Ultra‐short T₂ components imaging of the whole brain using 3D dual‐echo UTE MRI with rosette k‐space pattern

Abstract

Purpose

This study aimed to develop a new 3D dual‐echo rosette k‐space trajectory, specifically designed for UTE MRI applications. The imaging of the ultra‐short transverse relaxation time (uT₂) of brain was acquired to test the performance of the proposed UTE sequence.

Theory and Methods

The rosette trajectory was developed based on rotations of a “petal‐like” pattern in the k _x –k _y plane, with oscillated extensions in the k _z ‐direction for 3D coverage. Five healthy volunteers underwent 10 dual‐echo 3D rosette UTE scans with various TEs. Dual‐exponential complex model fitting was performed on the magnitude data to separate uT₂ signals, with the output of uT₂ fraction, uT₂ value, and long‐T₂ value.

Results

The 3D rosette dual‐echo UTE sequence showed better performance than a 3D radial UTE acquisition. More significant signal intensity decay in white matter than gray matter was observed along with the TEs. The white matter regions had higher uT₂ fraction values than gray matter (10.9% ± 1.9% vs. 5.7% ± 2.4%). The uT₂ value was approximately 0.10 ms in white matter .

Conclusion

The higher uT₂ fraction value in white matter compared to gray matter demonstrated the ability of the proposed sequence to capture rapidly decaying signals.

Short abstract

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1. INTRODUCTION

Conventional ¹H‐MRI sequences are widely used for in vivo imaging, which focus on detecting signals from tissues with relatively long transverse relaxation time (T₂). However, depending on the surrounding chemical environment, some protons in specific tissues in the human body have an ultra‐short T₂ (uT₂), which conventional MRI can hardly detect due to their relatively long TEs, on the order of milliseconds (ms). For example, the myelin bilayer in cerebral white matter (WM), ¹ cortical and trabecular bones, ² ligaments, ³ and tissues with high iron concentration ⁴ have uT₂ values. On the other hand, UTE MRI ⁵ sequences are capable of acquiring data with TEs on the order of microseconds (μs), which can provide images of tissues with uT₂ directly.

For UTE sequences, the readout gradients are applied immediately after the completion of the RF pulses. Therefore, to achieve the minimum possible TE, each data acquisition in UTE sequences needs to follow a center‐out trajectory. Although 2D UTE methods are available, they have limitations making it difficult to achieve an appropriate slice selection and a minimum TE due to eddy currents and imperfect gradients. ⁶ , ⁷ While some advanced techniques overcome the problems of 2D UTE, ⁸ the most common k‐space trajectory used in UTE MRI applications is a 3D radial center‐out readout. However, sampling the outer k‐space with a radial pattern may not be efficient. ⁹ Therefore, novel 3D k‐space trajectories with greater curvature per spoke have been proposed for a more efficient sampling strategy, e.g., the spiral‐like extended cones sampling. ⁹ , ¹⁰ Other state‐of‐the‐art 3D UTE techniques include density‐adapted 3D radial UTE, ¹¹ Fermat looped, orthogonally encoded trajectories UTE sequence ¹² and a 3D koosh ball trajectory UTE sequence. ¹³ Rosette k‐space trajectories, which allow a center‐out sampling pattern while providing more samples in the outer k‐space per spoke than radial trajectories, are also potential candidates for 3D UTE MRI. In addition, the rosette k‐space trajectory samples data in a more incoherent pattern than radial trajectories. Therefore, it offers the potential for further acceleration using higher under‐sampling factors and compressed sensing (CS) technique for reconstruction. ¹⁴ However, 3D rosette k‐space patterns have not yet been demonstrated in UTE applications.

Alternatively, a similar MRI‐based technique, zero TE (ZTE) MRI, has also been proposed for imaging uT₂ tissue. However, unlike UTE imaging, the readout gradients are applied before the RF pulse and are always on in ZTE sequences. ¹⁵ In addition, the center k‐space in the ZTE sequence is empty because of the dead time due to the switching from RF pulse excitation to data receiving, ¹⁵ which requires additional scans or interpolation based on an over‐sampling strategy to fill in the missing k‐space. ¹⁶ Nevertheless, a recent comparison study has shown that UTE and ZTE MRI sequences provide similar image quality and SNR. ¹⁷

One exciting application of 3D UTE and ZTE sequences is in imaging of the myelin bilayer in brain WM. Myelin constituents are water and dry mass, in which the dry mass is composed of about 80% lipids and 20% protein. ¹⁸ Since transverse relaxation of the lipid proton signal becomes shorter in this geometrically restricted environment, T₂ values vary from a few microseconds to milliseconds, where 75% of the myelin lipid signal manifests T₂ values below 100 μs. ¹⁹ Thus, conventional MRI sequences with TEs in the order of milliseconds or longer can hardly capture the rapid signal decay of the lipid bilayer.

