Comparison of Three MRI Measures of Brain Iron in Healthy and Cocaine Use Disorder Participants

Abstract

Several MRI measures for quantifying endogenous non-heme brain iron have been proposed. These correspond to distinct physical properties with varying sensitivities and specificities to iron. Moreover, they may depend not only on tissue iron concentration but also on the intravoxel spatial pattern of iron deposition, which is complex in many brain regions. Here the three MRI brain iron measures of $R_2^{*}$, magnetic field correlation (MFC), and magnetic susceptibility are compared in several deep gray matter regions for both healthy participants (HP) and individuals with cocaine use disorder (CUD). Their concordance is assessed from their correlations with each other and their relative dependencies on age. In addition, associations between the iron measures and microstructure in adjacent white matter regions are investigated by calculating their correlations with diffusion MRI measures from the internal capsule, and associations with cognition are determined by using results from a battery of standardized tests relevant to CUD. It is found that all three iron measures are strongly correlated with each other for the considered gray matter regions, but with correlation coefficients substantially less than one indicating important differences. The age dependencies of all three measures are qualitatively similar in most regions, except for the red nucleus where the susceptibility has a significantly stronger correlation with age than $R_2^{*}$. Weak to moderate correlations are seen for the iron measures with several of the diffusion and cognitive measures, with the strongest correlations being obtained for $R_2^{*}$. The iron measures differ little between the HP and CUD groups although susceptibility is significantly lower in the red nucleus for the CUD group. For the comparisons made, the iron measures behave similarly in most respects but with notable quantitative differences. It is suggested that these differences may be, in part, due to a higher sensitivity to the spatial pattern of iron deposition for $R_2^{*}$ and MFC than for susceptibility. This is supported most strongly by a sharp contrast between the values of the iron measures in the globus pallidus relative to those in the red nucleus. The observed correlations of the iron measures with diffusion and cognitive scores point to possible connections between gray matter iron, white matter microstructure, and cognition.

1 |. INTRODUCTION

Brain iron plays a key role in the synthesis of both myelin and neurotransmitters.^1,2 Disruption of brain iron homeostasis is associated with a variety of neurological and psychiatric disorders, including Parkinson’s disease, multiple sclerosis, Huntington’s disease, Alzheimer’s disease, and attention-deficit hyperactivity disorder.^1–3 The concentration of brain iron in humans is particularly high in several deep gray matter regions, such as the basal ganglia,⁴ to an extent that its presence is easily detected with MRI.^5–9 As a consequence, numerous studies have applied MRI as a noninvasive means of assessing brain iron abnormalities due to pathology.^10–20

However, the relationship between brain iron and MRI contrast is indirect, and each of the several proposed MRI measures of brain iron have important limitations. None of them should be regarded as a straightforward indicator of iron concentration. Rather, MRI measures of brain iron have varying degrees of specificity and are primarily useful in brain regions where the iron concentration is high enough for iron’s effect on the MRI signal to be relatively large. These include, in particular, several of the deep gray matter nuclei. Moreover, non-heme tissue iron in brain is not uniformly distributed on cellular length scales, but rather is concentrated within a subpopulation of glia.^21,22 The spatial pattern of these iron-rich cells may affect some brain iron measures and is potentially of clinical relevance,^23–25 in addition to the overall iron concentration.

Two commonly used MRI brain iron measures are the $R_2$ and $R_2^{*}$ transverse relaxation rates.^7–9 These are primarily sensitive to non-heme iron because of magnetic field inhomogeneities (MFIs) generated by iron-rich cells when placed inside an applied magnetic field, as within an MRI scanner. Non-heme tissue iron of healthy brain is believed to be mostly in the form of ferritin,^6,26 which is strongly magnetic having both paramagnetic and superparamagnetic components.²⁷ The MFIs have length scales ranging from a few microns (i.e., the size of glial soma) to several tens of microns for iron clusters that surround myelinated fiber bundles and blood vessels within the basal ganglia.^21,22 Since it is measured with a spin echo sequence, $R_2$ is mainly influenced by MFIs having length scales comparable to or smaller than the diffusion length for water, which is ~10 μm for typical MRI experiments, with the effect of longer length scale MFIs being suppressed by the refocusing pulse. For this reason, $R_2^{*}$ is expected to be more sensitive to iron than $R_2$, but not necessarily more specific. One factor limiting specificity is the presence of additional MFIs generated by air-tissue interfaces and by large blood veins. These mostly create MFIs with macroscopic length scales and thus typically alter $R_2^{*}$ more than $R_2$. In addition, both $R_2$ and $R_2^{*}$ can be influenced by several other relaxation mechanisms, including dipole-dipole interactions²⁸ and chemical exchange,⁹ which also lower their specificity to iron.

In order to improve specificity, magnetic field correlation (MFC) has been proposed as an alternative MRI measure of brain iron.^29–31 It is defined as the correlation between the local magnetic field shift (relative to the main field) experienced by individual water protons at two different times as they diffuse across the landscape of MFIs. The MFC is then sensitive to both the magnitude and spatial characteristics of the MFIs, as well as to the water diffusion coefficient. An advantage of MFC is that it is independent of the other relaxation mechanisms that influence $R_2$ and $R_2^{*}$. Empirically, substantial MFC values are mostly found in the brain regions with the highest iron content, such as the basal ganglia,³⁰ and the application of MFC has so far largely been limited to these areas.^{12,14,17,18,20,31} A notable exception is individuals with aceruloplasminemia who have elevated MFC values throughout much of the brain due to abnormally high iron levels.³⁰

More recently, quantitative susceptibility mapping (QSM)^33–35 has been applied to assess tissue iron by estimating the magnetic susceptibility (χ) for each voxel.^11,36–38 Its sensitivity to iron stems from iron’s aforementioned strong magnetic properties. Nonetheless, other tissue characteristics, such as myelin content, also contribute to χ. In addition, χ values estimated with QSM have associated uncertainties due to the required regularization schemes^33–35 and subtleties related to the anisotropic properties of magnetic susceptibility in brain.³⁹

In this paper, we compare in vivo $R_2^{*}$, MFC, and χ values for human brain from several deep gray matter regions known to have a high tissue iron content (globus pallidus, GP; putamen, PU; caudate nucleus, CN; red nucleus, RN), as well as from the thalamus (TH) which has a relatively lower iron content.⁴ Our goal is to investigate the similarities and differences in these three putative brain iron measures across brain regions and ages. We do this for both healthy participants (HP) and for individuals with cocaine use disorder (CUD), who may have associated alterations in brain structure^40,41 including some evidence of disrupted iron homeostasis.^42,43 In addition to comparing iron measures with each other, we also investigate their correlations with measures of diffusion in white matter regions adjacent to the basal ganglia and with measures of cognitive function. The inclusion of the CUD group is intended to increase the dynamic range of these parameters and thereby support a more comprehensive analysis. A central question to be addressed is the extent to which the three brain iron measures are redundant rather than complementary. The results of this investigation are also relevant to understanding the role of brain tissue iron in CUD and add to those of a closely related prior study by our group.⁴³

