Assessment of mesoscopic properties of deep gray matter iron through a model-based simultaneous analysis of magnetic susceptibility and R₂* - A pilot study in patients with multiple sclerosis and normal controls

Abstract

Most studies of brain iron relied on the effect of the iron on magnetic resonance (MR) relaxation properties, such as $R_2^{\ast }$, and bulk tissue magnetic susceptibility, as measured by quantitative susceptibility mapping (QSM). The present study exploited the dependence of $R_2^{\ast }$ and magnetic susceptibility on physical interactions at different length-scales to retrieve information about the tissue microenvironment, rather than the iron concentration. We introduce a method for the simultaneous analysis of brain tissue magnetic susceptibility and $R_2^{\ast }$ that aims to isolate those biophysical mechanisms of $R_2^{\ast }$-contrast that are associated with the micro- and mesoscopic distribution of iron, referred to as the Iron Microstructure Coefficient (IMC). The present study hypothesized that changes in the deep gray matter (DGM) magnetic microenvironment associated with aging and pathological mechanisms of multiple sclerosis (MS), such as changes of the distribution and chemical form of the iron, manifest in quantifiable contributions to the IMC. To validate this hypothesis, we analyzed the voxel-based association between $R_2^{\ast }$ and magnetic susceptibility in different DGM regions of 26 patients with multiple sclerosis and 33 age- and sex-matched normal controls. Values of the IMC varied significantly between anatomical regions, were reduced in the dentate and increased in the caudate of patients compared to controls, and decreased with normal aging, most strongly in caudate, globus pallidus and putamen.

1. Introduction

Iron has a paradoxical role in the human brain. On the one hand, iron is a vital contributor to many biochemical processes, including the binding of oxygen in the blood (heme-iron), adenosine triphosphate (ATP) generation in cellular respiration (iron-sulfur clusters), and myelin synthesis by oligodendrocytes (ferritin) (Todorich et al., 2009). On the other hand, free iron is toxic, in particular ferrous iron, because it promotes the generation of highly reactive hydroxyl radicals through Fenton and Haber-Weiss chemistry. A vast amount of imaging-based evidence exists for the association of iron load in the deep gray matter (DGM) with neurodegeneration in diseases such as multiple sclerosis (MS) (Bagnato et al., 2013; Ropele et al., 2017; Stankiewicz et al., 2014; Stephenson et al., 2014) and Parkinson disease (Ward et al., 2014). Most of these studies rely on the effect of iron on magnetic resonance (MR) relaxation properties. The effective transverse relaxation rate $\left(R_2^{\ast }\right)$, which comprises the reversible $\left(R_2^{\prime }\right)$ and irreversible $\left(R_2\right)$ transverse relaxation rates, has long been considered as the most sensitive technique for assessing brain iron load noninvasively. The presence of paramagnetic iron complexes, primarily ferritin, results in an increase of the micro- (≤ 10µm; sub-cellular) and mesoscopic (10 − 100µm; cellular) magnetic field inhomogeneity in the tissue, resulting in a loss of spin phase coherence that manifests as an echo-time dependent loss of signal intensity on gradient echo recalled (GRE) magnitude images.

With the recent advent of advanced numerical techniques for a physics-based analytical phase image reconstruction (Robinson et al., 2017; Schweser et al., 2017), an entirely new iron-measurement methodology has become feasible, referred to as quantitative magnetic susceptibility mapping (QSM) (Deistung et al., 2017; Haacke et al., 2015; Liu et al., 2015; Wang and Liu, 2015; Wang et al., 2017). This method quantifies the macroscopic voxel-average effect of iron on the MR’s static main magnetic field in the brain.

Inductively coupled plasma mass spectrometry (ICP-MS) of brain tissue has confirmed that both $R_2^{\ast }$ and magnetic susceptibility increase linearly with the tissue iron concentration in humans without neurological diseases (Langkammer et al., 2010; Langkammer et al., 2012; Ropele and Langkammer, 2017). However, being related to micro- and mesoscopic magnetic field inhomogeneities, $R_2^{\ast }$ theoretically depends not only on the voxel-average concentration but also on the distribution of iron in the tissue (Pintaske et al., 2006; Weisskoff et al., 1994; Yablonskiy and Haacke, 1994; Ziener et al., 2005). Bulk tissue magnetic susceptibility, as quantified by QSM, on the other hand, relies entirely on magnetic field variations on a macroscopic length scale (≈ 1mm) and, hence, at least what concerns the underlying physical model, is independent of the micro-distribution of iron. Furthermore, it has recently been acknowledged that substantial differences in electron spin relaxation times render $R_2^{\ast }$ about ten times more sensitive to ferric iron $\left({\text{Fe}}^{\text{3+}}\right)$ than to ferrous iron $\left({\text{Fe}}^{\text{2+}}\right)$, whereas the difference in magnetic moments (4 vs. 5 Bohr magnetons) of these iron forms has a relatively small effect on their magnetic susceptibility (Dietrich et al., 2017). Consequently, magnetic susceptibility may be regarded as a more direct measure of the iron concentration in the tissue than $R_2^{\ast }$.

The goal of the present study was to exploit the dependence of both measures on physical interactions at different length-scales to retrieve information about the tissue microenvironment in vivo. The present study hypothesized that changes in the DGM magnetic microenvironment associated with aging- or disease-related changes of the distribution and chemical form of the iron manifest in quantifiable contributions to observed $R_2^{\ast }$ values. To validate our hypothesis, we analyzed the voxel-based associations between $R_2^{\ast }$ and magnetic susceptibility in different DGM regions of patients with MS and normal controls.

2. Theory

2.1. Dependence of magnetic susceptibility and $R_2^{\ast }$ on tissue iron

Both the effective transverse relaxation rate, $R_2^{\ast }$, and the voxel-average bulk magnetic susceptibility, χ, depend linearly on the tissue iron concentration c_Fe (Langkammer et al., 2010; Langkammer et al., 2012):

$$R_2^{\ast }=R_{\text{Fe}}^{\ast }+R_{\text{other}}^{\ast }=r_{\text{Fe}}\cdot c_{\text{Fe}}+R_{\text{other}}^{\ast }$$ (1)

$$\chi ={\chi }_{\text{Fe}}+{\chi }_{\text{other}}=k_{\text{Fe}}\cdot c_{\text{Fe}}+{\chi }_{\text{other}}$$ (2)

where r_Fe and k_Fe are conversion factors that describe the sensitivity of $R_2^{\ast }$ and χ, respectively, on the iron concentration, and $r_{\text{other}}$ and ${\chi }_{\text{other}}$ are contributions to the respective measures from sources other than iron, such as diamagnetic myelin, calcium, or water. The conversion factors depend on the chemical form of the iron and, in the case of r_Fe, also on the micro- and mesoscopic distribution of the iron.