Many alternative MRI‐based methods have been proposed for myelin imaging, e.g., methods based on magnetization transfer effects, separation of myelin water signals, susceptibility imaging, and cortical myelin mapping. ²⁰ , ²¹ , ²² , ²³ However, while those methods provide an indirect measurement of myelin, UTE MRI can measure uT₂ components of myelin, which may be more specific and more precise. ¹⁰ , ²⁴

UTE MRI methods have shown great promise for imaging the signals arising from the phospholipid chains of myelin sheaths. Common techniques for the separation of myelin signals based on UTE acquisitions are the combination of inversion recovery suppression ¹ and dual‐echo subtraction. ²⁵ Even though those methods showed the potential to suppress signals originating from long‐T₂ components in both gray matter (GM) and WM, the inversion time of inversion recovery suppression is difficult to choose because of the wide range of longitudinal relaxation time (T₁) reported in WM (700 to 1100 ms at 3T). ²⁶ , ²⁷ An alternative method to quantify uT₂ components was using a dual‐exponential model fitting with data input based on a multiple TE acquisition, ranging from microseconds to milliseconds. ²⁸

This study aims to develop a novel rosette k‐space pattern for 3D UTE MRI and assess the sequence by directly and non‐invasively measuring the uT₂ components of whole‐brain. With the novel k‐space design, dual‐echo data are sampled in a single acquisition, allowing an extended TE coverage for the dual‐exponential complex model fitting. In addition, CS and low‐rank denoising were applied to reconstruct images from the acquired non‐Cartesian k‐space data.

2. THEORY

Rosettes are non‐Cartesian k‐space trajectories with high design flexibility. ²⁹ The rosette trajectories are well known for the multiple crossings of k‐space origin, ³⁰ which suggests the potential for multiple‐echo acquisition.

The following equations define the 3D rosette k‐space trajectory ³¹ :

$$\begin{array}{ll}\hfill K_{\mathit{xy}}(t)& =\mathit{Kx}(t)+i*\mathit{Ky}(t)\\ & =(K\max *\cos (\phi ))*\sin \left({\omega }_1*t\right)*e^{i{\omega }_{2}t+\beta }\end{array}$$ (1)

$$K_z(t)=(K\max *\sin (\phi ))*\sin \left({\omega }_1*t\right)$$ (2)

where $K\max$ is the maximum extent of k‐space, ${\omega }_1$ is the frequency of oscillation in the radial direction, ${\omega }_2$ is the frequency of rotation in the angular direction, $\phi$ determines the location in the z‐axis, and $\beta$ determines the initial phase in the angular direction.

In Figure 1A, a rosette trajectory is shown for the specific case where ${\omega }_1$ and ${\omega }_2$ are set to be equal. The origin of the k‐space is sampled at the beginning and the end of each TR, forming a petal‐like sampling pattern (Figure 1A). Dual‐echo images can be generated within a single acquisition with a manual separation at the middle of each data readout (Figure 1A,B). TE values are separately determined by the time of two crossings of the k‐space origin. The gradients of one petal trajectory are shown in Figure 1B. A specific gradient ramp‐up was used to keep the overall rosette shape (Supporting Information Figure S1, which is available online), which resulted in oversampling at the center k‐space. The ADC (analog to digital converter) was turned on during this gradient ramp‐up period to enable the shortest possible TE (details in Section 5). The separate k‐space trajectories in the x, y, and z directions are also shown in Figure 1B.

FIGURE 1.

Illustrations of the 3D rosette k‐space design. A, Selective spokes with varied rotations in the k _x –k _y plane and varied extensions in the k _z ‐axis are shown. Each spoke crosses the origin of k‐space at the beginning and the end, forming a “petal‐like” pattern. The dual‐echo acquisition (blue: first echo, red: second echo) was generated based on manual separation at the middle of each “petal‐like” pattern. B, The gradients in all three directions (red: gradients in the x‐axis, Gx; blue: gradients in the y‐axis, Gy; black: gradients in the z‐axis, Gz) of a selective spoke as shown in Figure 1A. The separated k _x , k _y , and k _z curves are also shown in Figure 1B (red dash line: k_x; blue dash line: k_y; black dash line: k_z). All gradients began at zero amplitude to avoid any potential delays caused by the gradients' ramp‐up. C, A 2D example to illustrate the differences between rosette (blue) and radial (red) acquisitions in peripheral (outer) k‐space coverage (regions between black dash lines). With greater curvature, rosette trajectory provides more samples in the peripheral k‐space than radial trajectory

The influence of the value of ${\omega }_1$ and ${\omega }_2$ is mainly on the speed of trajectory. For the dual‐echo acquisition, at the end of the readout duration, the trajectory needs to be located at the exact k‐space origin, which requires:

$${\omega }_1*\text{samples}\mathrm{per}\text{petal}*\text{dwell time}=\pi$$ (3)

where dwell time is 10 μs. In this study, ignoring the oversampling, 195 samples per petal were acquired (210 samples counting the oversampling). The parameters ${\omega }_1={\omega }_2$ are then calculated as:

$${\omega }_1={\omega }_2=\frac{\pi }{195*10}*1000=1.611\mathrm{kHz}.$$ (4)

The other parameters for the UTE acquisition with 2 × 2 × 2 mm³ spatial resolution were: $K\max =250\mathrm{m}$, number of total petals = 36100, samples per petal = 210, $\phi$ was sampled uniformly in the range of ($-\pi /2,\pi /2)$, and $\beta$ was sampled uniformly in the range of $(0,2\pi$). With 10 μs readout dwell time, the difference between first TE (TE₁) and second TE (TE₂) is equal to $210\times 10\mathrm{\mu s}=2.1\mathrm{ms}$ (other scan parameters are stated in the Section 3). Based on Nyquist criteria calculation, to avoid artifacts, the minimum number of total petals should be $4\pi *r^2\approx 45239$, where r represents half of the 1D matrix size (r = 60 in this paper). Due to the 3D rosette k‐space pattern (i.e., the curvature and k‐space coverage), this 80% (36 100/45 000) undersampling pattern did not suffer significant artifacts. The noise generated by the undersampling strategy was primarily removed by CS reconstruction. Because of these reasons, the trajectory with 36 100 petals is considered to be a fully sampled k‐space for the purpose of this study. The Nyquist criteria for samples per petal varied depending on $\varphi$ and $\beta$. It reaches the maximum required samples when $\varphi =0$, which is $\pi *r=189$ samples per petal (the number is for two TEs). Crusher gradients in all three directions were applied at the end of each readout gradient (not shown in Figure 1B).

