The quantitative analysis of biological tissues through MRI is a promising technique towards in vivo histology. A semi-empirical linear model relating the iron and sulfur concentrations (as markers for ferritin and myelin) to the MRI relaxation rates $$$R_1$$$ and $$$R_2^*$$$ was proposed and validated in human post mortem samples [1]. However, it remains unclear whether it would be possible to estimate, at least semi-quantitatively, myelin and ferritin concentration in brain tissues using an analogous model under different experimental conditions, both because the MRI parameters are known to vary significantly for different fixation procedures and for in vivo conditions, and because the model might not be accurate enough. Indeed recent works may indicate that a linear model, its underlying assumptions or the input data might be insufficient for fully explaining the tissue microstructure in the brain [2]. In this work we evaluated four different linear models for estimating myelin and iron content in the full brain from simultaneously measured relaxation rates [3] under in vivo conditions. Each of model uses a different set of assumptions, based on prior knowledge of relative composition, on the levels of myelin and ferritin concentrations in specific brain regions.

If the underlying model is linear with only two contributors, then it is possible to obtain semi-quantitative consistent information from only four (or six, if we assume non-vanishing offset) independent equations. Based on post mortem results [1], we identified two different brain areas with extreme myelin and ferritin content: (a) the posterior Corpus Callosum (pCC), high in myelin myelinated, MyH), but low in ferritin (FeL); (b) the Substantia Nigra (SN) high in ferritin (FeH), but low in myelin (MyL). Additionally, the (c) whole brain average were considered (MyA, FeA) as well as (d) the CerebroSpinalFluid (CSF) (My0, Fe0) [4,5]. The relaxation rates in these regions can be used to obtain the aforementioned equations.

(I):(MyH-FeH-MyA-FeA)

$$\begin{bmatrix}0.5\\0.5\end{bmatrix}=\begin{bmatrix}A_{0,0}A_{0,1}\\A_{1,0}A_{1,1}\end{bmatrix}\begin{bmatrix}R_1[c]\\R_2^*[c]\end{bmatrix}+\begin{bmatrix}B_0\\B_1\end{bmatrix}$$

$$1=A_{0,0}R_1[a]+A_{0,1}R_2^*[a]$$

$$1=A_{0,1}R_1[b]+A_{1,1}R_2^*[b]$$

(II):(MyH-FeH-MyA-FeA-My0-Fe0)

$$1=A_{0,0}R_1[a]+A_{0,1}R_2^*[a]$$

$$1=A_{0,1}R_1[b]+A_{1,1}R_2^*[b]$$$$\begin{bmatrix}0.5\\0.5\end{bmatrix}=\begin{bmatrix}A_{0,0}A_{0,1}\\A_{1,0}A_{1,1}\end{bmatrix}\begin{bmatrix}R_1[c]\\R_2^*[c]\end{bmatrix}+\begin{bmatrix}B_0\\B_1\end{bmatrix}$$

$$\begin{bmatrix}0\\0\end{bmatrix}=\begin{bmatrix}A_{0,0}A_{0,1}\\A_{1,0}A_{1,1}\end{bmatrix}\begin{bmatrix}R_1[d]\\R_2^*[d]\end{bmatrix}$$

(III):(MyH-FeL-MyL-FeH)$$\begin{bmatrix}1\\0\end{bmatrix}=\begin{bmatrix}A_{0,0}A_{0,1}\\A_{1,0}A_{1,1}\end{bmatrix}\begin{bmatrix}R_1[a]\\R_2^*[a]\end{bmatrix}+\begin{bmatrix}B_0\\B_1\end{bmatrix}$$

$$\begin{bmatrix}0\\1\end{bmatrix}=\begin{bmatrix}A_{0,0}A_{0,1}\\A_{1,0}A_{1,1}\end{bmatrix}\begin{bmatrix}R_1[b]\\R_2^*[b]\end{bmatrix}+\begin{bmatrix}B_0\\B_1\end{bmatrix}$$

(IV):(MyH-FeL-MyL-FeH-My0-Fe0)

$$\begin{bmatrix}1\\0.5\end{bmatrix}=\begin{bmatrix}A_{0,0}A_{0,1}\\A_{1,0}A_{1,1}\end{bmatrix}\begin{bmatrix}R_1[a]\\R_2^*[a]\end{bmatrix}$$

$$\begin{bmatrix}0.5\\1\end{bmatrix}=\begin{bmatrix}A_{0,0}A_{0,1}\\A_{1,0}A_{1,1}\end{bmatrix}\begin{bmatrix}R_1[b]\\R_2^*[b]\end{bmatrix}$$

$$\begin{bmatrix}0\\0\end{bmatrix}=\begin{bmatrix}A_{0,0}A_{0,1}\\A_{1,0}A_{1,1}\end{bmatrix}\begin{bmatrix}R_1[d]\\R_2^*[d]\end{bmatrix}$$

Quantitative $$$R_1$$$, $$$R_2^*$$$ ($$$0.6\;\mathrm{mm}$$$ isotropic nominal resolution) of the full brain were simultaneously acquired [3] in six healthy volunteer (2 females, age: $$$24-29\;\mathrm{yr}$$$), with a MAGNETOM 7T (Siemens, Erlangen, Germany) and a circularly-polarized Tx / 32-channels Rx Nova coil. The prior knowledge for CC and SN was obtained by calculating the group and region averages on manually drawn masks of $$$4-10\;\mathrm{px}$$$ diameter. The whole brain mask was obtained using FSL's BET2. The models were tested for the myelin and ferritin prediction by calculating the average and the standard deviation on the anterior CC (aCC) and on Red Nucleus (RN).

The simultaneously acquired maps for $$$R_1$$$, $$$R_2^*$$$ are reported in Fig.1. Myelin and ferritin abundance estimates for the four different models are reported in Fig.2-3. In Fig.4 we report the result of the test on the different regions. All four models predict higher myelination in CC compared to RN. For the ferritin, models (I), (II), and (IV) imply comparable ferritin content in aCC and RN. Instead, model (III) reports a substantially higher ferritin content in RN compared to aCC.

Despite the other models being more consistent, model (III) seems to better agree with previously published data, since the estimated ferritin ratio between the thalamus and the white matter [4] is in the order of $$$~4-5$$$ (the arbitrary offset excludes the possibility of a direct comparison).

The fact that three of the four model seems to fail may be related to relatively poor assumptions. In fact as soon as global assumptions are imposed to the model, the estimates fail. However, if a linear model with only two species acting as a source of contrast was valid, then model (I) and model (III) should have been very similar, with model (I) slightly superior has the content estimates should have aroused from deviation from the average value and thus should have been in the $$$(1,0)$$$ range. The inconsistency of these models with the previously reported estimates can be explained by other components playing a significant role in the generation of the $$$T_1$$$ and $$$T_2^*$$$ contrast. The possible success of the model (III), while requiring further validation, indicates the viability of such approach to extract information that might prove valuable.

Although further validation is required, linear modeling of the microstructural composition of brain tissues using relaxometric $$$R_1$$$ and $$$R_2^*$$$ for obtaining semi-quantitative myelin and ferritin information may provide results that are compatible with previous works. However, the failure of similar models may indicate the need for investigating the role of additional components to the generation of the MRI contrast.