scales in grey matter (L2=2Dτ). The values of Δω02 are in-line with expectations from the litterature2. The correlation of Δω02 with histological estimates of iron concentration ([Fe]) is shown in figure 3. Linear fit of Δω02 with [Fe] (Δω02 = p1*[Fe]+p0) gave p1=547 Hz2 (mg/100 g fresh wt)-1 and p0=2087 Hz2 (note the high value of the coefficient of determination R2).

### Discussion

Preliminary results are shown from the application of the Anderson-Weiss (AW) theory on in-vivo MRI data acquired at 3T. These results indicate that the AW theory may be used to extract histological measures of grey matter from the transverse relaxation of the MRI signal. In particular, the high correlation of Δω02 with iron concentration supports the validity of these biomarkers. Correction of susceptibility effects at the interface of brain tissue with air will improve the accuracy of the estimates.

### Acknowledgements

The author is grateful to Dr. Callaghan M.F., Dr. Mohammadi S and Prof. Weiskopf N. for fruitful discussions of this work.

### References

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

### Figures

Map of the parameter R2* 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 Δω02 (b) provided by the Anderson-Weiss theory in sub-cortical regions and cortical grey matter.

Linear correlation between the Δω02 parameter estimates and histological measures of iron concentration showing excellent correlation supporting the fact that Δω02 could act as a surrogate marker for iron concentration in vivo.

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