The 3D radius (including all x, y, and z directions) of the rosette trajectory is expressed with a sine function ($K\max *\sin \left({\omega }_1*t\right)$), which varies within $(0,K\max$). In addition, the 3D radius of the rosette trajectory has a fast rate of change at small radii of k‐space but a slow velocity at large radii of k‐space. With the constant readout dwell time, the k‐space velocity difference led to increased samples with the radii of k‐space for each readout spoke (about 43% of samples at radii of k‐space larger than $0.75K\max$). However, for each readout spoke, the 3D radius of the standard radial trajectory has a constant rate of change, which led to a uniform sampling with the 1D radii of k‐space (25% samples at radii of k‐space larger than $0.75\mathit{\text{Kmax}}$). A 2D example is illustrated in Figure 1C.

3. METHODS

For quantitative comparison of the sampling trajectories, the shift‐invariant point spread functions (PSFs) of full rosette k‐space patterns (first and second echoes), half undersampled rosette k‐space pattern, and 3D radial acquisition with golden angle, were calculated with a fast Fourier transform based method. ³²

The study was approved by the Institutional Review Boards of Purdue University. Five healthy subjects underwent brain scans with a whole‐body 3T MRI system (Prisma, Siemens, Erlangen, Germany), with a maximum gradient amplitude of 80 mT/m and maximum slew rate of 200 mT/m/ms isotropically. A vendor‐supplied 20‐channel receiver head coil was used for all volunteers. An magnetization‐prepared rapid gradient‐echo (MPRAGE) sequence was performed before the UTE sequence for the anatomical reference. The parameters used in the dual‐echo 3D UTE sequence with rosette k‐space sampling were: Field of view = 240 x 240 x 240 mm³, matrix size = 120 x 120 x 120, readout dwell time = 10 μs, flip angle = 7‐degree, TR = 7 ms, readout duration = 2.1 ms, and RF pulse duration = 10 μs. Ten repeated dual‐echo UTE scans were performed with varied TEs. The first TEs were 20, 40, 60, 80, 100, 150, 300, 600 μs; 1 and 1.5 ms. The second TEs were 2.12, 2.14, 2.16, 2.18, 2.2, 2.25, 2.4, 2.7, 3.1, and 3.6 ms. For one dual‐echo UTE acquisition, 36 100 petals were acquired (full k‐space acquisition without acceleration), resulting in a scan duration of 4.2 min (36 100 x 7 ms). The 10 repeated UTE scans lasted 42 min, and the total scan time was about 50 min for each volunteer.

Image reconstruction and post‐processing steps were performed in MATLAB (MathWorks, USA). The nonuniform fast Fourier transform was used to calculate the forward encoding transform of the acquired k‐space data. ³³ A CS approach was used for image reconstruction, using total generalized variation as the sparsifying penalty. ³⁴ The complex‐valued coil sensitivity maps were first extracted from the center of k‐space using ESPIRIT for coil combination. ³⁵ Then, the reconstructed complex image data were combined for each TE and resulted in the magnitude image data.

The post‐processing procedure was performed using FMRIB Software Library and Statistical Parametric Mapping software. The workflow of post‐processing steps was summarized in Figure 2, including registration to T₁‐weighted anatomy images, ³⁶ , ³⁷ brain tissue extraction, ³⁸ bias‐field correction, ³⁹ voxel‐wised LORA (low‐rank approximations) correction to reduce spurious fluctuations while preserving the relevant signal decays, ⁴⁰ and voxel‐wised dual‐exponential fitting based on the magnitude of the free induction decay signal. Ten dual‐echo UTE acquisitions allow to use additional 10 second TEs in the model for dual‐exponential fitting. The fitting model was expressed as the equation ²⁸ , ⁴¹ :

$$\begin{array}{cc}& S(\mathrm{TE})=S_{0,\text{short}}\exp \left(-\frac{\mathrm{TE}}{{{{\mathrm{T}}_2}^{*}}_{\text{short}}}\right)*\exp \left(2\pi ∆f_{\text{short}}\mathrm{TE}\right)\dots \\ & +S_{0,\text{long}}\exp \left(-\frac{\mathrm{TE}}{{{{\mathrm{T}}_2}^{*}}_{\text{long}}}\right)*\exp \left(2\pi ∆f_{\text{long}}\mathrm{TE}\right)\end{array}$$ (5)

