Phase-based fast 3D high-resolution quantitative T₂ MRI in 7 T human brain imaging

Abstract

Magnetic resonance imaging (MRI) is a powerful and versatile technique that offers a range of physiological, diagnostic, structural, and functional measurements. One of the most widely used basic contrasts in MRI diagnostics is transverse relaxation time (T₂)-weighted imaging, but it provides only qualitative information. Realizing quantitative high-resolution T₂ mapping is imperative for the development of personalized medicine, as it can enable the characterization of diseases progression. While ultra-high-field (≥ 7 T) MRI offers the means to gain new insights by increasing the spatial resolution, implementing fast quantitative T₂ mapping cannot be achieved without overcoming the increased power deposition and radio frequency (RF) field inhomogeneity at ultra-high-fields. A recent study has demonstrated a new phase-based T₂ mapping approach based on fast steady-state acquisitions. We extend this new approach to ultra-high field MRI, achieving quantitative high-resolution 3D T₂ mapping at 7 T while addressing RF field inhomogeneity and utilizing low flip angle pulses; overcoming two main ultra-high field challenges. The method is based on controlling the coherent transverse magnetization in a steady-state gradient echo acquisition; achieved by utilizing low flip angles, a specific phase increment for the RF pulses, and short repetition times. This approach simultaneously extracts both T₂ and RF field maps from the phase of the signal. Prior to in vivo experiments, the method was assessed using a 3D head-shaped phantom that was designed to model the RF field distribution in the brain. Our approach delivers fast 3D whole brain images with submillimeter resolution without requiring special hardware, such as multi-channel transmit coil, thus promoting high usability of the ultra-high field MRI in clinical practice.

Introduction

Non-invasive biomedical imaging provides high-impact medical diagnostics and offers an ideal means of promoting preventative medicine. This is indeed the case when it comes to ultra-high field (≥ 7 T) Magnetic Resonance Imaging (MRI)^1,2,3. One high-value diagnostic MRI method is based on estimating the T₂ relaxation time of tissues—either T₂-weighted⁴ imaging or quantitative-T₂ mapping^5,6,7. T₂-weighted MRI of the brain is one of the most widely employed routine diagnostic methods in cancer and neurodegenerative diseases. It is essential for the detection of hyperintense lesions pronounced in demyelinating diseases, such as multiple sclerosis^8,9,10, and in the monitoring of disease progression⁹. In multiple sclerosis, improved precision at early stages of lesion formation would allow their clear categorization and aid in developing new tools to delay or eliminate the relapse. Recent studies at 7 T MRI have shown that we can detect smaller lesions than previously possible and so better monitor disease progression⁸. However, the robust characterization of disease progression with MRI requires quantitative T₂ mapping, the use of which in clinics is impeded by its long scan duration. Novel fast methods^11,12,13 encounter extra challenges in ultra-high field MRI among which are the severe RF field inhomogeneity¹⁴, which reduces the accuracy of the quantification, and the increased power deposition that results in prolonged scan duration. Common T₂ methods are especially prone to the above drawbacks since they are spin-echo-based, requiring refocusing pulses that are high in Specific Absorption Rate (SAR)¹⁵ and whose effectiveness is sensitive to RF field inhomogeneity.

Recent studies have proposed another solution—called Magnetic Resonance Fingerprinting (MRF)^16,17. This method allows parametric MR mapping (including T₁ and T₂ maps), thus eliminating the dependence on the specific scan parameter or scanner. However, MRF is not easily translated into ultra-high field MRI, since overcoming the RF field inhomogeneity further complicates the acquired dataset¹⁷. Designs based on the steady-state gradient echo (GRE) pulse sequences offer a plethora of pathways toward multi-contrast fast acquisitions, among which are simultaneous multi-parametric acquisitions^18,19 as well as a design for T₁ and T₂ weighted images in highly inhomogeneous static magnetic fields²⁰. These include DESPOT2²¹ and phase-cycled balanced steady-state free precession^22,23,24 (bSSFP). A method called TESS^19,25 shows promising results for T₂ mapping without RF field dependence, however, currently it was demonstrated only as a 2D implementation for brain imaging²⁶. Finally, a method analyzing the complex signal of a set of unbalanced GRE scans at 7 T gave T₁ and T₂ maps¹⁸, but included a long total scan duration (16:36 min) and used parallel transmission to mitigate the transmit field inhomogeneity.

