T₂ contrast variation in human brain at 7 T and its potential contributors Open Access

The development of high-field MRI over the last two decades has been motivated by the promise of increased sensitivity and contrast for clinical neuroimaging. While high-field MRI has been beneficial for several applications, particularly significant improvements have been obtained with the use of T₂^*-weighted techniques that are sensitive to tissue magnetic susceptibility χ. These techniques are sensitive to subtle variations in χ associated with the presence of non-heme tissue iron and myelin, brain constituents relevant for healthy human brain function. Based on this, magnetic susceptibility contrast at 7 T has been used to study tissue iron accumulation in healthy aging (Betts et al., 2016; Buijs et al., 2017), Alzheimer’s disease (McKiernan & O’Brien, 2017), and Parkinson’s disease (Lehéricy et al., 2014; Schwarz et al., 2018). In multiple sclerosis, both white matter and cortical demyelinating lesions can be detected at 7 T (Liu et al., 2021; Nielsen et al., 2013), as well as aberrant iron deposition in and around the lesions that are associated with neuroinflammation (Absinta et al., 2016; Bagnato et al., 2011). This strong sensitivity provided by 7 T MRI offers opportunities to quantify local changes of tissue iron and myelin (Shin et al., 2021; Z. Li et al., 2023), potentially assisting diagnosis and monitoring of brain conditions and therapeutic interventions. In favor of readability, we will refer to non-heme tissue iron simply as iron in the following, noting the differences in relaxometry between non-heme and heme iron (Yablonskiy et al., 2021).

One of the outstanding problems with susceptibility contrast in MRI is its sensitivity to image artifacts around strong magnetic perturbations (e.g., from veins and air/tissue interfaces), which can compromise image quality and confound interpretation. These adverse effects can be further complicated by temporal field changes during the scan due to respiration and head motion (Liu et al., 2018; van Gelderen et al., 2007). In addition, quantitative evaluation of iron and myelin is affected by anisotropic microstructure (e.g., sensitivity to the orientation of white matter fibers relative to B₀) (Lee et al., 2010), an issue remaining incompletely resolved. Inclusion of fiber orientation data (e.g., from diffusion MRI) may help address this problem but requires extra scan time and novel reconstruction techniques (X. Li et al., 2012) that have not yet reached clinical standards.

An alternative approach to study brain iron and myelin is the use of T₂ contrast, which is less affected by artifacts from veins and air/tissue interfaces while maintaining sensitivity to iron (Drayer et al., 1986; Hasan et al., 2012; Langkammer et al., 2010; Vymazal et al., 1999) and myelin (Cho et al., 2023; Leppert et al., 2009; Miot-Noirault et al., 1997), albeit to a lesser degree than T₂^*. Like with T₂^*, the sensitivity of T₂ to tissue iron has been shown to increase with magnetic field at least up to 7 T (Bartzokis et al., 1993; Mitsumori et al., 2012; Schenck, 1995; van Gelderen et al., 2025). Exploiting the sensitivity of T₂ to iron for iron quantification is complicated by potential contributions of myelin to T₂ (van Gelderen et al., 2025). The sensitivity of T₂ to myelin has not been well explored at 7 T and above, and neither has the potential effect of white matter fiber microstructure and orientation on T₂. In part, this paucity of T₂ research relates to the difficulty in performing quantitative T₂ measurements at ultra-high-field, arising from increased RF power deposition and B₀- and B₁ nonuniformity. The latter compromise the ability to achieve accurate RF refocusing in spin echo (SE) generation required for sensitization to T₂.

Some of the above challenges with established approaches to measure T₂ may be alleviated by employing a method called Gradient Echo Sampling of Spin Echo (GESSE) (Cox & Gowland, 2010; Ma & Wehrli, 1996; Yablonskiy & Haacke, 1997), in which a single SE is generated and sampled with multiple gradient echoes (GEs). From an imaging practicality perspective, GESSE does not suffer from accumulating refocusing imperfections of multi-SE acquisitions, or time-inefficient measurement of T₂ with multiple single SE acquisitions at varying spin echo TE (sTE). These technical features make GESSE a more feasible approach for T₂ mapping at ultra-high-field, despite expected discrepancies in the obtained T₂ value when compared to that derived from conventional CPMG and Hahn-echo methods.

The goals of this study were to employ GESSE at 7 T to explore quantitative T₂ measures across the brain in both gray and white matter, and to investigate potential influences of white matter microstructure and orientation on measured T₂ values.

We implemented a modified GESFIDE/GESSE sequence that samples the Free Induction Decay (FID), as well as the dephasing and rephasing sides of the SE (Ni et al., 2015) (Fig. 1). The GE samples around the SE were used to estimate R₂ as proposed by the original GESSE study (Yablonskiy & Haacke, 1997) to take advantage of its features described above. The FID section was used to estimate R₂^* and χ, yielding quantitative images on par with those from commonly used GRE sequences with short TEs.