Expressing c_Fe by the number of iron-containing particles per volume (particles/m³), the conversion factor for susceptibility, k_Fe, may be expressed as a function of the effective number of Bohr magnetoms per atom ${\mu }_{\text{eff}}$ (Schenck, 1992), reflecting the chemical form of the iron,

$$k_{\text{Fe}}=\frac{{\mu }_0{\mu }_{\text{eff}}^2{\mu }_B^2}{3kT}.$$

For $R_{\text{Fe}}^{\ast }$, the relationship is more complicated because it depends non-linearly on tissue diffusion properties and the size of the iron-laden susceptibility inclusions (Hardy and Henkelman, 1989; Weisskoff et al., 1994), such as molecular complexes, cellular organelles, and cells. Theoretical models that describe the dependence of $R_{\text{Fe}}^{\ast }$ on microstructural properties in a multi-compartment tissue like brain are not available. Empirical models by Jensen and Chandra (Jensen and Chandra, 1999) and Yung (Yung, 2003) for the dependence of $R_{\text{Fe}}^{\ast }$ on diffusion describe the inverse of $R_{\text{Fe}}^{\ast }$ in the presence of impermeable spherical objects as the sum of the inverse relaxation rate $R_{\text{Fe}}^{\ast }\left(D=0\right)$ in the static dephasing regime (no diffusion) (Yablonskiy and Haacke, 1994) and the other extreme, the motional narrowing regime $R_{\text{MNR}}^{\ast }:{\left(R_{\text{Fe}}^{\ast }\right)}^{-1}={\left(R_{\text{Fe}}^{\ast }\left(D=0\right)\right)}^{-1}+{\left(R_{\text{MNR}}^{\ast }\right)}^{-1}$. Here,

$$R_{\text{Fe}}^{\ast }\left(D=0\right)=\frac{2\pi }{9\sqrt{3}}\gamma B_0\cdot \eta \cdot \Delta \chi ,$$ (3)

and

$$R_{\text{MNR}}^{\ast }=\frac{16}{1215}{\gamma }^2{B}_0^2\cdot \eta \cdot \Delta {\chi }^2\cdot \frac{R_c^2}{D}.$$ (4)

Note that the original publications used the cgs unit system whereas we use SI units. Here, B₀ is the externally applied, static magnetic field strength, D is the diffusion constant and γ = 267 10⁶ rad/s/T is the gyromagnetic ratio of protons. Further, η denotes the volume fraction of the magnetic particles in the voxel, the effective radius R_c of the particles, and their difference in susceptibility $\Delta \chi$ to their surroundings, i.e., $\eta \cdot \Delta \chi =k_{\text{Fe}}\cdot c_{\text{Fe}}$. After substituting η , the total contributions of iron to the inverse of the transversal relaxation rate can therefore be expressed as

$${\left(R_{\text{Fe}}^{\ast }\right)}^{-1}=\frac{1}{r_{\text{Fe}}\cdot c_{\text{Fe}}}=\frac{1215\cdot D}{16\cdot R_c^2{\gamma }^2{B}_0^2\Delta \chi \cdot c_{\text{Fe}}\cdot k_{\text{Fe}}\cdot }+\frac{9\sqrt{3}}{2\pi \cdot \gamma B_0\cdot c_{\text{Fe}}\cdot k_{\text{Fe}}}.$$ (5)

This model predicts an increase of the relaxation time with increasing diffusion if all other properties remain constant. Ziener et al. (Ziener et al., 2005) showed that this empirical model is a reasonably close approximation of the more exact Strong Collision Model of diffusion dynamics for all diffusion regimes.

Human brain tissue consists of multiple cellular and sub-cellular compartments that are differently diffusion restricted and iron appears in different highly localized areas, such as specific cells and cell organelles, and with a different concentration in various cells such as oligodendrocytes, astrocytes, and neurons (Meguro et al., 2008). Hence, Eq. (5), which assumes a two-compartment model with impermeable spheres, may not accurately describe the physical reality in brain tissues. Furthermore, Eqs. (3) and (4) strongly depend on the geometry of the susceptibility inclusions changing their absolute values (pre-factors) substantially when the inclusion geometry deviates from the spherical case (as assumed here).

However, we believe that there is a rational value in using the model equation to understand the qualitative dependency of $R_2^{\ast }$ measurements, which represent a cumulative measure from different compartments, on the underlying microstructural tissue properties.

2.2. Introduction of the Iron Microenvironment Coefficient (IMC)

Although the direct interpretation of susceptibility and $R_2^{\ast }$ values has been proven useful in numerous clinical studies, the dependencies of both quantities on other biophysical contrast properties renders their direct interpretation problematic. Here, we propose to disentangle the different biophysical contrast mechanisms based on the different dependence of r_Fe and k_Fe on the spin state and (sub-) cellular distribution of the iron. In particular, we propose to quantify the ratio of both quantities, ${\kappa }_{\text{Fe}}=k_{\text{F}e}/r_{\text{Fe}}$, which we will, in the following, refer to as the Iron Microenvironment Coefficient (IMC). Rearranging Eq. (5) leads to the following formula for the IMC:

$$\frac{1215\cdot D}{16\cdot R_c^2{\gamma }^2{B}_0^2\Delta \chi }+\frac{9\sqrt{3}}{2\cdot \pi \cdot \gamma B_0}=\frac{k_{\text{Fe}}}{r_{\text{Fe}}}={\kappa }_{\text{Fe}}.$$ (6)

Now, assuming a spherical particle and expressing the particles’ susceptibility difference relative to their surroundings, $\Delta \chi$, by the number of paramagnetic iron atoms N, and the volume of the particle $V=4/3\cdot \pi \cdot R_c^3$ (Schenck, 1992)

$$\Delta \chi =\frac{N}{V}\cdot \frac{{\mu }_0{\mu }_{\text{eff}}^2{\mu }_{\text{B}}^2}{3kT}=\frac{N}{4\pi \cdot R_c^3}\cdot \frac{{\mu }_0{\mu }_{\text{eff}}^2{\mu }_{\text{B}}^2}{kT},$$

we obtain:

$$\frac{R_c}{N}\cdot \frac{D}{{\mu }_{\text{eff}}^2}\cdot {\kappa }_{\text{MNR}}+\frac{9\sqrt{3}}{2\pi \cdot \gamma B_0}={\kappa }_{\text{Fe}},$$ (7)

Where ${\kappa }_{\text{MNR}}=\frac{1215\cdot 4\text{π}\cdot \text{kT}}{16{\gamma }^2{B}_0^2{\mu }_0{\mu }_{\text{B}}^2}$ is a constant that depends on tissue temperature and magnetic field strength. Under normal physiological body temperature, T=310K at B₀=3T, ${\kappa }_{\text{MNR}}=5.87\cdot {10}^{16}{\text{s}}^2{\text{m}}^{-3}$.

2.2.1. Experimental Determination of the IMC

Using Eqs. (1) and (2), the average IMC in a certain anatomical region may be quantified experimentally by simultaneously assessing magnetic susceptibility and $R_2^{\ast }$ in a region of interest (ROI) and fitting the following linear equation to the voxel values within the region:

$$\mathbf{\chi }\mathbf{=}\mathbf{\kappa }\mathbf{\cdot }{\mathbf{\text{R}}}_{\mathbf{2}}^{\mathbf{\text{*}}}\mathbf{+}\mathbf{\rho }\mathbf{,}$$ (8)

where $\rho =-\kappa \cdot R_{\text{other}}^{\ast }+{\chi }_{\text{other}}$ . Naturally, the calculated coefficient κ will be close to the region-average κ_Fe only if ρ does not vary systematically throughout the ROI, i.e., $\text{d}\rho \approx \text{0}$ throughout the region. Using the differential product rule, this requirement implies

$$\text{d}{\chi }_{\text{other}}-\text{d}{\kappa }_{\text{Fe}}\cdot R_{\text{other}}^{\ast }-\kappa \cdot \text{d}{R}_{\text{other}}^{\ast }\approx 0.$$ (8a)

Assuming that dκ is independent of both (not correlated with) $\text{d}{R}_{\text{other}}^{\ast }$ and ${\chi }_{\text{other}}$ and considering that myelin and calcium, the major non-iron players for brain susceptibility variations, have an opposite effect on susceptibility and $R_2^{\ast }\left(\text{d}{R}_{\text{other}}^{\ast }\propto -\text{d}{\chi }_{\text{other}}\right)$, the condition in Eq. (8a) is satisfied only if $\text{d}{R}_{\text{other}}^{\ast }\approx 0$ and $\text{d}{\chi }_{\text{other}}\approx 0$ throughout the ROI. In other words, κ will be a reliable estimate of κ_Fe if non-iron contributions to χ and $R_2^{\ast }$ are constant throughout the ROI. The average values of ${\chi }_{\text{other}}$ and $R_{\text{other}}^{\ast }$ within the ROI have no effect on κ.

