Spin-lock imaging of intrinsic susceptibility gradients in tumors

Abstract

Purpose:

Previous studies have shown that diffusion of water through intrinsic susceptibility gradients produces a dispersion of the spin-lattice relaxation rate in the rotating frame (R₁) over a low range of spin-locking amplitudes (0 < ω₁ < 100 Hz), whereas at higher ω₁ and high magnetic fields a second dispersion arises due to chemical exchange. Here, we separated these different effects and evaluated their contributions in tumors.

Methods:

Maps of R_1ρ and its changes with locking field were acquired on intracranial 9L tumor models. R_1ρ changes due to diffusion (R_1ρ^Diff) were calculated by subtracting maps of R_1ρ at 100 Hz (R_1ρ(100Hz)) from those at 0 Hz (R_1ρ(0Hz)). R_1ρ changes due to exchange (R_1ρ^Ex) were calculated by subtracting maps of R_1ρ at 5620 Hz (R_1ρ(5620Hz)) from those of R_1ρ at 100 Hz (R_1ρ(100Hz)). Measurements of vascular dimensions and spacing were performed ex vivo using three-dimensional confocal microscopy.

Results:

R_1ρ changes at low ω₁ in tumors (5.24±1.78s⁻¹) are substantially (p=3.7e-06) greater than those in normal tissues (1.36±0.70s⁻¹), which we suggest is due to greater contributions from diffusion through susceptibility gradients. Tumor vessels were larger and spaced less closely compared to normal brain, which may be one factor contributing the susceptibility within 9L tumors. The contrast between tumor and normal tissues for R_1ρ^Diff is larger than for R_1ρ^Ex and for the apparent R_2w.

Conclusion:

Images sensitive to the variations of spin-lock relaxation rates at low ω₁ provide a novel form of contrast that reflects the heterogeneous nature of intrinsic variations within tumors.

INTRODUCTION

Magnetic susceptibility variations within tissues can be induced by several agents including deoxyhemoglobin, calcifications, or iron deposits (1). The effects of changes in susceptibility on magnetic resonance images can be used to differentiate tissues with different vascularity or oxygenation, or those affected by other paramagnetic agents. Previously, tissue susceptibility effects have been assessed by their effects on the transverse relaxation rate R_2w* (2–4) or by susceptibility weighted imaging (SWI) (5–7), while dynamic susceptibility contrast-enhanced MR perfusion imaging (DSC-MRI) (8–10) has been used to exploit the effects of exogenous susceptibility agents. Recently, we performed finite-difference simulations (11) and experiments on samples containing beads (12) mimicking tissue local magnetic field variations as well as red blood cell suspensions (13) and showed that spin-lock sequences with low locking amplitudes (ω₁) are sensitive to the effects of susceptibility inhomogeneities to a degree that depends on the locking field and the spatial scale of the inhomogeneities. We derived theoretical expressions describing how water self-diffusion through intrinsic susceptibility gradients produces a dispersion of the spin-lattice relaxation rate in the rotating frame (R_1ρ) over a range of locking field amplitudes (11–14). Judicious selection of locking powers and combinations of data acquired with different powers can isolate the susceptibility effects from other non-susceptibility related effects, and potentially can be used to describe the scale and magnitude of intrinsic susceptibility gradients (11–13). Based on these previous studies in model systems, we propose that spin-locking at low amplitudes may be used to detect differences in tissues that reflect inhomogeneous susceptibility effects in vivo.

Many solid tumors are characterized by abnormal blood vessel organization and structure, often accompanied by increased vascularity (15) and variations in oxygenation (16,17) which are known to produce different intrinsic susceptibility gradients compared with those in normal tissues. Interest in characterizing such abnormal vasculature has spurred the development of techniques such as vessel size imaging (18) and blood oxygenation level dependent (BOLD) imaging of tumors (19–23). Here we report the results of spin-locking at low amplitudes in 9L rat brain tumors in vivo and interpret these in terms of differences in the magnitudes and spatial characteristics of susceptibility gradients within tumors compared to normal tissues.