After first implementing and optimizing the acquisition protocol at 7 T to enable whole-brain coverage, we performed R₂ (=1/T₂) analysis on a group of healthy volunteers. The latter was done using both surface- and volume-based analyses. Initial inspection of R₂ within the white matter revealed strong variation that appeared to be fiber tract-specific, indicating potential dependence of fiber diameter or fiber orientation in the main magnetic field (B₀). To investigate the effects of fiber diameter, we conducted sectional analysis of R₂ on the corpus callosum in sagittal images where fibers in each section were uniformly oriented perpendicular to B₀ but had varying diameters (Aboitiz et al., 1992). To investigate the contribution of fiber orientation, we performed voxel-wise fiber orientation calculation and fiber tract segmentation, followed by joint regression of the measured R₂ values on fiber orientation and diffusion-based fiber diameter index reported in S. Y. Huang et al. (2020).

The modified GESFIDE/GESSE sequence was implemented on a clinical 7 T MRI system (Terra, Siemens Healthineers, Erlangen, Germany) equipped with a single-channel transmit, 32-channel receive head RF coil array (Nova Medical, Wilmington, USA). In vivo experiments were conducted under a human subject research protocol approved by the Institutional Review Board at the National Institutes of Health.

Twelve healthy volunteers (4 males, 23–34 years) were scanned. Images were acquired from transverse-oblique slices parallel to the AC-PC line, with FOV 240 $×$ 180 mm², resolution 1.0 $×$ 1.0 mm², slice thickness 2 mm, slice gap 1 mm, 36–38 slices covering the entire brain, SE formation at sTE 40 ms, echo spacing (⁠$ΔTE$⁠) 1.30 ms, bandwidth 947 Hz/voxel, 6 GEs in the FID section (echo train TE 7.0–13.5 ms), 11 GEs in the rephasing section (echo train TE 25.7–40.0 ms), and 30 GEs in the dephasing section (echo train TE 40.0–79.0 ms). A tapered-sinc pulse with a time-bandwidth product of 6.0 was used for both excitation and refocusing. A slice refocusing factor of 1.5 (thickness ratio of refocused over excited slices) was used to alleviate the issue of imperfectly refocused slice profile. This was achieved by increasing the bandwidth of the refocusing pulse by a factor of 1.5, such that the slice-selection gradient remained the same for both pulses. This had the advantage of consistency between the excited and refocused slice positions in the presence of B₀ inhomogeneity. The refocusing RF pulse had a duration of 5 ms, constrained by limits on peak RF amplitude and power deposition (“SAR limit”). The excitation RF pulse length was 7.5 ms. TR was varied from 4.5–5.5 s to comply with the scanner prescribed “normal-mode” SAR limit (3.2 W/kg). A first-order navigator was acquired at TE = 5.4 ms to correct for the frequency fluctuations by instrumental and physiological sources. The scan time was approximately 15 min, which was achieved without the use of parallel imaging or partial Fourier acceleration. On subsequent GEs, there were small alternating image distortions along the readout direction corresponding to the positive-negative polarities of the odd/even numbered readout gradients in the presence of B₀ inhomogeneity, especially above the nasal sinus. These were corrected based on known readout gradient strength and B₀ field variations estimated by comparing images from a pair of subsequent GEs around the SE. Additionally, data with higher signal-to-noise ratio were acquired by collecting shorter scans (TR = 2 s) which were averaged over 3–4 repetitions. These data were acquired as transverse-oblique slices in 2 subjects for demonstration purposes, and sagittal images in 6 subjects were acquired to visualize the corpus callosum and the corticospinal tract.

A 3D T₁-MP2RAGE with 0.75 mm isotropic resolution was acquired as anatomical reference using the following parameters: 4600 ms TR, 840 ms TI1, 2370 ms TI2, and 2.3 ms TE. Flip angle was 5° and 6° for the 2 TIs respectively. The total acquisition time was 10 min.

The GESSE signal equation is as follows (Cox & Gowland, 2010; Yablonskiy & Haacke, 1997):

where $S$ denotes image magnitude, $M0$ is steady-state signal magnitude, $ΔTE$ echo spacing, and $n$ the distance from sTE in units of $ΔTE$⁠. GE pairs symmetric around sTE = 40 ms were used to calculate R₂ maps as follows

Empirically, it was found that R₂ maps corresponding to n = 6–11 (7.0–12.8 ms away from the SE top) had sufficiently high CNR to be averaged for further processing (Supplementary Fig. S1). $R2$ derived from this method (averaging of normalized ratios) was compared to exponential fitting to the signal $S$⁠, as well as linear fitting to the above function, both in the sense of least squared errors. Similar goodness of fit and R₂ values were obtained using these methods across representative tissue types (Supplementary Figs. S2 and S3). Therefore, we opted for the simple and fast “model-free” approach that does not require pixel-wise fitting.