where $S_{0,\text{short}}$ and $S_{0,\text{long}}$ are the proton density, and $∆f_{\text{short}}$ and $∆f_{\text{long}}$ are the frequency shift with short ${\mathrm{T}}_2^{*}({{{\mathrm{T}}_2}^{*}}_{\text{short}}$), and long ${\mathrm{T}}_2^{*}\left({{{\mathrm{T}}_2}^{*}}_{\text{long}}\right)$, respectively. After the fitting, the voxel‐wised ratio between $S_{0,\text{short}}$ and the total proton density $\left(S_{0,\text{short}}+S_{0,\text{long}}\right)$ was reported as uT₂ fraction map, and ${{{\mathrm{T}}_2}^{*}}_{\text{short}}$ and ${{{\mathrm{T}}_2}^{*}}_{\text{long}}$ were reported as uT₂ value and long‐T₂ value maps. All maps were registered to a standard brain atlas (MNI‐152) for better visualization and then were averaged across subjects for statistical analysis. The uT₂ fractions in total WM and total GM were reported individually and as mean across subjects. A two‐sample t‐test was used to test whether the uT₂ fractions were statistically different between GM and WM. In addition, the uT₂ fractions were quantified based on selected regions of interest (ROIs), including cingulum, corona radiata, internal capsule, corpus callosum, external capsule, fornix, and sagittal stratum.

FIGURE 2.

Workflow from data acquisition, image reconstruction to post‐processing. NUFFT, nonuniform fast Fourier transform; MPRAGE, magnetization‐prepared rapid gradient‐echo; LORA, low rank approximations.

A phantom and one volunteer were scanned using the dual‐echo 3D rosette UTE sequence and a 3D radial UTE sequence with golden angle acquisition ⁴² to compare the image quality after reconstruction. For this comparison, most of the imaging parameters were identical or the closest possible values between the two sequences, which were: Number of spokes (petals) = 36 100, TE_rosette = 20 μs, TE_radial = 30 μs, TR = 7 ms, flip angle = 7‐degree, field of view = 240 × 240 × 240 mm³, matrix size = 128 × 128 × 128, readout dwell time = 10 μs, and RF pulse duration = 10 μs. For the dual‐echo 3D rosette UTE sequence, 105 samples were acquired per petal per TE, while 128 samples were acquired per spoke for 3D radial UTE. Two reconstruction methods were performed: CS (as described above) and regular regridding applying a density compensated adjoint nonuniform fast Fourier transform. The reconstruction processing steps were kept identical for the data acquired by both the dual‐echo 3D rosette and radial UTE sequences. In addition, a Cartesian‐based fast low angle shot (FLASH) sequence was performed for comparison to evaluate the image quality (imaging parameters for phantom: Spatial resolution = 2 × 2 × 2 mm³, matrix size = 128 × 128 × 56, TE = 2.77 ms, TR = 7 ms, flip angle = 7‐degree, imaging parameters for in vivo: Spatial resolution = 2 × 2 × 2 mm³, matrix size = 128 × 128 × 128, TE = 2.59 ms, TR = 7 ms, flip angle = 4‐degree). The SNRs were calculated based on the mean signal intensities of the ROIs over the SD of the signal intensities in three background ROIs. In addition, image quality was assessed by the structural similarity index to the reference image acquired by the FLASH sequence.

4. RESULTS

The trajectory PSFs with dB unit are shown in Figure 3. The full rosette k‐space patterns (first and second echoes) have the highest PSF peak value, which is around −1.15 dB, and a full width at half maximum at (2.23, 2.23, 2.23 mm). In contrast, the half undersampled rosette k‐space pattern suffers further signal loss to have PSF peak value around −1.58 dB, and a full width at half maximum at (2.20, 2.20, 2.30 mm). The radial UTE with golden angle acquisition (same number of spokes compared to full rosette pattern) has the PSF peak value in between, which is −1.37 dB, and a full width at half maximum at (2.19, 2.19, 2.31 mm).

FIGURE 3.

Point spread function (PSF) comparison among different k‐space designs. The top figures represented the center slice in x–y plane of the 3D PSF. The bottom figures showed the center line in x‐axis (−70 to 70 mm) of the top figures. All results were converted into dB units to illustrate signal loss. The peak values of the PSF were also identified in the bottom figures. A, Rosette first echo k‐space trajectory. B, Radial UTE k‐space trajectory with golden angle acquisition. C, Rosette first echo k‐space trajectory with undersample factor = 2. D, Rosette second echo k‐space trajectory

Figure 4 (phantom) and Supporting Information Figure S2 (in vivo) compare the dual‐echo 3D rosette UTE sequence and the 3D radial UTE sequence. All the reconstructed images were normalized to have signal intensity ranging from 0 to 1. The standard regridding reconstruction method resulted in “ringing” artifacts for both acquisition methods (as shown in Figure 4B,D,F and Supporting Information Figure S2B,D,F), which had been minimized by the CS reconstruction method (as shown in Figure 4A,C,E and Supporting Information Figure S2A,C,E correspondingly). The reconstructed image quality by the dual‐echo 3D rosette UTE sequence was overall better than the 3D radial UTE, in terms of SNR (as shown in Figure 4A vs. 4E, and Supporting Information Figure S2A vs. S2E), and the ability to capture additional structural information (white dots as shown in Figure 4A, but not shown in Figure 4E). In addition, the dual‐echo 3D rosette sequence detected the rapid decaying signals originating from the foam pad used for positioning (Supporting Information Figure S3). However, the foam pad was not identified by the 3D radial sequence.

FIGURE 4.