Recently, a new method was introduced based on a steady-state spoiled gradient-echo (SGRE) acquisition that utilizes low flip angles and short repetition times (TRs) to obtain T₂ maps at 3 T MRI²⁷, assuming a uniform and a priori known flip angle. While most of the GRE-based studies have focused on magnitude images^20,21,28, in this study, phase information was highlighted, which offers a new and attractive method for T₂ mapping. Building on this work we elucidate the dependence of the phase-based method on the (unknown) excitation flip angle in addition to the RF pulse phase, with an eye to design an approach suited for T₂ mapping of the brain at 7 T. This new extension to the steady state method includes both T₂ and RF field estimation and is designed to cover the relevant flip angle range arising in the brain due to the RF field inhomogeneity at 7 T MRI (see Fig. 1). The advantage of this approach is its ability to simplify the signal dependencies and reduce the confounding variables. This includes the removal of the static magnetic field (B₀) dependence and a reduced dependence on the longitudinal relaxation time (T₁).

Figure 1

Schematics of the steady state method for T₂ and RF field estimation—its design and verification. Starting from simulations, through assessment of the estimation algorithm, via a 3D head-shaped brain-like phantom, to human imaging. Left—a design of a steady-state configuration based on Bloch simulations that provides θ(T₂,α) for specific φ_inc, which was thereafter utilized to generate T₂ and α in the 2D space (θ₁, θ₂). The new space allows to extract T₂ and α from θ₁ and θ₂. Center—the estimation algorithm was assessed via simulations and brain-like phantom measurements. In these measurements, a realistic signal $S$ was acquired, providing |S| and $\angle S$, from which the T₂ and α (or B₁ distribution) were estimated. Right—human imaging at 7 T MRI provided high-resolution whole-brain T₂ maps, while coping with the B₁ distribution.

Building on the phase-based approach by Wang^27,29, which departs from the traditional concepts based on spin-echo, our extension introduces a new T₂ mapping solution for ultra-high field MRI. This method can deliver quantitative T₂ mapping at 7 T MRI without requiring any additional hardware—such as dielectric pads or multi-channel transmit coil—to reduce the RF field inhomogeneity. Another advantage of this method is that it enables whole-brain imaging with high acceleration factors, as it relies on a 3D k-space acquisition.

Our study comprised three main steps (Fig. 1). First, we conducted Bloch simulations of the generated steady state signal for different scan parameters (such as RF flip angle, RF phase, and TR). Then, we looked for parameter combinations that support the range of flip angles, due to the RF field inhomogeneity, in 7 T brain imaging. Next, we developed and assessed an efficient estimation algorithm. Lastly, we performed human brain imaging on a 7 T MRI scanner. The estimation algorithm was assessed on synthetic signals from the Bloch simulations, as well as on actual measurements, in a realistic setting, via a 3D head-shaped phantom, which was designed to model the RF field distribution in the brain³⁰. For both the head-shaped phantom and the human brain imaging the phase-based method was compared with the gold-standard single-echo spin echo (SE–SE). Furthermore, we used the phase-based method to acquire whole-brain T₂ maps with sub-millimeter resolution.