T₂^* and QSM $χ$ maps were computed with JHU/KKI QSM toolbox v3.3 (https://github.com/xuli99/JHUKKI_QSM_Toolbox) (Bao et al., 2016; X. Li et al., 2019; van Bergen et al., 2016) using the FID data after the excitation pulse. Processing steps include phase unwrapping, brain extraction using BET in FSL (Smith, 2002), background field removal using VSHARP (kernel size 10 mm) (Wu et al., 2012), and dipole inversion using a modified structural feature collaborative reconstruction method (Bao et al., 2016). T₂^* and $χ$ maps were intrinsically registered to T₂ as they were from the same acquisition.

FreeSurfer (v7.2.0, https://surfer.nmr.mgh.harvard.edu/) was used to generate cortical surfaces and volumetric regions of interests (ROIs) using the “recon-all” command on the T₁-MP2RAGE. GE images at the TE (gTE) of 30 ms were affinely registered to the 3D T₁-MP2RAGE reference image set, yielding a registration matrix which was used to transfer data from the GE image space to the reference space (to generate R₂ cortical surface) and vice versa (to obtain ROI labels in the original R₂ space). For each subject, R₂ was averaged across 25% to 75% cortical depth to obtain a cortical surface map, and across -25% to -75% cortical depth to obtain a superficial white matter (SWM) map (i.e., white matter immediately below the cortical ribbon). The surface maps were topographically normalized to the “fsaverage” template for group averaging. Volumetric ROIs were taken from the “aparc+aseg.mgz” and “wmparc.mgz” output in the T₁-MP2RAGE reference space, including cortical functional areas, white matter areas within four brain lobes, as well as some subcortical nuclei. To alleviate partial volume effects, each binary ROI mask was tri-linearly transformed to the R₂ space separately, and a threshold of 0.9 was applied to re-generate a binary mask. The red nuclei and substantia nigra were not included in the segmentation; therefore, they were manually drawn for each subject on the GE images.

R₂ of the corpus callosum was analyzed on the central 3 sagittal slices located around the interhemispheric fissure, corresponding to a lateral width of 20 mm (2 mm slice thickness and 7 mm gap), in which fiber tracts are predominantly perpendicular to the B₀ field. The corpus callosum was manually segmented and divided from tip to tip into four equal-length sections. From anterior to posterior, these sections are genu, anterior body, isthmus, and splenium.

Effective fiber diameter was defined as the average fiber diameter weighted by the corresponding cross-sectional area, that is,

where $di$ and $fi$ are fiber diameter and frequency extracted from the histograms reported in Aboitiz et al. (1992, figure 4). Data from “anterior body” and “mid body” in that figure were combined into a single section of anterior body in this study, due to the limited number of MRI voxels in this narrow region of the corpus callosum.

To facilitate comparison of white matter fiber tract R₂ in this study with diffusion MRI-derived fiber diameter index reported by S. Y. Huang et al. (2020), we generated the same 20 fiber tract ROIs by implementing a similar post-processing pipeline based on NiftyReg (http://cmictig.cs.ucl.ac.uk/wiki/index.php/NiftyReg). First, a 3D GE volume (gTE = 30 ms) was registered to the T₂-weighted template in MNI-152 space from the Johns Hopkins University (JHU) white-matter probabilistic tractography atlas (Mori et al., 2008), using linear registration (“reg_aladin”) followed by nonlinear warping (“reg_f3d”). Then, the transformation was inverted to obtain the probabilistic tractography map in the subject native space for each fiber tract. A threshold of 0.25 was taken to generate binary ROIs. In the voxel-wise analysis, the apparent axonal diameter (⁠$d$⁠) for each individual GESSE voxel was set to the average diameter from (S. Y. Huang et al., 2020) for the fiber tract to which the voxel was assigned based on the registration to the JHU atlas.

To study the effect of fiber orientation on R₂, the same inverse transformation was applied to the fractional anisotropy (FA) map and principal eigenvector (PEV) images in the same JHU atlas. The PEV map was then combined with the slice orientation (axial or axial oblique) to calculate the angle $α$ between the primary fiber orientation and the B₀ field. White matter voxels in the native space with an FA larger than 0.4 and tract probability higher than 0.25 were included in this analysis, resulting in 49,967 valid voxels from the 12 subjects. Finally, $sin4α$ was calculated for each voxel to describe the orientation dependence of R₂ (Bartels et al., 2022; Gil et al., 2016; Knight et al., 2017). Voxels for each fiber tract were categorized into 10 bins based on their $sin4α$ values (ranging from 0 to 1) with a bin width of 0.1. The fitting described below was performed on the binned data to alleviate the heavy weighting on the fibers that were close to being aligned with or perpendicular to B₀ (Supplementary Fig. S4), a consequence of the natural head pose in supine position.

Multiple linear regression was performed using the following model:

where $a0,1,2,3$ are fitting coefficients, $d$ denotes the apparent axonal diameter (mean value over voxels belonging to the same fiber tract, as described above for $d$⁠), and $d¯$ is the mean diameter of all fiber tracts weighted by their corresponding number of voxels (calculated to be 4.46 μm). Using this “de-meaned” term of $(d−d¯)$ instead of $d$ helps to improve the interpretability of the intercept $a0$⁠, which represents the R₂ of a white matter voxel of average axonal diameter $(d−d¯=0)$ and with its fiber tract aligned with B₀ (⁠$sin4α=0$⁠). A subset of the coefficients was set to 0 to investigate the explanatory power of the remaining terms using the R² and adjusted R² metrics.