Decreased myelin or calcium content decreases $R_{\text{other}}^{\ast }$ and increases ${\chi }_{\text{other}}$, which results in an increase of ρ, and vice versa. Hence, an inverse proportional relationship exists between the amount of myelin and calcium and the true value of ρ at a certain location within the ROI. As a result, the stronger intra-ROI variations of susceptibility and $R_2^{\ast }$ values are correlated with the concentration of myelin or calcium, the stronger will the estimated IMC, κ, underestimate the true IMC, κ_Fe. In the most extreme case of an absence of iron in the ROI, variations of susceptibility and $R_2^{\ast }$ values are caused entirely by variations in myelin or calcium, resulting in a negative correlation of ρ with $R_2^{\ast }$ and, hence, a negative IMC is obtained using Eq. (8). For the remainder of this work, unless stated otherwise, we will assume that the effects of diamagnetic sources on the susceptibility and $R_2^{\ast }$ values are small within the DGM compared to the effect of iron, in line with most published studies.

If the underlying assumptions are valid, the evaluation of Eq. (8) transforms the simultaneously observed quantities χ and $R_2^{\ast }$ into two quantities of which one, the estimated IMC κ, depends on only the chemical form and distribution of the iron and the other, the offset ρ, comprises all referencing effects and non-iron contributions to χ and $R_2^{\ast }$.

2.2.2. Properties of the IMC

Several properties of the true IMC, κ_Fe, follow from Eq. (7):

1. The IMC obtains its minimum value in the absence of diffusion effects, D = 0. In the impermeable sphere model, ${\kappa }_{\text{Fe}}=\frac{9\sqrt{3}}{2\pi \cdot \gamma B_0}=3.1\hspace{0.33em}\text{ppb}\cdot \text{s}\left(B_0=3T\right)$.

2. In the presence of diffusion (D ≠ 0), the IMC increases linearly from its minimum value with increasing radius of the particles, R_C , and inversely with the number of iron atoms per particle, N, and the chemical form of the iron, reflected by the effective number of Bohr magnetoms, ${\mu }_{\text{eff}}$.

3. If diffusion and chemical iron form are similar, different IMC values reflect differences in the ratio of the particle radius (R_c) to the number of iron atoms (N). This relationship has interesting implications. It implies that for particles of different size with the same intracellular iron concentration, the IMC will be lower for those particles that are larger. For example, if iron is moved from a certain type of cell (e.g., oligodendrocyte) to another type of cell that has a different size (e.g., microglia), but the cellular iron concentration remains similar, the IMC may change. Furthermore, larger particles with the same iron load (number of atoms) as smaller particles, e.g., cell enlargement without a change in iron, have a greater IMC.

The following properties of the estimated IMC, κ, follow from Eq. (8):

1. It is independent of the region-average iron concentration or variations of voxel-average iron concentration, c_Fe, within the investigated anatomical region. According to Eqs. (1) and (2), variations in the iron concentration affect both χ and $R_2^{\ast }$ simultaneously so that an evaluation of Eq. (8) will yield the same value of κ. This property of the IMC illustrates that the IMC is a truly complementary (orthogonal) measure to region-average values of susceptibility and $R_2^{\ast }$. This property should not be confused with the dependence of the IMC on the number of iron atoms per particle, N (see properties ii and iii). While a change in c_Fe may be associated with a change in N (which would affect the IMC), it may also be related to an increased abundance of particles with the same N.

2. It is independent of the region-average values of non-iron contributions, R_other and χ_other, as long as these contributions are constant throughout the region of interest (see above).

3. It is independent of the chosen intra-subject reference of the susceptibility values (in this study: the whole brain; see below), which may itself be affected by aging or disease processes and often complicated the interpretation of previous QSM studies (Schweser et al., 2018).

2.2.3. Combined analysis of alterations in magnetic susceptibility and IMC

How can changes in the IMC and magnetic susceptibility be interpreted? In the following, we will try to answer this question by first discussing biophysical mechanisms that affect either IMC or magnetic susceptibility independently. Then we will discuss effects that affect both quantities in a coupled fashion.

Several microscopic processes can result in increased susceptibility without affecting the IMC, and vice versa. The IMC depends linearly on diffusivity (see Eq. 7). Hence, increased diffusivity increases the IMC. While the magnetic susceptibility is independent of diffusion properties, demyelination increases susceptibility because myelin is strongly diamagnetic $\left({\chi }_{\text{myelin}}<0\right)$. The IMC, on the other hand, is not affected by demyelination, as long as demyelination occurs homogeneously throughout the investigated region. Atrophy is another mechanism that can increase the magnetic susceptibility without any involvement of iron homeostasis and, hence, no change in the IMC: The removal (atrophy) of cells that do not contain a significant amount of tissue iron increases the tissue density of iron-containing cells, η, resulting in an increase in the region’s iron concentration c_Fe (but not iron mass!). Consequently, they both increase susceptibility and $R_2^{\ast }$. Analogously, a decrease in η may decrease the susceptibility without an accompanying change in IMC. Such a process could be, for example, a reduction of the number of iron-laden oligodendrocytes, without a change in the iron load of the remaining cells.

A prevailing hypothesis for pathological alterations in susceptibility and $R_2^{\ast }$ is that iron concentration is altered due to added or removed iron from the particular region (Eskreis-Winkler et al., 2017; Wang et al., 2017; Ward et al., 2014). Assuming the absence of other pathological mechanisms, such as atrophy, cellular uptake or depletion of iron from oligodendrocytes would increase and decrease, respectively, the number of iron atoms per cell, N, proportionally to the change in tissue iron concentration (susceptibility). Hence, regions affected by such a mechanism would be expected, in a first-order approximation, on a diagonal line spanning from quadrant A (cellular iron depletion) through the plot’s origin to quadrant D (cellular iron uptake). The slope of this line depends on other microscopic tissue properties.

Another effect that could result in coupled changes of IMC and susceptibility is related to a breakdown of the underlying assumption that dρ ≈ 0 throughout the ROI in Eq. (8). If myelin has a substantial effect on the IMC estimate (see above), demyelination may theoretically decrease the systematic, myelin-related underestimation of κ_Fe, resulting in an apparent increase of the estimated IMC. Regions affected by such a mechanism would be expected in quadrant B.

Figure 1 schematically visualizes the combined assessment of changes in susceptibility and IMC. Data points representing mechanisms with invariant susceptibility and IMC may be found near the plot’s origin. Regions with the aforementioned coupled shifts towards higher values of susceptibility and IMC will be found in quadrant B, and vice versa in quadrant C.

Figure 1:

Combined assessment of changes in susceptibility (horizontal) and the IMC (vertical) over time or between groups. The area around the figure’s origin characterizes no change in properties. Changes in iron concentration affect the susceptibility, while the IMC increases linearly with the radius R_c of iron containing cells as well as the diffusion constant and decreases with the number of iron atoms N within the cell (refer to Eq. 7). Phenomena shifting susceptibility and the IMC in one of the quadrants are discussed in section 2.2.3.

In summary, the combined analysis of changes in IMC and magnetic susceptibility approximately decouples biophysical effects due to diffusion, demyelination, and atrophy of cells without iron from changes in the cellular iron concentration, providing the chance to obtain complementary knowledge about pathological mechanisms.

3. Materials and Methods

This retrospective study was approved by the local Ethical Standards Committee at the University at Buffalo, and a written informed consent form was obtained from all participants.

Subjects

This study included a total of 59 participants of which 26 were MS patients and 33 were age-(p=0.98) and sex-matched (p=0.97) controls. The demographic and clinical characteristics of the study participants were determined by physical and neurological examinations. No subjects were included that were pregnant or had pre-existing medical conditions known to be associated with brain pathologies, such as cerebrovascular disease or positive history of alcohol dependence.

