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Gradient-Echo and Spin-Echo MRI Data from a Phantom Model of Tissue Microstructure

MRI data from suspensions of spherical polystyrene microbeads for research on gradient-echo and spin-echo signal decay in the presence of microstructural sources of magnetic susceptibility.

We are making available experimental MRI data for evaluating models of gradient-echo and spin-echo signal decay in the presence of microstructural sources of magnetic susceptibility. 

Many biological organs contain microstructure—such as myelin, iron deposits, and microvasculature—whose magnetic susceptibility differs from that of the surrounding tissue. This generates spatial variations in the static magnetic field of an MR scanner and alters the decay of gradient-echo (GRE) and spin-echo (SE) signals. In addition to increasing the rate of signal attenuation, microstructure produces characteristic nonexponential signatures in the decay curves, which depend on the spatial scale and magnetic susceptibility of the microstructure. 

Much theoretical work has been done to understand this signal behavior, with the ultimate goal of inverting the problem to extract microstructural information from MRI data. However, testing theoretical models requires controlled experiments, in which the properties of the microstructure are well defined and accurately measurable. 

This resource contains GRE and SE data acquired from phantoms containing spherical polystyrene microbeads of three different sizes. The experimental data and our theoretical models thereof are reported in a manuscript currently under review for Magnetic Resonance in Medicine.

We are sharing these data to enable other researchers to test alternative models of GRE and SE signal behavior in microstructure and to support the journal’s commitment to promoting reproducible research.

Polystyrene microbeads seen under a microscope.
Polystyrene microbeads seen under a microscope. The microbeads used in our experiments had nominal diameters of 10, 20, and 40 micrometers. Image courtesy of Microbeads AS.
Four pipettes: one with only gel, and three with microbeads 10, 20, and 40 micrometers in diameter, respectively.
From the top, three pipettes each containing microbeads with nominal diameters of 40, 20, and 10 micrometers, respectively; and one pipette filled with only gel as a control. Photo courtesy of Pippa Storey.

The MR data available here were acquired using a multi-echo GRE sequence and a customized SE sequence. They include magnitude signals from regions of interest (ROIs) in the phantoms, in addition to the original complex-valued images of the phantoms, which may be useful for scientists who wish to study the phase of the signal or apply their own processing methods.

In this section, we provide detailed information about the acquisition, processing, and formatting of the data. Each card below can be opened for a more specific description.

Phantom Design and Arrangement in the RF Coil

Phantoms consisted of pipettes filled with suspensions of spherical polystyrene microbeads in a doped gelatin medium. Three phantoms, each containing microbeads of a different size, were used to study the effects of microstructure. A fourth phantom containing the doped gelatin but without microbeads served as a control.

Phantom Design

Spherical polystyrene microbeads of 10 µm, 20 µm and 40 µm nominal diameter were purchased from Microbeads AS (Skedsmokorset, Norway). The beads had a relatively narrow size distribution, with median diameters of 11.1 µm, 23.0 µm, and 40.4 µm respectively. A representative example of the size distribution is shown in Figure 2 of the related manuscript.

For each bead size, a sample of the beads was suspended in a solution of 2% gelatin doped with 0.07% gadobutrol, such that the beads occupied a tenth of the total volume. Each suspension was loaded into a 25-mL serological pipette, which was sealed at both ends with a glue gun. The pipettes were placed in a sonicator to eliminate microbubbles, then rotated continuously for several minutes to ensure uniform mixing of the beads, before being plunged into a bath of ice water to trigger rapid gelling. A fourth phantom containing only the gel medium was constructed as a control.

Pipettes were chosen as containers for the phantoms because they provide a good approximation to an infinite cylinder, thereby minimizing macroscopic field inhomogeneity along most of their length.

Phantom Arrangement

The phantoms were arranged side-by-side in a wrist coil in the following order*:

  1. 20-µm bead suspension
  2. gel-only control
  3. 10-µm bead suspension
  4. 40-µm bead suspension

On GRE images, phantoms 1-4 appear left-to-right, with 1 at the left.

