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Abstract

Relative oxygen extraction fraction (rOEF) is a fundamental indicator of cerebral metabolic function. An easily applicable method for magnetic resonance imaging (MRI) based rOEF mapping is the multi-parametric quantitative blood oxygenation level dependent (mq-BOLD) approach with separate acquisitions of transverse relaxation times $_{T}^{2} *$ and T₂ and dynamic susceptibility contrast (DSC) based relative cerebral blood volume (rCBV). Given that transverse relaxation and rCBV in white matter (WM) strongly depend on nerve fiber orientation, mq-BOLD derived rOEF is expected to be affected as well. To investigate fiber orientation related rOEF artefacts, we present a methodological study characterizing anisotropy effects of WM as measured by diffusion tensor imaging (DTI) on mq-BOLD in 30 healthy volunteers. Using a 3T clinical MRI-scanner, we performed a comprehensive correlation of all parameters ( $_{T}^{2} *$ , T₂, $R_{2}'$ , rCBV, rOEF, where $R_{2}'$ =1/ $_{T}^{2} *$ –1/T₂) with DTI-derived fiber orientation towards the main magnetic field (B₀). Our results confirm strong dependencies of transverse relaxation and rCBV on the nerve fiber orientation towards B₀, with anisotropy-driven variations up to 37%. Comparably weak orientation-dependent variations of mq-BOLD derived rOEF (3.8%) demonstrate partially counteracting influences of $R_{2}'$ and rCBV effects, possibly suggesting applicability of rOEF as an oxygenation sensitive biomarker. However, unresolved issues warrant caution when applying mq-BOLD to WM.

Keywords

Anisotropy diffusion tensor imaging multi-parametric quantitative BOLD oxygen extraction fraction white matter

Introduction

The oxygen extraction fraction (OEF) is a fundamental marker of cerebral metabolic function, which is widely considered as an important indicator of brain health and tissue viability. For rapid in vivo assessment of regional OEF, the magnetic resonance imaging (MRI) based multi-parametric quantitative BOLD (mq-BOLD) approach is highly promising. In mq-BOLD, three separate measurements are conducted to obtain maps of the relative cerebral blood volume (rCBV) as well as the quantitative transverse relaxation rates $R_{2}^{*}$ and R₂. The rCBV is measured by dynamic susceptibility contrast (DSC) and the relaxation rates by gradient-echo (GRE) ( $R_{2}^{*}$ = 1/ $_{T}^{2} *$ ) and gradient spin-echo (GraSE) MRI (R₂ = 1/T₂). Based on those three parameter-maps, the semi-quantitative relative oxygen extraction fraction (rOEF) is calculated voxel-wisely.^1,2 However, derived values are considered to measure semi-quantitative, relative OEF, as relative CBV instead of venous CBV is used for calculation and obtained values are systematically elevated.¹ Compared to positron emission tomography (PET), the mq-BOLD technique is patient-friendly and easy to apply, as neither ionizing radiation nor arterial blood sampling are required.³ The technique has already been successfully applied in several studies comprising patients with glioma,^4–6 stroke⁷ and carotid artery stenosis.⁸

The mq-BOLD approach is based on a model representing a network of randomly oriented blood vessels by infinite length cylinders that possess homogenous magnetization and infinite length.^1,9 While these model assumptions are reasonable in gray matter (GM), known anisotropy effects in white matter (WM) contradict them. Anisotropy effects primarily arise from the highly oriented myelin sheaths within nerve fibers.¹⁰ Moreover, blood vessels are also expected to contribute to orientation effects,^11,12 because preferential orientation of blood vessels in WM parallel the fiber tracts.^13,14 As corroborated by simulations, the results of Hernández-Torres et al.¹² are in agreement with oriented vessels occupying about one-third of the vascular volume in WM. Thus, mq-BOLD application in highly ordered WM structures raises questions about its reliability.¹ Since WM is particularly affected by many vascular pathologies such as stroke and small vessel diseases,¹⁵ a deeper understanding of factors influencing mq-BOLD-derived rOEF values in WM as high clinical relevance.

Fiber bundles in WM consist of axons, running mainly parallel to each other, being wrapped by myelin. The surrounding myelin sheaths consist of lipid bilayers organized in a lamellar structure with alternating layers of lipid and water.¹⁶ Strong effects of the nerve fiber orientation towards the main static magnetic field (B₀) on effective transverse relaxation are well known and have been investigated extensively^11,16–31 and also demonstrated in the context of DSC-based perfusion imaging.¹² In addition, spin echo-derived T₂ was found to be affected by fiber orientation effects,²⁰ which was attributed to diffusion.¹⁸

Fiber orientation effects have been studied by different methods, including in vitro samples^{20,23,24,26,31} and scanning in different head positions.^11,18 However, determining fiber orientation via diffusion tensor imaging (DTI)³² allows voxelwise correlations with the parameter values,^{11,12,17,19,28,29} and thus appears most suitable for accurate in vivo measurements.

A number of studies attempted to characterize the $_{T}^{2} *$ -related orientation effects employing different models.^{9,16,20,22,24,27,28,31,33,34} Based on analytical modelling of highly aligned parallel cylinders with susceptibility differences to the surrounding tissue, it has been derived that $R_{2}^{*}$ and $R_{2}'$ , defined as $R_{2}^{*}$ –R₂, are modulated by sin²(θ) depending on their angle θ towards B₀.^9,34 However, more detailed experimental analyses of $R_{2}^{*}$ revealed deviations from this sin²(θ) term points to additional influences.^{17,20,24,29,31} This additional component was suspected to arise from susceptibility anisotropy^23,24,35 of myelin³⁰ and modeled by a sin⁴(θ) term.²⁴ To this end, the hollow cylinder fiber model (HCFM) with anisotropic magnetic susceptibility in the annular region was used to represent myelin sheaths surrounding the axons.²⁷ Alternative explanations for the additional orientation influences could be magic angle effects, arising from dipole–dipole interactions, which have been demonstrated in tendons and peripheral nerves with much thicker fiber bundles.³⁶ A detailed study compared both possible explanations and concluded that R₂ and $R_{2}^{*}$ orientation effects most likely originate from anisotropic susceptibility rather than magic angle effects.²⁰

Even though, the orientation effects of $_{T}^{2} *$ , T₂ and DSC-based rCBV in WM are well known, and complex effects on mq-BOLD-derived parameters are expected, their impact on mq-BOLD based rOEF measurements is unclear. Therefore, the aim of our study was to characterize the influence of orientation effects in WM on the calculated parameter values of mq-BOLD derived rOEF. To this end, we performed separate measurements of $_{T}^{2} *$ , T₂ and DSC-based rCBV in 30 healthy volunteers and assessed the angular dependencies of all parameters with respect to the main static magnetic field B₀ using DTI.