Example R₂, R₂^*, and $χ$ maps derived from a single modified GESFIDE/GESSE scan at 7 T are shown in Figure 2a. While iron-rich subcortical structures (e.g., basal ganglia, substantial nigra, red nucleus, and the pulvinar of thalamus) are conspicuous in all three contrasts, these maps show several notable differences. First, compared to R₂^* and $χ$⁠, R₂ is much less sensitive to the venous vasculature, as observed most prominently on the maximum intensity projection (MIP) images across slices (Fig. 2b). This is attributed to the fact that the spatial scale of susceptibility perturbations introduced by the veins is much larger than the diffusion distance between excitation and sTE (~5–10 μm), leading to effective refocusing (Boxerman et al., 1995; Weisskoff et al., 1994). Second, compared to R₂^*, stronger R₂ variation across the cortex can be observed, as well as stronger changes of the contrast between cortical gray matter versus superficial white matter. Third, within the deep white matter, there are sharp contrast transitions that appear to be fiber-tract specific. In the following, we study these features in more detail.

As is apparent from Figure 2, substantial R₂ variations are seen in both cortex and the underlying (superficial) white matter. This has been previously observed at 1.5 T, and tentatively attributed to variations in iron content (Zhou et al., 2001). The nature of these R₂ variations is further explored in Figures 3 to 5. Across the brain, contrast between cortical gray and superficial white matter is highly variable: in much of the frontal, temporal lobes and the insula, superficial white matter R₂ exceeds cortical R₂, while the reverse is true in the occipital and parietal lobes (Fig. 3a). A notable exception in the frontal lobe is the motor cortex R₂, where gray matter R₂ exceeds white matter R₂ (Fig. 3a). At the higher resolution of individual (native space) data, it appears that in the frontal and temporal lobes, a thin strip of high R₂ tissue closely follows the gray-white matter border (Fig. 3b), presumably originating from the thin layer of iron-containing U-fibers in the superficial white matter (Kirilina et al., 2020). This is also apparent on a previously published Perl’s iron stain (Fig. 3c).

The spatial variation of gray-white matter R₂ contrast is more evident when viewed from the cortical surface (Fig. 4). Cortical gray and superficial white matter R₂ generally follow Brodmann areas (BA) parcellations and display complementary patterns. Primary cortical areas such as the primary motor (BA 4), somatosensory (BA 3, 1, 2), and visual (BA 17) areas have higher R₂, potentially due to higher non-heme iron content. R₂ in the superficial white matter is lower, in contrast to that in the frontal and temporal lobes. These observations are consistent with, and nicely complemented by a recent study using high-resolution (250 μm) line-scanning GESSE at 7 T that reports higher R₂ in the primary visual, primary motor and somatosensory cortices, compared to adjacent white matter (Balasubramanian et al., 2022). In addition, superficial white matter R₂ in the occipital pole manifests clear correspondence to visual subareas, with the associative visual area (BA 18) having higher R₂ than its neighbors, the primary visual (BA 17) and associative visual (BA 19) areas. When taking the ratio of cortical and superficial white matter surfaces, a high-contrast map yields that is specific to functional areas, highlighting the sensorimotor, primary visual, primary auditory, and cingulate cortices. This resulted in an intriguing bi-modal distribution of the ratio values clearly seen on its histogram, which was absent for both cortical and SWM R₂. All surface maps are highly symmetric between left and right hemispheres.

In comparison to R₂, cortical susceptibility maps based on R₂^* and $χ$ are more strongly impacted by tissue-air interfaces and the venous vasculature (Fig. 5): The exceedingly high R₂^* values in the lower temporal and lower frontal lobes are due to their vicinity to the ear canals and nasal sinus, respectively, consistent with a previous report on cortical R₂^* at 7 T (Cohen-Adad et al., 2012). The high $χ$ areas are adjacent to the superior and inferior sagittal sinuses on the mid-sagittal plane, likely being results of incomplete dipole inversion near those strong susceptibility sources. These are consistent with the observations made in Figure 2.

R₂ results from volume and surface ROIs are summarized in Figure 6. Distinct from R₁ and R₂^* in which the white matter is typically higher (relaxing faster) than the cortex, R₂ of white matter and cortical areas at 7 T fluctuate within a similar range of 22-28 s^-1. The results corroborate our observations that the cortical-white matter R₂ contrast varies and even reverses across the brain. In particular, cortical R₂ is higher than the underlying white matter R₂ for the primary motor and visual cortices, consistent with the results in Figure 4. Nevertheless, such depth dependence was absent from the primary somatosensory and auditory cortices at the group level, which will be discussed below.

