Introduction

Iron homeostasis is a decisively important factor in maintaining the physiological functioning of the brain [1]. Using magnetic resonance imaging (MRI), iron can be visualized and measured by quantitative susceptibility mapping (QSM) techniques, which quantify magnetic susceptibility sources. Brain iron mapping with QSM has increasingly been in the focus of clinical attention in recent years, as increased iron levels have been described in patients with Parkinson’s disease (PD) [2], in the motor cortex of patients suffering from amyotrophic lateral sclerosis [3], as well as in the basal ganglia of patients with Huntington’s chorea [4].

A potential dysregulation of iron metabolism with subsequent alterations of the iron concentration has been implied as a potential factor or cofactor in neurodegenerative diseases such as dementia of the Alzheimer’s type (AD) and PD as well as in neuroinflammatory disorders such as multiple sclerosis [5–7]. For example, in the pathogenesis of PD, a strong line of evidence indicates a pivotal role of iron ions [8]. This is based on data from in vitro studies [9, 10], animal experiments [11], and human epidemiological and in vivo research [12, 13]. However, an increase in iron concentration in some regions of the brain is also viewed as a feature of normal aging [14, 15]. Interestingly, postmortem analysis of human brain tissue shows not only an increase in iron content in the affected brain areas but also a shift of the ratio of ferrous (Fe2+) to ferric iron ions (Fe3+) towards an increased content in ferric iron ions [16]. Whether iron is present in its ferric or ferrous form may have important implications for its biological effect and it would be desirable to noninvasively differentiate these forms in the brain in the in vivo situation.

The presence of iron in a sample or in tissue can be detected with MRI by relaxation-based methods [17–20] or by susceptibility-sensitive techniques [17, 19, 21–24]. Both approaches have been used for quantitative estimations of tissue iron concentrations. A wide range of slopes describing the linear dependence of relaxation rates and iron concentrations in brain tissue have been published (see Table 5 in ref. [17] for a review). However, these dependencies for iron-induced relaxation changes were determined in most cases without considering differences between the relaxivities of the ferric and ferrous form of stored iron [25–27].

The purpose of the present study is therefore to evaluate the MR imaging behavior of ferrous and ferric iron ions in order to develop a noninvasive technique to quantitatively differentiate between both forms of iron.

Methods

A phantom was built consisting of 21 cylindrical tubes (diameter 10 mm, length 40 mm) with different concentrations (0.0, 0.1, 0.3, 1.0, 3.0, and 10 mmol/L) of ferrous (FeCl2) and ferric (FeCl3) chloride solutions (Merck, Darmstadt, Germany); the solvent was purified water (H2O Millipore). Furthermore, four concentrations (0.0, 0.1, 1.0, 10.0 mmol/L) of ferric chloride were prepared with additional hydrochloric acid (HCl, pH = 2; Roth, Karlsruhe, Germany) since HCl suppresses the formation of Fe(OH)3, which is poorly soluble in water and would therefore precipitate. Four concentrations (0.0, 0.1, 1.0, 10.0 mmol/L) of ferrous chloride were prepared with sodium ascorbate (NaAsc, 10 mmol/L, Roth, Karlsruhe, Germany) since ascorbate suppresses the oxidation of unstable Fe2+ ions to Fe3+. Finally, one sample contained deferoxamine (10 mmol/L, Sigma-Aldrich, Munich, Germany) and one sample 1.0 mmol/L ferric chloride with deferoxamine, which chelates iron. All 21 tubes were positioned in an approximately rectangular box of size 200 × 100 × 55 mm3 molded with a polyvinyl alcohol cryogel (PVAc) [28, 29] (compare Fig. 1a). PVAc was transferred into its solid state via one freeze–thaw cycle and then stored at 4 °C. Before the measurements, the phantom was kept at room temperature (20 °C) for at least 4 h such that all 40-mL samples could reach room temperature.

Fig. 1
figure 1

Phantom with 21 samples and post-processing steps of quantification of magnetic susceptibility. a Magnitude data of a central slice (slice number 23 of 40) of the phantom. b Phase data of the same slice. c Internal magnetic field perturbations determined with the SHARP algorithm. d Dipole fit to the field map. e Map visualization of calculated magnetic susceptibility distribution

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The phantom was examined on a 3-T whole-body MRI system (Magnetom Verio, Siemens Healthcare, Erlangen, Germany) equipped with a 12-channel head coil. A multi-echo spoiled gradient-echo pulse sequence with eight echoes was used for both T 2* and quantitative susceptibility measurements. The echo times were TE = 10, 20, 30, 40, 50, 60, 70, and 80 ms (with monopolar/“flyback” readout) at a repetition time of TR = 95 ms; the flip angle was 20°. Magnitude and phase data (Fig. 1a, b) were acquired in coronal orientation with a matrix size of 320 × 260 × 40 voxels and a voxel size of 0.72 × 0.72 × 1.40 mm3; the receiver bandwidth was 130 Hz/pixel.