Phantom performance comparison between UTE sequences with 3D dual‐echo rosette trajectory and 3D radial golden angle trajectory. All the images were normalized to have signal intensity from 0 to 1. A, C, E, Reconstructed images based on compressed sensing (CS) technique from data sampled by the first echo of rosette trajectory (A), the second echo of rosette trajectory (C), and radial trajectory (E). B, D, F, Reconstructed images based on regridding (RG) technique from data sampled by the first echo of rosette trajectory (B), the second echo of rosette trajectory (D), and radial trajectory (F)

The results of the ROI‐based quantitative comparison are shown in Figure 5. The ROIs of phantom and in vivo images (reconstructed by regridding) were selected arbitrarily (red rectangular in Figure 5). The 3D rosette k‐space pattern reports higher SNR than 3D radial UTE acquisition with golden angle, based on phantom scans (rosette first TE: 315, rosette second TE: 211, vs. radial: 40) and in vivo scans (rosette first TE: 137, rosette second TE: 113, vs. radial: 43). The 3D rosette k‐space pattern has slightly higher similarity to the FLASH images than the 3D radial, based on both phantom scans (rosette first TE: 0.89, rosette second TE: 0.87, vs. radial: 0.86) and in vivo scans (rosette first TE: 0.72, rosette second TE: 0.66, vs. radial: 0.65).

FIGURE 5.

Quantitative performance comparison between UTE sequences with 3D dual‐echo rosette trajectory and 3D radial golden angle trajectory. All the images were normalized to have signal intensity from 0 to 1. The similarity was evaluated based on the ROI (red rectangular), using the structural similarity index with images acquired by the Cartesian FLASH sequence as reference. The SNR was calculated based on the mean signal intensity inside the ROI over the SD of the background (not shown in the Figure). A, anterior; L, left; P, posterior; R, right; FLASH, fast low angle shot.

In Figure 6A, brain image slices from a volunteer are shown for five representative TEs, 20 μs, 100 μs, 2.12 ms, 2.4 ms, and 3.6 ms. There was little or no contrast between WM and GM at the minimum UTE (TE = 20 μs), whereas the contrast between WM and GM increased at longer TE, as expected.

FIGURE 6.

A, Five brain image slices with 20 μs, 100 μs, 2.1 ms, 2.4 ms, and 3.6 ms TEs from a volunteer are shown. B, Signal decay curves from selected ROIs, which are identified as white matter (WM) ROI (left bottom corner) and gray matter (GM) ROI (right upper corner). All signals were normalized based on the shortest TE (∼20 μs). The stars showed the distribution of signals with different TEs from WM ROI (blue) and GM ROI (red). Black dash lines were used to identify the UTE region (below 0.15 ms). The fitting results of WM ROI: uT₂ fraction = 13.0%, uT₂ value = 0.13 ms, long T₂ value = 60.9 ms. The fitting results of GM ROI: uT₂ fraction = 8.7%, uT₂ value = 0.09 ms, long T₂ value = 74.9 ms

Figure 6B shows the differences in signal decay between WM ROI (blue) and GM ROI (red). The signal intensities with different TEs were normalized based on the detected signal at the shortest TE of 20 μs. WM and GM signal decay curves showed fast signal drop at UTE period (below 0.15 ms), which was about 5% in selected WM ROI and about 4% in GM ROI. The signal curve of WM ROI continued to drop (about 15% at TE = 3.6 ms), while the signal curve of GM ROI had a slower decay at longer TEs (about 10% at TE = 3.6 ms).

Table 1 summarizes the uT₂ fraction, uT₂ values, and long‐T₂ values in total GM and total WM individually and as mean across subjects. The voxels containing fitting results of uT₂ values longer than 1 ms were identified as outliers and excluded (portion of outliers: 0%–5% in WM, 3%–15% in GM). All subjects and the average indicated a significantly higher uT₂ fraction in WM than GM (P < 0.0001 for all subjects and the mean). The average WM uT₂ fraction across subjects was 10.9% ± 1.9%, and the average GM uT₂ fraction across subjects was 5.7% ± 2.4%. In addition, the average WM uT₂ value was 0.10 ± 0.06 ms, and the average WM long‐T₂ value was 54 ± 18 ms. In contrast, the average GM uT₂ value was 0.09 ± 0.12 ms, and the average GM long‐T₂ value was 57 ± 21 ms.

TABLE 1.

Individual and mean across subjects ultra‐short T₂ fractions, ultra‐short T₂ values, and long T₂ values in total white matter (WM) and total grey matter (GM). All values are shown as mean ± standard deviation. The voxels containing fitting results of uT₂ values longer than 1 ms were excluded. A two‐sample t‐test was used to test whether the ultra‐short T₂ fractions were statistically different between GM and WM, which P‐values were calculated

	uT2 fractions			uT2 values		Long T2 values
Subject number	Total GM	Total WM	P‐values	Total GM	Total WM	Total GM	Total WM
1	7.5% ± 1.1%	11.6% ± 0.9%	<0.0001	0.07 ± 0.10	0.07 ± 0.02	66 ± 17	54 ± 13
2	3.7% ± 1.4%	9.9% ± 1.3%	<0.0001	0.09 ± 0.16	0.07 ± 0.10	45 ± 19	43 ± 18
3	3.9% ± 2.1%	9.1% ± 1.0%	<0.0001	0.09 ± 0.08	0.09 ± 0.04	71 ± 15	67 ± 13
4	8.7% ± 1.4%	13.8% ± 1.2%	<0.0001	0.10 ± 0.08	0.12 ± 0.03	74 ± 13	64 ± 13
5	5.4% ± 1.6%	10.5% ± 1.1%	<0.0001	0.10 ± 0.11	0.11 ± 0.06	43 ± 14	38 ± 9
Total	5.7% ± 2.4%	10.9% ± 1.9%	<0.0001	0.09 ± 0.12	0.10 ± 0.06	57 ± 21	54 ± 18