In addition to the high contrast across gray matter, between the cortex and superficial white mater, and between different white matter regions, a strong R₂ variation of 6 s^-1, or 25%, can be observed within the white matter, with prominent tract specificity (Figs. 2a and 3a, b). For example, in the occipital lobe, the tapetum and the superior longitudinal fasciculus have notably lower R₂ than the optic radiation between them (Fig. 3b, enlarged in Fig. 3d). This variation is not readily explained by differences in iron content, as histological iron stains typically suggest low iron levels in most major fiber bundles in deep white matter (Drayer et al., 1986; Fukunaga et al., 2010) (Fig. 3c). This high level of spatial specificity is also absent from this area in myelin stain maps (Hametner et al., 2018). To investigate potential contributions from fiber microstructure, we performed tract-specific analysis.

We started from the corpus callosum, which consists of multiple fiber tracts traversing between left and right hemispheres. On sagittal images, these fiber tracts are arranged in segments from anterior to posterior with known variation in fiber diameter under electron microscopy (Aboitiz et al., 1992). This variation is associated with the functions these tracts subserve, with fibers connecting primary auditory cortex (in isthmus in Fig. 7c) being the largest and fastest signal carriers. Consistently high R₂ was found in the fibers of the genu that had smaller diameters, and low R₂ in the isthmus (Fig. 7a; Supplementary Fig. S5). R₂ values of the four sections studied showed a trend of inverse correlation with the effective fiber diameter (Fig. 7d). In addition, on the lateral slices, the corticospinal tracts are clearly visible with lower R₂. The gray matter structures it connects, that is, the globus pallidus and the motor cortex, are also discernable with higher R₂ (Fig. 7a).

Back to the whole-brain axial images, statistical analysis of R₂ within 20 major fiber tracts is shown in Figure 8. The tract-specific R₂ variation was consistent for left versus right hemispheres. Across white matter tracts, R₂ manifested a trend of inverse correlation with apparent axonal diameter $d$ from diffusion measures using high-performance gradients (S. Y. Huang et al., 2020). This result is consistent with the findings in the corpus callosum.

Figure 9 shows an example of fiber orientation calculation by registration to the JHU atlas, as an angle $α$ (range 0°–90°) with respect to the B₀. A positive correlation between R₂ and $α$ can be appreciated by comparing both images, and was confirmed by linear fits of R₂ to $sin4α$⁠. This was done separately for larger and smaller fibers with respect to the average diameter (4.46 μm), showing consistent angular dependence of R₂ in both cases.

With information about $α$ and $d$⁠, multi-linear regression of R₂ to (⁠$d−d¯)$ and $sin4α$ was performed and shown in Figure 10. An $R2$ value of 0.78 was found, superior to linear regression with either (⁠$d−d¯)$ or $sin4α$ alone (Table 1). Improvement with an additional term [(⁠$d−d¯)·sin4α$] was marginal in terms of $R2$⁠, and was absent after adjustment for number of variables, suggesting negligible interaction by multiplication between the two explanatory terms in our data.

Using modified GESFIDE/GESSE acquisition and GESSE-style analysis, we performed whole-brain R₂ mapping at 7 T MRI and observed sizable R₂ variations of ~25% or 6 s^-1 across the cortex, superficial white matter, and within deep white matter areas. In the cortical ribbon and superficial white matter, R₂ closely followed putative tissue iron content and clearly reflected functional parcellation, with diminished influence from confounding factors such as the venous vasculature compared to R₂^* and χ. Within deep white matter, R₂ inversely correlated with fiber diameter and additionally correlated with fiber orientation. These observations are consistent with the expected manifestations of irreversible transverse relaxation considering its strong dependence on micro- and meso-scopic susceptibility as well as diffusion effects. Although these physiological contributions to brain R₂ have been proposed and in some cases histologically validated (Balasubramanian et al., 2022; Hasan et al., 2012; Hervé et al., 2011; Kirilina et al., 2020; Yagishita et al., 1994; Zhou et al., 2001), this study offers a systematic investigation of their relative strengths in vivo at 7 T and their correspondences to whole-brain functional specialization.

The observation that the primary motor and visual cortices have much higher R₂ than the emanating projection fibers indicates that R₂ reflects iron content more strongly than myelination. This is also supported by the higher R₂ in the superficial compared to the deep white matter, in keeping with the iron content distribution. Our findings are consistent with a recent study using high-resolution (250 μm) line-scanning GESSE at 7 T (Balasubramanian et al., 2022). The high resolution achieved in that study allowed detection of a central R₂ peak across the cortical depth that closely follows non-heme iron distribution in contrast to myelin and microvasculature. A limitation of the study was the spatial coverage, which is now complemented by our whole-brain R₂ results.

