Riccardo Metere^{1} and Harald E. MÃ¶ller^{1}

Quantitative MRI maps are believed to strongly correlate with myelin and iron contents. Recently, a linear model combining prior information from non-MRI techniques was proposed for quantifying myelin and iron based on relaxometry (R_{1} and R_{2}^{*}) in post-mortem human brain samples. Here, we propose an adaptation of the linear relaxation model that is capable of predicting (with some limitations) the myelin and iron contents of the brain under in vivo conditions. It uses prior knowledge from the literature to calibrate the linear coefficients and was validated in a cohort of 10 subjects.

The analysis of the composition of biological tissues through quantitative MRI is a promising technique towards in vivo histology^{1}. A semi-empirical linear model relating the iron and sulfur/phosphorus concentrations (as markers for myelin) to the MRI relaxation rates $$$R_1$$$ and $$$R_2^*$$$ was proposed and validated in human post-mortem brain samples^{2}. However, those results are difficult to reproduce both ex vivo (because of the strong dependence of the parameters on the experimental conditions^{3}) and in vivo, as a result of the different relaxation regimes^{4}. The difficulty in obtaining similar non-MRI data under in vivo conditions has prevented the application of this model to the living brain. In this work, we propose an extension of the linear model to predict the myelin and iron content of brain tissue under in vivo conditions using relaxation information. This is achieved by estimating the model coefficients using simultaneously acquired $$$R_1$$$ and $$$R_2^*$$$ data^{5} combined with information of tissue composition from the literature^{6,7,8,9}. The results are then validated (or, more precisely, checked for self-consistency) using the newly obtained myelin $$$X_\mathrm{My}$$$ and iron $$$X_\mathrm{Fe}$$$ content (group averaged) maps.

The semi-empirical linear model of relaxation is given by^{2,10}:

$$\vec{P}=\boldsymbol{A}\vec{X} + \vec{P}_0$$

with $$$\vec{P}\equiv(R_1,R_2^*)$$$ and $$$\vec{X}\equiv(X_\mathrm{My},X_\mathrm{Fe})$$$. $$$A\equiv[[\mathcal{r}_{1,\mathrm{My}},\mathcal{r}_{1,\mathrm{Fe}}], [\mathcal{r}^*_{2,\mathrm{My}},\mathcal{r}^*_{2,\mathrm{Fe}}]]$$$ is defined in terms of the relaxivities $$$\mathcal{r}$$$ and $$$\vec{P}_0\equiv(R_1[\mathrm{bl}],R_2^*[\mathrm{bl}])$$$ are the baseline relaxations.

This can be rewritten as:$$\vec{X}=\boldsymbol{A}^{-1}(\vec{P}-\vec{P}_0)=\boldsymbol{A}^{-1}\vec{P}-\boldsymbol{A}^{-1}\vec{P}_0\equiv\boldsymbol{A}^{-1}\vec{P}+\vec{P}_{A,0}$$With sufficient knowledge of $$$\vec{X}$$$ and $$$\vec{P}$$$ in some Regions-Of-Interest (ROIs), it is possible to estimate $$$\boldsymbol{A}$$$ and $$$\vec{P}_0$$$, which can then be used to determine $$$\vec{X}$$$ in the brain.

Quantitative $$$R_1$$$, $$$R_2^*$$$ maps ($$$0.6\;\mathrm{mm}$$$ isotropic nominal resolution) of the full brain were simultaneously acquired using ME-MP2RAGE^{5} in 10 healthy volunteers (5 males, 5 females, age: $$$20-29\;\mathrm{yr}$$$), with a MAGNETOM 7T (Siemens, Erlangen, Germany) and a circularly-polarized Tx / 32-channel Rx Nova coil. The MRI maps were skull-stripped, co-registered to MNI space (using FSL^{11} and ANTs^{12}) and group averaged together. We extracted ROIs probabilistic masks from the Oxford-Harvard Cortical and Subcortical Atlases for which corresponding information on myelin (assumed to be equal to lipid) and/or iron contents are available. In such ROIs, the average (weighted for the inverse of the variance) $$$R_1$$$ and $$$R_2^*$$$ were calculated. These values, tabulated in Fig.[1], were used to determine optimal values for the coefficients $$$\boldsymbol{A}^{-1}$$$ and $$$\vec{P}_{A,0}$$$ using an Orthogonal Distance Regression (ODR) fit (separately for $$$X_\mathrm{My}$$$ and $$$X_\mathrm{Fe}$$$).

Then, the values of the coefficients are used to compute myelin and iron maps, whose values on the ROIs of Fig.[1] are validated (checked for self-consistency) with the literature.

