Non-invasive assessment of normal and impaired iron homeostasis in the brain

Strict iron regulation is essential for normal brain function. The iron homeostasis, determined by the milieu of available iron compounds, is impaired in aging, neurodegenerative diseases and cancer. However, non-invasive assessment of different molecular iron environments implicating brain tissue’s iron homeostasis remains a challenge. We present a magnetic resonance imaging (MRI) technology sensitive to the iron homeostasis of the living brain (the r1-r2* relaxivity). In vitro, our MRI approach reveals the distinct paramagnetic properties of ferritin, transferrin and ferrous iron ions. In the in vivo human brain, we validate our approach against ex vivo iron compounds quantification and gene expression. Our approach varies with the iron mobilization capacity across brain regions and in aging. It reveals brain tumors’ iron homeostasis, and enhances the distinction between tumor tissue and non-pathological tissue without contrast agents. Therefore, our approach may allow for non-invasive research and diagnosis of iron homeostasis in living human brains.

The theoretical basis for the r1-r2* relaxivity of brain tissue Brain tissue contains a complex milieu of iron compounds with variable iron binding capacities and aggregation states and includes myelin. Here we will expand the biophysical model of the r1-r2 * relaxivity ("In vivo iron relaxivity model" in Methods) for the case of a heterogenous iron environment and in the presence of myelin.
The r1-r2 * relaxivity measurement is defined as the linear dependency of R1 on R2 * (within an ROI in the brain, across in vitro samples or across each voxel's local neighborhood). This is equivalent to the total change in R1 values relative to the total change in R2 * values ( Δ 1 Δ 2 * ): S3) 1 2 * = ∑ (1, ) [ ]+ (1, ) [ ] ∑ (2, ) [ ]+ (2, )  The ambiguity in R1; R1 changes as a function of both iron environment and iron concentration. This is shown by calculating the median R1 value over biologically independent samples with high and low ironbinding protein concentrations (marked in (a); concentration ranges were chosen so that the number of data points in each range is relatively similar; N(low ferritin)=12), N(high ferritin)=11, N(high transferrin)=9). We find that R1 is greater for a higher ferritin concentration than for a lower ferritin concentration, but also find that R1 is greater for ferritin than for transferrin. For each box, the central line marks the median, the box extends vertically between the 25th and 75th percentiles, and the whiskers extend to the most extreme data points.

Supplementary Section 2 (Supplementary Figures 2,3)
The dependency of R1 and R2* on the iron concentration.
In Figure 2 we computed the iron relaxivity as the dependency of R1 and R2 * on the concentration of ironbinding proteins. We showed that different iron environments have different relaxivities. However, different proteins bind different amounts of iron. For example, ferritin binds three orders of magnitude more iron ions than does transferrin 3 . Therefore, we wanted to exclude the possibility that the different iron ion concentrations drive the different relaxivities of ferritin and transferrin.
We verified that the relaxivity changes according to the molecular type of iron, even when accounting for discrepancies in iron loading. We estimated the iron ion concentrations for ferritin and transferrin (see Methods section "Estimation of total iron content in phantoms") and tested whether those values can explain their different iron relaxivities. Importantly, after computing the iron relaxivity as the dependency of relaxation rates on the iron ion concentrations (rather than the concentration of iron-binding proteins), we still find that different iron environments have distinct relaxivities (Sup. Figure 2, p(one-sided ANCOVA)<10 -39 ).
To further stress the sensitivity of the r1-r2 * relaxivity to the iron environment, we compared the relaxivity of liposomal ferrous iron (Fe 2+ ) and iron bound to liposomal transferrin (Sup. Figure 3). Unlike ferritin and transferrin, these two iron compounds have relatively similar iron ion concentrations. Yet we find that they produce different iron relaxivities (p(one-sided ANCOVA)=1.3*10 -13 & 1.4*10 -5 for R1 and R2* respectively). The r1-r2 * relaxivities of these two iron environments are different as well (p(one-sided ANCOVA)=0.027). Therefore, the iron relaxivity and the r1-r2 * relaxivity are changing as a function of the molecular iron environment, even when accounting for the differences in iron binding.

