Supplementary A: PVE study on sodium MR images

Supplementary A: PVE study on sodium MR images
In-vivo proton and sodium MR images of human kidney were successfully acquired
using our developed dual-tuned 1H/23Na RF Coil (sFig. 1). Due to the sensitivity characteristics
of surface coil (proportional to the distance from the coil), higher signal intensity of sodium
image was acquired near the coil and gradually decreased into the deeper region. The intensity
inhomogeneity should be corrected by post-processing (see Supplementary B).
In order to evaluate the effect of spatial resolution on the measurement of [23Na] and
CMSG, we measured the intrinsic PSF of sodium MR image at nominal isotropic resolution of 3
mm, and simulated the change of CMSG value with different imaging conditions. The PSF of
sodium MR image under current experiment condition was measured using a homogeneous
saline phantom. The profiles of sodium image intensity change across the boundary of saline
phantom from the background were measured and fitted using
model, and then the
derivative was calculated as the PSF – therefrom, full width half maximum (FWHM) was
calculated at the half of peak point. In addition, the PVE on CMSG was investigated using a
kidney phantom which consisted of five concentric cylindrical containers (diameter of 12, 30, 46,
68, and 140 mm) filled with 4% agar gels with 150, 117, 83, 50, and 17-mM [23Na]. The
relationship between CMSG vs. cortico-medullary thickness and filter bandwidth was also
simulated using a simple triangle cortico-medullary [23Na] profile and a Gaussian PSF,
respectively. The slope of [23Na] change was calculated in only linear region of [23Na] change to
avoid a PVE bias at the region such as thin cortex and medullary pyramid in the kidney. Same
sodium MR parameters for the kidney phantom were applied as in sodium imaging of the human
The effects of different filter bandwidth (with 2.7, 1.6, 1.5, 1.3 and  in k-space) at
the reconstruction were tested to [23Na] signal changes due to the PVE around kidney medulla in
one healthy subject and 14-mm diameter cylindrical tube. Sodium signal of renal cortex-medulla
varied with the bandwidth of applied Hanning filter in k-space (sFig. 2A). Local maxima of
sodium signal were clearly shown at broad k-space filter (i.e., less smoothing in spatial image
space) but smeared out at narrow filter, while the mean signal was monotonically decreased with
the narrower filter (sFigs. 2A – C). The sodium signal in 14-mm diameter tubes was saturated
with the broad filter bandwidth (sFig. 2C), indicating that the effective PSF of sodium MR
imaging was narrower than ~7-mm dimension (i.e., half of the tube’s diameter). Indeed, the PSF
of sodium MR image (acquired at 3-mm resolution) had ~5-mm FWHM and was broader than
nominal imaging pixel resolution (sFig. 2D). In consideration of similar dimension of cortical
thickness (> 10 mm) with 2 × FWHM (~10 mm), the filtered signal in cortex-medulla region was
expected to be saturated with the broader k-space filter if the sodium profile was constant, but
kept increasing (sFig. 2C). According to the results of signal changes with the filter bandwidth,
the [23Na] profile from the cortex to medulla in sodium MR image was expected to be rather
tapered such as triangular (linear) shape but not step function.
Furthermore, the effect of broad PSF of sodium imaging on CMSG was tested using a
kidney phantom (sFig. 3). Sodium image intensity increased with given [23Na] (lower panel in
sFig. 3A) and showed the linear increase profile with distance (sFig. 3B). The measured sodium
gradient over 34-mm distance using sodium MR image acquired at 3-mm pixel resolution was
3.92 mM/mm which was consistent with given value 3.82 mM/mm (red line in sFig. 3B). The
relationship between the measurement accuracy of CMSG at given PSF (i.e., pixel resolution in
FWHM) and cortico-medullary thickness was simulated (sFig. 3C) – CMSG could be estimated
at > 95% accuracy for > 10-mm cortico-medullary thickness using sodium MR image acquired at
5-mm effective FWHM of (filtered) PSF. The simulation results explained the result of accurate
CMSG measurement using sodium MR imaging in the kidney phantom study.
Supplementary B: Imaging and data analysis
For the quantification of renal [23Na], B1 field inhomogeneity in sodium MR image was
measured in arbitrary unit using a 6-liter cylindrical phantom (diameter 200 mm, height 450 mm)
filled with 153-mM [23Na] homogeneous saline solution [1] . The phantom sodium MR image
was first smoothed by Gaussian function with 5-mm FWHM to remove the local change of
image intensity irrelevant to the field distribution. Sodium MR images of the native and
transplanted kidneys were normalized by the co-registered sodium image of the homogeneous
phantom for the B1 inhomogeneity correction, and scaled to 153-mM [23Na] value by comparing
image intensity of the 4 % agar 153-mM [23Na] saline reference marker [1]. We assumed T1 and
T2 relaxation time in 4 % agarose gel saline was similar to those in kidney [2]. For coregistration of two sodium images of the homogeneous phantom and the kidney, the reference
markers (14-mm diameter tubes) were segmented manually and the affine transformation were
applied by comparing two markers-only images, then the transformation matrix was applied to
sodium image of the homogeneous phantom.