METHODS

Contributions to R_1ρ

In biological tissues, R_1ρ can be expressed as the superposition of different terms (13),

$$R_{1\rho }\approx R_{1\rho }^{\mathit{\text{Diff}}}+R_{1\rho }^{Ex}+R_{2\text{w}}$$ (1)

where R_1ρ^Diff and R_1ρ^Ex are the relaxation rates due to diffusion through susceptibility gradients and chemical exchange effects, respectively. Values of R_1ρ decrease with the amplitude of the locking field, which is referred to as R_1ρ dispersion. The time scales of the exchange and diffusion processes are significantly different, so their dispersions occur over different ranges of ω₁. R_2w is the tissue water intrinsic transverse relaxation rate which is due mainly to dipolar relaxation effects and is largely independent of ω₁ (24). These different dependencies on ω₁ provide a means to separate them by judicious selection of ω₁ and by combination of data acquired with different ω₁.

In a complex medium the local magnetic field varies in space but may be characterized by an effective spatial frequency q that describes the mean scale of the variations (11,13). R_1ρ^Diff depends on q as well as the mean gradient strength (g) and the self-diffusion coefficient (D) (11,13).

$$R_{1\rho }^{\mathit{\text{Diff}}}=\frac{{\gamma }^2{g}^{2}D}{{(q^{2}D)}^2+{\omega }_1^2}$$ (2)

where γ is the gyromagnetic ratio. Eq. (2) indicates that R_1ρ^Diff depends not only on the mean gradient strength (which is the main factor that affects the signals measured by other susceptibility imaging methods) but also on the spatial frequency characteristic of the inhomogeneous magnetic field which in tissue reflects intrinsic microstructural inhomogeneities and, potentially, vascular geometry.

Note that R_1ρ^Diff decreases from a value γ²g²D/(q²D)² at ω₁ = 0 to half as much over the range 0 to ω₁ = q²D and to a quarter as much over the range 0 to ${\omega }_1=\sqrt{3}{q}^{2}D$. Thus by identifying the degree to which R_1ρ^Diff decreases over a range of locking fields, the value of q²D can be derived, and from that g may also be estimated. Moreover, to reasonable approximation we can model q as representing magnetic field variations caused by inhomogeneities of size R ≈ π/q.

Quantifying R_1ρ^Diff and R_1ρ^Ex

Previous studies and theoretical projections indicate that the contribution to R_1ρ from diffusion in intrinsic gradients induced by relevant tissue inhomogeneities (e.g. cells, capillaries, other microstructures) should be negligible at locking frequencies ω₁ beyond roughly 100 Hz (for example, according to Eq. (2), R_1ρ^Diff is reduced to under 10% of its value at ω₁ = 0 at ≈ 20 Hz for anything larger than R = 7 μm, and at ≈ 100 Hz for larger than R = 3 μm) and the R_1ρ dispersion (the change of R_1ρ values with varying ω₁) due to chemical exchange effects is very weak below ω₁ of 100 Hz (14). Here we choose two different ω₁ to quantify the ranges of R_1ρ^Diff and R_1ρ^Ex, respectively;

$$R_{1\rho }^{\text{Diff}}=R_{1\rho }(0Hz)-R_{1\rho }(100Hz)$$ (3)

$$R_{1\rho }^{\text{Ex}}=R_{1\rho }(100Hz)-R_{1\rho }(5620Hz)$$ (4)

where,

$$R_{1\rho }(0Hz)={R_{1\rho }|}_{{\omega }_1=0Hz},R_{1\rho }(100Hz)={R_{1\rho }|}_{{\omega }_1=100Hz},R_{1\rho }(5620Hz)={R_{1\rho }|}_{{\omega }_1=5620Hz}$$

5620 Hz is the highest power we can readily achieve on our MRI system, which is used to make R_1ρ relatively insensitive to the effects of chemical exchange. Thus, R_1ρ(5620Hz) should mainly reflect those processes that contribute to the intrinsic R_2w, although there may still be some residual chemical exchange effects from protons undergoing very fast exchange that are not completely reversed even at this high locking field. R_1ρ(100Hz) should reflect the sum of intrinsic R_2w and R_1ρ^Ex effects; R_1ρ(0Hz) should reflect the sum of intrinsic R_2w, R_1ρ^Ex, and R_1ρ^Diff effects.

