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.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 data^1,2,3. 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.

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, 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.

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 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 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 concentration^8,9.

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).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.