Principles of the modified-SGRE sequence for simultaneous T₂ and RF field mapping

The foundation for using phase increments during the RF pulse train was provided by Zur et al. in 1988^31,32. They showed that an RF pulse train with a quadratic phase φ_RF(n) = φ_inc∙(n² + n)/2 for the n-th pulse—using an appropriate φ_inc value in conjunction with a spoiling gradient—can achieve incoherent transverse magnetization, an effective spoiling better than simple gradient spoiling (φ_inc = 0 case). This is commonly called RF spoiling. Recent work by Wang²⁷ at 3 T provided another keystone, in which the authors showed that small φ_inc values have the opposite effect; they introduce coherent transverse magnetization, where the phase of the signal possess a strong dependence on T₂ (Fig. 2a). Figure 2a also shows the dependence of the phase of the signal on the excitation flip angle α. The α dependence curves have an extremum in the vicinity of 15°, i.e., the actual flip angle in that vicinity has a small effect on the phase. As the flip angle in the 3 T implementation was assumed to be given by the scan (due to relatively homogeneous RF field distribution), T₂ values could be extracted solely from the phase of the signal.

Figure 2

The phase of the steady-state signal as a function of T₂ and the flip angle. (a) θ(T₂, α, T₁) dependence (Bloch simulation results) for a representative small φ_inc (φ_inc = 2°). The dependence on T₂, α, and T₁ is shown in 1D plots and in 2D. (b) T₂ and α distributions in the new (θ₁, θ₂) 2D space. Two examples are shown: Top—(φ_inc1 = 2°_, α_scan1) with (φ_inc2 = 2°_, α_scan2 = 2α_scan1). Bottom—(φ_inc1 = 3°_, α_scan1) with (φ_inc2 = 1.5°_, α_scan2 = 2α_scan1). In each case, α (θ₁, θ₂) and T₂ (θ₁, θ₂) are shown with the equi-T₂ and equi-α lines.

In our study, however, the combined (T₂, α) dependence of the signal’s phase θ was exploited to cope with the RF field inhomogeneity at ultra-high field MRI. Neglecting, for now, the small T₁ dependence of the phase—for T₁ values relevant to brain tissues at 7 T, see Fig. 2a—the phase θ of the signal depends on the T₂ at the voxel and on the actual flip angle α there. This α is the target flip angle of the scan α_scan scaled by the RF field ratio at each voxel: α = α_scan∙RF_ratio, where RF_ratio is the normalized RF field distribution. As the phase θ(T₂, α) (see Fig. 2a) is not a one-to-one map of (T₂, α) to θ, at least two measurements, θ₁ and θ₂, are needed; thus defining a 2D space (θ₁, θ₂). To extract T₂ and α from θ(T₂,α), we need a convenient 2D space to represent T₂ and α in each voxel_. Based on the Bloch simulations, such a 2D space can be generated by two scans with two flip angles, α_scan1 and α_scan2 = R_FA∙α_scan1 (R_FA is a user set multiplication factor; for example, R_FA = 2). Furthermore, we found that varying φ_inc between the two scans—one scan with (φ_inc1, α_scan1) and a second with (φ_inc2, α_scan2 = R_FA∙ α_scan1)—provides greater flexibility in controlling the 2D (θ₁, θ₂) space and its mapping to (T₂, α). Figure 2b shows that different combinations of phase increment and flip angle pairs can be useful to adjust the range of viable flip angles and the T₂ of interest.