Material and methods

Participants

Thirty healthy elderly (17 females; mean age 70.3 ± 4.8 years; see Supplemental Table 1 for more details; normal test results in MMSE, STAI, BDI) participated in this prospective study. Participants were enrolled by word-of-mouth advertisement from May 2015 until May 2017. Examination of every participant included medical history, basic neurological examination and MRI. The study was approved by the medical ethical board of the Klinikum rechts der Isar, in line with Human Research Committee guidelines of the Technical University of Munich. All participants provided informed consent in accordance with the standard protocol approvals. Exclusion criteria for entry into the study were any neurological, psychiatric or systemic disease, clinically remarkable structural MRI (e.g. territorial stroke lesions, bleedings, or a history of brain surgery), severe chronic kidney disease or MR contraindications.

Imaging data acquisition

Scanning was performed on a clinical 3T Philips Ingenia MR-Scanner (Philips Healthcare, Best, The Netherlands) using a 16-channel head/neck-receive-coil. The Omega HP gradients allow a maximum amplitude of 45 mT/m and slew rate of 200 T/m/s. In order to calculate mq-BOLD-derived rOEF, the MRI protocol comprised quantitative mapping of intrinsic and effective transverse relaxation times T₂ and $_{T}^{2} *$ together with DSC MRI for rCBV assessment^37,38 as described previously.¹ T₁-weighted magnetization prepared rapid gradient echo (MPRAGE) and T₂-weighted fluid-attenuated inversion recovery (FLAIR) data were acquired to facilitate brain tissue segmentation and screening for lesions, respectively. Additionally, a contrast-enhanced angiography of the arteries of the neck and the aortic arch was performed to exclude relevant stenoses of the brain supplying arteries. DTI was performed to obtain fiber orientation within WM³⁹ and to assess orientation dependencies of the mq-BOLD related parameters (Figure 1).

Figure 1.

Overview of MRI protocol and derived parameters. DTI was used to derive the rotation matrix M, the main nerve fiber orientation vector-maps $\frac{}{V_{1}}$ and the fractional anisotropy (FA). MPRAGE was used for CSF and WM mask generation. FLAIR was used for structural lesion detection. The rotation matrix M was applied to transform $V_{1}$ vector-maps to the scanner coordinate system resulting in $V'_{1}$ . After application of a mask, selecting only oriented WM and excluding iron artefact related voxels (FA > 0.15, P_CSF < 0.05, P_WM > 0.95, $R_{2}'$ < 15 Hz), the spherical angles ϕ and θ (azimuthal and polar angles, respectively, between the main nerve fiber orientation and B₀) were calculated voxel-wisely (orange). The dependencies of the calculated mq-BOLD-related parameters (green) on ϕ and θ were analyzed in bins of 5°, each for ϕ and θ.

T2*-mapping used a 12 echo gradient echo (GRE) sequence featuring exponential excitation pulses to facilitate correction of magnetic background gradients^40,41 and duplicate acquisition of k-space center for motion correction⁴² with the following imaging parameters: TE₁ = ΔTE = 5 ms, TR = 1950 ms, α = 30°, mono-polar readout, 30 slices, matrix 112 × 92, voxel size 2.0 × 2.0 × 3.0 mm³, total acquisition time 6:08 min.

T2-mapping was based on an eight echo gradient-spin-echo (GraSE) sequence: TE₁ = ΔTE = 16 ms, TR = 8596 ms, echo planar imaging (EPI) factor = 7, 30 slices, gap 0.3 mm, matrix 112 × 91, voxel size 2.0 × 2.0 × 3.0 mm³, acquisition time 2:23 min.

DSC-imaging used dynamic acquisition of 80 single-shot gradient-echo EPI volumes during injection of a weight-adjusted Gd-DOTA bolus (concentration 0.5 mmol/ml, dose 0.1 mmol/kg, at least 7.5 mmol per subject, flow rate 4 ml/s, injection 7.5 s after DSC imaging onset) with TE = 30 ms, TR = 1513 ms, α = 60°, 26 slices, voxel size 2.0 × 2.0 × 3.5 mm³, acquisition time 2:01 min, following the ASFNR recommendations.⁴³

DTI used spin-echo EPI with 32 gradient directions, b = 800 s/mm², TE = 61 ms, TR = 12.9 s, Halfscan = 0.7, SENSE = 2, 60 slices, matrix 112 × 110, voxel size 2.0 × 2.0 × 2.0 mm³, NSA = 2, acquisition time 15:30 min. The DTI field-of-view (FOV) was individually aligned to the interhemispheric gap in the axial plane and tilted in the sagittal plane to exclude the participant's eyes.

Structural imaging comprised MPRAGE (TE = 4 ms, TR = 9 ms, α = 8°, TI = 1000 ms, shot interval 2300 ms, SENSE AP = 1.5, SENSE RL = 2.0, 170 slices, matrix 240 × 238, voxel size 1.0 × 1.0 × 1.0 mm³, acquisition time 5:59 min) and FLAIR (TE = 289 ms, TR = 4800 ms, α = 90°, inversion delay 1650 ms, α = 90°, TSE factor = 167, 163 slices, matrix 224 × 224, voxel size 1.12 × 1.12 × 1.12 mm³, acquisition time 4:34 min). Screening for ischemic brain lesions and grading of white matter hyper-intensities were based on diffusion-weighted imaging and FLAIR. The FLAIR lesions were graded by the Fazekas-score⁴⁴ (Rater: JG).