On the group analysis level, clear R₂ differences between the cortex and underlying white matter were not observed in the primary somatosensory and auditory areas, in contrast to the primary motor and visual areas. This is partly attributed to a relatively high R₂ in the white matter in somatosensory and auditory areas. For the primary somatosensory cortex, absence of observable R₂ differences may also be attributable to the heterogeneous cellular and chemical compositions across subregions (BA 3a, 3b, 1 and 2) (Geyer et al., 1999), and increased partial volume effects due to reduced thickness compared to the primary motor cortex (1.81 mm vs. 2.69 mm as reported in Fischl & Dale, 2000). For the primary auditory cortex, literature is scarce to support the relatively high iron concentration seen in the other primary areas. If cortical R₂ were indeed higher than the white matter, apparent differences may also be reduced by partial volume effects in this relatively thin cortical area, which is 2.34 mm thick on average according to Zoellner et al. (2019).

Based on our findings and relevant reports referenced above, we urge caution with using the ratio of T₁-weighted and T₂-weighted MRI data as indicator for cortical myelination at 7 T (Arshad et al., 2017; Glasser & Essen, 2011; Hagiwara et al., 2018), as the sensitivity of cortical R₂ to iron may confound this interpretation. This may be especially problematic with iron accumulation associated with aging or neurodegeneration. To what extent iron confounds the interpretation depends on the acquisition parameters of the T₁-weighted and T₂-weighted images, yet it is expected to increase with the B₀ field strength above 3 T as T₂ is more sensitive than T₁ to the increasingly stronger susceptibility effects from iron.

Because of its higher sensitivity to microscopic versus macroscopic susceptibility sources (Boxerman et al., 1995; Weisskoff et al., 1994), R₂ may complement R₂^* and χ (Cohen-Adad et al., 2012; Marques et al., 2017) to achieve higher specificity in high-field cyto- and myelo-architectural studies of the human cortex. Furthermore, R₂ may be combined with R₂^* and χ to separate paramagnetic and diamagnetic susceptibility sources that correspond to iron and myelin contributions respectively (Shin et al., 2021; Z. Li et al., 2023). Such separation may be enhanced by including T₁ (R₁) or quantitative magnetization transfer that are more specific to myelin (Marques et al., 2017; Sled, 2018; van der Weijden et al., 2021).

Iron concentration is known to increase with age in most of the brain (Hallgren & Sourander, 1958). Therefore, brain R₂ is expected to generally increase with age as well, which has been demonstrated in selected brain structures (Balasubramanian et al., 2019; Luo & Collingwood, 2022). We expect the observed correspondence between R₂ and cortical functional parcellation to remain with healthy aging, as the relative iron concentration of cortical areas roughly plateaus beyond the age of 40 years (Hallgren & Sourander, 1958). Nevertheless, other physiological and pathophysiological contributors to R₂ through susceptibility or alternative mechanisms may modify this pattern, including demyelination, vascular changes, calcification, and amyloid deposition. Importantly, R₂ is sensitive to the size of the underlying susceptibility sources, as observed in phantoms and demonstrated numerically to be related to diffusion distance (Weisskoff et al., 1994; van Gelderen et al., 2025). The notion is supported by the observation that sizable calcifications in the globus pallidus strongly change R₂^* while only mildly changing R₂ at 7 T (Balasubramanian et al., 2019). This again highlights the benefit of combining R₂ with other susceptibility imaging methods, but also the caveats when interpreting them in tandem.

Another finding of our study was the negative correlation between white matter R₂ and apparent axonal diameter, with an explanatory power of 0.63 by $R2$ in linear fitting. Observation of white matter heterogeneity on T₂-weighted MRI, particularly cortico-spinal tract (CST) hyperintensity, has been made early in the history of MRI (Curnes et al., 1988), and was attributed to the large fibers with thick myelination and wide translucent spaces in an joint MRI and histological study (Yagishita et al., 1994). Stanisz et al. discussed the interpretation of T₂ relaxation in terms of water compartments and how these may be influenced by axonal geometry including fiber diameter (Stanisz et al., 2005). A previous quantitative T₂ study at 7 T reported a 16% difference in T₂ between the CST and its neighboring fiber tract (Hervé et al., 2011). The underlying mechanism of this effect likely is a complicated combination of the effects of diffusion (Kiselev & Novikov, 2018), susceptibility (Weisskoff et al., 1994), intercompartmental magnetization exchange (Dula et al., 2010), surface relaxation (Barakovic et al., 2023), and their interactions. It is noteworthy that a handful of physiological features share a similar brain topographical distribution as axonal diameter, including myelin thickness (Liewald et al., 2014), inter-axonal spacing (Kitajima et al., 1996), fiber orientation dispersion (Friedrich et al., 2020), and microvascular distribution and perfusion (Aslan et al., 2011). These features can also modify R₂ to various extents. Separation of their contributions with current methodology is intractable due to the difficulty in manipulating them separately. Nevertheless, our results demonstrated that R₂ can reflect these microstructural features two orders of magnitudes smaller than the voxel size, and therefore may complement diffusion MRI techniques for studying axonal diameter variations between major fiber bundles.