Animal preparation

13 rats bearing 9L tumors were used in this study. Each rat was injected with 1 × 10⁵ 9L glioblastoma cells in the right brain hemisphere to induce tumors, and was then imaged after 2 to 3 weeks. The average tumor size (the diameter of the greater visible axis of the tumor) was measured to be 4.9 ± 2.1 mm based on the T₂ weighted images. All rats were immobilized and anesthetized with a 2%/98% isoflurane/oxygen mixture during imaging. Respiration rate was kept between 40 and 50/min, and a constant rectal temperature of 37°C was maintained throughout the experiments using a warm-air feedback system (SA Instruments, Stony Brook, NY). All animal experiments were approved by the Animal Care and Usage Committee at Vanderbilt University.

MRI and data analysis

Spin-lock experiments were performed on a 7 T Varian small animal system. A spin-lock preparation cluster was applied before image acquisitions. The cluster has an initial 90° flip, a pair of on-resonance locking pulses applied along the direction of the transverse magnetization with selectable amplitudes and durations and separated by a 180° refocusing pulse, followed by a −90° flip back to the z direction. R_1ρ dispersion curves were obtained by acquiring images with ω₁ from 0 Hz to 5620 Hz. Spin-locking times (SLT) were varied as 1, 25, 50, 75, 100 ms to enable derivation of R_1ρ rates. Spin-lock images were acquired using single-shot spin-echo Echo Planar Imaging (EPI) readouts with TE of 25 ms and TR of 4 s. Anatomic T₂ weighted images were also acquired with the same single-shot spin-echo EPI, but without the spin-lock preparation cluster. All images from 12 rats were acquired with matrix size 64 × 64, field of view (FOV) 30 mm × 30 mm, and a single slice scan with slice thickness of 2 mm. Regions of interest (ROIs) for tumors and contralateral normal tissues were manually outlined from each rat brain based on the anatomic images. Tumors were identified by their abnormal signal intensities (reflecting changes in water content and relaxation times) relative to the mean brain background signal. For comparison with histology, spin-lock images from one rat brain were also acquired with matrix size 64 × 64, FOV 30 mm × 30 mm, and slice thickness 1 mm. A 3D gradient echo image set for identifying the position of the spin-lock imaging slice was acquired with TE 4 ms, TR 100 ms, excitation flip angle 30°, slice thickness 30 mm, matrix size 128 × 128 × 128, and FOV 30 mm × 30 mm × 30 mm.

R_1ρ was obtained by fitting the spin-locking data S with a mono-exponential function $S={\text{S}}_0{e}^{-R_{1\rho }\cdot SLT}$ to derive R_1ρ. Student’s t-tests were employed to evaluate differences between results, which were considered to be statistically significant when p < 0.05.

Histology

Mean vessel (capillaries) diameters and spacings from several regions in rat brain bearing 9L tumor were estimated by histology and compared with R_1ρ^Diff from the corresponding regions in the MR images. To prepare the tissue samples, the rat vasculature was perfused and first labeled by intravenous injection of 100 μl (1mg/ml) dylight-649 labeled tomato lectin prior to cardiac perfusion that was performed with saline, 4%PFA and FITC hydrogel. After euthanasia, the rat brain was extracted and fixed overnight in 4% PFA at 4°C. 1 mm brain slices were sectioned matching the MRI orientation and cleared using the uDISCO method (25). 3D confocal imaging was performed on Zeiss LSM710/880 microscopes. A low-resolution overview image at 5x/0.25 numerical aperture (NA) and multiple high-resolution tiled z-stacks (1.5mm x1.5mm FOV at 0.5 μm2×0.6 μm resolution) with 20x/0.8 NA air or 40x/1.1 NA long distance (LD) water immersion objectives were acquired to image through the entire thickness of a section ~0.5 mm. Mosaic scan images were stitched and processed on IMARIS 9.1.2 (Bitplane, Zurich, Switzerland), Fiji and Matlab2017a (MathWorks, Natick, MA, USA) software to provide three dimensional data from which vessel diameters and spacings were obtained.

Two simple methods were adopted to describe the differences in diameters and vessel spacings. First, average diameters of segmented vessels from regions of interest in the tumor and normal brain were estimated for multiple sections. Second, the 3D stacks were projected onto a 2D space and the number of crossings of vessels with lines drawn at multiple angles was calculated. The number (representing the spacing in the projected data set) varied with the thickness of the section that was projected but the ratio of the normal tissue to tumors remained relatively constant, independent of thickness (see Table 1).