Data preprocessing and parameter calculation

All processing procedures used FMRIB Software Library⁴⁵ (FSL), SPM12⁴⁶ (Wellcome Trust Centre for Neuroimaging, UCL, London, UK) and custom programs in MATLAB R2016b (The MathWorks, Natick, MA, USA). MPRAGE data were segmented by SPM12 using six tissue classes and default settings for generation of a WM mask by applying a probability threshold of P_WM > 0.95. To reduce influences of partial volume effects, cerebrospinal fluid (CSF) was additionally excluded by applying a threshold of P_CSF < 0.05 (Figure 1).

mq-BOLD parameter maps

Multi-echo GRE data were corrected for macroscopic background gradients^40,41 and motion⁴² and subsequently fitted mono-exponentially for $_{T}^{2} *$ as described previously.¹ Quantitative T₂ parameter maps were derived by mono-exponential fitting of the even-echoes GraSE data to reduce the influence of stimulated echoes.^1,5 $_{T}^{2} *$ -maps were coregistered to the first echo of the T₂ GraSE sequence and visually checked (CP, SK). Both, $_{T}^{2} *$ and T₂ were smoothed with a 3D Gaussian filter-kernel of 3-mm prior to calculation of

R_{2}' = \frac{1}{T 2 *} - \frac{1}{T_{2}}

(1)

Since iron depositions are known to increase $R_{2}'$ , an empirically set threshold of $R_{2}'$ < 15 Hz was applied and carefully checked (CP, SK) to exclude iron induced focal increases of $R_{2}'$ . As macroscopic background, gradients up to about 250 μT/m can be corrected⁴⁰ and areas with higher gradients can also be removed via $R_{2}'$ thresholding,¹ remaining $R_{2}'$ was assumed to mainly reflect subvoxel susceptibility perturbations.¹⁸ DSC data were corrected for leakage contributions based on a reference curve technique⁴⁷ and processed as described previously.^37,38 Accordingly, DSC data were filtered using a 3D Gaussian spatiotemporal filter-kernel of 3-mm full width at half maximum (FWHM) with time as the third dimension. Relative CBV (rCBV) was calculated by first-pass integration of the area under the leakage corrected Δ $R 2^{*}$ (t) curve.³⁷ Subsequently, rCBV was normalized to 2.5% in normal appearing WM.^3,48 Following the mq-BOLD approach,¹ relative oxygen extraction fraction (rOEF) was calculated as

rOEF = \frac{R_{2}'}{c \cdot rCBV}

(2)

where

c = γ \cdot \frac{4}{3} \cdot π \cdot Δ χ \cdot B_{0}

and

B_{0} = 3 T

. Here, Δχ = Δχ₀ · Hct = 0.924 × 10⁻⁷ is the susceptibility difference between oxygenated and deoxygenated blood with the susceptibility difference between fully deoxygenated and fully oxygenated hemoglobin Δχ₀ = 0.264 × 10^{−6 49,50} and the small-vessel hematocrit Hct = 0.35.⁵⁰ The gyromagnetic ratio is γ = 2.675 × 10⁸ s⁻¹ T⁻¹. For quality assessment,

_{T}^{2} *

, T₂, rCBV and rOEF parameter maps were screened especially for motion artefacts (raters CP, SK). Based on these ratings, two subjects were excluded from the final evaluation.

DTI-based fiber orientation mapping

DTI-data were processed using FSL.⁴⁵ Eddy current effects and motion were corrected by the FSL FLIRT toolbox^51,52 and non-brain voxels removed by the FSL brain extraction tool.⁵³ Eigenvalues and corresponding eigenvectors were calculated with the tensor fitting routine of FSL FDT.^54,55 Fractional anisotropy (FA) values were calculated and thresholded at FA > 0.15 to exclude voxels with isotropic structures. We assumed the nerve-fibers to be collinear with the main eigenvector, which is associated with the highest eigenvalue.¹⁰ Thereby, the tensor fitting revealed voxelwise vectors $V_{1}$ describing the main nerve fiber orientation within the coordinate system defined by the DTI-FOV (Figure 2).

Figure 2.

Overview of main nerve fiber vector map calculation and angular transformations. (a) Tensor fitting of the DTI-data within the DTI-FOV coordinate system (DTI_CS, green) revealed the main nerve fiber orientation for each voxel, described by the vector $V_{1}$ corresponding to the largest eigenvalue λ₁. (b) The rotation matrix M, individually derived from the DTI image header for each participant, was applied to transform the $V_{1}$ vector-maps to the MRI-scanner coordinate system (Scanner_CS, orange) resulting in $V'_{1}$ vector-maps. (c) Vector-maps of $V'_{1}$ were transformed to spherical coordinates, yielding the polar angle θ and the azimuthal angle ϕ for each voxel.

Spatial coregistration

For further evaluation, all individual MR images and parameter maps (MPRAGE, tissue segments, $_{T}^{2} *$ -, T₂-, $R_{2}'$ -, rCBV- and rOEF-maps) were spatially coregistered to the individual participant's DTI-data using SPM12 and very carefully checked for transformation-related artefacts by two experienced researchers (CP, SK).

Angulation processing

The orientation information about the DTI-FOV was extracted from the DTI nifti headers. The resulting matrix M describes the rotation between the DTI-FOV and the MR-scanner coordinate system and was applied to the main nerve fiber orientation vectors $V_{1}$ resulting in $V'_{1}$ (Figure 2).^30,56 Thereby, each voxel's $V_{1}$ vector was rotated to the scanner coordinate system with z′ ‖ B₀. Subsequently, $V'_{1}$ vectors were transformed from Cartesian to spherical coordinates. The resulting polar angle θ describes the angulation between the main nerve fiber orientation and B₀. The azimuthal angle ϕ describes the orientation of $V'_{1}$ projected onto the x′-y′-plane (⊥B₀) (Figure 2). As fiber-direction is irrelevant, we analyzed angle ranges from θ = 0° to 90°^11,12,17 and ϕ = −90° to 90°. Further analysis was restricted to oriented WM voxels outside of regions with iron-artefacts or uncorrectable macroscopic magnetic field gradients, defined by FA > 0.15, p_WM > 0.95, p_CSF < 0.05 and $R_{2}'$ < 15 Hz. Within this mask, anisotropy effects of the individual parameters $_{T}^{2} *$ , T₂, $R_{2}'$ , rCBV and rOEF were evaluated in 5° bins. All previously described processing was conducted individually for each participant. On the group-level, median values were calculated within a given angle-bin for each parameter. Standard deviations (SDs) of the parameters were calculated by dividing the SD of all voxels and all participants within a given angle-bin by the square-root of the number of evaluated participants. Histograms of $_{T}^{2} *$ , T₂, $R_{2}'$ , rCBV and rOEF maps vs. θ and ϕ were prepared using median values and SDs across all oriented WM voxels from all participants.