On SE images, phantoms 1-4 appear bottom-to-top, with 1 at the bottom.

At the longest echo time, the gel-only control phantom has the highest intensity.

We chose the order above because the sensitivity of the coil is highest at the edges, and this arrangement helped boost the signal-to-noise ratio of the 20-µm and 40-µm bead suspensions, whose signal decayed fastest with echo time.

*In the experiment conducted on June 20, 2021, we imaged two additional phantoms containing 40-µm beads to test the sensitivity of the results to bead volume fraction. In one phantom (far left on the images) the bead density was higher by 2%, and in the other (far right) the bead density was lower by 2%.

Data Acquisition

The data were acquired on a 3-Tesla Prisma MRI system (Siemens, Erlangen) using a multi-echo gradient-echo (GRE) sequence and a customized spin-echo (SE) sequence as described in the manuscript.

Five experiments were performed, each with a fresh set of phantoms.

  • For each experiment, the four phantoms were arranged side by side in a 15-channel wrist coil, with their long axes oriented along the long axis of the bore.
  • A multi-echo GRE sequence was run in all five experiments. In the last three experiments, a customized SE sequence was added to the protocol (see the related manuscript for more detail).
  • In every experiment, noise-only data were also acquired by setting the transmit voltage to zero. These data provided an estimate of the noise covariance among coil elements, which was used to optimize SNR in the reconstructed images.
  • Immediately before and after each GRE and SE sequence, we ran an EPI diffusion sequence to estimate the apparent diffusion coefficient of the gel medium.
  • In addition, we made independent measurements of the susceptibility difference between the beads and the gel medium using the method illustrated in Figure 3 of the related manuscript.

Complex-valued Image Data and Methodology

Complex-valued image data from GRE and SE sequences are provided in MATLAB format. A description of the files and a summary of the reconstruction methods used to compute the complex-valued images from the raw k-space data are given here.

Files Containing Gradient-Echo Image Data

The files containing the multi-echo GRE image data are labeled using the following convention: gre_image_data_YYYY_MM_DD.mat, where YYYY_MM_DD is the study date. These files contain the following variables:

Variable Name Size Class Description
complex_image_data_4d 224 x 224 x 80 x 32 complex double Complex-valued images from 80 slices and 32 echoes
te_ms 1 x 32 double Echo times in milliseconds

Files Containing Spin-Echo Image Data

The files containing the SE image data are labeled using the following convention: se_image_data_YYYY_MM_DD_run_Z.mat. These files contain the following variables:

Variable Name Size Class Description
complex_image_data_3d 96 x 36 x 25 complex double Complex-valued images from 25 echoes in a single slice
te_ms 1 x 25 double Echo times in milliseconds
Summary of the differences among runs of the SE sequence.
Date Run TE Order Plane Position Slice Thickness Receiver Gain Coil Group
2021/08/08 1 ascending axial H0.0 mm 10.0 mm High HW1
2 descending axial H0.0 mm 10.0 mm High HW1
3 ascending oblique H0.0 mm* 10.0 mm High HW2*
4 descending oblique H0.0 mm 10.0 mm High HW2
5 ascending axial H0.0 mm 10.0 mm High HW2
6 descending axial H0.0 mm 10.0 mm High HW2
2021/09/26 1 ascending axial H0.0 mm 10.0 mm High HW2
2 descending axial H0.0 mm 10.0 mm High HW2
3 ascending axial H0.0 mm 10.0 mm Low HW2
4 descending axial H0.0 mm 10.0 mm Low HW2
5 ascending axial H0.0 mm 20.0 mm Low HW2
6 descending axial H0.0 mm 20.0 mm Low HW2
2022/02/06 1 ascending axial H0.0 mm 10.0 mm Low HW2
2 descending axial H0.0 mm 10.0 mm Low HW2
3 ascending axial H20.0 mm 10.0 mm Low HW2
4 ascending axial F20.0 mm 10.0 mm Low HW2
* On 2021/08/08, the table was repositioned between run 2 and run 3, so the slice positions are not comparable between runs 1-2 and runs 3-6.