R2-based relaxivity
Similarly to R2 * , R2 is also sensitive to the effects of iron on the transverse relaxation 3,4 . Theoretically, the dependency of R1 on R2 could also be used as an in vivo estimation of the iron relaxivity. To test this, R2 measurements of different iron environments were assessed. This analysis (Sup. Figure 4) shows that different iron environments have distinct R2-iron relaxivity (p(one-sided ANCOVA)=2.6*10 -73 ). Comparing the R2-iron relaxivity (Sup. Figure 4) and the R2 * -iron relaxivity (Figure 2c) we find similar contrast between iron environments (e.g. highest relaxivity for ferrous iron and lowest relaxivity for transferrin). This contrast is different from the R1-iron relaxivity. For example, while the R1-iron relaxivity of ferritin is similar for free and liposomal states (Figure 2c), both the R2-iron relaxivity and the R2 * -iron relaxivity are different for liposomal and free ferritin (Sup. Figure 4a-b, Figure 2c). Therefore, these results suggest that R2 could be used instead of R2 * when calculating the relaxivity. To test this, we estimated the r1-r2 relaxivity for different iron environments (Sup. Figure 4c-d). We found that different iron environments have distinct r1-r2 relaxivity (p(one-sided ANCOVA)=1.2*10 -40 ). Moreover, we found great agreement between the experimental results and the theoretical predictions for the r1-r2 relaxivity based on the ratio of iron relaxivities (eq. 2, Sup. Figure 4d). Interestingly, while the theoretical prediction for the r1-r2 * relaxivity of ferrous iron and liposomal transferrin was a bit higher than the experimental results ( Figure   2e), the theoretical prediction of these experimental results is more accurate for the r1-r2 relaxivity.
Therefore, we believe that estimating the r1-r2 relaxivity may also be a useful marker of the iron homeostasis. Technically, acquiring R1 and R2 * with standard MRI protocols can be shorter than acquiring R1 and R2. Both R1 and R2 * can be estimated from the same widely available sequence (spoiled gradient echo with multiple echoes). However, if measurements of both R1 and R2 are available, we believe that an estimation of the r1-r2 relaxivity also could contribute to the in vivo characterization of the iron homeostasis. By joining several iron relaxivity measurements, it might be possible to further disentangle the contributions of different iron environments to the MRI signal.
Sup. Figure 4 Supplementary Figure 5 Sup. Figure 5 ). Therefore, the r1-r2 * relaxivity is sensitive to the paramagnetic properties of iron-binding proteins and not to the proteins themselves.
We tested the theoretical formulation presented in eq. S1-S3 (Sup. Section 1) in an artificial environment of multiple iron compounds. For this aim, we constructed phantom experiments containing both ferritin and transferrin in a liposomal environment. In this synthetic toy model, the transferrin-ferritin fraction represents an example for a feature of the molecular iron environment which should affect the r1-r2 * relaxivity. To test this assumption, the biophysical model shown in Sup. Section 1 can be further developed under the conditions of these phantom experiments: When ferritin, transferrin and myelin are present, eq. S1-S2 can be expressed as: (1, ) [ ] + (1, ) [ ]
Assuming the transferrin-ferritin fraction ( ) remains fixed across the in vitro samples over which the r1-r2 * relaxivity is calculated: In the ferritin-transferrin mixtures experiments, the liposomal fraction, which mimics the effect of myelin, was fixed at 17.5%. Therefore, in this case [Δ ] = 0 and eq. S8 reduces to: S9) Using the ferritin and transferrin relaxivities ( (1/2, / ) ) measured for each liposomal iron compound individually ( Figure 2a-c), we could test the prediction of this model. Notably, the theoretical r1-r2 * relaxivities calculated with eq. S9 were in agreement with the experimental r1-r2 * relaxivities (Sup. Figure   8), validating the presented biophysical framework in vitro. Moreover, the differences in the r1-r2 * relaxivities measured for different transferrin-ferritin fractions were above the detection limit of this MRI measurement as estimated in a scan-rescan experiment (MAE=3.9*10 -4 , Sup. Figure 9). Therefore, this toy example demonstrates that the heterogeneity in the iron environment can produce measurable changes in the r1-r2 * relaxivity, which are in agreement with the biophysical modeling of this measurement.
Sup. Figure    The effect of hemoglobin of the r1-r2* relaxivity.
We evaluated the effect of non-heme iron (ferritin, transferrin and ferrous iron) on the iron relaxivity.
However, brain tissue also includes high concentration of hemoglobin in the blood 3 . In order to assess the effect of hemoglobin on the r1-r2 * relaxivity, we performed additional in vitro experiments containing hemoglobin. First, we assessed the r1-r2 * relaxivity of hemoglobin. Next, we examined whether the r1-r2 * relaxivities of ferritin and transferrin change in the presence of hemoglobin (two different hemoglobin concentrations were tested). The hemoglobin concentrations in this experiment were constrained by its solubility (20mg/mL for hemoglobin alone, and lower when it is in a mixture with other iron-binding proteins). Sup. Figure 10a-b shows the dependency of R1 and R2 * on the iron compound concentration.  5 . We divided the R1 and R2 * relaxivity of deoxyhemoglobin to get an estimation for the r1-r2 * relaxivity (eq. 2). The prediction from the literature is presented in a red data point in Sup. Figure 10e. We find great agreement between our estimation of the hemoglobin r1-r2 * relaxivity, and the literature reported values. Next, we tested whether the r1-r2 * relaxivities of ferritin and transferrin are affected by the presence of hemoglobin (Sup. Figure 10e). We found that even in hemoglobin mixtures, ferritin and transferrin have distinct relaxivities (p<0.005 when comparing all ferritin-containing samples to all transferrin-containing samples, bonferroni-corrected ANCOVA test).

Sup. Figure 10: the effect of hemoglobin on the r1-r2* relaxivity. (a-b)
Adding hemoglobin to ferritin and transferrin did not have significant effect on the r1-r2 * relaxivity (p>0.05 bonferroni-corrected ANCOVA test). Notably, we scanned the hemoglobin samples twice, immediately after the preparation and a week later. While the rest of our in vitro experiments were stable and reproducible for different scan times, hemoglobin samples scanned a week after the preparation showed aggregation, visible both by eye and in the MRI scans. This aggregation was less visible in the first scan, immediately after the preparation. Therefore, we used results from the first scan for the analysis.
However, aggregation processes may still impact these results.
Importantly, these in vitro experiments may not capture fully the effect of hemoglobin on the r1-r2 * relaxivity in the in vivo brain. Particularly, the hemoglobin concentration in the blood is very high. We can simulate to what extent hemoglobin can affect the in vivo r1-r2 * relaxivity. In normal gray-matter and white-matter, approximately 4-6% and 1-3% of the tissue volume is occupied by blood 6 . Assuming an extreme scenario where all blood volume is occupied by deoxyhemoglobin, and that the r1-r2 * relaxivity of deoxyhemoglobin in blood is as reported in the literature 5 , the r1-r2 * relaxivity effect in a voxel with 6% blood volume would be: This is less than 1% percent of the average r1-r2 * relaxivity measured in the in vivo brain. Therefore, based on this simulation, hemoglobin is not expected to be the main source governing the r1-r2 * relaxivity contrast in the brain. Nonetheless, it could be that some of the r1-r2 * relaxivity effects that we measured in the brain are related to hemoglobin. We therefore believe that the r1-r2 * relaxivity in the brain is probably not sensitive exclusively to ferritin and transferrin. Hemoglobin and many other aspects of the iron homeostasis could be reflected in the r1-r2 * relaxivity measurement.