Table 1.

Mean vessel spacings for section thickness of 50 μm and 100 μm. The values in the brackets are the ratio of the mean vessel spacings between Ctrl1 and the corresponding tumor regions.

	Section thickness 50 μm	Section thickness 100 μm
Ctrl1	15.56 ± 0.65 μm	9.86 ± 0 μm
#1	17.97 ± 2.07 μm (0.87)	10.79 ± 2.33 μm (0.91)
#2	19.76 ± 2.40 μm (0.79)	12.69 ± 2.07 μm (0.77)
#3	18.32 ± 1.87 μm (0.85)	11.61 ± 0.51 μm (0.85)

RESULTS

Fig. 1 shows the average R_1ρ dispersion curves from tumors and contralateral normal tissues for the 12 rat brains. Note that two distinct R_1ρ dispersions are apparent, one in the range from 0 Hz to 100 Hz (especially in tumors) and the other from 100 Hz to 5620 Hz. According to previous studies and theory (11–14), the R_1ρ dispersion from 0 Hz to 100 Hz is due to diffusion through intrinsic susceptibility gradients, and the R_1ρ dispersion from 100 Hz to 5620 Hz should be mainly due to chemical exchange effects.

FIG. 1.

R_1ρ dispersions from tumors (red) and contralateral normal tissues (blue) in rat brains. Error bars are standard deviations from 12 rats. Circles represent the R_1ρ values acquired with ω₁ of 0 Hz, 100 Hz, and 5620 Hz.

By using Eq. (3) and (4), the R_1ρ contributions due to these two different mechanisms were quantified. As illustrated in Fig. 2, over 12 rats, the amplitudes of R_1ρ^Diff were 5.24 ± 1.78 s⁻¹ in tumors and 1.36 ± 0.70 s⁻¹ in contralateral normal tissues; the amplitudes of R_1ρ^Ex were 6.70 ± 0.69 s⁻¹ in tumors and 7.99 ± 0.84 s⁻¹ in contralateral normal tissues; the amplitudes of other relevant R_1ρ values R_1ρ(0Hz), R_1ρ(100Hz), R_1ρ(5620Hz) were 20.08 ± 2.00 s⁻¹, 14.75 ± 0.88 s⁻¹, and 8.04 ± 0.64 s⁻¹, respectively, in tumors and 20.42 ± 0.55 s⁻¹, 19.06 ± 0.78 s⁻¹, and 11.07 ± 0.19 s⁻¹, respectively, in contralateral normal tissues. The differences between tumor and normal brain were statistically significant for R_1ρ^Diff, R_1ρ^Ex, R_1ρ(100Hz), and R_1ρ(5620Hz), but not for R_1ρ(0Hz). Note that empirically R_1ρ^Diff provides the strongest contrast between tumors and contralateral normal tissues.

FIG. 2.

Mean values of R_1ρ(0Hz) (a), R_1ρ(100Hz) (b), R_1ρ(5620Hz) (c), R_1ρ^Diff (d), and R_1ρ^Ex (e) from 12 rat brains bearing 9L tumors. Error bars are standard deviations from 12 rats. (*p<0.05)

Fig. 3 shows maps of R_1ρ(0Hz), R_1ρ(100Hz), R_1ρ(5620Hz), R_1ρ^Diff, and R_1ρ^Ex from a representative rat brain. Maps of these imaging contrasts from the other 11 rats are shown in the Supporting information Figures S1–S11. Note that tumor can be clearly identified in the R_1ρ^Diff map. Also note that tumor in the R_1ρ(0Hz) image is more inhomogeneous than at R_1ρ(100Hz) or R_1ρ(5620Hz), and the tumor boundary in the R_1ρ(0Hz) image is not as distinct as in the R_1ρ(100Hz) and R_1ρ(5620Hz) images.

FIG. 3.

Anatomical T₂ weighted image (a), maps (s⁻¹) of R_1ρ(0Hz) (b), R_1ρ(100Hz) (c), R_1ρ(5620Hz) (d), R_1ρ^Diff (e), and R_1ρ^Ex (f) from a representative rat brain bearing a 9L tumor (rat #1).