The group average and standard deviation of the measured relaxation maps are shown in Fig.[2]. Note the overestimation of the $$$R_2^*$$$ values near the nasal cavity, which appears as a darkening in the bottom part of the coronal view of the group average $$$R_2^*$$$ map. A graphical representation of the fits is show in Fig.[3]. The corresponding parameter values are:

$$\boldsymbol{A}^{-1}=\left[\begin{array}{cc}47.2\pm{}4.6&-0.50\pm{}0.10\\-205\pm{}58&5.48\pm{}0.84\\\end{array}\right]$$

$$\vec{P}_{A,0} = \left[\begin{array}{c}-7.8\pm{}1.6\\16\pm{}31\\\end{array}\right]$$

These were used to compute myelin and iron content maps as presented in Fig.[4]. The error caused by $$$R_2^*$$$ overestimation propagated to both myelin and iron maps. The myelin and iron content estimated from the newly calculated maps is compared with the literature values on the selected ROIs in Fig.[5].

The determination of the model coefficients enables the computation of $$$X_\mathrm{My}$$$ and $$$X_\mathrm{Fe}$$$ maps with realistic values matching relatively well the literature data.

The $$$X_\mathrm{My}$$$ estimations are more consistent than those for $$$X_\mathrm{Fe}$$$ as indicated by the values of the residual variance. However, further conclusions cannot be drawn, given the reduced number of points available for fitting.

The $$$R_2^\prime$$$ component in $$$R_2^*$$$ maps is likely to be responsible for the overestimations near the nasal cavity, and future models should consider refining/replacing this parameter, or developing correction schemes, although this may require new ex vivo validations and more complex acquisition and/or post-processing techniques.

Of note, the myelin estimates are inaccurate in the Globus Pallidus (the negative values obtained there are meaningless!). This might be an indication that a purely linear model is inappropriate for such estimations over the whole range of brain tissues, as previously suggested for $$$R_1$$$^{10,13,14}. We suggest that myelin estimates co-localized with high iron content are less reliable.

We would like to thank the following people for insightful discussions: Carsten Stüber, Laurentius Huber, Henrik Marschner, Robert Trampel, Evgeniya Kirilina and Nikolaus Weiskopf.

Funded by: EU through the 'HiMR' Marie Curie ITN (FP7-PEOPLE-2012-ITN-316716), the Max Planck Society through IMPRS NeuroCom, and the Helmholtz Alliance 'ICEMED - Imaging and Curing Environmental Metabolic Diseases'.

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**Fig.1: Regions-Of-Interest (ROIs) used for determining model parameters.**

The myelin $$$X_\mathrm{My}$$$ content (assumed to be identical to the lipid content) was obtained from [^{7,9}] while the iron content $$$X_\mathrm{Fe}$$$ was obtained from [^{6,8}]. Units are % for myelin and ppm for iron, both measured as mass to wet mass ratio. The $$$R_1$$$ and $$$R_2^*$$$ values were obtained from ME-MP2RAGE acquisitions^{5}, with the exception of $$$R_1$$$ for cerebrospinal fluid (CSF), which (ME-)MP2RAGE typically estimates incorrectly, and whose value is determined from literature^{15}. Blank cells indicates that the data is not available in the sources.

**Fig.2: The group average and standard deviation of the relaxation maps.**

$$$R_1$$$ and $$$R_2$$$ are the longitudinal and transverse relaxation maps obtained using ME-MP2RAGE with the same acquisition parameters as in [^{5}] ($$$600\;\mathrm{\mu m}$$$, $$$T_{I,(1,2)}=750,2900\;\mathrm{ms}$$$, $$$\alpha_{1,2}=3,6°$$$, $$$T_R=6000\;\mathrm{ms}$$$, $$$T_{E,i}=2.35,6.59,10.63,14.77\;\mathrm{ms}$$$). The black borders surrounding the brain tissues are a registration artifact. The group standard deviation of $$$R_1$$$ is significantly less than that of $$$R_2^*$$$, indicating the higher level of reproducibility of $$$R_1$$$, consistent with the findings in [^{5}].

**Fig.3: Results of the ODR affine fits on the priors.**

Visual representation of the Orthogonal Distance Regression (ODR) fits for both macromolecules and iron content. This regression method is suited when the errors on the independent variables cannot be ignored. The fits were performed separately for the two relaxing agents. The numerical results of the fits, including their standard errors, are reported, in addition to the (relative) residual variance, i.e. the fraction of the variance in the dependent variable that cannot be explained by the model.

**Fig.4: The group average and the standard deviation of the myelin and iron maps.**

$$$X_\mathrm{My}$$$ and $$$X_\mathrm{Fe}$$$ are myelin and iron maps obtained by applying the linear model (with the parameter values obtained with the ODR fits) to the relaxation maps $$$R_1$$$ and $$$R_2^*$$$. Realistic values are reproduced in almost all voxels. The larger biases and inferior reproducibility originating from $$$R_2^*$$$ maps affects both estimates similarly.

**Fig.5: ROI-based validation of the myelin and iron maps.**

The mean values of the myelin and iron content group averages are calculated in each Region-Of-Interest (ROI) (and weighted for the inverse of the group variance). These are compared with the values from the literature^{5,6,7,8} (as reported in Fig.[1]). For all ROIs the values are within their respective standard deviations. The abbreviations for the ROIs were introduced in Fig.[1].