2 |. METHODS

2.1 |. Physical basis of iron measures

Each of the three iron measures considered here represents a distinct physical property and is estimated by MRI in a different manner. To determine $R_2^{*}$, one fits the signal magnitude as a function of echo time for a gradient echo sequence to a monoexponential function. The decay constant thereby obtained corresponds to $R_2^{*}$ by definition. The MFC, on the other hand, is defined as

$$\text{MFC}\left(t_2-t_1\right)\equiv {\gamma }^2\langle \left[B\left(t_1\right)-B_0\right]\left[B\left(t_2\right)-B_0\right]\rangle ,$$ (1)

where $B\left(t\right)$ is the local magnetic field experienced by a water proton at a time $t$, $B_0$ is the applied field, and $\gamma =$ 2.675 × 10⁸ s⁻¹/T is the proton gyromagnetic ratio.²⁹ The angle brackets indicate an ensemble average over all water protons within any given voxel. The local field changes with time as water molecules diffuse through the landscape of MFIs. The MFC only depends on the difference between the initial time $t_1$ and the final time $t_2$ because of time translation invariance. For large time differences, the MFC tends to zero as the local magnetic field shifts become uncorrelated. The MFC can be estimated with MRI by using an asymmetric spin echo sequence.²⁹ For isotropic materials with linear magnetic properties, the magnetic susceptibility is defined (in SI units) as

$$\chi \equiv \frac{\mu M}{B_0}\approx \frac{{\mu }_{0}M}{B_0},$$ (2)

where $M$ is the magnetization, $\mu$ is the magnetic permeability, and ${\mu }_0=4\pi \times {10}^{-7}$ H/m is the magnetic permeability of free space.⁴⁴ For biological tissues, $\mu$ and ${\mu }_0$ differ only slightly. QSM provides a method of estimating $\chi$ for each imaging voxel from the phase of the gradient echo signal.^33–35 This is formally an ill-posed problem necessitating the use of one of several regularization schemes, and estimates for $\chi$ will depend somewhat on which one is chosen. The QSM calculation of $\chi$ is nonlocal in that the value for any given voxel depends on the phase from all other voxels. Thus, imaging artifacts in the MRI signal data can propagate across voxels. This is in contrast to the calculations for $R_2^{*}$ and MFC, both of which use only local information. In addition, QSM estimates of $\chi$ have an unknown offset so that only relative values are physically meaningful,^35,45 and there are outstanding technical issues related to the fact that the magnetic properties of white matter are anisotropic.³⁹ Nonetheless, established QSM approaches are able to generate impressive maps in which iron-rich brain regions are prominent.^36–38 Figure 1 highlights the physical meanings of $R_2^{*}$, MFC, and χ.

FIGURE 1:

Physical meanings of three different brain iron measures. (A) $R_2^{*}$ is defined as the decay constant for the signal magnitude (S) from a gradient echo sequence. (B) The magnetic field correlation (MFC) is proportional to the correlation between local magnetic field shifts experienced by water protons at two different times as they diffuse across the landscape of magnetic field inhomogeneities (MFIs) generated by magnetized tissue components such as iron-rich glia. (C) The magnetic susceptibility χ for any voxel is determined by the ratio of its magnetization M to the magnitude of the applied field B₀. The arrows indicate the directions of magnetic field and magnetization vectors, which are parallel for simple materials, and the square represents an imaging voxel with a magnetic permeability μ, which typically differs only slightly from the free space permeability μ₀.

2.2 |. Random sphere model

To illustrate the relationship of $R_2^{*}$, MFC, and χ to tissue iron and guide the interpretation of our data, we consider a simple model of water diffusing through a set of uniformly magnetized spheres placed independently of each other at random. We assume the diffusion is unrestricted and isotropic with a diffusivity $D$. The spheres are considered permeable (so that water molecules can freely enter and exit) and occupy a volume fraction $f$. All the spheres have the same radius $R$ and the same susceptibility ${\chi }_0$. In a uniform applied field, the spheres become magnetized and thereby generate MFIs. This model is qualitatively similar to water diffusing in deep gray matter regions with iron-rich glia being analogous to the magnetized spheres. However, iron-rich glia are not uniformly distributed as both isolated cells and aggregations surrounding myelinated fiber bundles and small blood vessels are prominent.^21,22 Therefore, the random sphere model provides only a rough, semi-quantitative description of the complex landscape of MFIs generated by iron rich cells. (While we employ SI units throughout this paper, some of the prior work referred to in this subsection uses CGS units, for which magnetic susceptibility is smaller by a factor of 4π.⁴⁴)

For this model, $R_2^{*}$ can be calculated analytically to leading order in ${\chi }_0$ as

$$R_{2,W}^{*}={\left(\gamma B_0{\chi }_0\right)}^2\frac{8f{R}^2}{225D},$$ (3)

with the subscript $W$ being added to indicate that this is for weakly magnetized spheres.^46,47 Thus $R_{2,W}^{*}$ depends both on the volume fraction of spheres as well as the sphere radius. For a fixed volume fraction, $R_{2,W}^{*}$ grows as $R$ is increased showing that the extent to which the magnetized material is clustered affects the relaxation rate. However, for large ${\chi }_0$ and assuming $f\ll 1$, the strong field (or static dephasing) approximation applies and gives

$$R_{2,S}^{*}=\frac{2\pi }{9\sqrt{3}}f\gamma B_0{\chi }_0,$$ (4)

which is independent of sphere radius and thus insensitive to clustering.^48–50 An established interpolation formula that covers the full range of susceptibilities is^50–52

$$R_2^{*}=\frac{R_{2,W}^{*}{R}_{2,S}^{*}}{R_{2,W}^{*}+R_{2,S}^{*}}=R_{2,S}^{*}\frac{R^2}{R^2+R_c^2}$$ (5)

where

$$R_c\equiv \frac{5}{2}{\left(\frac{\pi D}{\sqrt{3}\gamma B_0{\chi }_0}\right)}^{1/2}.$$ (6)