Fig. 4 compares the mean vessel spacings and diameters estimated by histology with R_1ρ^Diff from several regions of one rat brain bearing 9L tumor. Table 1 and 2 list the values of the mean vessel spacings and diameters, respectively. Note that the mean vessel spacing, irrespective of the thickness of section projected, is higher in all tumor regions than in the normal brain; the mean vessel diameter is also higher in all tumor regions than in the normal brain, which is in agreement with R_1ρ^Diff, suggesting that the change of R_1ρ^Diff may reflect the change in the vasculature in 9L tumors. Fig. 5 shows the binarized histological images from a tumor region and the contralateral normal brain, which clearly show that the vessel spacings and diameters are higher in the 9L tumor than in the normal brain;

FIG. 4.

Histological images (a) and R_1ρ^Diff MRI image (b) from one rat brain bearing 9L tumor. Mean vessel spacing with section thickness 50 μm (c) and 100 μm (d), mean vessel diameter estimated by histology (e), and R_1ρ^Diff (f) from four ROIs including one region from the contralateral normal tissue (Ctrl1) and three regions from the tumor (#1, #2, and #3). Error bar shows the standard deviation.

Table 2.

Mean vessel diameters

Ctrl1	5.68 ± 1.55 μm
#1	7.32 ± 2.99 μm
#2	6.58 ± 2.30 μm
#3	6.15 ± 2.46 μm

FIG. 5.

Binarized histological images from a tumor region (left) and the contralateral normal brain (right).

DISCUSSION

This report describes the application of spin-locking techniques to assess 9L tumors in an animal model at 7 T. By subtraction of R_1ρ values at two different locking fields ω₁, greater contrast can be produced compared to other types of images including R_1ρ(0Hz), R_1ρ(100Hz), R_1ρ(5620Hz), and R_1ρ^Ex, and we suggest the resultant maps may be interpreted in terms of the contribution of dephasing effects caused by diffusion within intrinsic gradients. In Fig. 2, the reduced values of R_1ρ(5620Hz) in tumors compared to normal brain are expected as a reduction of the intrinsic R_2w caused by increased water content; the reduced R_1ρ^Ex values in tumors may also be due to the decrease in concentrations of macromolecules and exchanging species in, for example, peptides and neurotransmitters (26). There was no statistical difference in the average R_1ρ(0Hz) values between tumors and contralateral normal tissues, though the tumors appear more inhomogeneous in maps of R_1ρ(0Hz) and their margins are unclear. At lower magnetic fields R_1ρ(0Hz) in tumors is often lower than in normal brain because R_2w is lower, but at high magnetic fields diffusion and exchange effects counteract this difference. The R_1ρ^Diff contrast between tumors and contralateral normal issues is significantly larger than other spin-locking contrasts, suggesting that R_1ρ^Diff may be useful for the detection of 9L tumors. Based on theory and previous studies in model systems (11,12,13), we propose this contrast may be due to the changes in vascular size and density, oxygenation level, or hemorrhage in 9L tumors that cause intrinsic susceptibility gradients.

Fig. 4 suggests that the higher R_1ρ^Diff values in the 9L tumors may be due to the larger mean vessel diameters and spacings and smaller q values as predicted by theory. Previously, the specific tumor line used has been extensively studied in rodents and the differences in tissue microstructure and vasculature compared to normal brain have been extensively documented. For example, Kim et al. (27) performed microscopic imaging of 9L microvasculature and reported significant increases in fractional vascular volume, average vessel diameter, number of vessel branches per volume, total vessel length per volume and vessel tortuosity in 9L tumors compared to normal brain, while the mean vessel length was reduced. These differences are predicted to produce increased gradient dephasing, as shown for example, by Semmineh et al. (28) using computational simulations of microvascular tree structures.