The 3D sodium images were reformatted to generate coronal images parallel to
longitudinal axis of the kidney for improved delineation of renal anatomy in sodium MR images.
The same reformat procedure was applied to the proton anatomy images.
SNR and [23Na] in native and transplanted kidneys:
The SNR of the sodium kidney MR images was calculated by the ratio of the signal
intensity of the kidney and the background noise. The 3D cubic region (fully covering the
kidney) was manually selected. The mean and STD of signal intensities within the region were
calculated; the pixels with higher signal than mean ± STD in the region were considered in the
SNR measurement (see dotted contour in sFig. 4A). Noise was computed from the STD of a 10cm3 ROI placed in the background.
Cortico-medullary sodium gradient (CMSG):
Spatial variation of the [23Na] was measured on a pixel-by-pixel basis along corticomedullary axis as previously described [1; 3; 4]. Measurements were performed on coronal
sodium images, using proton images as anatomical reference; 4 ± 2 renal pyramids were used for
the measurement (see black-dotted lines in sFig. 4B). For each pyramid, five cortico-medullary
lines with 2-mm gap were traced perpendicular to the cortex (see red-solid and -dotted lines in
sFig. 4B). [23Na] profiles were measured in the cortico-medullary axis and averaged together.
Only linear region of [23Na] profile was selected and the slope (i.e., CMSG) was calculated by 1st
order polynomial fitting.
For more accurate CMSG measurement multiple coronal images were included in the CMSG
measurement because the peak positions of each pyramid were not co-aligned in same slice
position; the same cortico-medullary lines were automatically propagated to seven adjacent
slices spanned with 15-mm depth. The CMSG values were measured for each seven slices and
then fitted with 2nd order polynomial function along slice-depth direction to find the pyramidal
peak value (sFig. 5).
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sFig. 1 In-vivo dual-tuned proton and sodium MR images of human abdomen using a flexible
dual-tuned 1H/23Na RF coil. No post-processing was applied to images and the intensity is in
arbitrary unit. The proton imaging only covered the region of kidney to reduce total acquisition
time. 1 – liver, 2 – kidney, 3 – intervertebral disc, 4 – muscle and 5 – cerebral spinal fluid.
Reference markers are indicated by red arrows. Note than both nucleus MR images are selfcoregistered each other.
sFig. 2 PSF of sodium MR image. A and B, Sodium MR images of healthy native kidney and
agar phantom (14-mm diameter tube), respectively. Hanning filter is applied in in k-space.
Black-dotted circles are the tubes’ boundary. C, Mean intensity changes with the filter
bandwidth within region of interest (black contours in A). The intensity are normalized with the
intensity at the filter size . D, PSF measurement. Profile of sodium image intensity is measured
along white line (inset), repeated for multi-slices over 46-mm depth and averaged (black trace).
Red-dotted trace is the PSF and the FWHM was measured as 4.8 mm. Note that the sodium
signal linearly increases from the cortex to the medullary pyramid.
sFig. 3 PVE on sodium gradient measurement. A, proton (upper panel) and sodium MR image
(lower panel). Phantom is filled with 4% agarose gels with 150 (5), 117 (4), 83 (3), 50 (2), and
17 mM (1) [23Na]. Green-solid circles are markers’ boundary. Five plastic containers are marked
with green-dotted circles determined based on proton image and overlaid on sodium image. Red
contours represent the coil frame. White arrow indicates the ghost artifacts in proton image. B,
Image intensity profile following white-dashed line in A. C, Simulation of sodium gradient
change with FWHM of sodium image and cortex-medullar thickness.
sFig. 4 ROI selection (A) and CMSG measurement (B). Black-dotted contour in A is selected in
the medullary region by threshold of sodium image. In the re-oriented coronal slice, the corticomedullary axis (a-b red line in B) is drawn and neighboring other 4 parallel lines (red dotted lines
in B) are selected for the CMSG measurement. White-dotted contour is the boundary of kidney.
 – Noisy area out of calibration phantom.
sFig. 5 CMSG measurement considering its variation in slice direction. A and B, Proton and
sodium MR images in multiple slices in coronal view. M1, M2, and M3 are the medullar
pyramids; white and black arrowheads point M1 and M2, respectively. White-dashed contour is
the boundary of kidney determined based on 1H image.  – Area out of proton imaging. C,
CMSG variation with the slice. The 2nd order polynomial fitting is applied to calculate the peak
CMSG value (red arrows).