Figure 7 shows the mean uT₂ fraction map (Figure 7A), the mean uT₂ value map (Figure 7B), and the mean long‐T₂ value map (Figure 7C) in MNI‐152 space. The uT₂ fraction map (Figure 7A) indicated a generally homogeneous uT₂ fraction among voxels in WM, which was higher than the uT₂ fraction among voxels in GM. A generally slightly faster uT₂ value was observed in GM than in WM. The long‐T₂ component value map indicated an increased T₂ value across GM and the CSF compared to the WM, which is in line with previous reports. ²⁸ , ⁴³ (The uT₂ fraction and uT₂ value maps from two subjects are shown in Supporting Information Figure S4). The mean frequency shift ($∆f_{\text{short}}-∆f_{\text{long}})$ map is shown in Supporting Information Figure S5. A significant difference in frequency shift is observed between WM (around −5 to −40 Hz) and GM (around −150 to −200 Hz).

FIGURE 7.

The results of dual‐exponential fitting: the mean ultra‐short T₂ components (uT₂) fraction map (A), the mean uT₂ value map (B), the long T₂ value map (C). Please note that some voxels were black in Figure 7B (primarily located in cerebrospinal fluid and gray matter), caused by high uT₂ values reaching the top threshold of the color bar. A, anterior; L, left; P, posterior; R, right;

Figure 8 summarizes the mean and SD of the uT₂ fraction among different ROIs across five subjects (cingulum, corona radiata, internal capsule, corpus callosum, external capsule, fornix, and sagittal stratum). The ROI locations are indicated on the left and right sides of Figure 8. All the ROIs were identified as WM‐rich regions and reported about 10% as the uT₂ fraction. The lowest reported ROI‐based uT₂ fraction value, 9.4% ± 1.0%, was in the corpus callosum. The highest reported ROI‐based uT₂ fraction value, 12.2% ± 1.6%, was in the fornix.

FIGURE 8.

The mean (blue columns) and SD (red) of ultra‐short T₂ components (uT₂) fraction among different ROIs across subjects, quantified based on the five individual uT₂ fraction maps. The locations of the ROIs are indicated on the left and right sides of the image. CC, corpus callosum; CR, corona radiata; IC, internal capsule

5. DISCUSSION

This study developed a novel 3D dual‐echo UTE sequence based on a rosette k‐space trajectory. The advantages of this novel design included: (1) increased sampling density in the outer k‐space, (2) improved PSF and SNR compared to radial acquisition, (3) a smooth transition (zero‐delay) between the two echoes of dual‐echo acquisition. As a result, a statistically significantly higher uT₂ fraction value was found in WM compared to GM. In addition, the uT₂ fraction value was homogeneously distributed among WM voxels.

The achievement of the shortest TE in UTE sequences is limited by the system hardware, not only by the dead time ¹⁵ but also by the slew rate limitation if the initial gradient amplitude is high in any direction. In this 3D rosette k‐space design, a specific gradient ramp‐up was used to maintain the overall rosette shape. In the meantime, the ADC was turned on during ramp‐up time to provide UTE. The strategy was to gradually increase the ${\omega }_1$ and ${\omega }_2$ to the designed value of 1.611 kHz at the beginning of each TR. With this strategy, the maximum slew rate was about 140 mT/m/ms for all three directions separately. In addition, the initial sampled data still followed the originally designed rosette trajectory, which was used for image reconstruction. This resulted in an over‐sampling at the center k‐space (about 20% of samples located in radii of k‐space smaller than $0.25K\max$), which could improve the SNR. Similar to ZTE applications, this study used a small flip angle (7‐degree). Although large flip angles are allowed in UTE acquisition, a small flip angle could minimize the T₁ influence on the detected signals. ⁴⁴

The volume of the 3D k‐space is proportional to the cube of the radius of the acquired k‐space. The volume of radii larger than $0.75K\max$ (considered as peripheral k‐space) occupied about 58% (= [1³ – 0.75³]/1³) of the entire volume of 3D k‐space with the radius of $K\max$. However, the volume of radii smaller than $0.25K\max$ (considered as center k‐space) only occupied about 2% (= 0.25³/1³) of the entire volume of k‐space. This resulted in a much larger peripheral k‐space than the center k‐space volume in 3D cases. Therefore, the conventional radial acquisition, which samples uniformly along with the 1D radius of k‐space (25% of samples at center k‐space, and 25% of samples at peripheral k‐space), may not be efficient at the large radii of 3D k‐space. Under the specific circumstances, e.g., 80% undersampling number of spokes, the PSF analysis demonstrated that the 3D radial acquisition suffered more noise with a lower peak value than the 3D dual‐echo rosette trajectory. The reconstructed images acquired by the 3D radial pattern confirmed that disadvantage, which resulted in noise amplification and the loss of structural details. In addition to the insufficient samples at the large radii of 3D k‐space, the suboptimal imaging parameters, such as the insufficient number of spokes and long TR set to match 3D dual‐echo rosette UTE, further contributed to the degraded performance of 3D radial acquisition. The structural similarity index indicated a higher value of phantom images (around 0.9) than in vivo images (around 0.7), compared to the reference acquired by the Cartesian FLASH sequence. This may be because the contrast of in vivo images is highly related to the imaging parameters, including TE, TR, and flip angle. However, the inner plastic gridding mainly determines the contrast of phantom images.