Supplementary Section 6 (Supplementary Figures 11-13)
The dependency of the iron relaxivity on the liposomal fraction.
R1 and R2 * measured in the brain are known to be sensitive to myelin content 4,7-12 . Myelin is composed mainly of lipids, though it also includes proteins. We tested the effect of the myelin fraction on iron relaxivity by varying the liposomal and protein (BSA) fractions in our phantoms.
In histological studies of brain iron, the iron concentrations often are reported relative to the wet weight, as this is considered more accurate 4 . To match our in vitro analysis to brain histology as much as possible, we calculated the iron-binding proteins' concentrations relative to the water fraction ([mg/wet ml]). This was done by computing the ratio between the iron concentration and the water fraction (which is complementary to the liposomal or protein fractions). The iron relaxivities shown in Figure 2 were therefore calculated as the linear dependencies of relaxation rates on the iron-binding protein concentration relative to the water fraction. Sup. Figure   fractions along the iron relaxivity's linear fits. Therefore, while the non-water fraction has an effect on the relaxation rates, it does not disrupt the sensitivity of the iron relaxivities to the molecular type of iron.
We further estimated the effect of the liposomal (or BSA) fractions on the r1-r2 * relaxivity. In Sup. Figure   11e we show the same r1-r2 * relaxivities presented in Figure 2, but now the liposomal (or BSA) fractions are indicated by different symbols. Similarly to the iron relaxivities, the r1-r2 * relaxivities of different iron environments were distinct, even though they were calculated across varying liposomal (or BSA) fractions. Moreover, we estimated the r1-r2 * relaxivity separately for each liposomal (or BSA) fraction (Sup. Figure 11f). We find that the r1-r2 * relaxivity differences between iron compounds are greater than the differences within each iron compound for the variable liposomal (or BSA) fractions.
The dependency of R1 on the macromolecular tissue volume (MTV) was associated with lipid composition in our previous work 13 . We tested this finding in the presence of iron by calculating the R1-MTV dependencies for different types of lipids mixed with iron (Sup. Figure 12a-b). Notably, in the current study we sampled only three liposomal fractions, and therefore the variation in the iron concentration between the samples was much richer than the variation in lipid concentration. Still, we were able to replicate our finding regarding the sensitivity of the R1-MTV dependency to lipid type. We find that the R1-MTV dependencies are different for two types of lipid mixtures (phosphatidylcholine (PC) and phosphatidylcholine-sphingomyelin (PC-SM)) mixed with ferrous (Fe 2+ ) iron (Sup. Figure 12a). In the presence of ferritin, the difference between the R1-MTV dependencies of the two lipids is smaller (Sup. Figure 12b).
Unlike the R1-MTV dependency, the r1-r2 * relaxivity is insensitive to the lipid composition (Sup. Figure   12c): different lipids mixed with ferritin have a similar r1-r2 * relaxivity (p(one-sided ANCOVA)=0.11). The variability in the r1-r2 * relaxivity was much bigger when comparing these different liposomal ferritin samples to liposomal transferrin (p(one-sided ANOCVA)<10 -7 ). Compared to the R1-MTV dependencies, we find that the r1-r2 * relaxivity provides a better distinction between iron compounds. Sup. Figure 13 presents the r1-r2 * relaxivities and the R1-MTV dependencies for different iron compounds. One-sided ANCOVA tests for the R1-MTV dependencies reveal that the only significant distinction is between the BSA-ferritin mixture and all the liposomal iron compounds (p(ANCOVA)<10 -5 ). The rest of the iron environments are indistinguishable in terms of their R1-MTV dependencies. On the contrary, all iron environments were distinguishable in terms of their r1-r2 * relaxivity (p(ANCOA)<10 -32 ).