The two phase measurements, θ₁ for scan parameters (φ_inc1, α_scan1) and θ₂ for scan parameters (φ_inc2, α_scan2), are functions of φ_inc1, φ_inc2, T₂ and the (actual) flip angles, i.e., θ₁ = θ(φ_inc1, α₁, T₂) and θ₂ = θ(φ_inc2, α₂, T₂), where α₁ and α₂ are the actual flip angles. Although α₁ and α₂ are unknown, their ratio must obey α₂/α₁ = α_scan2/α_scan1 $\equiv$ R_FA. Thus, renaming α₁ as α, we have θ₁ = θ(φ_inc1, α, T₂) and θ₂ = θ(φ_inc2, R_FA∙α, T₂), or in a shorthand notation θ₁ = θ₁(α, T2) and θ₂ = θ₂(α, T₂), where the functions θ₁() and θ₂() contain the known φ_inc1, φ_inc2, and R_FA parameters. One can now map T₂ and α to the new (θ₁, θ₂) 2D space, written as T₂(θ₁, θ₂) and α(θ₁, θ₂). Figure 2b shows that equi-T₂ and equi-α lines are nearly orthogonal, when we are well inside the “balloon” (the support region), which is an indication of the robust estimation for a given set of (θ₁,θ₂) there. At the “balloon” edges of low or high α values the solution is ill-posed and can provide more than one solution, thus increasing the variability and bias of the estimation at that region. Having now the simulated (θ₁, θ₂) 2D space for T₂ and for α, one can point with any measured (θ_1meas.,θ_2meas.) to that space and provide the expected T₂ and α values by a simple interpolation. This representation is useful to explore and characterize optimal choices of flip angles and φ_inc to achieve minimal variability and bias. Figure 2b shows that the set (φ_inc1 = 3°_, α_scan1) and (φ_inc2 = 1.5°_, α_scan2 = 2α_scan1) covers a larger flip-angle range than set (φ_inc1 = 2°_, α_scan1) and (φ_inc2 = 2°_, α_scan2 = 2α_scan1). We performed a detailed analysis to determine the optimal regime for whole-brain imaging, the results of which are summarized in Fig. S1–S4.

Variability and bias evaluation + SAR considerations

We examined the variability and bias of the method in the range of flip angles relevant for brain imaging. To do so, noise was added to the simulated signal and the variability and bias of the method were examined as a function of T₂ and α. The noise in the simulations was calibrated so the resulting synthetic signal to noise ratio (SNR) matched the measured SNR in agar tubes for the same α and T₂, where the agar T₂ was in a range matching white matter (WM) and gray matter (GM) at 7T¹⁸. The signal dependence on flip angle and phase increment showed that the phase of the signal is high for low φ_inc (φ_inc < 10°) (Fig. S1). It can be seen that the combination (φ_inc1 = 3°_, α_scan1) and (φ_inc2 = 1.5°_, α_scan2 = 2α_scan1) provides a lower variability (i.e., lower std(T₂^est.)) and a smaller bias (i.e., lower |ave(T₂^est.) − T₂^true|) for a larger range of flip angles (Fig. S2). We also examined three criteria (Fig. S3): the average estimation variability for 30 < T₂ < 50 ms and 5° < α < 17°, and both the minimal and maximal flip angles that provide std(T₂^est.) < 5 ms. The result of a combined minimization of the three criteria (shown in Fig. S3d) is a pair of scans with (φ_inc1 = 3°_, α_scan1) and (φ_inc2 = 1.5°_, α_scan2 = 2α_scan1) that provides a good combination of the lowest average std(T₂^est.) and supports a flip angle range of 3.7–35° (in which std(T₂^est.) < 5 ms).

Figure S4 shows three additional aspects that were included to establish the final configuration, including the repetition time (TR), the R_FA in a realistic experiment and reduction of the cerebrospinal fluid (CSF) signal. Although the combination (φ_inc1 = 3°_, α_scan1) and (φ_inc2 = 1°_, α_scan2 = 2α_scan1) provides a better flip angle range (2.4–35°), in practice, φ_inc1 = 1° generates a high CSF signal. This can result in an extra signal and a residual artifact in the proximity of the ventricles. To reduce the CSF signal’s effect, it was found worthwhile to use φ_inc2 = 1.5° (Fig. S4a). As the change in relative variability as a function of TR (Fig. S4b) is insignificant, the choice of TR can be made by balancing between SAR limitations, on the one hand, and scan duration, on the other hand. A TR of 10 ms provided a practical tradeoff. Our examination of the effect of the R_FA on the flip angle range showed that the higher the R_FA, the better (Fig. S4c). However, to keep SAR within the “Normal” level, it was found that R_FA in the range of 1.6–2 (with TR = 10 ms) provides a suitable flip angle range. In case of adopting “First level” SAR limit, one can increase the range of the flip angles.