Of the 26 MS patients, 16 had the relapsing-remitting (RR) form of MS and ten had secondary progressive (SP) MS. The average age of the patients was 52.9±10.3 years (mean±std), and the sex ratio was 2.25 (18 female, eight male). Patients were diagnosed using the revised McDonald criteria (Polman et al., 2011). The average disease duration was 19.6±9.7yrs (mean±std). The Expanded Disability Status Scale (EDSS) was obtained by an experienced neurologist (more than 30 years of experience).

All healthy controls had a normal neurological examination and no history of neurologic disorders or chronic psychiatric disorders. The mean age of the controls was 52.1±11.1yrs (mean±std), and the sex-ratio was 2.3 (23 female, ten male).

Data acquisition

We performed MRI at a clinical 3 Tesla magnet (Signa Excite HD 12.0; General Electric, Milwaukee, WI, USA) using an eight-channel head-and-neck coil. No hardware or software upgrades occurred between the first and the last exams included in the study.

Data for QSM were acquired using an axial, un-accelerated 3D single-echo spoiled GRE pulse sequence with first-order flow compensation in read and slice directions, a matrix of 512×192×64 and a nominal resolution of 0.5×1×2 mm³ (FOV=256×192×128 mm³), flip angle = 12°, TE/TR=22ms/40ms, bandwidth=13.89 kHz, and a total measurement time of 8 minutes and 46 seconds. Due to the lack of a phase-reconstruction mechanism on the MRI scanner, we stored the raw k-space data for each receiver channel. Data for $R_2^{\ast }$ mapping were acquired with a separate axial, bipolar multi-echo GRE (MGRE) pulse sequence using a matrix of 384×172×126 and a nominal resolution of 0.625×1×1 mm³ (FOV=240×180×126 mm³), flip angle = 15°, 11 echoes, TE₁/∆TE/TR=1.17ms/2.96ms/34.8ms, bandwidth=41.67 kHz, and elliptical sampling, resulting in a total measurement time of 6 minutes and 40 seconds. For this sequence, the scanner software had reconstructed the magnitude images, which were exported in DICOM format.

Image reconstruction

Magnitude and phase images of the GRE sequence were reconstructed offline on a 512×512×64 spatial grid using sum-of-squares and scalar phase matching (Hammond et al., 2008), respectively. To obtain an isotropic in-plane resolution, the k-space was zero-padded in phase-encoding direction before the processing. In-plane distortions due to imaging gradient non-linearity were compensated for based on the gradient coil’s spherical harmonics (Polak et al., 2015). We computed the susceptibility maps by unwrapping the phase images with a best-path algorithm (Abdul-Rahman et al., 2007), background-field correction with V-SHARP (Schweser et al., 2011) (radius 5mm; TSVD threshold 0.05), and conversion to magnetic susceptibility maps using the HEIDI algorithm (Schweser et al., 2012). We referenced (0 ppb) all susceptibility maps to the average susceptibility of the brain (Straub et al., 2016), a reference region which was chosen to minimize bias due to potentially pathology-related changes in a smaller anatomical reference region.

We used the magnitude images of the six odd echoes of the multi-echo sequence to calculate $R_2^{\ast }$ using logarithmic calculus (mono-exponential) and accounting for Rician noise bias with the power-method (Miller and Joseph, 1993). To account for the sensitivity of the $R_2^{\ast }$ reconstruction to signal noise, all magnitude images were denoised with gradient anisotropic diffusion filtering prior to the fitting (ITK, Version 3.20.0, www.itk.org, (Perona and Malik, 1990); 6 iterations, conductance = 1, time step 0.1152; empirically determined parameters to preserve structural details on the final $R_2^{\ast }$ maps).

All processing was performed by fully automated pipelines on a Linux workstation (Ubuntu 12.04) with 48 cores (Intel Xenon E5–2697v2 at 2.7Ghz) and 396 GB RAM. In particular, all QSM- and $R_2^{\ast }$-related processing steps relied on in-house developed MATLAB programs (2013b, The MathWorks, Natick, MA).

Image processing

Susceptibility maps were normalized to an in-house generated susceptibility brain template using Advanced Normalization Tools (ANTs; version 2.0.0; http://stnava.github.io/ANTs) with diffeomorphic Greedy-SyN transformation model. We created the template independently of the current study with an intensity normalization technique from susceptibility maps of ninety subjects of 3 groups (30 HC, 30 RRMS, 30 SPMS), with age and sex having been matched one-to-one, and ages spread out between 18–70 years. Details of the template generation technique (DIR-R strategy) have been described previously (Hanspach et al., 2016). The template is shown as an inset in Figure 2.

Figure 2:

Processing pipeline employed in the present study. The simulated magnitude images from the MGRE-sequence were registered to the magnitude images of the GRE sequence. The obtained non-linear transformation matrix was then applied to the $R_2^{\ast }$ maps using ANTs, which transformed $R_2^{\ast }$ and $\chi$ into the same space. Finally, to enable a voxel-wise comparison, we warped the susceptibility maps to a dedicated susceptibility brain template and applied the computed warp fields to the $R_2^{\ast }$ maps.

To enable the multi-voxel analysis of $R_2^{\ast }$ and magnetic susceptibility values in Eq. (8), we transformed also the $R_2^{\ast }$ maps into the susceptibility template space. To facilitate this transformation, we used the multi-echo data to forward-simulate for each subject a magnitude image with an image contrast similar to the (single-echo) GRE magnitude images. This simulation was achieved using a mono-exponential signal decay model with the fitting coefficients obtained from the $R_2^{\ast }$ reconstruction (see above). We calculated the effective image intensities in all voxels at an echo time of 22ms. While we did not systematically evaluate the benefit of this simulation strategy over the use of a single volume from the MGRE sequence at an echo time close to 22ms (8^th echo; 21.9ms), we expected that the increased signal-to-noise ratio of the simulated images would increase the registration stability. The individual echo images of the MGRE sequence suffered from relatively low signal-to-noise ratio due to the high readout bandwidth used. We affine registered the simulated images onto the GRE magnitude images using ANTs. The resulting deformation transform was then applied to the $R_2^{\ast }$ maps, followed by a warp of the transformed maps to the template space based on the existing warp-field of the susceptibility maps. Figure 2 illustrates the entire processing pipeline.

Calculation of the IMC

We studied the IMC in all major deep gray matter (DGM) regions. To this end, a trained image analyst created a custom DGM atlas by outlining the following bilateral 3D ROIs on the susceptibility template using the label map editor of 3D Slicer (version 4, www.slicer.org; (Fedorov et al., 2012)): caudate (CAU), dentate (DEN), globus pallidus (GP), nucleus ruber (NR), pulvinar nucleus of the thalamus (PUL), thalamus without the pulvinar nucleus (THA*), whole thalamus (THA), and putamen (PUT). We avoided partial-volume effects at the region boundaries by defining the ROIs slightly smaller than the actual visibility of the anatomical region and joined regions across the left and right hemispheres to reduce the number of comparisons. For each region of the atlas, we carefully inspected both the $R_2^{\ast }$ and χ maps of every individual subject with respect to the presence of obvious imaging and reconstruction artifacts or improper registration. If a subject showed artifacts or signal degradation in a particular ROI, this region of the subject was excluded from subsequent analyses. Details of the quality control are provided in Supplementary Material A.1.

To determine the validity of Eq. (8) in human DGM, we first correlated the voxel values of magnetic susceptibility and $R_2^{\ast }$ in each ROI. If Pearson correlation reached statistical significance (p < 0.05), we fitted Eq. (8) to the voxel values using a total least-squares algorithm (Krystek and Anton, 2007), as we considered both QSM and $R_2^{\ast }$ to be affected by measurement errors.

Statistical analysis

We statistically analyzed the obtained IMC values. Also, we analyzed the regional susceptibility and $R_2^{\ast }$ values to facilitate a comparison with previous studies and to exploit the approximate orthogonality of IMC and susceptibility.