Supplementary Section 7 (Supplementary
The intercept of the R1-R2 * linear fit represents the residual R1 not explained by R2 * . Therefore, this measurement has the potential to be sensitive to biological sources affecting exclusively R1 and not R2 * .
Based on the relaxivity model ("In vivo iron relaxivity model" in methods), the expression for intercept can be deduced: S10) 1 = (1, ) [ ] + (1, ) S11) 2 * = (2, ) [ ] + (2, ) Substituting Eq. S10 in Eq. S11: ). We first tested the biophysical interpretation of the intercept in vitro. Sup. Figure   15 shows the intercept of different iron forms. Interestingly, the intercept seems to be less sensitive to the molecular environment of the iron forms compared to the r1-r2 * relaxivity. For example, the r1-r2 * relaxivity varied greatly between free and liposomal ferritin (Figure 2e, p<10 Sup. Figure  For each box, the central mark is the intercept, and the box shows the 95% confidence bounds of the linear fit.
Next, we tested the intercept of the R1-R2 * linear fit in vivo. Sup. Figure 16 shows the R1-R2 * linear fit for four brain regions of a single subject. Sup. Figure 16b shows the variability of the intercept across young subjects for different brain regions. Interestingly, while white-matter regions tend to have high R1, R2 * and r1-r2 * relaxivity values, they have low intercept. Therefore, in the white-matter, most of the variability in R1 is explained by R2 * , implying for shared biological sources that govern both relaxation mechanisms in this tissue. On the contrary, gray-matter and subcortical regions have higher intercept, suggesting that in these regions there is a residual R1 relaxation not explained by R2 * . This residual R1 could be attributed to biological sources affecting R1 exclusively.
R1 relaxation mechanisms are affected by local molecular interactions, while R2 * is sensitive to more global effects of extended paramagnetic interactions at the mesoscopic scale 14 . Therefore, it could be that the intercept is more sensitive to local molecular interactions that do not involve extended paramagnetic effects. Further work may provide insights into biological substrates that are characterized by such relaxation. To conclude, while we exploit the slope of the R1-R2 * fit (r1-r2 * relaxivity) for information on the iron homeostasis, the intercept might capture important information as well.
Analyzing both the relaxivity and the intercept may contribute complementary information and allow better in vivo characterization of brain tissue.
Sup. Figure 16: Supplementary Section 8 ( Supplementary Figures 17-19) Voxel-wise r1-r2* relaxivity visualization. Figure 3 and Figure 5 compare the contrast of R1 and R2 * in the brain to the contrast generated by the r1-r2 * relaxivity. The measurement of the r1-r2 * relaxivity is calculated across all the voxels of a specific ROI in the brain (see "r1-r2 * relaxivity computation for ROIs in the human brain" in Methods). Therefore, the contrasts are presented across different entire brain regions. In order to demonstrate a visualization of a voxel-wise r1-r2 * relaxivity contrast, we generated representative maps of the local r1-r2 * relaxivity in a healthy young subject and in a Meningioma patient. For this purpose, we used a moving-window approach, in which the r1-r2 * relaxivity of each voxel is based on the local linear dependency of R1 on R2 * in that voxel and all its neighboring voxels (125 voxels total, for more details see "Generating voxel-wise r1-r2 * relaxivity visualizations" in Methods).
A comparison of the voxel-wise r1-r2 * relaxivity to the R1 and R2 * maps in the healthy brain can be seen in Sup. Figure 17. Similarly to the ROI-based approach (Figure 3), this voxel-wise comparison also shows that the r1-r2 * relaxivity generates a unique contrast in the brain compared to R1 and R2 * . Interestingly, this local relaxivity contrast highlights the differences between superficial and deep white-matter. Such contrast was previously suggested to be driven by the microscopic iron distribution 15 .
In meningioma patients, we show that the ROI-based approach for the r1-r2 * relaxivity allows to enhance the contrast between tumor tissue and non-pathological tissue without contrast agent injection ( Figure   5). A comparison of the voxel-wise r1-r2 * relaxivity to the R1 and R2 * maps and to the Gd-enhanced contrast in a representative meningioma patient can be seen in Sup. Figure 18. In this example, the boundaries of the tumor can be separated from the surrounding non-pathological tissue based on the voxel-wise contrast of the r1-r2 * relaxivity. Importantly, for this patient we were able to replicate our ROIbased results on the voxel-wise level (Sup. Figure 19). Across voxels, we find that the r1-r2 * relaxivity allows to distinguish between tumor tissue and non-pathological tissue better than R1 and R2 * (for example, effect size for the difference between tumor and gray-matter is more than 10 times larger in the r1-r2 * relaxivity compared to R1 and R2 * ).
Nonetheless, these representative visualizations merely provide preliminary evidence for the adaptiveness of the r1-r2 * relaxivity approach for voxel-wise analyses. Notably, the presented implementation still has some limitations. First, the moving-window approach used for calculating the local r1-r2 * relaxivity leads to inherent smoothing. As a result, this approach is sensitive to partial volume effects for voxels on the border between tissue types, which could be driving the observed contrast between superficial and deep white-matter and between tumor tissue and non-pathological tissue. In addition, the local computation of the r1-r2 * relaxivity uses fewer voxels compared to the ROI-based approach. It also does not include the binning procedure prior to the fitting which we used in the ROIbased approach. Therefore, this computation is less stable and is more sensitive to the inherent SNR of R1 and R2 * , which is affected by magnetic field inhomogeneities, imperfections of the shim, and the heterogeneous magnetic susceptibility of the head. As a result, some of the calculated values in the brain are negative (4% of the voxels in the healthy subject and 11% of the voxels in the meningioma patient).
These limitations should be accounted for prior to any future implementation of this voxel-wise approach for purposes other than visualization.
Sup. Figure 17: Voxel-wise comparison of the r1-r2 * relaxivity map to R1 and R2 * maps in the in vivo healthy brain. The maps of R1 (left) and R2 * (middle) are compared to the local r1-r2 * relaxivity visualization (right) on a representative young healthy subject. The voxel-wise visualization of the r1-r2 * relaxivity in the brain was generated based on the local linear dependency of R1 on R2 * using a moving-window approach (for more details see "Generating voxel-wise r1-r2 * relaxivity visualizations" in Methods).