Global phase corrections

In practice, the phase ($\angle S$) of the signal S at a voxel is comprised of the steady-state phase θ(α, T₂, T₁) plus a global phase θ₀. The global phase θ₀ arises from several factors, with a dominant contribution from B_0. It can be eliminated by repeating the scan twice, once with + φ_inc and once with -φ_inc, and setting θ(α, T₂, T₁) = $\angle \left({S}_{{+\varphi }_{inc}}\cdot conj\left({S}_{{-\varphi }_{inc}}\right)\right)/2$ (as was shown in Ref.²⁷). The implemented acquisition thus includes four scans: the two scans (φ_inc1, α_scan1) and (φ_inc2, α_scan2) and their repetition with a negative phase increment to remove θ₀. Calculating the θ₁ and θ₂ in this method does not result in phase wrapping, since after the global phase removal, the signals’ phase is in the range of 0° to ~ 50°.

Estimation algorithm

The actual estimation algorithm included two main steps, per voxel, namely the removal of the global phase (θ₀) and an estimation of T₂ and α from (θ₁,θ₂) using linear interpolation. An additional step was established for low flip angles because low flip angles result in (θ₁,θ₂) measurement pairs close to the edges of the “balloon” (Fig. 2b), a region where interpolation is an ill-posed problem. Low flip angles are relevant for whole-brain imaging because despite the flip angle of the first scan being set to α_scan1 = 15° , the actual whole-brain RF field distribution results in a flip angle in the range of ~ 4° to 22° (even reaching below 4° for some regions, see a representing distribution in Fig. 1). Brain regions where very low flip angles (~ 4–6°) are typically reached are the cerebellum, midbrain, and brainstem, as well as some regions in the temporal lobe. The added step to handle low flip angles takes advantage of two aspects: i) that α changes slowly in space, and ii) that for small flip angles (α < 20°) the phase $\theta$ is linear with T₂, and that the slope itself is linear with the flip angle α. Detailed description of this step are in the “Materials and methods” section. Figure S5 shows the improvement attained using the second step for the low flip angles. Additional steps were also performed to improve the estimation for the expected low values of (θ₁,θ₂), which, due to noise, results in negative values (see “Materials and methods”).

T₁ corrections

As mentioned, phase dependence on T₁ is small, but it can account for ~ 15% of the final T₂ estimation. To reduce the error due to T₁ in human imaging voxels were classified as either “high” or “low” T₁ by empirically thresholding $\left|{S}_{{\alpha }_{\text{scan2}}}\right|/\left|{S}_{{\alpha }_{\text{scan1}}}\right|$. Separate maps—T₂(θ₁, θ₂) and α(θ₁, θ₂)—were used for each classification, based on T₁ = 1 s (representing WM) and T₁ = 2 s (the rest). With this correction, the error was further reduced (shown in Fig. S6). A detailed description of the algorithm is provided in the “Materials and methods” section.

Results

To examine the estimation bias and estimation variability we conducted two imaging experiments with phantoms, one with tubes filled with agarose suspension, the other with a 3D head-shaped phantom. In the first experiment (Fig. 3a), the variability was × 1.4 smaller than with SE–SE (0.5 ms compared to 0.7 ms). The a_slope and the relative deviation error (see Eq. 1) calculated between the T₂ from this method and the T₂ from SE–SE were 1.01 and 0.5%. Thus, the phase-based method provides a small bias and a lower variability compared to SE–SE, while the scan duration is × 2.3 faster.