Fitting model

Recently, Lee et al.²⁴ proposed a model for highly aligned networks of parallel fibers including anisotropy of magnetic susceptibility to describe $R_{2}^{*}$ orientation effects depending on the polar angle θ. According to that, the orientation dependence of the measured signal was fitted by

S (θ) = c_{0} + c_{1} sin (2 θ + φ_{0}) + c_{2} sin (4 θ + φ_{1})

(3)

with the orientation-independent coefficient c₀, the two orientation-dependent coefficients c₁ and c₂ and two sinusoidals to account for highly non-random, non-isotropic perturber distributions and magnetic susceptibility anisotropy. The model can be applied to R₂(θ)²⁰ and

R_{2}'

(θ).³⁴ In this work, we also analyzed whether this model is capable to describe rCBV(θ) and rOEF(θ) orientation effects. All fits were performed by the least-square curve fitting routine ‘lsqcurvefit’ (MATLAB R2016b, The MathWorks, Natick, MA, USA) with default settings.

Results

The calculated maps of the polar angle θ and azimuthal angle ϕ show excellent agreement with the expected fiber tract directions as demonstrated in Figure 3, showing data from a prototypical participant (see Supplemental Figure 1 for more details).

Figure 3.

Exemplary parameter maps of a healthy volunteer in one axial slice. $T 2 *$ (a), T₂ (b), rCBV (c), rOEF (d), MPRAGE (e), FA (f), the polar angle θ (g) and the azimuthal angle ϕ (h) overlaid on MPRAGE. The mask of oriented WM was already applied to the orientation maps (g, h). Fibers in FH-direction correspond to θ = 0° in case of small DTI-FOV angulations. Fibers in AP-direction correspond then to θ = 90° and ϕ = ±90°. Fibers in LR-direction correspond to θ = 90° and ϕ = 0°.

On group level, $_{T}^{2} *$ median values strongly depended on θ with $_{T}^{2} *$ (θ) ranging from 48.2 ms to 54.7 ms, which corresponded to an absolute difference of Δ $_{T}^{2} *$ (θ) = 6.5 ms and a variation of 13.5% between fibers parallel and perpendicular to B₀ (Figure 4(a)). Accordingly, $R_{2}^{*}$ (θ) median values were measured within the range of $R_{2}^{*}$ (θ) = [18.3–20.8] Hz and Δ $R_{2}^{*}$ (θ) = 2.5 Hz (data not shown). Analysis of T₂ revealed an angulation-dependent range of median values T₂(θ) = [78.4–84.3] ms corresponding to ΔT₂(θ) = 5.9 ms and a variation of 7.5% (Figure 4(c)) or ΔR₂(θ) = 0.9 Hz (data not shown). Both, $_{T}^{2} *$ and T₂ were almost independent of the orientation within the plane perpendicular to B₀, described by the azimuthal angle ϕ (Figure 4(b) and (d)). $R_{2}'$ yielded a θ-dependent range of median values $R_{2}'$ (θ) = [6.5–8.2] Hz corresponding to a variation of 26.5% (Figure 5(a)). Relative CBV median values varied between rCBV(θ) = [2.0–2.8]%, representing a variation of 37.1% (Figure 5(c)). The resulting range of rOEF median values was rOEF(θ) = [0.94–1.09] corresponding to a variation of 15.0% between lowest and highest values (Figure 5(e)). Similar to $_{T}^{2} *$ and T₂, the median values of $R_{2}'$ , rCBV and rOEF were almost independent of ϕ (Figure 5(b), (d) and (f)).

Figure 4.

Orientation dependencies of $T 2 *$ and T₂ on group level. The dependencies of $T 2 *$ (a, b) and T₂ (c, d) on polar angle θ (a, c) and azimuthal angle ϕ (b, d) are depicted (median across all participants ± SD). Parameter values were evaluated within 5° bins. The plots show a clear orientation dependency of $T 2 *$ (a) and T₂ (c) on θ, which describes the fiber orientation relative to B₀. As expected, no major angle dependencies of any parameter were observed in the x′-y′ plane perpendicular to B₀ (b, d).

Figure 5.

Orientation dependencies of $R_{2}'$ , rCBV and resulting rOEF on group level. Plots of $R_{2}'$ (a, b), rCBV (c, d) and rOEF (e, f) are shown (median across all participants ± SD) depending on the polar angle θ (a, c, e) and the azimuthal angle ϕ (b, d, f). Parameter values were evaluated within 5 ° bins. $R_{2}'$ was derived from $T 2 *$ and T₂ and shows strong orientation dependence on θ (a). Relative CBV shows a similar behavior with an even stronger dependence on θ (c). As rOEF is proportional to the ratio of $R_{2}'$ and rCBV (equation (2)), the resulting anisotropy artefacts of rOEF are driven by the different slopes of $R_{2}'$ (a) and rCBV (c). Thereby, rOEF shows a lower dependency on θ (e). In the x′-y′ plane perpendicular to B₀, no major angular dependency effects were observed (b, d, f).

Figure 6.

Histograms of the numbers of contributing voxels depending on the polar angle θ and the azimuthal angle ϕ. The dotted blue line represents the average number of measured voxels per participant depending on θ (a). For comparison, the solid black line indicates equally populated orientations (a). The average number of voxels per participant depending on ϕ, perpendicular to B₀, is shown by the red dotted line and compared to the mean of all voxels, represented by the solid black line (b).