In the statistical analysis only those subjects that showed a positive correlation between magnetic susceptibility and $R_2^{\ast }$, i.e., κ > 0 in Eq. (8) were included. When a subject showed a negative association between the measures in a region, we excluded it from the pool of subjects for the particular region, because negative slopes indicate a failure of the underlying assumption that intra-regional variations in $R_2^{\ast }$ and χ are dominated by variations in iron concentration (see also below). While the fitting offset values, ρ, contain principally relevant information about non-iron tissue compartments, their interpretation is difficult due to their implicit dependence on the IMC and the intra-subject susceptibility reference. Hence, we did not systematically analyze them in the present study.

The normality of sample distributions was assessed using the Shapiro-Wilk test. Group differences were assessed with an independent samples t-test. To test if sample distributions differed significantly between ROIs within HCs or MS patients, we applied a one-way analysis of variance (ANOVA) with Tukey’s HSD (Honestly Significant Difference) post-hoc analysis. Univariate analysis of covariance (ANCOVA) with age and sex as covariates revealed if the mean values of ROIs differed between controls and patients. The ANCOVA was conducted in an unweighted manner for $R_2^{\ast }$ and χ mean values. For the IMC values, we used a weighted ANCOVA to incorporate additional information about the robustness of the IMC value estimation, i.e., the stability of the linear fitting. We used the uncertainty of the fitting coefficient κ as weights, i.e., the ratio of the mean coefficient and its standard error obtained from the total least squares fitting routine.

We used a p-value threshold of 0.05 to define statistical significance. To reduce the family-wise error rate (FWER), we employed a Bonferroni correction for eight comparisons (8 ROIs) resulting in a p-value threshold of 0.05/8=0.00625 for statistical significance. To limit the number of false negative findings in this exploratory study, we report results with 0.00625 ≤ p < 0.05 as statistical “trends,” i.e., results that were statistically significant before the Bonferroni correction (but not after). The effect size of group differences was assessed using Cohen’s d.

To characterize the effects of sex and healthy aging, we applied a linear model with age as a covariate and sex as a fixed factor in the HC group. If there were no significant associations with sex, we further applied a linear least-squares fit to reveal the dependencies of the IMC, $R_2^{\ast }$ and χ on age. For the IMC, the linear least-squares fit was weighted with the aforementioned relative errors. The statistical significance of differences in fitting coefficients between groups were assessed based on the overlap of 95% confidence intervals.

Association of the IMC with EDSS was tested using sex as fixed factors, and age and disease duration as covariates. Due to the inherent specificity limitations of the EDSS score, we hereafter used the pyramidal functional score (FS) as a more reliable marker of motor disability regardless of the stage of the disease. In the absence of a significant association, we repeated the analysis using a binarized form of the pyramidal sub-score (<2 and ≥2, respectively). The pyramidal score is more specific to motor disability, and binarizing was justified by the non-linear rank nature of the score.

All statistical analyses were performed in SPSS (version 24.0; IBM Corp, Armonk, NY) or MATLAB.

4. Results

In the following, if not stated otherwise, results are presented as mean value ± 95% confidence interval.

4.1. Quality control

The quality control of the $R_2^{\ast }$ and susceptibility maps led to the exclusion of 55 ROIs (12%). Between 5% and 13% of the subjects had to be excluded in each region, except for the DEN. Here, about one third of the subjects was excluded primarily due to a loss of magnitude signal at the inferior edge of the imaging slab. In THA, THA*, and PUL, ROIs were excluded primarily due to a significant contamination with the signal from veins. In all other regions, magnetic field inhomogeneity and respiration artifacts were the primary reasons for exclusion.

4.2. Group differences in magnetic susceptibility and $R_2^{\ast }$ values:

Figure 3 (top and middle) summarizes the group-average susceptibilities and relaxation rates for patients and HCs. Details may be found in the Supplementary Materials (Tables A.3 and A.4). Differences of magnetic susceptibility did not reach significance after Bonferroni correction, but trends (0.00625 ≤ p < 0.05) were observed toward higher susceptibility in patients in the CAU (p = 0.011, d = +0.674), DEN (p = 0.007, d = +0.737), and GP (p = 0.008, d = +0.712), and toward lower susceptibility in patients in the THA (p = 0.021, d = −0.64) and THA* (p = 0.024, d = −0.628).

Figure 3:

Mean values of susceptibility χ, relaxation rate $R_2^{\ast }$, and IMC κ for the 8 ROIs in controls and patients, represented with their respective 95% confidence intervals. The plots visualize values listed in Tables A.3, A.4 and 1, respectively. A detailed overview of the distribution of κ can be found in Figure A.1. Significant differences between the groups (p < 0.006) corrected for multiple comparisons are denoted by **, trends (p < 0.05) by *.

Findings based on $R_2^{\ast }$ resembled those based on susceptibility in all regions, with lower values in PUL, THA, and THA* of patients and higher values in all other regions. However, statistical significance was reached only in the DEN (p = 0.001, d = +0.878). We observed trends toward higher $R_2^{\ast }$ values in CAU (p = 0.034, d = +0.563) and in the GP (p = 0.033, d = +0.576 ).

4.3. Iron Microenvironment Coefficient (IMC):

We found significant positive correlations between $R_2^{\ast }$ and χ in the DEN, GP, NR, and PUT of all subjects, which is consistent with the hypothesis that variations in DGM voxel values are dominated by variations in iron concentration. Three exemplary significant correlations are visualized in Figure 4. The correlations did not reach significance in the THA, THA*, CAU, and PUL of 2.2% to 4.4% of the subjects (see Table A.1 for details). The IMCs followed normal distributions with the only outliers being negative coefficients, κ < 0, which were observed in a total of 3.6% of the regions (see Figure A.1 in the Supplementary Material). After the exclusion of the subjects with negative coefficients (Table A.1) the resulting sub-groups for each ROI were still age- and sex-matched (p ≥ 0.45).

Figure 4:

Quantification of the association between χ and $R_2^{\ast }$ by total least-squares fitting of Eq. (8) to the voxel value distributions in each ROI. Shown are three exemplary sample distributions and corresponding regression lines from different anatomical regions of healthy female controls with ages between 47 to 54 years.

The average of the IMC over all ROIs was (6.2±0.2) s·ppb in the HCs and (6.0±0.2) s·ppb in the MS patients (±95% confidence intervals). The difference between the groups was not significant when all ROIs were combined (p ≥ 0.066).

Table 1 and Figure 3 (bottom) show the average values of the IMC in the different regions. In all regions except PUT and CAU (trend, p = 0.015, d = +0.641), the IMCs were lower in patients than in controls, but differences reached significance only in the DEN (p = 0.001, d = −1.16).

Table 1:

Mean values (± 95% confidence intervals) of the IMC in the HC $\left({\overline{\kappa }}_{\text{HC}}\right)$ and MS groups $\left({\overline{\kappa }}_{\text{MS}}\right)$. The p-values were determined by conducting a weighted ANCOVA on each region with disease as a fixed factor; and d is the effect size. The unit of κ is s·ppb. Statistically significant results after Bonferroni correction are indicated by **, trends by *. N denotes the number of analyzed cases, as shown in detail in Table A.1.

	$\overline{\kappa }$	$\overline{\kappa }$	p	d	N
CAU	4.8±0.3	5.5±0.6	0.015*	+0.641	47
DEN	6.9±0.5	5.7±0.5	0.001**	−1.16	39
GP	5.7±0.5	5.4±0.4	0.231	−0.271	56
NR	5.3±0.4	5.1±0.3	0.426	−0.172	56
PUL	5.7±0.6	5.7±0.7	0.809	−0.018	52
THA*	6.9±0.6	6.5±0.5	0.281	−0.272	49
THA	7.7±0.7	7.3±0.6	0.351	−0.214	50
PUT	6.5±0.4	6.8±0.5	0.115	+0.342	53

A General Linear Model using region as a fixed factor and IMC values as dependent variables showed no statistically significant interaction effects between IMC and region or group. However, a similar post-hoc analysis using only IMC values in DEN, GP, NR, PUL, and THA* showed that the reduction of IMC values in patients compared to controls was statistically significant (p = 0.007). A similar analysis using CAU and PUT showed a statistically significant increase of the IMC in patients compared to controls (p = 0.009).