Here $R_c$ is a critical radius that governs the crossover from the weak field behavior of Equation (3) to the strong field behavior of Equation (4). The effect of the magnetized material on $R_2^{*}$ is thus greatest when $R\gg R_c$, small when $R\ll R_c$, and half its maximum value when $R=R_c$. On the time scales relevant to most MRI experiments, the diffusivity in gray matter is about $D=0.9$ μm²/ms,⁵³ and ${\chi }_0$ for iron-rich glial cells has been estimated as ~10⁻⁶.⁵⁴ For $B_0=3$ T, we then find $R_c\approx 3.6$ μm. Since the soma for oligodendrocytes, the most common iron-rich glial cell,²¹ have radii of roughly 5 μm,⁵⁵ cell clusters should alter $R_2^{*}$ more than an equal number of well separated individual cells with the same total iron content. This dependence of $R_2^{*}$ on sphere size has been demonstrated experimentally in suspensions of polystyrene microspheres,⁵⁶ and the interpolation formula of Equation (5) is consistent with Monte Carlo simulations.^50,51 The dependence of $R_2^{*}$ on $R$ predicted by Equation (5) is plotted in Figure 2 for $R_c=3.6$ μm.

FIGURE 2:

Dependence of $R_2^{*}$ and MFC on sphere radius R for water diffusing through MFIs generated by magnetized random spheres. For a fixed volume fraction, both measures increase as the radius grows, showing how the degree to which the magnetized material is clustered affects their values. The plot for $R_2^{*}$ is obtained from Equation (5) with $R_c=$ 3.6 μm, and the plot for MFC is obtained from Equation (7) with $\sqrt{Dt}=4.2$ μm. These parameter choices are relevant to practical MRI experiments in deep gray matter at a field level of 3 T. The two curves indicate that MFC achieves half its maximum sensitivity at a substantially larger radius than does $R_2^{*}$. Therefore the MFC is expected to be relatively less affected than $R_2^{*}$ by smaller (~10 μm) iron clusters.

The MFC for random permeable spheres is given by

$$\text{MFC}\left(t\right)=\frac{4f}{45}{\left(\gamma B_0{\chi }_0\right)}^{2}U\left(\frac{Dt}{R^2}\right),$$ (7)

where $t$ is the time interval over which the MFC is measured and

$$U\left(x\right)\equiv \frac{1}{\sqrt{\pi }}\left\{\sqrt{\pi }\text{erf}\left(\frac{1}{\sqrt{x}}\right)+2x^{3/2}\left[1-\text{exp}\left(-\frac{1}{x}\right)\right]-x^{1/2}\left[3-\text{exp}\left(-\frac{1}{x}\right)\right]\right\}$$ (8)

with $\text{erf}\left(x\right)$ being the error function.^29,46 Figure 2 shows how the MFC increases monotonically with $R$, demonstrating the effect of aggregating the magnetized material. The maximum sensitivity occurs for large spheres, and the MFC achieves half its maximum value when $R\approx \sqrt{10Dt}$. Again using $D=0.9$ μm²/ms and setting $t=20$ ms, which is typical for an MFC imaging experiment, one finds that the MFC achieves half its maximum sensitivity at radii of approximately 13.4 μm, which is substantially larger than the size of oligodendrocytes. Thus, the MFC is relatively insensitive to individual iron rich cells, but should be able to detect clusters of a few cells or more. By varying the time interval $t$, MFC imaging has been previously applied to yield estimated iron cluster sizes in deep gray matter of 10 to 20 μm,⁵⁷ which is broadly consistent with the size of iron clusters associated with fiber bundles in the basal ganglia.^21,22 As suggested by Figure 2, the iron sensitivity of MFC is expected to be more strongly weighted toward larger clusters than is $R_2^{*}$.

The total magnetic susceptibility for the random sphere model is simply $\chi =f{\chi }_0$ and is therefore independent of the clustering. For this reason, QSM should ideally not be sensitive to the intravoxel spatial distribution of iron-rich cells, although there may be subtle influences due to imperfections of the algorithms employed to calculate $\chi$. The three brain iron measures considered here thus have markedly different dependencies on the degree to which iron occurs in individual cells or clusters of cells. However, for a fixed cluster size, the random sphere model suggests that all three measures increase linearly with the volume fraction of iron-rich glial cells.

Our assumption of fully permeable rather than impermeable spheres has been made here for the sake of mathematical convenience. Nonetheless, the effect of a finite permeability would be modest. For example, if the permeability were set to zero, Equation (3) is unchanged except for an additional factor of 10/9,⁴⁷ while Equation (4) is unaltered. The actual permeability of cell membranes in gray matter is not well established, but recent work does support rather high intercellular exchange rates exceeding 100 s⁻¹.⁵⁸

2.3 |. Test for impact of spatial pattern of iron deposition

The GP and RN are the two brain iron regions with the highest tissue iron concentrations, which are similar as the GP has just 9% more iron than RN on average.⁴ However, histochemical assessment indicates their spatial patterns of iron deposition to be quite different.²² Large iron clusters with radii of up to 500 μm are observed around blood vessels in GP but not RN. Also, GP contains numerous myelinated fiber bundles that stain heavily for iron while iron in RN is mainly concentrated within individual glial cells or diffusively spread throughout the neuropil in fine submicron granules. Hence, as a test of the effect of the spatial pattern of iron deposition, we will compare in these two regions the three iron measures considered here. As suggested by the random sphere model, the magnetic susceptibility should be similar in both regions, but because of the greater degree of iron clustering within GP, both $R_2^{*}$ and MFC are expected to have relatively larger values in GP than in RN, beyond what one would naïvely expect based just on these regions’ iron concentrations.

2.4 |. Participants

For this study, 23 HP and 22 individuals with CUD were recruited and provided informed consent under a protocol approved by the Institutional Review Board of the Medical University of South Carolina. One HP was excluded from the study due to a failure to complete the required MRI scan. The demographics of the remaining 44 participants are summarized in Table 1.

TABLE 1.

Demographics

	Healthy	Cocaine Use Disorder
Number	22	22
Age, Years, Mean ± SD	44.0 ± 11.4	49.8 ± 10.7
Age Range, years	18–59	20–61
Sex, Male:Female	7:15	14:8
Ethnicity/Race	17 Non-Hispanic White; 5 Non-Hispanic Black/Other	2 Non-Hispanic White; 20 Non-Hispanic Black/Other
Years of Education	15.5 ± 2.3	13.0 ± 2.8
Percent Smokers	36%	77%
Years of Cocaine Use, Mean ± SD	0	20.5 ± 9.8
Years of Cocaine Use, Range, years	0	3–41

The participants with CUD used cocaine at least 4 times per month for at least 3 years. In addition, they identified cocaine as their drug of choice and did not meet the Diagnostic and Statistical Manual of Mental Disorders (5^th edition)⁵⁹ criteria for substance use disorder for any other drugs (not including caffeine, nicotine, or cannabis). The HP did not meet these criteria for substance use disorders for drugs other than caffeine, nicotine, or cannabis. No participants included in this study had a history of neurological or psychiatric disorders other than CUD, and none had a previous head injury or contraindication to completion of MRI procedures.