The distribution of the number of voxels within oriented WM contributing to the presented median values within the θ bins of 5° was well described by a sinusoidal curve (Figure 6(a)), indicating that fiber orientations towards the main magnetic field are almost homogenously distributed within the investigated volumes. Conversely, the voxel distribution depending on the azimuthal angle ϕ was almost constant, also indicating a homogenous distribution, with a slight preference for left-right and anterior-posterior orientations (Figure 6(b)).

Although the Fazekas-scores revealed a mean of 1.0 ± 0.9 (range 0–3, for details see Supplemental Table 1) indicating minor microangiopathic changes, none of the participants had subacute or older territorial infarct lesions. Including participants with Fazekas-scores above 1 had no obvious effect on the observed orientation dependencies (Supplemental Figure 2). Separate evaluations of the data from female and male participants did not reveal significant effects of gender on rOEF(θ) (Supplemental Figure 3). Additional measurements of $_{T}^{2} *$ , T₂ and DTI in a small cohort of young healthy controls provided evidence that observed orientation dependencies were not influenced by age (Supplemental Figure 4).

Fitting of Lee's model (equation (3)) to the median values of $_{T}^{2} *$ (θ) revealed excellent agreement (R² > 0.999, Figure 7(a)), with the two fitted sinusoidal components being incoherent in phase (Figure 7(b)). Accordingly, fitting of $R_{2}^{*}$ (θ) revealed c₀ = 19.54 Hz, c₁ = 1.11 Hz, Φ₀ = 67.33°, c₂ = 0.07 and Φ₁ = 0.61° (data not shown). Applying the same model (equation (3)) to T₂(θ), $R_{2}'$ (θ) and rCBV(θ) median values, showed excellent agreement (R² > 0.997, Figure 7(c) to (f)) as well. Even fitting of rOEF(θ) shows very good agreement to Lee's model (equation (3)) (R² > 0.991, Figure 7(f)).

Figure 7.

Fittings of all mq-BOLD-related parameters. All parameters were fitted with the same function (equation (3)). Median values on group-level and SDs are shown in blue, fitted curves are indicated by dashed orange lines. The fit parameters are noted in the red framed boxes (a, c–f). Analysis of the two sinusoidal fit components of $T 2 *$ shows phase incoherence (b). All fittings of $T 2 *$ (a), T₂ (C), $R_{2}'$ (d), rCBV (e) and rOEF (f) reveal excellent agreement with sum-of-squared-errors R² > 0.99.

Discussion

In this study, we presented a DTI-based quantitative orientation analysis method using an automated coordinate system transformation to spherical coordinates and applied it to characterize anisotropy effects of mq-BOLD related parameter maps in WM. Orientation effects were measured for multiple parameters, namely $_{T}^{2} *$ , T₂, rCBV and rOEF. Using DTI-derived nerve fiber orientations, tissue orientation effects were quantified along the polar angle θ towards B₀. Observed dependencies of $_{T}^{2} *$ (θ), T₂(θ) and rCBV(θ) are in excellent agreement with the literature.^{11,12,17–21,24,28,29} In addition, orientation effects of rOEF(θ) were demonstrated and quantified. All observed angular dependencies could be well described by fitting a model including susceptibility anisotropy (equation (3)) in good agreement with previous reports.^{20,21,24,28,29} Contrary to intuition, the impact of WM orientation on calculated parameter values of rOEF is comparably weak because contributions of $R_{2}'$ and rCBV partly compensate.

Influence of WM orientation on T $2 *$

Our measured differences Δ $_{T}^{2} *$ (θ) = 6.5 ms or Δ $R_{2}^{*}$ (θ) = 2.5 Hz fully agree with previously reported in vivo measurements.^{11,17–21,24,28,29} The details of $_{T}^{2} *$ (θ) and $R_{2}^{*}$ (θ) angular dependencies (Figure 4(a)) resemble those observed in previous studies.^11,28,29 Though, our measured $_{T}^{2} *$ (θ) dependency appears more pronounced than demonstrated by Denk et al.,¹⁷ which might be explained by our improved, automated coordinate system transformation and rigorous thresholding to exclude artefacts.

The major contributors to anisotropy effects driving orientation dependencies of effective transverse relaxation are still under discussion. Most likely, the angular dependencies are caused by sub-voxel susceptibility effects arising from anisotropic sources, namely highly ordered myelin-fiber structures^{12,17–24,57} and effects of oriented WM vasculature^11,12,22 being preferentially aligned parallel to axonal-fibers.^12–14

Lee's model (equation (3)) includes highly oriented cylinders, which can represent the fibers and vessels, as well as anisotropic susceptibility in the annular region, representing myelin.²⁴ Fitting Lee's model (equation (3)) to $_{T}^{2} *$ (θ) reveals excellent agreement (Figure 7(a)) in accordance with the literature.^20,24,29,57 While the fitted $_{T}^{2} *$ (θ) curve closely resembles the data, we did not observe phase coherence of the two sinusoidal components (Figure 7(b)), which represent influences by highly non-random, non-isotropic perturbers and magnetic susceptibility anisotropy, in contrast to Lee et al.²⁴ Other studies applied a similar model without sinusoidal phase shifts to $R_{2}^{*}$ (θ), yielding very similar results.^29,57 Our results are, therefore, in accordance with assuming major contributions to $_{T}^{2} *$ (θ) orientation effects from highly ordered myelinated fiber structures and the vasculature.

Influence of WM orientation on T₂

We also observed a strong T₂(θ) orientation effect with ΔT₂(θ) ≈ 6 ms or ΔR₂(θ) ≈ 1 Hz in accordance with Oh et al.²⁰ Minor discrepancies to their ex vivo study can be explained by cell swelling as well as further molecular changes¹⁸ in their formalin fixed tissue samples scanned at room temperature, which also influences the transverse relaxation rates.²⁰ Moreover, their study was conducted at 7T and they averaged over larger ROIs without actually measuring fiber orientation. While orientation dependencies can be expected to be more prominent at higher field strength, the latter rather decreases the observed effects.