In HCs, ANOVA indicated that values of the IMCs in the DEN (p < 0.001) and PUT (p < 0.03) differed significantly from those in CAU and NR. The values in CAU, GP, NR, and PUL were significantly different from the values in THA and THA* (p < 0.05). Corresponding observations in patients were similar to those in HCs with significantly different values in CAU, DEN, GP, NR, and PUL from those in the THA (p < 0.002). Values in the NR were significantly different from those in the THA* (p < 0.005). PUT was significantly different from CAU, and GP from NR (p < 0.009). A more detailed overview of the ANOVA-results may be found in Figure A.2 in the Supplementary Materials.

4.3.1. Age and Sex Dependency of Magnetic Susceptibility, Relaxation Rate, and IMC Values in Healthy Controls

In the CAU, we observed a significant positive correlation of susceptibility (p = 0.001, R² = 0.315) as well as a trend towards a positive correlation of $R_2^{\ast }$ (p = 0.012, R² = 0.188) with age. We found trends in the GP towards positive associations with susceptibility (p = 0.009, R² = 0.201) and $R_2^{\ast }$ (p = 0.017, R² = 0.169). In PUT, this trend was also found for susceptibility (p = 0.021, R² = 0.308), but not for $R_2^{\ast }$ (p = 0.099, R² = 0.171). In the NR, we observed a significant positive correlation of susceptibility with age (p = 0.004, R² = 0.243) and a trend for $R_2^{\ast }$ (p = 0.008, R² = 0.207). Associations between susceptibility and age were negative in both THA* (p = 0.013, R² = 0.182) and THA (p = 0.045, R² = 0.123). The IMC decreased in all regions with age, although this association reached significance only in CAU (p = 0.005, R² = 0.29). Trends toward a negative association of the IMC with age were found in GP (p = 0.02, R² = 0.174) and PUT (p = 0.017, R² = 0.199).

The univariate model revealed trending associations of sex towards higher values of susceptibility in HCs in the PUT for females (p = 0.032) and as well as higher values of $R_2^{\ast }$ in the DEN (p = 0.017). We did not find statistically significant associations of the IMC with sex (p > 0.16).

Table 2 and Tables A.5 and A.6 in the Supplementary Materials lists the detailed results of the linear regression with age for the IMC, susceptibility, and the relaxation rate, respectively. Figure 5, 6, and 7, respectively, visualize the associations between the observed quantities and age in regions with trending or significant associations.

Table 2:

Coefficients of the linear correlation (± 95% confidence intervals) of the IMC with age in healthy controls. The p-values represent the Pearson correlation coefficient. Statistically significant results after Bonferroni correction are indicated by **, trends by *. Significant correlations are also shown in Figure 7.

	Slope in s ppb 10–3 /year	Intercept in s–1	p	R2
CAU	−47±27	7.1±1.5	0.005**	0.29
DEN	−7±38	7.2±2.1	0.807	0.003
GP	−40±39	7.6±2.1	0.02*	0.174
NR	−20±31	6.2±1.7	0.152	0.072
PUL	−27±51	6.6±2.7	0.141	0.071
THA*	−13±46	7.2±2.5	0.65	0.008
THA	−14±55	8±2.9	0.434	0.023
PUT	−38±30	8.3±1.6	0.017*	0.199

Figure 5:

Age-dependency of the magnetic susceptibility in HCs. The solid lines represent the linear fits with the dashed line being 95% confidence intervals calculated with the Working-Hotelling procedure (Kutner et al., 2005). Significant correlations are denoted with **, trends with *. Fitting coefficients are listed in Tab. A.5 in the Supplementary Materials.

Figure 6:

Age-dependency of $R_2^{\ast }$ in HC. The solid lines represent the linear fits with the dashed line being 95% confidence intervals calculated with the Working-Hotelling procedure (Kutner et al., 2005). Significant correlations are denoted with **, trends with *. Fitting coefficients are listed in Tab. A.6 in the Supplementary Materials.

Figure 7:

Age-dependency of IMCs. HCs and patients are indicated by hollow circles and red diamond symbols, respectively. The solid lines represent the linear fits to the HC data with the dashed line being 95% confidence intervals calculated with the Working-Hotelling procedure (Kutner et al., 2005). Significant correlations in HC are denoted with **, trends with *. Fitting coefficients are listed in Tab. 2.

4.3.2. Dependency of Disease Duration (dd) and Disability on the IMC:

The correlation between disease duration (dd) and IMC did not reach statistical significance in any of the regions (p > 0.07). We also did not find significant associations of the IMC with EDSS (p > 0.19), binarized pyramidal EDSS scores (p > 0.12), or age (p > 0.09) in patients.

4.3.3. Combined assessment of susceptibility and IMC changes in MS

Figure 8 visualizes the group differences in IMC and susceptibility in the orthogonal coordinate system spanned by the two quantities (Fig. 1). The plot shows no regions in quadrant A, CAU and PUT in quadrant B, thalamic regions in quadrant C, and NR, GP, and DEN in quadrant D.

Figure 8:

Dependency of differences in IMC over differences in susceptibility between HC and MS in the respective regions (cf. Fig. 1). Positive values of Δκ represent higher values of κ in HC compared to MS.

5. Discussion

In this work, we introduced a method for the simultaneous analysis of brain tissue magnetic susceptibility and $R_2^{\ast }$ that aims to isolate those biophysical mechanisms of $R_2^{\ast }$-contrast that are associated with the mesoscopic distribution of iron. The technique yields a new measure that we refer to as the Iron Microstructure Coefficient (IMC). The IMC may be understood as being, to some degree, complementary to the voxel-average magnetic susceptibility, potentially providing a new window to illuminate the contentious processes underlying alterations of iron homeostasis in the human brain. In the present pilot study with healthy subjects and patients with MS, we found significant differences in IMC values between anatomical regions, a dependency of the IMC on age, and differences between patients and controls.

5.1. Comparison with previous studies

Our tissue susceptibility and $R_2^{\ast }$ measurements were widely in-line with previously published findings, confirming the comparability of our cohort and methods used: We found increasing values with age in all regions but thalamus and increased values in patients compared to controls in most DGM regions (Al-Radaideh et al., 2018; Elkady et al., 2017; Fujiwara et al., 2017; Hagemeier et al., 2017; Langkammer et al., 2013; Rudko et al., 2014; Schweser et al., 2018), but decreased values in the thalamus (Al-Radaideh et al., 2018; Burgetova et al., 2017; Hagemeier et al., 2017; Schweser et al., 2018).

Several previous clinical studies have analyzed and compared both magnetic susceptibility and $R_2^{\ast }$. However, most of these studies considered susceptibility and $R_2^{\ast }$ as similar means with only potentially different sensitivity to assess the same underlying physical tissue property, namely the iron concentration, c_Fe, with susceptibility being a mere evolution of $R_2^{\ast }$-based iron assessment. Few studies have attempted a truly simultaneous analysis of both measures that exploits their differences in sensitivity on the underlying biophysics of contrast generation as proposed in the present work. A recent study by Elkady et al. (Elkady et al., 2017) employed a sparse classification approach to disentangle the contributions of iron and myelin to $R_2^{\ast }$ and magnetic susceptibility changes in MS, showing no significant effects of myelin in the DGM. Another study from the same group (Sun et al., 2015) correlated the average $R_2^{\ast }$ values in the major DGM regions of three HCs and three MS patients with their corresponding average susceptibility values at 4.7T. Under the assumption of a linear field-strength dependence of $R_2^{\ast }$ (Peters et al., 2007; Yao et al., 2009), the original values can be converted to those at 3T (the field strength used in the present study), arriving at equivalent values for 3T between 5.8 and 8.7 s·ppb. Li et al. (Li et al., 2014) correlated average DGM values from 191 normal subjects across a wide range of ages at 3T and reported an average of 7.9 s·ppb. Using the COSMOS technique to determine susceptibility in nine young normal controls at 7T, Deistung et al. (Deistung et al., 2013) reported a 3T-equivalent value of 6.37 s·ppb. These previously estimated values are similar to our values of 6.2±0.2 s·ppb (HC) and 6.0±0.2 s·ppb (MS) when averaged over all ROIs. Compared to the minimum value of the IMC predicted by the impermeable sphere model (Eqs. 6 and 7), the observed values were about twice as high.