2.5 |. Imaging

All MRI scans were performed on a 3 T Prisma^fit scanner (Siemens Healthineers, Erlangen, Germany) using a 32-channel head coil. The pulse sequences employed included a multi-echo gradient echo sequence for estimating $R_2^{*}$, a four-shot echo planar asymmetric spin echo sequence for estimating MFC, and a second multi-echo gradient echo sequence optimized for QSM. The asymmetric spin echo sequence was repeated 4 times for the sake of signal averaging and to allow for the discarding of scans with substantial motion artifacts (which this sequence is prone to). In order to determine diffusion properties in white matter, a bipolar diffusion-weighted single shot echo planar sequence was used to acquire two b-value shells (b = 1000 and 2000 s/mm²) with 64 diffusion encoding directions in each shell and phase encoding in the anterior-to-posterior direction. Applying the same sequence, 10 image volumes were also obtained with the b-value set to zero and anterior-to-posterior phase encoding together with a second set of 10 b = 0 image volumes obtained with posterior-to-anterior phase encoding, which allowed for correction of susceptibility distortion of all the diffusion images.⁶⁰ Finally, both T1-weighted and T2-weighted scans were performed for anatomical reference. The main imaging parameters are listed in Table 2. The full protocol required 32 min and 58 s of scan time. For two participants (1 HP and 1 CUD), the $R_2^{*}$ gradient echo sequence was not run due to time constraints. In some of the scans, excessive motion artifacts were observed for the asymmetric spin echo sequence during the acquisition, in which case they were repeated additional times in order to ensure data integrity.

TABLE 2.

MRI pulse sequence parameters

Parameter	Gradient Echo for $R_2^{*}$	Asymmetric Spin Echo for MFC	Gradient Echo for QSM	Diffusion sequence	T1-weighted (MPRAGE)	T2-weighted (turbo spin echo)
Number of slices	82	70	64	54	192	49
Slice thickness (mm)	1.5	1.7	2	2.5	1	2.7
Field of view (mm2)	220 × 220	220 × 220	240 × 240	220 × 220	256 × 256	260 × 260
Acquisition matrix	128 × 128	128 × 128	256 × 256	88 × 88	256 × 256	192 × 192
Acceleration factor	2 (phase)	-	2 (phase)	2 (phase) 2 (slice)	2 (phase)	2 (phase)
TR (ms)	4380	5080	55	3600	1900	6100
Phase partial Fourier	off	off	3/4	off	off	off
Number of echoes	10	1	8	1	1	11 (turbo factor)
First echo time (ms)	4.92	40	3.6	85	2.26	85 (effective TE)
Echo spacing (ms)	4.92	-	5.91	-	-	9.46
Refocusing pulse shifts (ms)	-	0, −4, −16	-	-	-	-
Flip angle	20°	90°	15°	90°	9°	120°
Bandwidth (Hx/px)	260	1346	240	1496	200	223
b-values (s/mm2)	-	-	-	0, 1000, 2000	-	-
Number of diffusion directions	-	-	-	64	-	-
Number of acquisitions	1	4	1	1	1	1
Acquisition time	5′ 34″	6′ 4″	6′ 18″	9′ 27″	4′ 26″	1′ 9″

Parametric maps of $R_2^{*}$ were generated by fitting the multi-echo signal data for the associated gradient echo sequence to the expression

$$S\left(t\right)=S_0\text{exp}\left(-R_2^{*}t\right),$$ (9)

where $S\left(t\right)$ is the signal magnitude as a function of time $t$ and $S_0\equiv S\left(0\right)$. This was accomplished using a custom MATLAB (MathWorks, Natick, MA) script.

For the MFC maps, the images from the different asymmetric spin echo images were averaged for each refocusing pulse time shift ($t_s$), after excluding any image volumes with excessive motion artifacts. Then the averaged images were fit to

$$S\left(t;t_s+t/2\right)=S\left(t;t/2\right)\text{exp}\left[-2t_s^2\text{MFC}\left(t/2\right)\right],$$ (10)

where $S\left(t;t\prime \right)$ is the signal magnitude at an echo time $t$ with the 180° refocusing pulse placed at a time $t\prime$.^29,30 In our experiment, the echo time was $t=40$ ms so that the MFC is estimated at a time $t/2=20$ ms. The pulse shifts were $t_s=$ 0, −4 ms, and −16 ms with a minus sign indicating that the refocusing pulse is shifted towards shorter times. A custom MATLAB script was again used for the fitting.

The QSM data were analyzed using the Morphology Enabled Dipole Inversion (MEDI) method⁶¹ as implemented by the MEDI Toolbox (http://pre.weill.cornell.edu/mri/pages/qsm.html), which yielded susceptibility maps for each participant. The λ regularization parameter was set to 1000, the spherical mean value parameter was set to 5 mm, and the “unwrapPhase” option was used for phase unwrapping. Since the susceptibilities computed in QSM are only relative and not necessarily consistent across participants, we further calculated maps of $\Delta \chi$, where $\Delta \chi$ in a given voxel is the difference between the voxel’s QSM susceptibility and the susceptibility in a small region of interest (ROI) within the deep frontal white matter.³⁵ We chose deep frontal white matter as a reference region because this has been shown to minimize inter-scan variability.⁴⁵ With this convention, white matter then appears dark in $\Delta \chi$ maps, as illustrated in Figure 3. We note that other studies have used either different white matter regions or cerebrospinal fluid as the susceptibility reference.⁶² Figure 3 also shows examples of representative $R_2^{*}$ and MFC maps obtained from an HP and a CUD participant.

FIGURE 3:

Representative T1-weighted, $R_2^{*}$, MFC, and Δχ maps for similar anatomical slices from a healthy participant (HP, first row) and an individual with cocaine use disorder (CUD, second row). Each of the three brain iron measures provides a unique contrast. The calibration bar for the $R_2^{*}$ maps is given in units of s⁻¹, and the calibration bar for the MFC maps is given in units of s⁻². The Δχ maps show the magnetic susceptibility relative to deep frontal white matter, which is why white matter regions appear dark, with the calibration bar indicating parts per billion. Some image distortion may be noticed due to imperfect spatial normalization.