Regarding origins of T₂(θ) orientation effects, contributions from susceptibility effects are actually expected to be minimized by the GraSE refocusing pulses, in contrast to GRE-based $_{T}^{2} *$ mapping.²⁰ However, mediated by diffusion, the same susceptibility gradients causing $_{T}^{2} *$ decay are expected to decrease T₂.^18,20 The signal decay due to diffusion of spins through inhomogeneous magnetic fields can be modeled with the Carr-Purcell method by adding a diffusion term to the intrinsic spin-spin dephasing. This additional exponential term, representing the signal decay due to diffusion, can be approximated by a Taylor expansion resulting in a sum of sin(2θ) and sin(4θ) terms. For a rough estimate of diffusion effects on T₂(θ), we rely on Le Bihan et al.,¹⁰ who analyzed anisotropic diffusion in WM⁵⁸ and found diffusion perpendicular to nerve fibers to be impeded by approximately 60%. Based on this, the maximum strength of the GraSE sequence's readout gradients (≈20 mT/m) could well explain T₂ orientation effects within the observed range. Since fitting of Lee's model (equation (3)) to T₂(θ) shows excellent agreement (Figure 7(c)), it appears reasonable to attribute dependencies of T₂ on θ to diffusion effects.

Application of Lee's model (equation (3)) to T₂(θ) was further supported by Oh et al.,²⁰ who compared the anisotropic susceptibility model with pure magic angle effects of R₂(θ) as well as a model of isotropic susceptibility in superposition with magic angle effects. In agreement with their data, pure magic angle effects cannot explain our measured T₂(θ) dependency (see Figure 7(c)). In general, our fittings of $_{T}^{2} *$ and T₂ resemble their findings. However, as differences of the models including higher order terms are very subtle, we cannot exclude some additional influences of magic angle effects based on our data.

Influence of WM orientation on $R_{2}'$

Since, in our approach, $R_{2}'$ (θ) is calculated from $_{T}^{2} *$ and T₂ (equation (1)), a strong orientation effect of approximately 27% was found, according to expectations (Figure 5(a)). Again, fitting of the model (equation (3)) is in excellent agreement with the measured $R_{2}'$ (θ) dependency (Figure 7(d)).

Influence of WM orientation on rCBV

As could be expected from the fact that DSC-MRI is based on $_{T}^{2} *$ -weighted EPI, our measurements revealed a pronounced dependency of rCBV on θ. This dependency is characterized by an almost angulation independent section for θ = [0°–15°] followed by a steep increase of rCBV for θ = [15°–90°] (Figure 5(c)). These findings are in full accordance with a previous study by Hernández-Torres et al.,¹² who analyzed DSC-based rCBV with a very similar methodology. The authors concluded anisotropic vascular architecture to significantly contribute to the observed CBV orientation effects, as histological staining demonstrated blood vessels running preferentially parallel to WM fibers.^13,14 Furthermore, via simulations they found evidence that one-third of the WM vascular volume is comprised of vessels aligned to the fiber tracts.¹²

Again, fitting Lee's model (equation (3)) to rCBV(θ) revealed excellent agreement (Figure 7(e)). Interestingly, the ratio of the orientation-dependent fit coefficients c₁ and c₂ to the orientation independent coefficient c₀ is much higher for the rCBV(θ) fitting compared to $_{T}^{2} *$ (θ) and T₂(θ) (Figure 7(a), (c) and (e)). This is related to the very strong orientation dependence of rCBV(θ) (≈37%) and implies enhanced effects due to oriented vasculature in contrast agent-based DSC-imaging.

Distribution of orientations

Even though the subvoxel WM structures are highly anisotropic, as indicated by high FA values within oriented WM (Figure 3), the orientations across all WM voxels are almost equally populated (Figure 6). Regarding the polar angle θ, measured voxel distributions closely resemble a sinusoidal shape, representing equal populations (Figure 6(a)). Those results are in accordance with data from a similar approach by Denk et al.¹⁷ However, our results are even closer to equal population, which might be due to different FA thresholds, our additional WM and CSF thresholds, larger sample size, higher number of DTI gradient directions and improved, automated coordinate transformation. Analysis of the voxel distribution with respect to the azimuthal angle ϕ reveals almost equal population, too (see Figure 6(b)). However, angles around ϕ = 0° and ϕ = ±90° tend to be somewhat higher populated indicating a slight preference for fiber orientations in right-left and anterior–posterior orientations. Those findings are in accordance with DTI and histological examination of highly ordered structures such as the corpus callosum.⁵⁹

Previous studies analyzing orientation effects by voxel-wise parameter correlations with DTI investigated either only the polar angle^12,17,29 or showed somewhat contra intuitive dependencies on the Euler angles relative to the x-axis and y-axis.¹¹ Those uncertainties could be resolved in our study by introducing spherical coordinates to describe the fiber orientation within the scanner coordinate system. Overall, the distribution of orientations underlines the successful implementation of the introduced automated coordinate system transformation. Moreover, it strongly indicates the validity of our DTI-based orientation analysis.

Influence of WM orientation on rOEF

A pronounced dependence of mq-BOLD-derived rOEF on θ was expected, since the contributing parameters $R_{2}'$ and rCBV demonstrate a distinct anisotropy in WM. However, the observed variation between lowest and highest values of 15% is rather weak compared to the strong variations of $R_{2}'$ (θ) (≈27%) and rCBV(θ) (≈37%). Interestingly, rOEF(θ) shows an angular dependency that appears distinctly different from the $R_{2}'$ (θ) and rCBV(θ). This is due to counteracting influences of $R_{2}'$ and rCBV, causing rOEF orientation artefacts to depend on their different slopes in the ratio of $R_{2}'$ (θ) and rCBV(θ) (equation (2)) (Figure 5(a), (c) and (e)). Moreover, a closer analysis reveals that average orientation induced variation of rOEF(θ) is rather low when accounting for the voxel distribution depending on θ. The highest orientation induced variation of rOEF(θ) was observed at low angles θ < 30° (Figure 5(e)), which actually corresponds to a small fraction of voxels (Figure 6(a)). Thus, the average variation, calculated via bin-wise deviations from the overall mean rOEF and weighting by the number of voxels within each angle-bin, is 3.8%. Those findings imply that mean values of WM rOEF are only weakly affected by orientation effects. Interestingly, fitting Lee's model (equation (3)) to rOEF(θ) shows good agreement (Figure 7(f)) even if the underlying orientation effects of $_{T}^{2} *$ , T₂ and rCBV are expected to arise from different origins and form complex superpositions within the mq-BOLD model (equation (2)).