For evaluation, each sample tube was manually segmented in all slices, resulting in 21 volumes of interests (VOI). Quantitative evaluation was restricted to six central slices (slice numbers 20 to 25 from 40), which showed the lowest levels of artifacts due to field inhomogeneity.

The transverse relaxation rate, R 2* = 1/T 2*, was determined by nonlinear exponential fitting (\( S\ \left(\mathrm{TE}\right)={S}_0 \exp \operatorname{}\left(-{R}_2^{\ast}\cdot \mathrm{TE}\right) \)) based on the mean signals, S(TE), of all eight echoes in each slice and each sample; then, the mean value and the standard deviation of R 2* over the six evaluated slices were calculated (thus, allowing an estimation of the variability of the calculated values).

The susceptibilities, χ, of the samples were calculated separately for the acquisitions with TE = 10, 20, and 30 ms, since phase data at longer TEs showed high levels of artifacts. First, the acquired phase data were unwrapped using the “best path” 3D phase unwrapping algorithm [30]. The “Sophisticated Harmonic Artifact Reduction for Phase data” (SHARP) algorithm [31, 32] was applied to the unwrapped phase data for background field removal (with a kernel radius of 6 mm and a regularization parameter of 0.05), resulting in (internal) field maps ϕ(r; TE) for each of the three echo times based on the sample susceptibilities only (Fig. 1c). Then, the magnetic unit dipole response with a kernel size of 103 × 103 × 53 pixels was numerically convolved with the shape of each individual sample tube (i.e., each segmented VOI), resulting in 21 spatial field distributions f n (r), n = 1, …, 21. Finally, 21 susceptibility coefficients χ n were determined for each evaluated slice Slc(k) using nonlinear least-squares optimization to fit the superposition of the 21 field distributions to the measured internal field map:

$$ {\left\{{\chi}_n\right\}}_{n=1\dots 21}= \arg \underset{\left\{{\chi}_n\right\}}{ \min}\sum_{\boldsymbol{r}\in \mathrm{Slc}(k)}{\left(\phi \left(\boldsymbol{r};\mathrm{TE}\right)-{\sum}_{n=1}^{21}{\chi}_n{f}_n\left(\boldsymbol{r}\right)\right)}^{2.} $$

(i.e., the difference between measurement ϕ(r; TE) and model was minimized simultaneously for all pixels r ∈ Slc(k) in slice number k.) This procedure, which was similar to an approach proposed by de Rochefort et al. [33], resulted in 18 sets (6 slices × 3 echo times) of 21 susceptibility values (Fig. 1d, e); each susceptibility was averaged over all slices and echo times (with calculation of the standard deviation).

To analyze the different behaviors of ferrous and ferric chloride solutions, we determined the relaxation rate changes ΔR 2*(c Fe) = R 2*(c Fe) − R 2*(c Fe = 0) and the susceptibility changes Δχ(c Fe) = χ(c Fe) − χ(c Fe = 0) for all concentrations, since (ferric or ferrous) ions are expected to influence ΔR 2*(c Fe) and Δχ(c Fe) directly proportional to the iron concentration, c Fe. From these difference values, the linear slopes of ΔR 2*(c Fe) and Δχ(c Fe) as functions of the iron concentration were calculated using linear regression analysis; these slopes quantitatively describe the strength of the influence of (ferrous or ferric) ions on relaxation and susceptibility (the slope of ΔR 2*(c Fe) is simply the relaxivity of ferrous or ferric chloride). Finally, the “relaxation-to-susceptibility” ratio ΔR 2*(c Fe) / Δχ(c Fe) was calculated for all samples, since this quantity was hypothesized to differentiate between ferrous and ferric chloride solutions.

For statistical evaluation, the slopes of ΔR 2*(c Fe) of samples with ferrous and with ferric chloride solutions were compared using the z test [34]; the same comparison was performed for the slopes of Δχ(c Fe). We used Fisher’s exact test (two-tailed) to evaluate the performance of the relaxation-to-susceptibility ratio ΔR 2*(c Fe) / Δχ(c Fe) for the differentiation of Fe2+ and Fe3+. P values lower than 0.05 were considered to indicate statistically significant differences. All mathematical evaluations were performed with GNU Octave 3.8.2 (<https://gnu.org/software/octave>) and all statistical evaluations were performed with R version 3.1.1 (The R Foundation for Statistical Computing, Vienna, Austria; <http://www.R-project.org>).