Sup. Figure 18: Voxel-wise comparison of the r1-r2 * relaxivity map to R1 and R2 * maps and to the Gdenhanced contrast in the in vivo brain of a meningioma patient.
Representative visualization of R1, R2 * , the voxel-wise r1-r2 * relaxivity map and the Gd-enhanced contrast for a meningioma patient. Tumors are marked with arrows. The voxel-wise r1-r2 * relaxivity map was generated based on the local linear dependency of R1 on R2 * using a moving-window approach (for more details see "Generating voxel-wise r1-r2 * relaxivity visualizations" in Methods).

Sup. Figure 19: The voxel-wise r1-r2 * relaxivity enhances the contrast between tumor tissue and nonpathological tissue on a representative meningioma patient. Replication of the ROI-based results presented in figure 4d-f on the voxel-wise level. The contrast between the white-matter (WM, N=60647 independent voxels), gray matter (GM, N=44251 independent voxels) and tumor tissues (N=313 independent voxels) is presented for R1, R2 * and the voxel-wise r1-r2 * relaxivity. The variation in each box is calculated across voxels in a representative meningioma patient (Sup. Figure 11). The 25th, 50th and 75th percentiles and extreme data points are shown for each box, whiskers show maximal and minimal values. The d-values represent the effect size (Cohen's d) of the differences between tissue types.
Across voxels, the r1-r2 * relaxivity allows to distinguish between tumor tissue and non-pathological tissue better than R1 and R2 * . Estimates in non-pathological tissues are for the tumor-free hemisphere.

The correlations of MRI parameters with MTsat. The qMRI measurement of the magnetization transfer saturation (MTsat) vs. R1, R2 * and the r1-r2 * relaxivity measured in vivo across younger (aged 23-63 years, N =26) and older (aged 65-77 years, N=13) subjects (different marker shapes) in 10 brain regions (different colors). Data points show mean values and error bars show the mean absolute deviation across subjects. Unlike R1 and R2 * , the r1-r2 * relaxivity is not significantly correlated with MTsat. p-values are for one-sided F-test corrected for multiple comparisons (FDR).
Supplementary Figure 22 Sup. Figure 22:

The correlations of MRI parameters with MD. The qMRI measurement of the mean diffusivity (MD) measured in vivo across younger (aged 23-63 years, N =25) and older (aged 65-77 years, N=12) subjects vs. R1, R2 * and the r1-r2 * relaxivity measured in vivo across younger (aged 23-63 years, N =26) and older (aged 65-77 years, N=13) subjects (different marker shapes) in 10 brain regions (different colors). Data points show mean values and error bars show the mean absolute deviation across subjects.
Unlike R1 and R2 * , the r1-r2 * relaxivity is not significantly correlated with MD. p-values are for one-sided Ftest corrected for multiple comparisons (FDR).
The phantom experiments of ferritin and transferrin mixtures (Sup. Section 4) allowed us to establish a theoretical framework for the r1-r2 * relaxivity in an in vitro environment where only the iron concentration changes, and the liposomal fraction mimicking the myelin is fixed ([Δ ] = 0). In the brain, we estimate the r1-r2 * relaxivity across all voxels of an anatomically-defined ROI. Within brain tissue ROIs, both the iron and the myelin concentration may vary 15 .
Importantly, rearranging eq. S8 we find that the strength of the myelin effect on the r1-r2 * relaxivity depends on how variable is the myelin content within an ROI relative to how variable is the iron content In these analyses we aim to simulate realistic concentrations of ferritin, transferrin and myelin, in order to achieve brain-like R1 and R2 * values. Next, we follow our analysis pipeline; binning of the R2 * and R1 measurements, excluding bins with small number of voxels, and assessing the r1-r2 * relaxivity across the binned values. By varying the simulated content of the myelin and iron compounds we test to what extent each biological source contributes to the measurement of the r1-r2 * relaxivity. First, we will examine our hypothesis that changes in the molecular iron environment, reflected by the transferrinferritin fraction, but not in the iron concentration, affect the r1-r2 * relaxivity. We will then evaluate how the r1-r2 * relaxivity is modulated by myelin. We will show that non-physiological conditions are required in order for the myelin by itself to fully explain the r1-r2 * relaxivity changes measured in the brain.
Each numerical simulation was designed to mimic an ROI in the brain containing 1M voxels, with a fixed transferrin-ferritin fraction ( ) across all voxels and varying myelin, transferrin and ferritin concentrations (Sup.