Possible limitations

Values of rOEF derived by mq-BOLD are systematically elevated, as previously reported.^1,4,7,60 Furthermore, WM values (average rOEF_WM = 0.94) are elevated compared to GM values (average rOEF_GM = 0.60; for more details, see Supplemental Table 2). This contradicts PET-based OEF measurements, and primarily arises from systematic errors of the mq-BOLD method. While approximating the venous CBV by total DSC-based CBV certainly contributes to GM-WM contrast, systematic bias in T₂ measurement mainly causes general overestimation.¹ Improved quantitative T₂ mapping has already been demonstrated to statistically significantly reduce rOEF elevations towards lower, physiologically more realistic values.⁶¹ In this study, we could demonstrate that orientation effects do not primarily contribute to neither rOEF elevations nor the GM-WM contrast. Despite of this and successful applications of mq-BOLD in different pathologies,^1,4,7,60 future studies are necessary to further validate and improve the method. Furthermore, observed diffusion-dependent T₂(θ) orientation effects indicate that the assumption of static dephasing in mq-BOLD might be violated. In any case, caution should be exercised when evaluating rOEF by mq-BOLD in WM. To minimize detrimental influences of unphysiological GM-WM contrast, mq-BOLD evaluations should not mix values from GM and WM.

Generally, the large variations of $_{T}^{2} *$ , T₂ and $R_{2}'$ values and error propagation due to mq-BOLD modeling² limit the ability to differentiate between the different origins of anisotropy (see Appendix 1). The observed non-orientation-dependent parameter variations can be explained by further factors influencing transverse relaxation such as insufficiently corrected macroscopic magnetic background gradients, myelination and non-heme iron content or physiological differences.^11,17 Nevertheless, orientation effects of all investigated parameters could be clearly extracted by the presented methodology of automated coordinate system transformation, rigorous thresholding and averaging of all participant's data to minimize potential systematic errors.

Further limitations may apply. Measurements of $_{T}^{2} *$ and T₂ are known to depend on the echo sampling.^62,63 In addition, mono-exponential fitting to compute $_{T}^{2} *$ - and T₂-maps is a simplification as multi-compartmental effects in WM are well known.^18,27,28,64 But even if multi-exponential relaxation was contributing, our analysis depicts the dominant term.

Influences of age and WM pathology on the observed orientation effects may be suspected. To limit application of contrast agent in DSC-imaging, we investigated orientation effects in the elderly control group, which was also acquired for a physiological MRI study.⁸ Additional control analyses revealed that higher Fazekas-scores of some of our elderly participants have no obvious impact on the observed orientation effects (Supplemental Figure 2). This is in accordance with Haller et al. who concluded that periventricular FLAIR hyperintensities are in many cases not associated with demyelination.⁶⁵ In order to control for age effects on $_{T}^{2} *$ (θ), T₂(θ) and R₂(θ) orientation dependencies, we compared the presented data to those of young healthy participants and found the same orientation dependencies, independent of age (Supplemental Figure 4).

Anisotropy effects of oriented susceptibility perturbations also depend on the magnetic field strength, where we expect stronger orientation dependencies with increasing B₀. Furthermore, sequence-dependent influences may for example arise from the voxel size, as the aspect ratio in GRE was found to affect the sensitivity to veins and may thereby also influence measured orientation dependencies.¹⁷

Another potential limitation is the scanning at only one head orientation. However, in vivo scanning at different head positions is experimentally very challenging and limited on both, reachable angles and the number of scanned angles.¹⁷ In contrast, our investigation of tissue orientation effects based on analysis of DTI-data requires scanning at only one head position while deriving precise information about voxel-wise fiber orientations. Even though errors of DTI-based fiber orientation mapping induced by crossing fibers within single voxels cannot be corrected with the presented methodology,³² thresholding of FA values reduced errors by excluding isotropic voxels.

A disadvantage of the DTI-based method may arise from patient movement between the mq-BOLD and the DTI acquisitions, but careful immobilization of the participant's head with foam pads and image coregistration could minimize motion-related errors. But in spite of careful inspection, small misalignments after coregistration cannot be ruled out completely. Nevertheless, the validity of the results is strongly supported by the excellent agreement of θ dependent fittings with previous studies.

Analysis of orientation effects assumes B₀ to be parallel to the z′-axis in our as well as previous studies.^{11,12,17,28,29} However, magnetic field inhomogeneities, shimming and measurements off the iso-center may violate this assumption. Nevertheless, analysis of the azimuthal angle ϕ revealed independency on the fiber orientation perpendicular to B₀, strongly indicating correct orientation analyses and generally high consistency of the presented data.

Partial volume effects are another potential error source affecting both, DTI orientation analysis and the mq-BOLD parameter estimates. However, those influences could be reduced by rigorous application of individual oriented WM masks excluding CSF.

Impact of orientation effects

Tissue microstructure orientation effects may have far reaching consequences on many MRI parameters in WM. While we demonstrated mq-BOLD-derived rOEF to be only moderately affected by WM orientation effects, $_{T}^{2} *$ , T₂, $R_{2}'$ and rCBV strongly depend on the orientation. Moreover, orientation effects in WM are also known to affect arterial spin labeling and functional connectivity imaging.⁶⁶ Due to pial vessels orientation effects in the cortex, orientation dependencies were shown in GM, too.⁶⁷ Pathologies affecting the vessel architecture or the myelinisation may have additional influences, also by changing orientation effects regionally. This needs to be considered, especially when comparing different brain regions or hemispheres.

A promising method to further disentangle orientation effect origins by myelinated nerve fibers and oriented vessels is cortical surface modeling of GM.⁶⁷ Veins can be modelled depending on the cortical surface orientation to exclusively characterize vessel-related orientation effects.