The diffusion MRI (dMRI) data were processed using the DESIGNER pipeline⁶³ as implemented by the PyDesigner software package (https://github.com/muscbridge/PyDesigner).⁶⁴ This yielded parametric maps of the mean diffusivity (MD), fractional anisotropy (FA), and mean kurtosis (MK). The MD is an indicator of the amplitude of water diffusion, the FA is an indicator of diffusion anisotropy, and MK is an indicator for the heterogeneity of the intravoxel diffusion environment.^65,66 All three are therefore influenced by tissue microstructure. In white matter, data from developing brain suggest that greater myelination is associated with lower MD, higher FA, and higher MK.^67,68

To facilitate acquiring consistent ROI values across participants, FreeSurfer⁶⁹ was applied to the T1-weighted images for each participant to automatically generate ROIs for GP, PU, CN, and TH. For RN, the ROIs were drawn manually using the T2-weighted images as anatomical reference. All images, parametric maps, and ROIs were then spatially normalized to a common space using the Automatic Registration Toolbox software with the transformations being based on the T1-weighted images.⁷⁰ Guided by the normalized FA maps, ROIs were also drawn manually for the anterior limb of the internal capsule (ALIC) and posterior limb of the internal capsule (PLIC). The ALIC and PLIC are white matter regions adjacent to GP, PU, CN, and TH, but not to RN. All ROIs were visually inspected in the common space for each participant and, if needed, adjusted manually. All manually defined ROIs and manual adjustments were performed by a single investigator (JV). Examples of the ROIs considered are given in Figure 4 for two anatomical slices.

FIGURE 4:

The brain regions considered for quantitative analysis indicated on T1-weighted images for two different anatomical slices from a single participant. Iron measures were quantified in five deep gray matter regions: globus pallidus (GP), putamen (PU), caudate nucleus (CN), thalamus (TH), and red nucleus (RN). The GP, PU, CN, and RN all have relatively high iron concentrations.⁴ The diffusion measures were quantified in the anterior limb of the internal capsule (ALIC) and the posterior limb of the internal capsule (PLIC). These two white matter regions were selected since they are in close proximity to the GP, PU, CN, and TH. Some of the considered regions of interest extended onto anatomical slices not shown in the figure.

Our dMRI imaging processing pipeline also produced maps for the axial diffusivity, radial diffusivity, axial kurtosis, and radial kurtosis. However, these were not considered in our analysis since the complex geometrical organization of the internal capsule, with intermingled intersecting fiber bundles,⁷¹ obscures their biophysical meaning.

2.6 |. Cognitive assessments

A primary rationale for including individuals with CUD in this study was to support an investigation of connections between brain iron and cognitive functioning, which is known to be altered in this group.^72–76 In order to assess cognition quantitatively, a battery of six different standardized tests were administered to all participants. These were: 1) Shipley-2 for crystallized knowledge and fluid reasoning;^77,78 2) Digit Span for attention and working memory;⁷⁹ 3) Auditory Oddball Task for attention and cognition control;⁸⁰ 4) Wisconsin Card Sorting Test for abstract thinking;^81,82 5) Monetary Choice Questionnaire for impulsivity;⁸³ and 6) Symbol Digit Modalities Test for overall cognitive dysfunction.⁸⁴ For each of these tests, a single measure was selected as a summary statistic. These were: 1) Shipley-2 total scaled score (S-TSS); 2) Digit Span scaled score (DS-SS); 3) Auditory Oddball Task d′ (AOT-d′); 4) Wisconsin Card Sorting Test percent preservative error (WCST-PPE); 5) Monetary Choice Questionnaire overall k (MCQ-Ok); and 6) Symbol Digit Modalities Test standardized score (SDMT-SS). Prior studies have reported that individuals with CUD differ from HP in Digit Span,⁷⁴ Wisconsin Card Sorting Test,^72,74,75 Monetary Choice Questionnaire,⁷⁶ and Symbol Digit Modalities Test.⁷³

2.7 |. Statistical Analysis

Pearson’s correlation coefficients (r) were used to quantify the associations between each of the iron measures from the gray matter ROIs as well as their associations with age. The iron measures in GP, PU, CN, and TH were compared, using linear regression and Pearson’s correlation coefficients, to estimates of tissue iron concentration obtained from published equations derived by fitting to postmortem biochemical assay data as a function of age.^4,32 The statistical significance of each of these correlations was assessed using a general linear mixed model with random subject effects and unstructured covariance matrix, to account for the fact that there were iron measures from multiple regions per subject. The RN was not included in this comparison to estimated iron concentration since a fit for the iron concentration in RN as a function of age is not available (to the best of our knowledge). However, as described above, the mean RN iron was directly compared to the mean GP iron. Comparison of the iron, dMRI, and cognitive measures were made for the HP and CUD groups using ANCOVA⁸⁵ to assess for significant differences after controlling for age.

Partial Spearman rank correlations (ρ) were used to investigate the associations between the regional iron and dMRI measures and between the regional iron and cognitive measures. These correlations were adjusted for age, given its association with brain iron concentration, and with cocaine use, a key study design variable. Age-adjusted correlations were also calculated separately for the HP and CUD groups and compared to each other using Sheskin’s approach that incorporates Fisher Z-transformations.⁸⁶ For the CUD group, partial Spearman rank correlations, adjusted for age, were used to assess associations between iron measures and years of cocaine use. P-values ≤ 0.05 were considered to be statistically significant. Given the hypothesis-generating nature of this study, p-values were not adjusted for multiple comparisons.⁸⁷ These analyses were performed using SAS v9.4 (SAS Institute, Cary, NC, USA).

The two participants without $R_2^{*}$ values were excluded from all analyses related to this parameter, but otherwise included. Thus comparisons involving $R_2^{*}$ were based on 21 HP and 21 CUD participants, while other comparisons were based on 22 HP and 22 CUD participants.

3 |. RESULTS

The three iron measures are compared in Figure 5 across the five gray matter regions. They are all strongly correlated with each other, but the correlations are still substantially less than unity, indicating that these quantities are not redundant. The highest correlation is found between $R_2^{*}$ and $\Delta \chi (r=0.839, p<{10}^{-4})$, and the lowest correlation is found between MFC and $\Delta \chi (r=0.653, p<{10}^{-4})$.

FIGURE 5:

Correlations between the three iron measures for data pooled from all five deep gray matter regions across all 44 participants. All three measures are strongly correlated with each other. Data for the HP group are indicated with green symbols while data for the CUD group are indicated with red symbols.