Sup. Table 1: Simulation parameters.
We synthetically generated R1 and R2 * values for each voxel based on eq. S4-S5. The relaxivities of ferritin and transferrin ( (1/2, ) , (1/2, ) ) were taken from the results of our phantom experiments (Figure 2). In order to generate simulations that are as realistic as possible, the rest of the parameters were adapted from the human brain. The mean ferritin and transferrin concentrations (across all voxels of the ROI) were estimated based on post-mortem findings [16][17][18] . The myelin characteristics were simulated based on the qMRI measurement of the macromolecular tissue volume (MTV) 19 , defined as 1-water fraction, which was shown to approximate the myelin content [20][21][22][23][24] . The myelin relaxivity ( (1/2, ) ) is defined as the dependency of relaxation rates on the myelin concentration 13 . We estimated the myelin relaxivity as the linear dependency of R1 and R2 * on MTV, averaged across 16 ROIs in the brains of 21 young subjects. In order to assess the changes in myelin content within brain ROIs ([Δ ]), we calculated the range of MTV values within white-matter (WM) or gray-matter (GM) regions averaged across 8 ROIs in the brains of 21 young subjects (Sup. Figure 23). Finally, the changes in ferritin and transferrin concentrations within brain were determined based on the range of R2 * values within 16 WM and GM regions in the brains of 21 young subjects. We assumed that the changes in R2 * not explained by MTV are related to changes in iron concentration (Sup. Figure 24): We found that the total change in R2 * within ROIs in the human brain is on average Δ( ) 2 * =9.0 1/sec, from which about 61% (Δ( ) 2 * =5.6 1/sec) could be related to changes in iron concentration.
Therefore, the simulated variably in the ferritin and transferrin concentrations were set to satisfy this requirement. An example result of the numerical simulation is presented in Sup. Figure 25a. It is evident that both the changes in myelin concentration across voxels of the simulated ROI (represented by different colors) and the changes in ferritin and transferrin concentrations across voxels (represented by the symbols size) affect the measured r1-r2 * relaxivity. In our analysis pipeline we first bin the R1 and R2 * values within the ROI and next calculate r1-r2 * relaxivity over the binned values. Therefore, the variability in R1 for a given R2 * bin is collapsed to an average R1 value (black data points). We assume that this approach eliminates some of the variability related to myelin. We hypothesized that the r1-r2 * relaxivity is sensitive to the iron environment. Indeed, in our simulations we find that by setting different physiological transferrin-ferritin fractions and leaving the myelin parameters constant, the r1-r2 * relaxivity changes considerably (Sup. Figure 25).

Sup. Figure 24: Myelin-and iron-related changes in
In addition, we hypothesized that the r1-r2 * relaxivity is less sensitive to the iron concentration and is more sensitive to the iron environment. To test this, we run two numerical simulations with the same transferrin-ferritin fraction but with different transferrin and ferritin concentrations. As expected, R1 and R2 * values changed with increased ferritin and transferrin concentrations but the r1-r2 * relaxivity did not change (Sup. Figure 26). This indicates that the r1-r2 * relaxivity measurement is less sensitive to absolute changes in the iron concentration and is sensitive to the interplay between iron compounds, reflected in the simulations by the transferrin-ferritin fraction. In the brain, changes in the myelin content between GM and WM are known to substantially affect the measurements of R1 and R2 *4,7-12,25,26 . To test the potential contribution of the myelin to the r1-r2 * relaxivity, we changed the myelin concentration in our simulation while keeping the rest of the parameters fixed. Setting the myelin concentration to that typical for GM or WM (as estimated in vivo by MTV) led to considerable changes in R1 and R2 * , but did not produce any change in the r1-r2 * relaxivity (Sup. Figure 27). The theoretical formulation presented here indicates that it is not the myelin concentration, but the variability in myelin within an ROI ([Δ ]), that is important for determining the r1-r2 * relaxivity (eq. S14).

Sup. Figure 25: The
However, estimating the variability in myelin within ROIs in vivo based on the myelin marker MTV, we find that it only explains ~30% of the variation in the in vivo r1-r2 * relaxivity measurements across the brain (Sup. Figure 28). In the simulations, setting both the range and concentration of myelin to the ones typical for WM or GM (as estimated by MTV, Sup. Figure 23), slightly changed the r1-r2 * relaxivity (0.002, Sup. Figure 29). Importantly, changing the transferrin-ferritin fraction between the physiological values of 0.1-0.2 led to a change of 0.026 in the r1-r2 * relaxivity (Sup. Figure 25). Therefore, the simulated changes related to the molecular iron environment were one order of magnitude bigger (Sup. Figure 25).