However, our work goes beyond these previous studies by exploiting the intra-regional multi-voxel variation of $R_2^{\ast }$ and susceptibility, allowing the comparison of the association between the two measures in different anatomical regions. Using this approach, we showed significant differences in IMC between anatomical regions (Figs. 3 and A.2). The ability to obtain the IMC in more than 96% of the regions demonstrated the practical feasibility of our approach.

5.2. IMC decreases with normal aging

The observed age-related increase in susceptibility and $R_2^{\ast }$, and the decrease of the IMC (Tab. 2) in all regions (but the thalamus) suggest that the well-established age-related increase in tissue iron concentration (Hallgren and Sourander, 1958) is due to cellular iron uptake, corresponding to an increase of N in Eq. (7). Since most of the tissue iron is found in oligodendrocytes (Bagnato et al., 2011; Francois et al., 1981; Haider et al., 2014; Hill and Switzer III, 1984; Meguro et al., 2008), our results suggest that the observed increase in iron concentration is due to an oligodendroglial iron uptake and not a mere increase in oligodendrocyte density due to atrophy affecting other tissue components (see discussion below). If our IMC estimations were biased by contributions from myelin (see above), demyelination – which occurs in normal aging – would likely result in decreased bias and, hence, increasing IMC values with age. Consequently, it may be assumed that the observed age-effect in our study is underestimating the true IMC changes with age. In theory, however, the decreased IMC may also be affected by an aging-related decrease in diffusivity (Chen et al., 2016). Since we did not acquire diffusion-weighted data in this study, a direct analysis of the impact of diffusion was infeasible and will remain to be explored in future studies.

5.3. Differences in IMC between patients and controls support the differential iron homeostasis and oligodendroglia stress hypothesis

Interpretations of changes in IMC remain speculative until an analytical model of brain $R_2^{\ast }$ is available. However, assuming that changes in IMC are driven by mechanisms related to iron-laden cells, primarily perineuronal oligodendrocytes in the DGM (Verkhratsky, 2013), the impermeable sphere model underlying Eqs. (6) and (7) may lead to qualitative insights on the cause of IMC changes. We believe that this model bears value for the interpretation of IMC changes because the distribution of iron-laden oligodendrocytes resembles the isolated, focal, scattered pattern of susceptibility perturbation underlying the impermeable sphere model. Accepting this model, Eq. (7) suggests that mechanisms increasing the IMC are increased diffusivity (D), a growth of iron-containing cells (R_C), decreased cellular iron load (N), and decreased magnetism of iron (µ_eff); and vice versa for decreasing IMC.

A consensus exists in the literature that diffusion is increased in several DGM brain regions of MS patients compared to controls (Cappellani et al., 2014; Fabiano et al., 2003; Homos et al., 2017; Schmierer et al., 2004), including the anterior (THA*) and posterior (PUL, +0.041 mm²/s) thalamus, lentiform nucleus (GP and PUT, +0.042 mm²/s), and bilateral CAU (+0.025 mm²/s); all stated values taken from (Hasan et al., 2009)). This pathological increase in diffusivity has been attributed to microstructural injury secondary to trans-synaptic and retrograde degeneration and may explain the increased IMC in patients compared to controls in the CAU (p = 0.015) and, albeit it did not reach statistical significance, also in the PUT. As discussed in the context of aging, the increased values may, theoretically, also be related to a diminishing bias from myelin due to demyelination in the patients.

However, a follow-up QSM study (Hagemeier et al., 2017) recently provided an alternative explanation for increased IMC. The authors have suggested that the increase in susceptibility of the CAU in MS patients compared to controls cannot be explained solely by an atrophy-related increase in oligodendrocyte density, which would be represented by an increased value of η. The authors concluded that pathological mechanisms must have removed iron from the region. Moreover, Hametner et al. (Hametner et al., 2013) have recently shown that iron depletion in the WM of MS patients is associated with a shift of iron from oligodendrocytes to activated microglia. This process would be associated with an increase of the IMC because activated microglia are larger than oligodendrocytes (R_c). However, histopathology needs to confirm that a similar relocation of iron also occurs in the DGM. Furthermore, controlled phantom experiments will have to demonstrate that changes in the cell populations cause measurable changes in the IMC. In the CAU, the group difference was driven by six patients (27%) that showed IMC values exceeding 6.7 s·ppb (see Fig 7). A detailed analysis of this group did not reveal any apparent differences between these patients and other patients (see Supplementary Materials A.2). Future research will investigate if these extreme IMC values in the CAU are reproducible and have, e.g., prognostic value.

All other regions showed decreased or similar IMC values in patients compared to controls, which excludes increased diffusivity or diminishing myelin-bias as the driving force for changes in the IMC. An increase in cellular iron load that occurs in addition to an atrophy-related increase in iron concentration (increase in 5) seems to be the most plausible explanation for the decreased IMC in the DEN, NR, and GP (quadrant D in Fig. 8) because of the following considerations: First, both $R_2^{\ast }$ and susceptibility were increased relative to controls in all regions but thalamus. Second, it is currently unknown what form of iron would be more magnetic and available in a concentration sufficient to affect MRI signal (Ropele and Langkammer, 2017). Although evidence exists for demyelination in the DGM of MS patients (Haider et al., 2014), we consider it as unlikely that demyelination is the driving force of pathology-related changes in susceptibility for the following reasons:

1. DGM nuclei, in particular CAU, DEN, PUL, and PUT, contain a relatively low amount of myelin (Schaltenbrand et al., 1977), with GP, NR, and some thalamic nuclei being the most highly myelinated DGM regions (Schaltenbrand et al., 1977);

2. While the CAU, which showed a significant increase in susceptibility (Fig. 4), is the region in which Haider et al. (Haider et al., 2014) have found the highest volume-percentage of demyelinated tissue, the GP, which also showed increased susceptibility, has been reported to demonstrate the lowest percentage of demyelinated tissue among all DGM nuclei (Haider et al., 2014);

3. The previously mentioned study by Elkady et al. (Elkady et al., 2017), aiming to reveal local inverse associations between $R_2^{\ast }$ and susceptibility indicative for demyelination, did not observe significant demyelination in any MS group and DGM region studied.

Nevertheless, future studies should assess both myelination and diffusion properties in conjunction with the IMC.

DEN showed the highest effect size in both susceptibility and $R_2^{\ast }$ differences between the groups. Due to its independence from iron concentration, a change in $R_2^{\ast }$ and susceptibility is not necessarily associated with a change in the IMC. Still, DEN showed the highest effect size in all measures, susceptibility, $R_2^{\ast }$ , and IMC, leading to an alternative explanation of IMC changes in patient dentates: Retention of linear gadolinium-based contrast agents (GBCA). Several recent studies have demonstrated that linear GBCA is retained in both dentate and globus pallidus (Radbruch et al., 2015), leading to locally increased T₁ (Radbruch et al., 2015; Robert et al., 2015) and magnetic susceptibility (Hinoda et al., 2017). Due to its seven unpaired electrons, the effective number of Bohr magnetons of the Gd³⁺ ion is µ_eff=15, which is substantially higher than µ_eff=3.78 of ferritin (Schenck, 1992). Furthermore, due to the inverse relationship between µ_eff and κ (Eq. 7), Gadolinium deposition would indeed decrease the IMC. The IMC may potentially aid the understanding of the level of GBCA deposition in patients in future studies by disentangling the gadolinium-related effects on tissue properties from those of tissue iron.