Results

The results of all quantitative measurements are listed in Table 1. Overall, we found increasing relaxation rates, R 2*, and susceptibilities, χ, with increasing concentrations of iron. At the highest concentration (10 mmol/L), the relaxation rates increased by about 120–130 s−1 for ferric ions and by about 7–10 s−1 for ferrous ions (relative to the values at an iron concentration of 0). The susceptibility of both ferric and ferrous ions increased by about 0.6–1.0 ppm at the highest iron concentrations.

Table 1 Mean values (standard deviations) of relaxation rates (R 2*) and susceptibilities (χ)
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Ferric ions with added HCl behaved very similarly to pure ferric chloride solutions; in contrast, deferoxamine reduced the relaxation rate change at 1 mmol/L ferric ions. Ferrous ions with added sodium ascorbate showed a slightly higher increase of both ΔR 2* and Δχ at the highest iron concentrations.

To estimate the dependence of the relaxation rate and the susceptibility on the iron concentration quantitatively, we combined the results for Fe3+ with and without HCl, and we also combined the results for Fe2+ with and without sodium ascorbate; the data combination was performed to reduce the statistical fluctuations of the measured data. With these data, we calculated a linear slope of the relaxation rate of (12.5 ± 0.4) s−1/(mmol/L) for Fe3+ and a slope of (0.77 ± 0.09) s−1/(mmol/L) for Fe2+. These two slopes were significantly different (Z = 26.8, P < 0.0001). The linear slopes of the susceptibility were (0.088 ± 0.003) ppm/(mmol/L) for Fe3+ and (0.079 ± 0.006) ppm/(mmol/L) for Fe2+. These slopes were not significantly different (Z = 1.46, P = 0.14). The combined values of ΔR 2* and Δχ as well as the calculated slopes are shown in Figs. 2 and 3.

Fig. 2
figure 2

Dependence of relaxation rate change ΔR 2* on the iron concentration shown for Fe3+ (blue solid line) and Fe2+ (red dashed line). Plotted data are shown as mean values with standard deviations from evaluations in six slices (and sample combination as described in the “Results” section)

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Fig. 3
figure 3

Dependence of susceptibility change Δχ on the iron concentration shown for Fe3+ (blue solid line) and Fe2+ (red dashed line). Plotted data are shown as mean values with standard deviations from evaluations at three different TEs in six slices (and sample combination as described in the “Results” section)

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The ratio ΔR 2*/Δχ was greater than 40 s−1/ppm for all five concentrations of ferric solution and lower than 20 s−1/ppm for all but one (i.e., for 4) of the concentrations of ferrous solution (the single exception was the concentration of 0.3 mmol/L ferrous chloride, which is displayed as visual outlier in Fig. 4). Using a threshold of 30 s−1/ppm, the sensitivity and specificity of the relaxation-to-susceptibility ratio for the detection of Fe2+ were 80% and 100%, respectively, resulting in an accuracy of 90% (Fisher’s exact test demonstrated statistical significance with P = 0.0476).

Fig. 4
figure 4

Relaxation-to-susceptibility ratio ΔR 2*/Δχ of relaxation rate and susceptibility changes. The suggested threshold (green dashed line) for differentiation between ferric and ferrous chloride is 30 s−1/ppm. The single data point with deviating behavior (open circle, 0.3 mmol/L ferrous chloride) is discussed in the main text; this data point has been included in all evaluations and also in the plots in Figs. 2 and 3

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Discussion

Our results illustrate a significant difference between the T 2* relaxivity of ferrous and ferric chloride solution. This difference has previously been analyzed for T 1 and T 2 relaxation times in the context of NMR applications [25] of Fricke gels for radiation dosimetry [27]. The difference is caused by different correlation times of the dipolar interactions between iron ions and water protons; in particular, substantial differences of the electron spin relaxation times are described to be the reason for a much more efficient relaxation process of water protons in the neighborhood of Fe3+ than of Fe2+ [25, 26]. On the other hand, both forms of iron similarly influence the magnetic susceptibility of the sample, which basically reflects the additional magnetic field of the paramagnetic iron ions (an effect that is widely independent of molecular dynamics and correlation times); the magnetic moments of ferrous and ferric ions are 4 μB (μB, Bohr magneton) and 5 μB, respectively [35], and hence of comparable magnitude. These different mechanisms responsible for relaxation changes on the one hand and susceptibility changes on the other hand can be exploited by determining the relaxation-to-susceptibility ratio ΔR 2*/Δχ, which provides a good (and statistically significant) differentiation between both forms of iron ions. Thus, the change of iron concentration (independent of the oxidation state) can be determined quantitatively based on magnetic susceptibility differences and, simultaneously, ferric and ferrous iron ions can be differentiated based on MR relaxometry.