Sup. Figure 29: The r1-r2 * relaxivity in two simulated ROIs with different myelin concentrations, different ranges of myelin concentrations ([ ]), and similar transferrin-ferritin fractions (Tf/(Tf+Ft)); (A) WM; a higher myelin concentration and a larger range of myelin variability, the transferrin-ferritin fraction is 0.1; (B) GM; a lower myelin concentration and a lower range of myelin variability, the transferrin-ferritin fraction is 0.1. Each figure shows the dependency of R1 on R2 * for 1,000 representative simulated voxels. The colors of the data points indicate the variability in myelin concentration across voxels, and their sizes indicate the variability in iron compounds concentration across voxels (the simulated concentrations are shown in the text box, myelin is in units of [fraction] as MTV, transferrin and ferritin are in units of [mg/ml]). As in our in vivo pipeline, R2 * and R1 values were binned (black data points represent the bins' median), and a linear fit was calculated (black line). The slopes of the linear fit (shown in the title)
represent the dependency of R1 on R2 * (r1-r2 * relaxivity) and vary slightly with the range of myelin variability ([ ]).
We further tested what are the myelin properties that would generate similar r1-r2 * relaxivity effect as the effect observed when changing the transferrin-ferritin fraction (a change of 0.026 in the r1-r2 * relaxivity, Sup. Figure 25). As changing the myelin concentration does not change the r1-r2 * relaxivity (Sup. Figure 27), we changed the variability in myelin concentration within the ROI ([Δ ], Sup. Figure 29).
We found that in order to generate a change of 0.026 in the r1-r2 * relaxivity only through myelin-related changes (when the iron-related properties are fixed), the variability in MTV within the simulated ROI should be in the order of 0.187 [fraction] (Sup. Figure 30). Evaluating the in vivo variability in MTV within WM, GM and subcortical ROIs across 21 young subjects, the typical variability is ~ 0.09 [fraction], and the most extreme variability that was measured was 0.13 [fraction] (in the WM, Sup. Figure 23). Even this atypical value is still much lower than that required to generate a change of 0.026 in the r1-r2 * relaxivity (0.187 [fraction] in MTV). Thus, while the variability in myelin within ROIs can affect the r1-r2 * relaxivity, there are no physiological myelin properties that would fully explain the r1-r2 * relaxivity effect measured in the brain. The iron and myelin contents of brain tissue are tightly related, as iron is required for the formation of myelin 4 . To test how this affects the r1-r2 * relaxivity measurement, we simulated a case where iron and myelin are completely correlated. Importantly, even in this extreme case, different transferrin-ferritin fractions exhibited different r1-r2 * relaxivity (Sup. Figure 31). To conclude, we simulated a brain-like environment in order to test the biological sources affecting the r1-r2 * relaxivity measurement. We found that physiological changes in the molecular iron environment, represented in the simulations by the ferritin-transferrin fraction, led to considerable changes in the r1-r2 * relaxivity (0.026). This effect could not be attributed to the absolute concentrations of iron compounds, only to the ratio between them. To estimate whether the effect of changing the molecular iron environment is measurable in vivo, we assessed the detection limit of the r1-r2 * relaxivity measurement using scan-rescan experiments (Sup. Figure 14). We found that the changes in the r1-r2 * relaxivity simulated by different physiological transferrin-ferritin ratios are well above the detection limit of this MRI measurement in vivo (MAE~0.0035). Importantly, our arguments regarding the sensitivity of the r1-r2 * relaxivity to the molecular iron environment are demonstrated in the simulations based on the example of the transferrin-ferritin ratio. However, it is evident from our theoretical formulation (eq. S14) that the variability in iron concentration within an ROI contributes to the r1-r2 * relaxivity as well. Therefore, while the transferrin-ferritin ratio was used as an example, other features of the iron environment such as the spatial variability of iron compounds, their binding capacities and aggregate sizes, could affect the r1-r2 * relaxivity as well. Next, we confirmed that changes in the myelin concentration affect the measurements of R1 and R2 * , but not the r1-r2 * relaxivity. The myelin variability within an ROI can affect the r1-r2 * relaxivity. However, we found that in vivo estimates of this myelin characteristic explain only 30% of the variation in the in vivo r1-r2 * relaxivity measurement across the brain. In the simulation, setting the myelin variability within an ROI to typical GM and WM values led to a slight change in the r1-r2 * relaxivity.

Sup. Figure 31: The r1-r2 * relaxivity in two simulated ROIs with different transferrin-ferritin fractions (Tf/(Tf+Ft)) and a correlation between iron and myelin concentrations across voxels; (A) The transferrin-ferritin fraction is 0.1; (B) the transferrin-ferritin fraction is 0.2. In both A and B iron and
However, we found that unrealistic myelin variability is required in order to produce the r1-r2 * relaxivity effect observed for realistic changes in the transferrin-ferritin fraction. Therefore, while the myelin substantially affects the measurements of R1 and R2 * , it is not the main component governing the measurement of the r1-r2 * relaxivity, and under physiological conditions it cannot by itself explain the measured variability in the r1-r2 * relaxivity across the brain. Figures 32-34) Comparison of the r1-r2* relaxivity and T1w/T2w. The semi-quantitative T1w/T2w imaging is widely used as a myelin marker 27 . Both the r1-r2 * relaxivity and the T1w/T2w approaches represent combinations of transverse and longitudinal relaxation. Due to the underlying similarities between these methods we wanted to verify that the r1-r2 * relaxivity is less sensitive to myelin compared to T1w/T2w. Mathematically, it can be shown that the T1w/T2w enhances the myelin contribution, while the r1-r2 * relaxivity reduces the myelin contribution. T1w is proportional to R1, and T2w is proportional to 1/R2. Therefore, T1w/T2w is proportional to R1*R2. Assuming both R1 and R2 are linearly related to myelin, then T1w/T2w is proportional to myelin squared (as argued by Glasser et al 27 ). On the contrary, the r1-r2 * relaxivity (i.e., the slope of the R1-R2 * linear fit) represents the change in R1 relative to the change in R2 * (ΔR1/ΔR2 * ), and is therefore less sensitive to the magnitude of these relaxation rates and more sensitive to their shared variation. While the myelin concentration has a large effect on the magnitudes of R1 and R2 * , its effect of the shared variation of R1 and R2 * (ΔR1/ΔR2 * ) is minimal. ΔR1/ΔR2 * is mostly related to the variability in myelin concentration within ROIs (ΔM) Sup. Figure 32: Simulations of the sensitivity of R1*R2* (a-d) and r1-r2* relaxivity (e-h) to different biophysical sources. The variability in R1*R2* and r1-r2* relaxivity was tested across the physiological ranges of transferrin-ferritin fraction (a,e), myelin concentration (b,f), myelin range (ΔM , c,g) and iron compounds concentrations (d,h). Simulations were performed under the same framework as in Supplementary Section . In each simulation we changed one biological component while keeping the rest fixed.

Supplementary Section 10 (Supplementary
(Sup. Section 9). We show in simulations that non-physiological values of ΔM are required to produce the r1-r2* relaxivity values measured in the brain. To demonstrate the differences between T1w/T2w and the r1-r2 * relaxivity, we performed simulations of r1-r2 * relaxivity and R1 * R2 * (similar to R1 * R2 which is proportional to T1w/T2w). We tested these parameters across the physiological ranges of transferrinferritin fraction, myelin concentration, myelin range (ΔM) and iron compounds concentrations. In each simulation we changed one biological component while keeping the rest fixed. These simulations follow the same framework presented in Sup. Section 9. Sup. Figure 32 demonstrates that R1 * R2 * changes mostly with the myelin and iron concentrations, but also with the transferrin-ferritin fraction. On the other hand, the r1-r2 * relaxivity changes mostly with the transferrin-ferritin fraction. It also changes with the myelin variability (ΔM), but to a smaller extent (Sup. Section 9). Nevertheless, the simulated r1-r2 * relaxivity does not change with the myelin and iron concentrations.