Research into noninvasive measurement of brain white matter fiber diameter using MRI has been a vibrant field, propelled mainly by advanced diffusion-weighted MRI techniques (Assaf et al., 2008; Fan et al., 2020; S. Y. Huang et al., 2020). This is a challenging endeavor, as the majority of human brain fibers have a diameter of less than 1 μm, necessitating extremely strong gradient hardware (S. Y. Huang et al., 2015) and meticulous modeling with consideration of complex tissue microstructures (Jelescu et al., 2020) for a faithful estimation of statistical parameters reflecting features of the underlying diameter distribution. Recent development using combination of relaxometry and diffusion may alleviate such demanding requirements and allow direct estimation of fiber diameters (Barakovic et al., 2023). A key step to their clinical applications is validation against histology, and cross-validation between in vivo methods, for which R₂ mapping may be a viable candidate.

The orientation dependence of white matter transverse relaxation is a well-established effect, originating from the anisotropic magnetic susceptibility effect described by $sin2α$ and/or $sin4α$ terms (Oh et al., 2013; Wharton & Bowtell, 2012), and secondarily the magic-angle effect described by a $(3cos2α−1)2$ term (Bydder et al., 2007; Henkelman et al., 1994). In in vivo brain, such orientation dependence may be described using a single $sin4α$ term (Bartels et al., 2022; Gil et al., 2016; Knight et al., 2017). The range of R₂ orientation dependence observed in this study was 5.34 s^-1, which is a factor of 2.43 compared to 2.2 s^-1 at 3 T in Tax et al. (2021). This is close to the ratio of the field strengths 7/3 = 2.33, suggesting a close-to-linear scaling of R₂ orientation dependence with B₀. Intriguingly, based on R₂ data from different head poses, Gil et al. (2016) reported that coefficients of the orientation-independent and dependent terms vary across fiber tracts, pointing to tract-specific R₂ modifiers that were suggested to associate with fiber microstructures. This is in line with our findings of fiber diameter effects on orientation dependence. However, our data is limited to a single head pose in the supine position, which did not allow direct comparison with that study. In addition, using a multi-TE multi-shell diffusion spin echo EPI data acquired in two head-tilting positions (supine and 18$°$ pitch), Tax et al. (2021) report that absolute R₂ is higher and its orientation dependence much stronger for the extra-axonal signal than the intra-axonal signal. These findings together warrant further investigation of white matter R₂ orientation dependence at 7 T by water compartmentalization and tissue microstructure.

Comparison of the orientation dependence of R₂ and R₂^* may elucidate their physiological origin. R₂^* is known to be strongly orientation dependent primarily due to the diamagnetic susceptibility of myelin combined with water compartmentalization in white matter fibers (Duyn & Schenck, 2016). In the current study, we observed a R₂^* variation of 5.60 s^-1 across fiber tracts with the natural orientation dispersion in the supine position, similar to the value of 5.34 s^-1 for R₂. This similarity is in agreement with studies at 3 T, as Tax et al. (2021) report R₂ variation of 2.2 s^-1, and Bender and Klose (2010) report R₂^* variation of 2.68 s^-1, both pooling whole-brain white matter voxels. However, the strength of orientation dependence varies across fiber tracts, particularly for R₂ (Gil et al., 2016; Tax et al., 2021), which may reflect the tract differences in microstructure such as fiber diameter and myelin thickness. Therefore, studies of orientation dependence of single fiber tracts with multi-orientational data would be more revealing. For example, in in vivo marmoset brain at 7 T, a 15 s^-1 increase in R₂^* was found in the optic radiation when the fiber tract was perpendicular versus parallel to the B₀ (Sati et al., 2012).

A confounding factor with our fiber-tract specific R₂ analysis is the variation in fiber diameter and orientation within regions of interest (Jeurissen et al., 2019). Notably, orientation dispersion of fine fibers itself might not strongly affect R₂ of the voxel through susceptibility effects as measured by GESSE in this study, because of the diffusion averaging effect associated with the long TE of 40 ms (van Gelderen et al., 2025; Yablonskiy & Haacke, 1997). The practical effect of multiple fiber orientations and/or fiber diameters within a voxel is a “noisy” appearance of the R₂ distribution within white matter (Bender & Klose, 2010; Gil et al., 2016; Tax et al., 2021). We alleviated this effect by limiting the analysis to voxels with an FA larger than 0.4 and tract probability higher than 0.25, effectively selecting voxels dominated by a single tract. Such approach can be further enhanced by measuring subject-specific diffusion images to avoid misregistration to standard templates. This will also open new opportunities for joint analysis of R₂ with advanced diffusion-derived biomarkers such as neurite density and orientation dispersion index (H. Zhang et al., 2012), non-Gaussian diffusion (Steven et al., 2014), axonal diameter distributions (Assaf et al., 2008), compartment-specific parameters (Gong et al., 2020), among others.