The newly proposed 3D rosette trajectory has increased samples at larger radii of k‐space, which provides greater sampling density in peripheral k‐space. The advantages of the newly proposed 3D rosette trajectory (i.e., trajectory curvature and k‐space coverage) may have the potential for further acceleration by acquiring fewer petals without losing image quality. As stated in the Theory section, the number of petals (spokes) used to compare the dual‐echo 3D rosette and the 3D radial trajectories is an 80% undersampling pattern. However, using the CS reconstruction, the reconstructed dual‐echo 3D rosette images did not suffer from significant artifacts. They did not lose structural information compared to the images acquired by the 3D radial scan. In addition, although the regridding method resulted in sharper images, they suffered from “ringing” artifacts, which could be caused by gradient imperfections or sampling density compensation. In this study, the CS reconstruction was tuned to minimize the “ringing” artifact, with the cost of some loss of effective spatial resolution. Adapting this dual‐echo 3D rosette trajectory to retain image quality with an undersampling strategy may lead to future directions. For example, with an additional undersampling factor = 2 (40%) or 4 (20%), the total scan time of the 10 dual‐echo UTE sequences can be shortened to between 21 and 10 min, which could be acceptable in clinical settings (reconstructed images with undersampling factor = 2 were tested for further acceleration purpose and are shown in Supporting Information Figure S6).

Instead of combining inversion recovery suppression and dual‐echo subtraction, ¹⁰ dual‐exponential complex fitting was performed in this study, offering uT₂ fraction and uT₂ value maps. Although the quantitative analysis of the uT₂ fraction and value maps still needs validation, ¹⁰ this method showed a potential way to compare across subjects. The setback of this method was the need for a multiple TEs acquisition, which increased total scan time. However, with the dual‐echo rosette sequence proposed in this study, 20 images with different TEs could be acquired in a reasonable total scan time. A clinically acceptable scan time can be achieved by further reducing acquisition duration with an undersampling strategy. Some publications used a three‐component exponential model with an additional intermediate T₂ range of around 10 ms for regression. ²⁸ This model might be more accurate. However, it significantly increases the unknown parameters that need to be estimated. The current TE samples may not support a fitting with a three‐component model, as the fitting results within some voxels were already unreliable with the current two‐component exponential model. In addition, a series of TEs in a wider range (i.e., including TE at 10 ms) may better describe the free induction decay curve of the long‐T₂ component. However, including TE at 10 ms will significantly increase TR (longest TE = 3.6 ms and TR = 7 ms in this study), which correspondingly increases the total scan time.

Overall, the results of uT₂ components quantification, acquired by the dual‐echo 3D rosette sequence, agree with previous publications with 3D radial or 3D cones trajectories. ¹⁰ , ⁴⁵ First, little or no contrast at short TEs (i.e., below 100 μs) was achieved without IR suppression. Second, larger signal decay in WM than in GM was observed, which increases the contrast between WM and GM at longer TEs. Third, the uT₂ components were mainly distributed in WM voxels, resulting in a generally higher uT₂ fraction value in WM compared to GM. Additionally, the uT₂ fraction values based on ROIs aligned with previous publications, ⁴⁶ , ⁴⁷ , ⁴⁸ around 10% to 12% in most WM‐rich brain regions.

One disadvantage of the 3D rosette k‐space pattern is that more samples per acquisition were needed (1.5 times more samples than radial). In addition, the long readout duration of this rosette trajectory (2.1 ms for dual‐echo acquisition, which means 1.05 ms for the first echo acquisition) may suffer image blurring caused by the fast signal decay. ⁶ A previous study has shown that the ideal sampling duration is 0.81*T₂ of the imaging tissue for radial UTE. ⁴⁹ However, such a short sampling duration would result in spatial resolution loss because not enough samples would be acquired. ⁶ Therefore, the sampling duration of two to four times T₂ of the imaging tissue was typically used. ⁶ For the myelin imaging applications, the sampling duration was usually set to 0.3 to 1 ms. ¹ , ²⁵ , ⁵⁰

One of the significant issues of model‐based processing is to fit a large number of parameters, long and ultra‐short signal decay rates, and respective frequency shifts. This results in complications with the degradation of the accuracy and precision of the parameter estimations. Although stable frequency differences between WM and GM were observed, ⁵¹ the frequency shift values may not be reliable because this study used magnitude data for the complex model. On the other hand, we attempted to use the complex data for the complex model. ²⁸ However, the estimations hit the boundary conditions and resulted in unstable and hence inhomogeneous estimates of parameters in two out of five subjects (data were not shown). This might be due to the relatively long acquisition duration for both echoes (2.1 ms), propagation of phase errors due to eddy currents, gradient delays, and breathing. One can overcome these limitations using field cameras. ⁵² Alternatively, the gradient impulse response function can be calculated to mimic the gradient chain's behavior and then used for the image reconstruction retrospectively. ⁵³

Recent publications showed that the brain iron content led to inaccurate results of the myelin water fraction (about 26%–28% decrease after iron extraction by reductive dissolution of brain slice samples) by myelin water imaging technique. ⁵⁴ Although 3D UTE rather than myelin water imaging was used in this study, the influence of iron content on the results was not ruled out. The presence of iron increases the magnetic field inhomogeneity, resulting in a shorter T₂*. As a result, some protons which have relatively long‐T₂ may be shortened into the uT₂ range ⁵⁵ within substantia nigra, ⁵⁶ putamen, ⁵⁷ and globus pallidus ⁵⁸ regions, which have potential age‐related iron accumulation. Those regions had high signal intensities in our reconstructed images of the novel dual‐echo 3D rosette acquisition with the shortest TE (∼20 μs). A new model for fitting could regress the iron effect out. ⁵⁹ In addition, quantitative susceptibility mapping ⁶⁰ may be applied for iron measurement since the proposed sequence allows a dual‐echo acquisition.