Supplementary Section 11 (Supplementary
The voxel-wise division of R1 and R2 * (the R1/R2 * ratio) may provide a simple approximation of the r1-r2 * relaxivity, which has the benefit of allowing higher spatial resolution. However, we demonstrate that the R1/R2 * ratio has a different biophysical interpretation compared to the r1-r2 * relaxivity. Mainly, the R1/R2 * ratio depends on the relative magnitudes of R1 and R2 * . On the other hand, the slope of the R1-R2 * linear fit (i.e. the r1-r2 * relaxivity) represents the change in R1 relative to the change in R2 * (ΔR1/ΔR2 * ), and is therefore less sensitive to the magnitude of these relaxation rates and more sensitive to their shared variation. To demonstrate this point, we performed simulations of the R1/R2 * ratio and the r1-r2 * relaxivity across the physiological ranges of transferrin-ferritin fraction, iron compounds concentration, myelin concentration and myelin variability (ΔM). In each simulation we changed one biological component while keeping the rest fixed. These simulations follow the same framework presented in Sup. Section 9. Sup. Figure 35 demonstrates that the R1/R2 * ratio changes with several Sup. Figure 35: Simulations of the sensitivity of the R1/R2* ratio and the r1-r2* relaxivity to different biophysical sources. The variability in R1/R2* and r1-r2* relaxivity was tested across the physiological ranges of transferrin-ferritin fraction (a), iron compounds concentration (b), myelin concentration (c) and myelin variability (ΔM , d). In each panel only one biological property is changing while the rest are kept fixed. Simulations were performed under the same framework as in Sup. Section 9.
physiological properties; the transferrin-ferritin fraction, the iron compounds concentration and the myelin concentration. On the other hand, the r1-r2 * relaxivity changes mostly with the transferrin-ferritin fraction. It is also sensitive, but to a smaller degree, to changes in ΔM (Sup. Section 9). Changes in the myelin and the iron compounds concentrations do not affect the simulated r1-r2 * relaxivity. Therefore, the R1/R2 * ratio and the r1-r2 * relaxivity have different biophysical sources.
To further demonstrate the differences between the r1-r2 * relaxivity and the R1/R2 * ratio, we provide a comparison between these measurements in vivo. Sup. Figure 36 shows that across subjects and brain regions, the r1-r2 * relaxivity is different compared to the R1/R2 * ratio.
Sup. Figure 37 emphasizes that the contrast of the R1/R2 * ratio across the brain is different from the r1-r2 * relaxivity contrast (Figure 3b). Namely, the contrast between different white-matter regions that was observed in the r1-r2 * relaxivity (Sup. Figure 20) vanishes in the R1/R2 * ratio. The contrast between different gray-matter regions is also different between these measurements. Another example for the differences between the measurements is that the hippocampus, which has the second lowest r1-r2 * relaxivity, is similar to the thalamus and is closer to white-matter regions in terms of its R1/R2 * ratio.
These analyses validate that the r1-r2 * relaxivity is inherently distinct from the R1/R2 * ratio. It highlights the unique nature of the relaxivity measurement, which does not depend on the magnitude of the relaxation rates but rather on Sup. Figure 36: comparison between the R1/R2* ratio (yaxis) and the r1-r2* relaxivity (x-axis) across different brain areas (different colors) for all healthy human subjects (N=39).
Sup. Figure 37: The R1/R2* ratio across the brain. The variation across young subjects (age 27±2, N = 21) in the R1/R2* ratio in different brain regions. The 25th, 50th and 75th percentiles and extreme data points are shown for each box. their shared variation. This reduces the effect of the myelin and iron concentrations on the r1-r2 * relaxivity, and enhances its sensitivity to the iron homeostasis.
The pallidum is unique in terms of its paramagnetic properties: it is highly rich in iron, but also contains iron oxides and metal depositions 3,28,29 which might affect the measurement of the r1-r2 * relaxivity.
For young subjects, R1 and R2 * values in the pallidum were the highest among all regions tested, and the r1-r2 * relaxivity was the lowest (Figure 3). To make sure our results are not driven by the outlier values in the pallidum, we tried to exclude it from the comparisons between MRI and iron histology we show in Figure 4b-c. The correlation of the r1-r2 * relaxivity with the iron concentration did not survive after excluding the pallidum (Sup. Figure 39). On the contrary, the correlations of R2 * with the iron concentration and of the r1-r2 * relaxivity with the iron mobilization remained significant even when the pallidum was excluded from the analysis (Sup. Figure 39). Figure 5b- Therefore, the correlation of the r1-r2 * relaxivity with the iron concentration was driven mostly by the distinct behavior of the pallidum, while its correlation with the iron mobilization was stronger and more stable. These analyses demonstrate the enhanced sensitivity of the r1-r2* relaxivity to the iron homeostasis rather than to the absolute iron concentration.

Sup. Figure 39: The correlations of MRI parameters with the iron environment when excluding the pallidum. Replication of
Supplementary Table 3 Sup.