Although spin-locking imaging in tumors has been previously reported (29–37), there have been relatively few studies that explored variations of R_1ρ with the applied locking field, or the origins of the dispersion of R_1ρ at higher magnetic fields. A previous study (37) reported spin-locking experiments with a broad range of ω₁ (85 Hz to 5960 Hz) and apparent R_2w (which can be looked as R_1ρ(0Hz)) on tumors at 4.7 T. Although this study evaluated spin-locking signals at different ω₁ and spin-locking changes between 85 Hz and 640 Hz and between 850 Hz and 5960 Hz, it did not report the dispersion at lower magnetic fields, between 0 Hz and 85 Hz. However, consistent with our findings at higher magnetic field, differences in (R_1ρ(85Hz) - apparent R_2w) between tumor and normal tissue can be observed in their paper, and this dispersion increased as tumors developed. According to our analysis, the spin-locking dispersion in this low ω₁ range is due to the effect of intrinsic gradients which were not identified in previous studies. This earlier paper also noted significant contrast between tumor and normal tissue for the apparent R_2w, but was performed at lower magnetic field. Our results show significant contrast between tumor and normal tissue for R_1ρ with ω₁ > 100 Hz, but not for R_1ρ(0Hz). This difference could be due to the fact that spin-locking signals are more sensitive to chemical exchange effects at high magnetic fields (14,38), which increases R_1ρ^Ex, and less dependent on low frequency dipolar effects which contribute to R_2w. In addition, the different tumor cell lines may be another reason for the different results in these two papers. Fig. 1 suggests that diffusion and exchange may contribute in opposite directions to the contrast between tumor and normal tissue at 7 T, which causes the margins of tumors in R_1ρ(0Hz) images to be less clear in Fig. 3b. A spin-locking measurement with ω₁ ~100 Hz can thus enhance the contrast compared to 0 Hz (or an apparent R_2w measurement). Previously, it was reported that the apparent R_2w measured using Carr-Purcell (CP) sequences with different echo spacings can achieve contrast resembling R_1ρ at low locking field (36,39). However, the CP sequence with varied echo spacing has a range of echo pulse rates limited by power and pulse length constraints and is less able to fully document relaxation rate dispersion.

The value of R_1ρ at low locking fields is sensitive to intrinsic gradients of different spatial scales including smaller size microvasculature. Moreover, the analysis of the dispersion of R_1ρ allows estimates of the scale of the dominant intrinsic gradients independent of the magnitude of the susceptibility changes that cause them, though the strength of those gradients may also then be calculated. For example, in our data, the mean value of R_1ρ^Diff is 5.24, so using simple linear interpolation of values (a reasonable approximation over a small range), if R_1ρ^Diff is negligible at 100 Hz, then at 50 Hz the locking field ω₁ = q²D. If D = 2 × 10⁻⁵ cm²s⁻¹ then we estimate R ≈ π/q ≈ 7.9 μm, indicating the scale of the inhomogeneities producing the gradients are of the order of microvessels. Moreover, using the same values, the mean gradient amplitude g at a magnetic field of 7 Tesla may be estimated to be of order 0.0536 ppm/μm. Given the approximate nature of the model, this is consistent and to the same order as the values for gradients created within the tissue by inhomogeneities with the susceptibility of deoxygenated blood (≈ 0.1 ppm). Our previous studies also indicated that by judicious selection of ω₁ between 0 Hz and 100 Hz, R_1ρ could be made selectively sensitive to a specific size of microvasculature and changes in blood oxygenation (12,13,40).

Experimentally, because of R_2ρ effects, R_1ρ is sensitive to B₀ shifts at lower ω₁. For example, previously, we reported that the apparent value of R_1ρ may gradually increase with ω₁ in a range from 100 Hz to 526 Hz at 9.4 T (41) in the presence of significant B₀ inhomogeneities. Here we did not observe an increase of R_1ρ when ω₁ > 100 Hz, which may be due to the better magnetic field homogeneity and shimming obtained at 7 T. Better shimming and improvements in RF pulses to reduce such R_2ρ effects may increase the application of R_1ρ weighted acquisitions for susceptibility-weighted and microvascular imaging. Future studies on the correlations between R_1ρ^Diff and histological estimates of vessel size may further validate this contrast mechanism, but even without such confirmation it is clear that empirically this metric provides increased contrast between 9L tumors and normal brain. Note that to estimate R_1ρ^Diff, only low locking powers are required so this method is not limited by specific absorption rate (SAR) and can safely be translated to higher magnetic field human studies.

CONCLUSION

We show that spin-locking dispersion imaging at low locking power can be applied to obtain images with novel contrast that we suggest reflects intrinsic gradients induced by susceptibility inhomogeneities in tissues in vivo, and these are markedly different in 9L tumors. The behavior of the dispersion is consistent with dephasing by water diffusing amongst gradients at microvascular scale caused by blood and may be a feature of abnormal microvasculature in tumors.