Methodology

K-space data were saved at the end of each experiment and processed offline. Noise-only data were used to estimate the noise covariance among coil elements. For each slice and echo of the image data, the noise covariance matrix was used to combine the separate images from individual coil elements into a single complex-valued image with optimized SNR, Rician noise statistics, and a noise standard deviation of one.

The coil sensitivities were estimated for each voxel by calculating the relative signals among coil elements in that voxel and averaging over all echoes. Due to the large number of echoes and the high signal within the phantoms across all echoes, this averaging process minimized the introduction of correlations between the coil sensitivity vector and the noise itself, thereby preserving the accuracy of the signal time course and the Rician character of the noise statistics.

Note that the signals from different coil elements in a given voxel differ both in magnitude and phase, so the coil sensitivities are complex-valued, as is the resulting combined signal. While the relative phase of the combined signal among echoes contains information about the physics of the system, most notably the local Larmor frequency in the case of the gradient-echo sequence, there remains an overall phase factor that can be set arbitrarily. This factor was chosen such that the phase of the combined signal on the first echo equaled zero.

The above method was applied to all voxels in the imaging volume. However, since voxels in the background contain no true signal, the algorithm used to calculate the coil sensitivities fails in those regions. As a consequence, the calculated values do not accurately reflect the coil sensitivities in the background, and they are not completely free of correlations with the noise itself (although averaging over echoes reduces the correlations substantially). As a consequence, the standard deviation of the noise in the background of the combined images is slightly greater than one. This is true for all echoes except the first, where the phase was set to zero as described above.

Files containing the complex-valued image data after coil combination are available in this repository for both gradient echo and spin echo sequences.

Region-of-Interest Data and Methodology

Magnitude signals as a function of echo time from regions of interest (ROIs) in each phantom are provided in MATLAB format for both GRE and SE sequences. A description of the files and a summary of the methods used to compute the ROI data from the complex-valued images are given here.

Files Containing Gradient-Echo ROI Data

The files containing the signal intensity time courses as a function of echo time from ROIs in the GRE images are labeled using the following convention:gre_ROI_data_YYYY_MM_DD.mat. They contain the following variables:

Variable Name Size Class Description
uncorrected_intensities_X_sliceY 1 x 32 double intensity time course in phantom X from slice Y, before correction for noise rectification
corrected_intensities_X_sliceY 1 x 32 double intensity time course in phantom X from slice Y, after correction for noise rectification
roi_X_sliceY 224 x 224 logical ROI in phantom X from slice Y
te_ms 1 x 32 double Echo times in milliseconds
center_frequency_MHz 1 x 1 double Larmor frequency at isocenter of scanner in megahertz
adc_um2perms 1 x 1 double Apparent diffusion coefficient of gel medium in µm2/ms

Files Containing Spin-Echo ROI Data

The files containing the signal time courses as a function of echo time from ROIs in the SE images are labeled using the following convention: se_ROI_data_YYYY_MM_DD_run_Z.mat. They contain the following variables:

Variable Name Size Class Description
uncorrected_intensities_X 1 x 25 double intensity time course in phantom X, before correction for noise rectification
corrected_intensities_X 1 x 25 double intensity time course in phantom X, after correction for noise rectification
roi_X 96 x 36 logical ROI in phantom X
te_ms 1 x 25 double Echo times in milliseconds
center_frequency_MHz 1 x 1 double Larmor frequency at isocenter of scanner in megahertz
adc_um2perms 1 x 1 double Apparent diffusion coefficient of gel medium in µm2/ms

Methodology

Magnitude images were obtained by calculating the absolute value of the complex-valued image data. For each slice, an ROI was selected in each phantom on the image with longest echo time. The ROIs were then copied to the corresponding images for all other echo times. The final echo was used for ROI selection because image artifacts (most notably point-like susceptibility artifacts on the gradient-echo images) were most prominent at long echo times, and clear visualization of the artifacts was essential to exclude them from the ROI.