The iron distribution in the brain is on the verge to become an additional technique in the MRI-based diagnosis of neurodegenerative diseases such as PD and AD [36, 37]. Analogous to postmortem analysis of human brain tissue that shows a shift of the ratio of ferric to ferrous iron ions towards ferric iron ions [16], we showed in the present study that it is in principle possible not only to obtain MRI-based measurements of iron content in fluids but also to differentiate quantitatively between ferric and ferrous iron ions. We consider this work a first step in the assessment of shifts in ferric and ferrous iron ion ratios by MRI in vivo.

A consequence of our results is that MRI measurements of tissue iron concentrations based on relaxation effects (i.e., on the measurement of T 2* or R 2*) may require a particularly careful interpretation: When iron concentrations are quantified based on R 2* values, the oxidation state of iron may also influence the relaxation rates in vivo and thus influence the reliability of the quantification.

To control systematic errors of our measurements, we prepared samples with HCl or sodium ascorbate added to the ferric and ferrous chloride, respectively. Similar results for all our FeCl3 measurements with and without HCl demonstrate that during the experiment no relevant amount of Fe3+ ions was extracted from the solution by the formation of Fe(OH)3. Comparing Fe2+ samples with and without sodium ascorbate demonstrates that no relevant oxidation occurred during the experiments—if relevant oxidation had occurred, relaxation rates would have been expected to be substantially lower in the presence than in the absence of ascorbate. In contrast, the addition of deferoxamine to FeCl3 solution resulted in a lower relaxation rate, since the interaction of water molecules and ferric ions can be expected to be reduced due to the chelation of the ions.

These observations justified the combination of the Fe3+ results with and without HCl as well as of the Fe2+ results with and without sodium ascorbate for quantitative analysis. This analysis resulted in a relaxivity (i.e., slope of the relaxation rate), which was about an order of magnitude (i.e., a factor of 16) higher (and significantly different) for Fe3+ than for Fe2+ ions. In contrast, the slopes of the susceptibility were similar for both forms of iron and only about 10% lower for Fe2+ than for Fe3+ (which is compatible with the small difference of the magnetic moments of both ions).

A limitation of our study is the occurrence of systematic errors in the individual results. These errors are caused predominantly by magnetic field inhomogeneities (visualized by the phase distribution in Fig. 1b and by the R 2* variability in Fig. 5), which influence the accurate determination of both R 2* and of the susceptibility, χ. In addition, the influence of low concentrations of iron (i.e., 0.1 or 0.3 mmol/L) on R 2* and χ is small and therefore difficult to quantify. For instance, R 2* relaxation rates between about 0.5 and 4 s−1 (corresponding to relaxation times between 250 and 2000 ms) are difficult to measure with feasible echo times between 10 and 80 ms. A consequence of these effects is large relative errors of the data points at low iron concentrations (c Fe ≤ 0.3 mmol/L). In particular, the visual outlier in Fig. 4 can be explained by an incorrect systematic deviation towards too low values of the measured susceptibility of Fe2+ at a concentration of 0.3 mmol/L.

Fig. 5
figure 5

R 2* maps of the phantom a in coronal orientation (as acquired), b reformatted in axial orientation, and c reformatted in sagittal orientation. The white arrows indicate the B 0 magnetic field orientation. The position of the six central evaluated slices is shown as white box in b and c. These maps are meant as illustration of the R 2* distribution in the phantom; the actual evaluation of R 2* was not based on this map but was performed using the averaged signal intensities S(TE) in circular regions (in the six central slices) within each sample

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Conclusions

Ferrous and ferric chloride show significantly different relaxation behaviors in MRI but similar influences on the susceptibility. These properties can be used to differentiate ferrous and ferric samples in our phantom based on the relaxation-to-susceptibility ratio. Future work is required to investigate if this approach is also feasible for measurements of (changes of) Fe2+ and Fe3+ concentrations and of the ratio of Fe2+ to Fe3+ in biological tissue in vivo.