Conclusion

Our results demonstrate reliable in vivo characterization of WM anisotropy effects in mq-BOLD imaging with high sensitivity at reasonable scan time. We confirmed strong dependencies of transverse relaxation and rCBV on the nerve fiber orientation towards B₀. In contrast, observed orientation effects in rOEF values are comparably low in our healthy, elderly cohort indicating an average orientation induced variation of 3.8%. This is due to a partial compensation of anisotropy effects in $R_{2}'$ and rCBV and indicates rather minor influences of orientation effects on mq-BOLD-derived rOEF in WM. In any case, caution should be exercised when evaluating mq-BOLD-derived rOEF in WM and further mq-BOLD validations are clearly necessary.

Supplemental Material

Supplemental Material1 - Supplemental material for Characterizing white matter fiber orientation effects on multi-parametric quantitative BOLD assessment of oxygen extraction fraction

Supplemental material, Supplemental Material1 for Characterizing white matter fiber orientation effects on multi-parametric quantitative BOLD assessment of oxygen extraction fraction by Stephan Kaczmarz, Jens Göttler, Claus Zimmer, Fahmeed Hyder and Christine Preibisch in Journal of Cerebral Blood Flow & Metabolism

Supplemental Material

Supplemental Material2 - Supplemental material for Characterizing white matter fiber orientation effects on multi-parametric quantitative BOLD assessment of oxygen extraction fraction

Supplemental material, Supplemental Material2 for Characterizing white matter fiber orientation effects on multi-parametric quantitative BOLD assessment of oxygen extraction fraction by Stephan Kaczmarz, Jens Göttler, Claus Zimmer, Fahmeed Hyder and Christine Preibisch in Journal of Cerebral Blood Flow & Metabolism

Supplemental Material

Supplemental Material3 - Supplemental material for Characterizing white matter fiber orientation effects on multi-parametric quantitative BOLD assessment of oxygen extraction fraction

Supplemental material, Supplemental Material3 for Characterizing white matter fiber orientation effects on multi-parametric quantitative BOLD assessment of oxygen extraction fraction by Stephan Kaczmarz, Jens Göttler, Claus Zimmer, Fahmeed Hyder and Christine Preibisch in Journal of Cerebral Blood Flow & Metabolism

Supplemental Material

Supplemental Material4 - Supplemental material for Characterizing white matter fiber orientation effects on multi-parametric quantitative BOLD assessment of oxygen extraction fraction

Supplemental material, Supplemental Material4 for Characterizing white matter fiber orientation effects on multi-parametric quantitative BOLD assessment of oxygen extraction fraction by Stephan Kaczmarz, Jens Göttler, Claus Zimmer, Fahmeed Hyder and Christine Preibisch in Journal of Cerebral Blood Flow & Metabolism

Supplemental Material

Supplemental Material5 - Supplemental material for Characterizing white matter fiber orientation effects on multi-parametric quantitative BOLD assessment of oxygen extraction fraction

Supplemental material, Supplemental Material5 for Characterizing white matter fiber orientation effects on multi-parametric quantitative BOLD assessment of oxygen extraction fraction by Stephan Kaczmarz, Jens Göttler, Claus Zimmer, Fahmeed Hyder and Christine Preibisch in Journal of Cerebral Blood Flow & Metabolism

Footnotes

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the Friedrich-Ebert-Stiftung (grant to SK), the Dr.-Ing. Leonhard Lorenz-Stiftung (grant to JG: 915/15), by the Faculty of Medicine of the Technical University of Munich (grant to JG: KKF E12), by a postdoc fellowship of the German Academic Exchange Service (DAAD) (grant for JG) and the German Research Foundation (DFG) – Project number PR 1039/6-1 (grant to CP). FH was supported by NIH grants (R01 MH-067528, R01 NS-100106, P30 NS-052519).

Acknowledgements

We thank Andreas Hock (Philips Healthcare, Hamburg, Germany) for his support with the DTI orientation transformation.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Author's contributions

SK: study design, data acquisition, data analysis, interpretation of the results, manuscript writing.

JG: data acquisition, data analysis, interpretation of the results, manuscript editing.

CZ: study design, study supervision.

FH: interpretation of the results, manuscript editing.

CP: study design, study supervision, interpretation of the results, manuscript editing.

Supplemental material

Supplemental material for this paper can be found at the journal website:

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Supplementary Material

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Characterizing white matter fiber orientation effects on multi-parametric quantitative BOLD assessment of oxygen extraction fraction

Abstract

Keywords

Introduction

Material and methods

Participants

Imaging data acquisition

Data preprocessing and parameter calculation

mq-BOLD parameter maps

DTI-based fiber orientation mapping

Spatial coregistration

Angulation processing

Fitting model

Results

Discussion

Influence of WM orientation on T 2 *

Influence of WM orientation on T2

Influence of WM orientation on R 2 '

Influence of WM orientation on rCBV

Distribution of orientations

Influence of WM orientation on rOEF

Possible limitations

Impact of orientation effects

Conclusion

Supplemental Material

Supplemental Material1 - Supplemental material for Characterizing white matter fiber orientation effects on multi-parametric quantitative BOLD assessment of oxygen extraction fraction

Supplemental Material

Supplemental Material2 - Supplemental material for Characterizing white matter fiber orientation effects on multi-parametric quantitative BOLD assessment of oxygen extraction fraction

Supplemental Material

Supplemental Material3 - Supplemental material for Characterizing white matter fiber orientation effects on multi-parametric quantitative BOLD assessment of oxygen extraction fraction

Supplemental Material

Supplemental Material4 - Supplemental material for Characterizing white matter fiber orientation effects on multi-parametric quantitative BOLD assessment of oxygen extraction fraction

Supplemental Material

Supplemental Material5 - Supplemental material for Characterizing white matter fiber orientation effects on multi-parametric quantitative BOLD assessment of oxygen extraction fraction

Footnotes

Funding

Acknowledgements

Declaration of conflicting interests

Author's contributions

Supplemental material

References

Supplementary Material

Influence of WM orientation on T $2 *$

Influence of WM orientation on T₂

Influence of WM orientation on $R_{2}'$