The mean signal intensity within each ROI was calculated for each echo time and corrected for noise rectification (i.e. the bias introduced into the mean by the use of magnitude images rather than complex-valued images). Since the SNR was high across all echoes, the correction was very small, even at the longest echo time.

The gradient-echo sequence was run in a 3D coronal slab that encompassed the phantoms, and therefore yielded several slices for ROI selection. Large ROIs that extended along most of the length of each phantom were selected in each slice.

The spin-echo sequence was applied in a single 2D axial plane, which allowed for the selection of only one small ROI per acquisition. However, since the sequence was repeated several times (in different locations or with different chronological ordering of the echoes) several ROIs could be chosen for each phantom per experiment.

Files containing the signal intensity time courses for each ROI, with and without correction for noise rectification, are available in this repository for both gradient-echo and spin-echo sequences.

Magnetic Susceptibility Data and Notes

Measurements are provided of the magnetic susceptibility of the polystyrene beads relative to the doped gelatin medium. A description of the file and notes regarding the acquisition and interpretation of the data are given here.

Files Containing Magnetic Susceptibility Data

The file is labeled: gre_ROI_data_YYYY_MM_DD.mat and contains the following variables:

Variable Name Size Class Description
delta_chi_X_beads_wrt_gel 5 x 1 double magnetic susceptibility difference in SI units between the polystyrene material of the beads and the surrounding gel medium, as measured using bead size X
study_date 5 x 1 cell date of the experiment in which the measurements were made

Notes

The magnetic susceptibility difference between the polystyrene material of the beads and the surrounding gel medium was estimated using the method described in the related manuscript and illustrated in Figure 3 therein. The measurements were repeated for each experiment, since any inaccuracy in the concentration of gadobutrol in the gel medium would cause corresponding changes in the susceptibility of the medium. Slight variations in the magnetic susceptibility value were therefore expected among experiments, and were indeed observed.

However, since all beads were manufactured from the same material, the magnetic susceptibility value was not expected to differ significantly among bead sizes. Nevertheless, the smaller beads consistently yielded higher values than the larger beads. This may be due in part to less uniform mixing of the larger beads (which tended to sink more rapidly during phantom preparation than the smaller beads). Another possible factor may be contributions from higher-order cumulants to the phase evolution of the signal as a function of echo time. In calculating the frequency maps for the susceptibility measurements, the phase was fitted with a linear function of TE, thereby ignoring higher-order cumulants. Those cumulants would have been more important for the larger beads than the smaller beads.

In the interests of full transparency, all measurements are included in the file. However, we have more confidence in the results for the small (10-µm) beads than the larger beads for the reasons outlined above.


Pippa Storey and Dmitry Novikov
Signatures of microstructure in gradient-echo and spin-echo signals.
Under review at Magnetic Resonance in Medicine.

Get the Data

This resource is 9.10 GB in size.

The data available on this page are provided free of charge and come without any warranty. CAI²R and NYU Grossman School of Medicine do not take any liability for problems or damage of any kind resulting from the use of the files provided. Use of the data is solely at the user’s own risk. The data provided are not medical products and must not be used for making diagnostic decisions.

The data are provided for non-commercial, academic use only. Usage or distribution of the data for commercial purpose is prohibited. All rights belong to the author (Pippa Storey) and NYU Grossman School of Medicine. If you use the data for academic work, please give credit to the author in publications and cite the related publications.

Please spell out your affiliation (e.g. “New York University” rather than “NYU”).

Contact

Questions about this resource may be directed to Pippa Storey, PhD.