In Figure 6, the iron measures from the GP, PU, CN, and TH are plotted as a function of the estimated tissue iron concentration based on regression curves given by Hallgren and Sourander⁴ (GP, PU, and CN) and by Adisetiyo and coworkers³² (TH). For all four regions, these regression curves are based on the postmortem data of Ref. 4. The Pearson correlation coefficients exceed 0.8 for all three measures, supporting a strong association with tissue iron. Comparable results for individual iron measures have been reported in prior work.^{30,32,36,43,88–91}

FIGURE 6:

Correlations of iron measures with estimated tissue iron concentrations for the GP, PU, CN, and TH based on postmortem data from Ref. 4. The Pearson correlation coefficients (r) all exceed 0.84. Data for the HP group are indicated with green symbols while data for the CUD group are indicated with red symbols. The correlation coefficients and equations shown on the plots are for best fit lines to the pooled data with both groups combined.

The differences between the iron measures in the GP and RN are given in Figure 7 for the combined group of all participants (All), HP group, and CUD group. Across groups, these differences are similar. For the All group, $R_2^{*}$ is 21% ± 3% higher in GP, MFC is 68% ± 8% higher, and $\Delta \chi$ is 12% ± 6% higher. This can be compared to the expectations based on the simple correlations with the iron concentration provided by the regression lines shown in Figure 6, which predict that $R_2^{*}$ should be 6% higher, MFC should be 9% higher, and $\Delta \chi$ should be 11% higher. Clearly, only the difference for $\Delta \chi$ is in agreement with these estimates. However, the discrepancies for $R_2^{*}$ and MFC are at least qualitatively in accord with histological observations of markedly different spatial patterns of iron deposition for GP and RN.²² As discussed above, iron in GP is more clustered than in RN so that both $R_2^{*}$ and MFC should be relatively less sensitive to RN iron. This effect is especially pronounced for MFC, which may reflect its lower sensitivity to smaller iron clusters as illustrated in Figure 2. The strong linear correlations of Figure 6 for all three measures are consistent with similar degrees of iron aggregation in GP, PU, CN, and TH.

FIGURE 7:

Comparison of iron measures for GP and RN. (A) Compared to RN, $R_2^{*}$ in GP is 21% ± 3% higher for the All (HP+CUD) group, 18% ± 4% higher for the HP group, and 23% ± 6% for the CUD group. (B) MFC in GP is 68% ± 8% higher for the All group, 64% ± 10% higher for the HP group, and 72% ± 12% for the CUD group. (C) Δχ in GP is 12% ± 6% higher for the All group, 8% ± 7% higher for the HP group, and 17% ± 10% for the CUD group. A prior postmortem study found the GP iron concentration to be about 9% higher than in the RN.⁴ This is comparable to results for Δχ, but not for $R_2^{*}$ and MFC, which may reflect the greater sensitivity of these two measures to the details of the spatial pattern of iron deposition. This effect is especially pronounced for the MFC, consistent with theoretical expectations. The indicated uncertainties are standard error estimates.

The correlations of the iron measures with age in the All group are shown in Figure 8 for the deep gray matter regions. These are positive in GP, PU, and CN as expected from the known general increase of iron with age in these regions.⁴ However, the correlations are only significantly different from zero for $R_2^{*}$ and MFC in GP and for $R_2^{*}$ in PU and CN. In the TH, the correlations are all close to zero and largely consistent with biochemical assays showing a gradual decline in iron concentration after 40 years of age.⁴ For the GP, PU, CN, and TH, the correlations in each region are not significantly different from each other across the iron measures. However, in the RN, the correlations for $R_2^{*}$ and $\Delta \chi$ are different (p = 0.048). For $\Delta \chi$, the correlation is also significantly different from zero (p = 0.017) with a positive sign. Prior results for the age dependence of iron in the RN based on biochemical assay are limited and insufficient to draw definitive conclusions for the age range of our study,⁹² but an increase in magnetic susceptibility with age has been previously reported.⁹³

FIGURE 8:

Correlation of iron measures with age for the All group. $R_2^{*}$ is found to increase significantly with age in GP, PU, and CN, MFC is found to increase significantly with age in GP, and Δχ is found to increase significantly with age in RN (solid lines). Data for the HP group are indicated with green symbols while data for the CUD group are indicated with red symbols. Dotted regression lines have slopes that are not significantly different from zero.

Figure 9 provides a comparison of the iron measures for the HP and CUD groups. After controlling for age, the only significant difference observed is a lower $\Delta \chi$ in RN for the CUD group (p = 0.02). A similar observation of lower susceptibility in RN for CUD participants has been previously reported.⁴² Prior work has also found higher susceptibility and MFC in GP for individuals with CUD,^42,43 which we do not replicate here. However, important methodological differences relative to our study include a larger sample size⁴² and subdivision of GP into external and internal segments.^42,43

FIGURE 9:

Comparison of iron measures between HP and CUD groups. No significant differences are found except that Δχ in RN is lower for the CUD group. The indicated uncertainties are standard error estimates. *p < 0.05 after controlling for age.

As shown in Figure 10, no significant group differences are seen in ALIC and PLIC for the three diffusion measures of MD, FA, and MK, except that FA in ALIC is lower for the CUD group after controlling for age (p = 0.01). In contrast, one large prior study did not find FA differences in ALIC for CUD participants but did find a lower FA in this region for nicotine users.³⁸ Since our CUD group has a higher proportion of smokers than the HP group (77% vs 36%), our results may be reflecting this discrepancy. The CUD group also has a higher proportion of males (64% vs 32%), which could have affected our results since some studies have found sex differences in FA for ALIC and PLIC.^94–96 However, only higher FA for males in either ALIC or PLIC are described. Therefore, sex imbalance is unlikely to be causing the lower FA in ALIC for the CUD group. It should be noted that at least one study reports no significant FA differences between healthy males and females in ALIC and PLIC.⁹⁷

FIGURE 10:

Comparison of diffusion measures between HP and CUD groups. No significant differences are found except that fractional anisotropy (FA) in ALIC is lower for the CUD group. The indicated uncertainties are standard error estimates. MD = mean diffusivity, MK = mean kurtosis. *p < 0.05 after controlling for age.