Decades of relaxometry research have demonstrated that irreversible transverse relaxation in a complex environment such as biological tissues is dependent on a myriad of effects (e.g., nature of interaction of water with other molecules, water diffusion, magnetization exchange, and magnetic susceptibility) and their interactions, rendering it non-exponential and TE-dependent in nature. Therefore, T₂ values obtained through quantitative MRI heavily depend on the method of measurement and should be considered “apparent” T₂ that partially reflects the underlying irreversible transverse relaxation. For example, multi-echo spin echo in the CPMG regime is well-established to reduce effects of tissue intrinsic diffusion as are encountered in Hahn T₂ (Carr & Purcell, 1954); However, diffusion weighting from the imaging gradients becomes significant when imaging at high spatial resolution (Oakden & Stanisz, 2014) or in the presence of imperfect refocusing as a result of B₁ heterogeneity (Weigel & Hennig, 2012). GESSE T₂ has similar diffusion contributions as Hahn T₂ (van Gelderen et al., 2025), yet discrepancies may arise when TEs of Hahn SEs are different from that of GESSE due to multi-compartmental relaxation in tissues.

To estimate R₂, we followed the original GESSE method (Yablonskiy & Haacke, 1997) that took the ratio of symmetric echo pairs around the spin echo. This model-free approach is insensitive to the underlying frequency distribution, which may deviate from Lorentzian. For example, in some brain regions at high field, Gaussian distributions were found to be superior to Lorentzian (Mulkern et al., 2015). A flexible distribution model may improve quality of fitting when both irreversible and reversible transverse relaxation characteristics are of interest (Steidle & Schick, 2021).

The T₂ data presented here were acquired in 1 × 1 × 2 mm³ resolution, which is rather modest to state-of-the-art T₂^* acquisitions commonly performed at 7 T. When using a large (3 mm) slice separation as done here, misregistration and partial volume effects can compromise accuracy of R₂ on the cortical and SWM surfaces. We attempted to minimize the adverse effects by using high-resolution T1MPRAGE for cortical parcellation, supplying a T₂(T₂^*)-weighted image to “bbregister” with the “-t2” option enabled, and checking individual alignment. Higher resolution R₂ data would allow more accurate study of the dependence of R₂ on cortical area and depth, but would require further technical development to obtain substantial volume coverage within a practical scan duration. This could be addressed by imaging acceleration using parallel imaging and multi-shot EPI methods (Uğurbil et al., 2013; Z. Zhang et al., 2022; Y. Huang et al., 2024). Combination with low-rank signal modelling for continuously acquired GE trains may further improve scanning efficiency (Cao et al., 2022; Wang et al., 2022) to allow higher resolution. Caution needs to be taken as effects such as magnetization transfer, intercompartmental exchange and refocusing RF efficiency can impact the observed R₂. Such effects need to be considered in pulse sequence design or modeled in post-processing to achieve higher consistency and reproducibility. An alternative approach for acceleration of the image acquisition would be multiband or simultaneous multislice imaging (Larkman et al., 2001). One caveat would be the increased RF power deposition and maximum RF amplitude, which may be alleviated by further reducing pulse bandwidth, lowering flip angle, or using PINS pulses (Norris et al., 2014). Research efforts in these directions are warranted considering the unique value afforded by brain R₂ in 7 T studies of healthy aging and neurodegenerative diseases.

Whole-brain R₂ maps can be robustly acquired at 7 T with the GESSE approach and show dominating contributions of iron in both cortical and deep gray matter regions. Robust against the confounding contrast from venous vasculature characteristic of susceptibility-weighted techniques, R₂ may contribute to assessing gray matter iron content. In major white matter fiber bundles, both fiber diameter and orientation relative to B₀ show an apparent contribution to R₂, complicating its interpretation.

The underlying data and code that support the findings of the study are available from the corresponding author upon reasonable request, and subject to institutional policies.

Yicun Wang: Conceptualization, Methodology, Software, Formal analysis, Investigation, Visualization, Data Curation, Writing—original draft, and Project administration. Peter van Gelderen: Conceptualization, Methodology, Investigation, Validation, and Writing—review & editing. Maxime Donadieu: Methodology, Investigation, and Writing—review & editing. Jiaen Liu: Methodology, Software, and Writing—review & editing. Jacco A. de Zwart: Investigation, Software, Data Curation, and Writing—review & editing. Jiazheng Zhou: Investigation, Data Curation, and Writing—review & editing. Govind Nair: Investigation, Writing—review & editing. Daniel S. Reich: Conceptualization, Methodology, and Writing—review & editing. Jeff H. Duyn: Conceptualization, Methodology, Supervision, Writing—original draft, and Writing—review & editing.

All participants gave written informed consent, and ethical approval was granted by the Institutional Review Boards of the National Institutes of Health (Protocol 00-N-0082).

The authors declare no conflict of interest.

The authors thank Susan Guttman and Steven Newman for help with volunteer recruitment; Dr. Kenichi Oishi for providing the principal eigenvector atlas; Drs. Alan Koretsky and Xu Li are acknowledged for constructive discussions. This research was supported by the Intramural Research Programs of the National Institute of Neurological Disorders and Stroke, National Institutes of Health.

Supplementary material for this article is available with the online version here: https://doi.org/10.1162/IMAG.a.67.