Although we found a significant difference between the IMC in THA and PUL, supporting previously distinct processes in the PUL compared to the rest of the thalamus (Schweser et al., 2018), the IMC was relatively unaffected by the disease in all thalamic regions, while magnetic susceptibility was decreased in MS, consistent with several previous studies (see Discussion in (Schweser et al., 2018)). Similar to the CAU, decreased thalamic magnetic susceptibility might be related to a depletion of iron from oligodendrocytes (Schweser et al., 2018). Our data did not indicate an increased IMC in the thalamus, despite the previously reported increase in diffusion in the PUL (see above), which would be expected as a consequence of oligodendroglial iron depletion in this region. However, the relatively high stability of thalamic IMCs (PUL: d=−0.018) suggests that processes decreasing the IMC compensated for the diffusion-related effects on the IMC, such as shrinkage of oligodendrocytes. Oligodendrocyte stress has been associated with a withdrawal of processes (Rone et al., 2016), significantly reducing the effective size of these cells (R_c). This shrinkage alone would not affect the voxel-average magnetic susceptibility, leaving a combination of cellular shrinkage, oligodendrocyte death and clearance of debris, including iron, as a possible explanation of the observed tissue property changes in the thalamus, in line with the hypothesis of oligodendroglial stress in the thalamus.

5.4. Limitations

The conceptual elegance of the IMC stems from the possibility of acquiring both magnetic susceptibility and $R_2^{\ast }$ with the same multi-echo GRE sequence, which renders both quantities intrinsically co-registered. However, due to the retrospective nature of the present study and technical limitations of the employed MRI system, we did not have access to the phase images of the multi-echo sequence for the calculation of susceptibility maps. Hence, we relied on two individual pulse sequences for the acquisition of susceptibility maps and $R_2^{\ast }$. The acquisition of both quantities with the same pulse sequence will allow for a calculation of the IMC in the native subject space without the laborious co-registration of the two image contrasts used in the present work. Since co-registration always induces smoothing effects due to the interpolation of voxel values, which is problematic for the multi-voxel correlation required in the calculation of the IMC, we expect that the simultaneous acquisition and the thereby enabled calculation in the native subject space will yield IMCs with substantially improved stability and accuracy in future studies. It can be expected that those studies will observe a dramatically increased effect size compared to the present pilot study.

Another limitation of our pilot study is that we could not validate the obtained IMC values with an independent technique and we did not perform dedicated phantom measurements to validate the association of the observed IMC changes with micro- and mesoscopic tissue properties. However, various previous studies have performed such experiments (Dietrich et al., 2017; Tanimoto et al., 2001; Weisskoff et al., 1994; Yung, 2003), providing substantial evidence for the dependence of $R_2^{\ast }$ on micro- and mesoscopic iron distribution and binding properties.

In the present study, between 5% and 13% of the ROIs (depending on region) had to be excluded from the analysis. While we do not expect that this exclusion introduced bias into our study (groups were tested for demographic differences after exclusion), it has reduced the statistical power of our analysis. We expect that the number of corrupted ROIs will be lower in future studies that derive the IMC from the same sequence because of a reduced overall measurement time (reduced motion artifacts), fewer registration steps, and smaller voxel volumes for the $R_2^{\ast }$ calculation (less dependence on macroscopic field gradients).

The interpretation of negative IMC values, which were observed and excluded primarily in thalamic regions, remains unclear. Negative IMC values imply a breakdown of the underlying assumptions if Eq. (8) with systematic variations in non-iron contributions representing the most likely cause. In particular, with an iron concentration similar to white matter, the thalamus has the lowest region-average iron concentration of all DGM regions (Hallgren and Sourander, 1958) and some recent studies have suggested that iron concentration is even reduced further in patients with MS (Hagemeier et al., 2017; Schweser et al., 2018; Zivadinov et al., 2018). In addition, thalamic nuclei show different degrees of myelination, with the lateral nuclear region being most densely myelinated and the PUL showing only very little myelin (Schaltenbrand et al., 1977). While these observations may explain the observed negative IMC estimates in thalamic regions, we do not expect that variations in myelin or calcium content will have a significant effect on the estimated IMC values in regions in which iron content is higher and not necessarily correlated with the concentration of myelin. Moreover, the myelin content is relatively low in all other DGM regions except the GP (Schaltenbrand et al., 1977). With regards to the comparison of patients and controls, one would expect that homogeneous demyelination within the ROI reduces the underestimation of the true IMC value using Eq. (8), resulting in a bias toward higher IMC values in patients compared to controls. The only regions in which MS patients showed higher IMC values than controls in the present study were CAU and PUT. Although consistent with Haider’s (Haider et al., 2014) finding of the highest volume-percentage of demyelinated tissue in the CAU, the region is only weakly myelinated (Schaltenbrand et al., 1977) and shows more than twice the iron concentration of the thalamus (Hallgren and Sourander, 1958). This finding renders it unlikely that a reduced underestimation bias due to demyelination can explain a group-average IMC increase by more than 10% in patients (Tab. 1). Furthermore, a potential homogeneous aging-related demyelination cannot explain the decreasing IMC observed in NC with increasing age.

The effect of focal demyelination (lesions) within an ROI on the estimated IMC value depends on the tissue iron content at the location of the demyelinating lesion. If visualized by MRI, lesions should be excluded: On the one hand, focal demyelination in a sub-region with a relatively high iron content will further increase χ, but decrease $R_2^{\ast }$. As a result, the IMC would be over-estimated, depending on the size of the lesion and the degree of demyelination. On the other hand, if a low-iron region is demyelinated, the increased χ and decreased $R_2^{\ast }$ will result in an underestimation of the IMC. In general, lesions will likely increase the variation of IMC values in the patient group, reducing statistical power. In the present study, we observed similar variances in IMC values in both groups (Tab. 1), except for the CAU, where the group of systematic outliers caused the higher variance (see above). Hence, it is unlikely that focal lesions substantially affect the IMC values in our study.

While these foundations illustrate the general difficulty of interpreting quantitative in vivo MRI findings, we would like to emphasize that the discussed potential bias due to demyelination does not affect only the present study but all studies using susceptibility-related imaging metrics such as $R_2^{\ast }$ and QSM. In particular, one should consider that it is currently established practice to interpret changes in the regional average values of susceptibility or $R_2^{\ast }$ in the DGM as changes in regional iron concentration. The proposed IMC technique, although limited by underlying assumptions introduces a new dimension into the analysis of susceptibility MRI measurements that exploits the intra-regional multi-voxel correlation between the measures to disentangle the underlying relationship between them. Future studies should compare IMC measurements with specific measures of diffusivity and myelination to provide better insights into the usefulness of this new measure to reveal additional information on disease mechanisms.

6. Conclusion

This pilot study introduced a new methodology for the simultaneous analysis of magnetic susceptibility and effective transverse relaxation rate in the deep gray matter. The new measure, referred to as Iron Microstructure Coefficient (IMC), reflects distribution properties of iron on the (sub-)cellular scale. Despite limitations regarding the quantitative interpretation of IMC values, our study illustrated that $R_2^{\ast }$ values and bulk magnetic susceptibility carry partially complementary information and should not be understood as equivalent metrics of tissue iron concentration. The IMC partially disentangles the additional microstructural and chemical effects on $R_2^{\ast }$ that manifest in changes with age, vary between anatomical regions, and between healthy controls and patients with MS.

Highlights.

• Voxel-wise analysis of $R_2^{\ast }$ and susceptibility reveals their differential dependency on brain iron

• The Iron Microstructure Coefficient (IMC) varies with brain regions and decreases with age

• Multiple Sclerosis is associated with increased IMC in dentate and decreased IMC in caudate.