Partial Spearman rank correlations for the All group between the iron and diffusion measures are listed in Figure 11. Significant positive correlations are found for FA in ALIC with $R_2^{*}$ in PU, CN, and TH and with MFC in PU, for MK in ALIC with $R_2^{*}$ in GP and PU and with MFC in GP, for MD in PLIC with MFC in TH, and for MK in PLIC with MFC in GP. However, no significant correlations were found with $\Delta \chi$. A possible explanation for this is that the implied associations between iron and white matter microstructure are being driven by the spatial pattern of iron deposition rather than the iron concentration. The strongest correlations are for FA in ALIC with $R_2^{*}$ in PU (ρ = 0.427, p = 0.006) and for MK in ALIC with $R_2^{*}$ in GP (ρ = 0.471, p = 0.002). Interestingly, FA in ALIC also has a significant correlation with MFC in PU (ρ = 0.331, p = 0.032), and MK in ALIC also has a significant correlation with MFC in GP (ρ = 0.319, p = 0.039). Physical connections for ALIC with PU and GP are plausible as these are adjoining structures linked by numerous neuronal projections. In contrast, no significant correlations were found for iron measures in RN, which is adjacent to neither ALIC nor PLIC.

FIGURE 11:

Partial Spearman rank correlations for the All group between diffusion measures in the internal capsule and iron measures in deep gray matter regions. Significant correlations are observed for FA in ALIC with $R_2^{*}$ in PU, CN, and TH and with MFC in PU, for mean kurtosis (MK) in ALIC with $R_2^{*}$ in GP and with MFC in GP, for mean diffusivity (MD) in PLIC with MFC in TH, and for MK in PLIC with MFC in GP. No significant correlations are observed for any diffusion measures with Δχ in any gray matter regions. *p < 0.05, **p < 0.01.

After controlling for age, four of the six cognitive measures differ between groups. Specifically, these are S-TSS (p < 0.001), DS-SS (p = 0.023), AOT-d′ (p = 0.022), and SDMT-SS (p < 0.001) while no significant differences are found for MCQ-Ok (p = 0.09) and WCST-PPE (p = 0.614). Several significant partial Spearman rank correlations for the All group are also observed between the iron and cognitive measures, as shown in Figure 12. Most of these are for $R_2^{*}$, but one is found between SDMT-SS and $\Delta \chi$ in GP (ρ = −0.363, p = 0.027) while none are obtained for MFC. For $R_2^{*}$, the strongest correlation is its value in GP with MCQ-Ok (ρ = 0.404, p = 0.015). No significant correlations are obtained for DS-SS and WCST-PPE.

FIGURE 12:

Partial Spearman rank correlations for the All group between cognitive measures and iron measures in deep gray matter regions. Significant correlations are observed for Shipley total standard score (S-TSS) with $R_2^{*}$ in GP, for Auditory Oddball Task $\text{d}\prime$ (AOT-d′) with $R_2^{*}$ in TH, for Monetary Choice Questionnaire overall $\text{k}$ (MCQ-Ok) with $R_2^{*}$ in GP, for Symbol Digit Modalities Test scaled score (SDMT-SS) with $R_2^{*}$ in PU and TH and with Δχ in GP. No significant correlations are observed between any cognitive measures with MFC in any gray matter regions. DS-SS = Digit Span scaled score, WCST-PPE = Wisconsin Card Sorting Test percent preservative error. *p < 0.05.

The comparison of the partial Spearman rank correlations when calculated separately for the HP and CUD groups showed very few significant differences. The exceptions were MD in PLIC with MFC in CN (p = 0.019), S-TSS with $\Delta \chi$ in TH (p = 0.043), and DS-SS with $\Delta \chi$ in PU (p = 0.012). For the CUD group, no significant correlations were found between any of the iron measures and years of cocaine use.

4 |. DISCUSSION

Because of its relevance to a variety of pathologies, there has long been an interest in quantifying brain tissue iron with MRI.^5–9 For the most part, efforts in this direction have focused on deep gray matter regions with high iron content where it is sensible to a try to disentangle iron’s impact on MRI contrast from other competing factors such as myelin and water content.⁹ Since putative MRI brain iron measures are all indirect, relying on the measurement of some iron-related property that is invariably influenced by more than just the iron concentration, they have important limitations and attendant caveats.

The most conventional iron measures are the $R_2$ and $R_2^{*}$ relaxation rates,⁹ which are easily determined using simple pulse sequences and elementary calculational methods. However, both of these measures are lacking in specificity and not completely well-defined in being inextricably tied to MRI with some inherent dependence on the details of the pulse sequences used to measure them. MFC and $\Delta \chi$ are alternatives based on quantities with clear physical meanings independent of MRI, which can potentially help alleviate some of the limitations of $R_2$ and $R_2^{*}$ as brain iron measures. Here we have compared $R_2^{*}$, MFC, and $\Delta \chi$ in several deep gray matter regions for both healthy adults and adults with CUD. The inclusion the CUD group adds heterogeneity in terms of iron deposition, white matter microstructure, and cognition, allowing us to investigate more fully how the iron measures are related to these properties.

A crucial, but underappreciated, aspect of iron in deep gray matter is its complex pattern of spatial deposition, which varies considerably between regions.^21,22 In particular, a substantial portion of tissue iron is concentrated in isolated iron-rich glial cells as well as in larger aggregations with sizes of up to several hundred microns. Both $R_2^{*}$ and MFC are influenced by the details of this pattern, thereby encoding relevant information. Since it directly quantifies intravoxel variations in the magnetic field landscape, the MFC is tightly linked to the deposition pattern and is mainly sensitive to iron clusters larger than about 10 μm, as suggested by Figure 2. In contrast, iron affects $\Delta \chi$ in gray matter primarily through the average iron concentration inside a voxel, with the degree of iron clustering being less important. For this reason, $R_2^{*}$, MFC, and $\Delta \chi$ should be regarded as complementary measures of brain iron, with each providing distinct information, as highlighted in Figure 7 in the comparison of values for GP and RN. Using two or more of these quantities in tandem may then support a more comprehensive characterization of brain tissue iron.

Despite their differences, we do observe strong correlations of the iron measures with each other (Figure 5) presumably reflecting their common association with tissue iron. The lowest correlation is between MFC and $\Delta \chi$ (r = 0.653), which might reflect these two being the most divergent in their sensitivities to iron clustering with $R_2^{*}$ being somewhat intermediate in this respect. In addition, their correlations with age are similar in most regions (Figure 8), with the exception of RN.

In our data, we do not find significant group differences between HP and individuals with CUD for the iron measures other than $\Delta \chi$ in RN (Figure 9). In contrast, two prior studies reported significant differences also in GP for MFC and $\Delta \chi$.^42,43 However, our results are not necessarily inconsistent due to methodological discrepancies including ROI definition and number of participants. Most notably, both prior studies used separate ROIs for the internal and external GP, which are not generated by the software used in our analysis pipeline. Still, our data indicate that CUD has no more than modest effects on iron concentration and pattern of deposition in the brain regions considered.