Supplementary Material

Supplementary

Supporting information Figure S1. Maps of anatomy (a), several R_1ρ contrasts (b-f), and the normalized root mean square error (NRMSE) for fitting R_1ρ(0Hz) (NRMSE(0Hz)) (g), R_1ρ(100Hz) (NRMSE(100Hz)) (h), and R_1ρ(5620Hz) (NRMSE(5620Hz)) (i) from rat #2.

Supporting information Figure S2. Maps of anatomy (a), several R_1ρ contrasts (b-f), and the normalized root mean square error (NRMSE) for fitting R_1ρ(0Hz) (NRMSE(0Hz)) (g), R_1ρ(100Hz) (NRMSE(100Hz)) (h), and R_1ρ(5620Hz) (NRMSE(5620Hz)) (i) from rat #3.

Supporting information Figure S3. Maps of anatomy (a), several R_1ρ contrasts (b-f), and the normalized root mean square error (NRMSE) for fitting R_1ρ(0Hz) (NRMSE(0Hz)) (g), R_1ρ(100Hz) (NRMSE(100Hz)) (h), and R_1ρ(5620Hz) (NRMSE(5620Hz)) (i) from rat #4.

Supporting information Figure S4. Maps of anatomy (a), several R_1ρ contrasts (b-f), and the normalized root mean square error (NRMSE) for fitting R_1ρ(0Hz) (NRMSE(0Hz)) (g), R_1ρ(100Hz) (NRMSE(100Hz)) (h), and R_1ρ(5620Hz) (NRMSE(5620Hz)) (i) from rat #5.

Supporting information Figure S5. Maps of anatomy (a), several R_1ρ contrasts (b-f), and the normalized root mean square error (NRMSE) for fitting R_1ρ(0Hz) (NRMSE(0Hz)) (g), R_1ρ(100Hz) (NRMSE(100Hz)) (h), and R_1ρ(5620Hz) (NRMSE(5620Hz)) (i) from rat #6.

Supporting information Figure S6. Maps of anatomy (a), several R_1ρ contrasts (b-f), and the normalized root mean square error (NRMSE) for fitting R_1ρ(0Hz) (NRMSE(0Hz)) (g), R_1ρ(100Hz) (NRMSE(100Hz)) (h), and R_1ρ(5620Hz) (NRMSE(5620Hz)) (i) from rat #7.

Supporting information Figure S7. Maps of anatomy (a), several R_1ρ contrasts (b-f), and the normalized root mean square error (NRMSE) for fitting R_1ρ(0Hz) (NRMSE(0Hz)) (g), R_1ρ(100Hz) (NRMSE(100Hz)) (h), and R_1ρ(5620Hz) (NRMSE(5620Hz)) (i) from rat #8.

Supporting information Figure S8. Maps of anatomy (a), several R_1ρ contrasts (b-f), and the normalized root mean square error (NRMSE) for fitting R_1ρ(0Hz) (NRMSE(0Hz)) (g), R_1ρ(100Hz) (NRMSE(100Hz)) (h), and R_1ρ(5620Hz) (NRMSE(5620Hz)) (i) from rat #9.

Supporting information Figure S9. Maps of anatomy (a), several R_1ρ contrasts (b-f), and the normalized root mean square error (NRMSE) for fitting R_1ρ(0Hz) (NRMSE(0Hz)) (g), R_1ρ(100Hz) (NRMSE(100Hz)) (h), and R_1ρ(5620Hz) (NRMSE(5620Hz)) (i) from rat #10.

Supporting information Figure S10. Maps of anatomy (a), several R_1ρ contrasts (b-f), and the normalized root mean square error (NRMSE) for fitting R_1ρ(0Hz) (NRMSE(0Hz)) (g), R_1ρ(100Hz) (NRMSE(100Hz)) (h), and R_1ρ(5620Hz) (NRMSE(5620Hz)) (i) from rat #11.

Supporting information Figure S11. Maps of anatomy (a), several R_1ρ contrasts (b-f), and the normalized root mean square error (NRMSE) for fitting R_1ρ(0Hz) (NRMSE(0Hz)) (g), R_1ρ(100Hz) (NRMSE(100Hz)) (h), and R_1ρ(5620Hz) (NRMSE(5620Hz)) (i) from rat #12.