There are some other limitations of this study. First, the sample pool of five healthy volunteers was limited. Due to its nature as proof of concept, the sensitivity of the novel 3D rosette trajectory UTE sequence and/or the dual‐exponential model‐fitting method to detect diseased states (e.g., demyelination) is undetermined. A prospective study is required to address this limitation. Second, other macromolecules with similar uT₂ values may contribute to the detected signals. ⁵⁵ For future studies, patients (and/or animals) with different stages of myelination diseases will be recruited to test the performance of this novel rosette k‐space trajectory. In addition, a comparison of the 3D rosette dual‐echo UTE sequence to other MRI‐based methods, e.g., myelin water imaging and magnetization transfer, is another potential future direction.

In conclusion, this study proposed a novel dual‐echo 3D rosette k‐space trajectory, specifically for UTE MRI and MR spectroscopic imaging applications. ⁶¹ , ⁶² The higher uT₂ fraction value found in WM compared to GM demonstrated the ability of this sequence to capture rapidly decayed signals. In addition, the fitting based on the dual‐exponential model provided quantitative results of the uT₂ fraction, which could be used for myelination assessment in the future.

CONFLICT OF INTEREST

The authors have no conflict of interest to disclose.

Supporting information

FIGURE S1 Details of the oversampling strategy. (A) The trajectory of one petal located at x‐y plane without using oversampling strategy. (B) The trajectory of the same petal shown in (A), but with oversampling strategy. Zoomed‐in trajectories are shown at the right corner of (A) and (B) to show the locations of initial samples up to 6 m ky value. (C) The gradients waveform for (A) trajectory. (D) The gradients waveform for (B) trajectory

FIGURE S2 In vivo performance comparison between UTE sequences with 3D dual‐echo rosette trajectory and 3D radial golden angle. All the images were normalized to have signal intensity from 0 to 1. (A, C, E) Reconstructed images based on compressed sensing (CS) technique from data sampled by (A) the first echo of rosette trajectory; (C) the second echo of rosette trajectory; (E) radial trajectory. (B, D, F) Reconstructed images based on regridding (RG) technique from data sampled by (B) the first echo of rosette trajectory; (D) the second echo of rosette trajectory; (F) radial trajectory. A, anterior; I, inferior; L, left; P, posterior; R, right; S, superior

FIGURE S3 Performance comparison between UTE sequences with dual‐echo 3D rosette trajectory and 3D radial golden angle trajectory based on the phantom scan. All the images were reconstructed using the compressed sensing technique described in the Methods section and were normalized to have signal intensity in the range of 0 to 1. A colorbar with a reduced threshold (0 to 0.1) was used to highlight the foam pad used for positioning. The dual‐echo 3D rosette sequence with ultra‐short TE (20 μs) (A) detected the rapid decaying signals originating from the foam pad. However, the foam pad was not identified by the dial‐echo 3D rosette sequence with longer TE (2.12 ms) (B) or by the 3D radial sequence with ultra‐short TE (30 μs) (C)

FIGURE S4 Two representative subjects' results of ultra‐short T₂ components (uT₂) fraction maps and ultra‐short T₂ value maps are illustrated. (A, B) uT₂ fraction maps (A) and ultra‐short T₂ value maps (B) from one volunteer. (C, D) uT₂ fraction maps (C) and ultra‐short T₂ value maps (D) from another volunteer (different volunteer). A, anterior; I, inferior; L, left; P, posterior; R, right; S, superior

FIGURE S5 The results of mean frequency shift ($∆f_{\text{short}}-∆f_{\text{long}})$ after dual‐exponential regression. A, anterior; I, inferior; L, left; P, posterior; R, right; S, superior

FIGURE S6 Reconstructed brain image slices based on compressed sensing technique for the dual‐echo 3D rosette with TEs of 20 μs, 100 μs, 2.12 ms, 2.4 ms, and 3.6 ms from a volunteer are shown. All the image slices were normalized to have signal intensity in the range of 0 to 1. (A) Reconstruction results from full k‐space acquisition (number of petals = 36 100, 4.2 min for one dual‐echo acquisition). (B) Reconstruction results from 50% k‐space acquisition (undersampling factor = 2, number of petals = 18 050, 2.1 min for one dual‐echo acquisition)

FIGURE S7 Reconstructed brain image slices based on compressed sensing technique for the dual‐echo 3D rosette from a volunteer are shown. All the image slices were normalized to have signal intensity in the range of 0 to 1. (A) Reconstruction results of first echo and second echo from full k‐space acquisition. (B) Reconstruction results of first echo and second echo from 50% k‐space acquisition

Shen X, Özen AC, Sunjar A, et al. Ultra‐short T₂ components imaging of the whole brain using 3D dual‐echo UTE MRI with rosette k‐space pattern. Magn Reson Med. 2023;89:508‐521. doi: 10.1002/mrm.29451