We observe some weak to moderate correlations for $R_2^{*}$ and MFC in deep gray matter with white matter microstructure in the internal capsule as assessed with dMRI (Figure 11). These are seen for GP, PU, CN, and TH, but not for RN. For $R_2^{*}$, significant correlations occur only with ALIC, but also with PLIC for MFC. Somewhat similar results have been reported in macaque brain using QSM to measure magnetic susceptibility in deep gray matter regions and myelin water fraction imaging for white matter.⁹⁸ Specifically, significant correlations are described between susceptibility in the GP, PU, and CN and white matter myelin content in ALIC and PLIC. Interestingly, no significant correlations for white matter with susceptibility are found in our data, which suggests that the spatial pattern of iron deposition may be relevant to the observed associations between white matter and the basal ganglia. A relationship between deep gray matter iron and internal capsule microstructure is plausible given their proximity and many neuronal interconnections. In addition, since iron plays an essential role in myelination,⁹⁹ iron trafficking from the basal ganglia to adjacent white matter regions provides one conceivable mechanism. Indeed, we find both $R_2^{*}$ and MFC to be positively correlated with FA and MK. Since greater myelination is generally expected to increase FA and MK, this suggests that higher iron concentration and/or enhanced iron clustering in the basal ganglia is positively associated with more heavily myelinated axons in the internal capsule. In the aforementioned macaque study, a positive correlation between iron and myelination is also demonstrated.⁹⁸ The associations with ALIC may be of particular relevance for CUD given its involvement with cognition and executive function.¹⁰⁰ In view of the differences shown in Figure 11 for the three iron measures, future investigation of links between gray matter iron and white matter may benefit from a multimodal iron mapping approach.

For the cognitive measures, we find several significant correlations with $R_2^{*}$ and $\Delta \chi$, but none with MFC (Figure 12). Most notably, the SDMT-SS has negative correlations with $R_2^{*}$ in PU and TH and with $\Delta \chi$ in GP, which suggests elevated iron concentration and/or stronger iron clustering in deep gray matter may be associated with greater cognitive dysfunction. In addition, the positive correlation of MCQ-Ok with $R_2^{*}$ in GP indicates that increased iron concentration/clustering is associated with greater impulsivity, while the negative correlation of S-TSS with $R_2^{*}$ in GP points to increased iron concentration/clustering being related to lower levels of crystalized knowledge and fluid reasoning. Overall, higher iron concentration/clustering in GP, PU, and TH is seen to predict poorer cognition. A prior study by Ghadery and coworkers has similarly found that higher $R_2^{*}$ in the basal ganglia correlates with cognitive impairment in normal aging.¹⁰¹ Ferroptosis is one proposed mechanism for such a relationship.¹⁰² Indeed, $R_2^{*}$ values in PU have been found to be predictive of its shrinkage with aging.¹⁰³

As we have emphasized, an important caveat for our results is that all proposed MRI measures of brain iron are indirect and can potentially be affected by tissue properties unrelated to iron. Most importantly, myelin content may influence $R_2^{*}$, MFC, and $\Delta \chi$ because its magnetic susceptibility differs from other tissue components.^39,104 In addition, background magnetic field gradients generated by tissue interfaces and spin-spin relaxation may have an impact.⁹ However, in the brain regions with the highest iron content, which include GP, PU, CN, and RN, it is plausible that tissue iron makes a relatively larger contribution to the measured values for $R_2^{*}$, MFC, and $\Delta \chi$, as supported by the strong correlations with estimated tissue iron shown in Figure 6. Nonetheless, the possibility that the observed associations for the iron measures with white matter microstructure and cognition are altered by tissue properties other than iron content or clustering should be borne in mind. Since such properties are expected to have somewhat different effects on $R_2^{*}$, MFC, and $\Delta \chi$, findings that are concordant among these three quantities are more likely to be iron-related.

This study has two limitations that should be noted. First, our sample size is modest, and the participants have particular demographic characteristics, which may restrict the generalizability of our results. In particular, the CUD group has a higher proportion of males and smokers than the HP group. Second, this study is intended as exploratory and consequently no adjustments for multiple comparisons have been made to the calculated p-values.⁸⁷ This is most relevant for the correlations of the iron measures with white matter properties (Figure 11) and with cognition (Figure 12), which should be regarded as preliminary and in need of replication.

5 |. CONCLUSION

The three iron measures of $R_2^{*}$, MFC, and $\Delta \chi$ are strongly correlated with each other in deep gray matter regions and have similar dependencies on age. Nevertheless, they differ considerably with respect to their sensitivity to intravoxel iron clustering, with MFC being the most sensitive and $\Delta \chi$ the least. Associations were observed for $R_2^{*}$ and MFC with dMRI properties of the internal capsule, pointing to a possible interplay between deep gray matter iron and microstructure in adjacent white matter. Associations were also observed for $R_2^{*}$ and $\Delta \chi$ with several cognitive scores, suggesting a link between iron and cognition. However, despite cognitive differences for the HP and CUD groups, no significant group differences in deep gray matter iron were observed, except for $\Delta \chi$ in RN. Since $R_2^{*}$, MFC, and $\Delta \chi$ have distinct strengths and weaknesses as iron measures, it may be advantageous to adopt a multimodal approach for the characterization of brain iron in order to better capture the complexities associated with its heterogenous spatial distribution and to help control for confounding factors that limit their individual specificities.

Abbreviations used:

ALIC

anterior limb of the internal capsule

AOT-d′

Auditory Oddball Task d

CN

caudate nucleus

CUD

cocaine use disorder

dMRI

diffusion MRI

DS-SS

Digit Span scaled score

FA

fractional anisotropy

GP

globus pallidus

HP

healthy participants

MCQ-Ok

Monetary Choice Questionnaire overall k

MD

mean diffusivity

MEDI

Morphology Enabled Dipole Inversion

MK

mean kurtosis

MFC

magnetic field correlation

MFIs

magnetic field inhomogeneities

PLIC

posterior limb of the internal capsule

PU

putamen

ROI

region of interest

QSM

quantitative susceptibility mapping

RN

red nucleus

SDMT-SS

Symbol Digit Modalities Test scaled score

S-TSS

Shipley-2 total scaled score

TH

thalamus

WCST-PPE

Wisconsin Card Sorting Test percent preservative error

DATA AVAILABILITY STATEMENT

Research data are not shared.