Figure 3

Assessment of estimation bias and variability in phantoms. (a) Comparison of the T₂ obtained with the phase-based method and SE–SE in agar tubes. Top—a central slice of the T₂ maps and magnitude images. Bottom—estimated T₂ for each tube as a function of T₂ with SE–SE; a_slope = 1.01, relative deviation error = 0.5%. The average standard deviation was 0.5 ms for the phase-based method, and 0.7 ms for SE–SE. (b–d) Comparisons using a 3D-head-shaped brain-like phantom. (b) T₂ and α maps estimated by the phase-based method. (c) T₂ map estimated with SE–SE. And (d) α map estimated using the vendor’s RF field mapping scan. Two main cross-sections are shown for all cases, Sagittal and Axial. For comparison, the average T₂ and standard deviation was calculated in the same region of interest (marked by a blue contour for the phase-based method and a red contour for SE–SE). The average deviation between the α maps of the phase-based method and of the vendor’s RF mapping was calculated to be 0.56° for the Sagittal plane and 0.84° for the Axial plane.

In the second experiment, a specially designed 3D head-shaped brain-like phantom was used to examine the capability to cope with an RF field distribution similar to that in the brain. The “brain” had a uniform T₂, which helped to separate the two parameters we sought to estimate, α and T2. Our results show low variability in T₂ (std(T_{2 phase-based-method} )/std(T_{2 SE–SE}) = 0.46) and an RF field map estimation with little bias (a 4% average deviation from the map acquired with the vendor’s pulse sequence), see Fig. 3b. Even low flip angles, in the ill-posed area of the “balloon”, were well determined using the implemented estimation algorithm (Fig. S8).

The contribution of the B₁ correction to the T₂ estimate can be seen in Fig. 4. It compares T₂ maps extracted from a set of four scans (two pairs) to T₂ maps extracted from a single pair—as in Ref.²⁷—using either of the pairs (either pair 1: φ_inc1 = 3° and φ_inc1 = − 3°, with α_scan1; or pair 2: φ_inc2 = 1.5° and φ_inc2 = − 1.5°, with α_scan2). It can be seen that for both phase increments the RF field inhomogeneity results in either underestimated or overestimated T₂ values, depending on the actual flip angle in each voxel (see Fig. 2a for phase dependence on flip angle). The 4-scans result, which combines both phase increments, provides a uniform T₂ map of the “brain” tissue in the 3D-head shaped phantom, as expected by the design.

Figure 4

Comparison of T₂ maps extracted with (a) 4-scans, (b) single pair with (φ_inc1, α_scan1) and (c) single pair with (φ_inc2, α_scan2). (d) For each case a plot for a line shown in the Sagittal and Axial scans. The images show 3D-head shaped phantom (left) and human imaging (right). The human axial plane image in (a) shows the regions that were examined and summarized in Table 1.

Table 1 Estimated T₂ in sample regions of white matter, grey matter and CSF (see Fig. 4).

Figure 4 also shows the estimated T₂ maps, for human imaging, based on either 4-scans or a single scan-pair. Although more challenging to observe, due to the heterogeneous T₂ distribution in the brain and to the very high T₂ values in the CSF regions, it can also be seen that T₂, estimated from a single pair, is either underestimated or overestimated compared to 4-scans. This can be observed, for example, in regions such as the cerebellum and the temporal lobes. Table 1 summarizes the results by giving sample T₂ values in white matter, grey matter and CSF. For each tissue 2 sampled regions were chosen as shown in Fig. 4—WM1 and WM2 in white matter tissue, GM1 and GM2 in the grey matter tissue and CSF1, CSF2 in the CSF. The table also shows T₂ values reported in Ref. ¹⁸. Note: the CSF values are underestimated with the current method, as further elaborated in the Discussion section.

Continuing with human imaging, Fig. 5 compares the phase-based method with 1.5 mm isotropic voxels to the gold standard SE–SE, for a T₂ mapping comparison, and to the vendor RF mapping, for an RF field mapping comparison. The α map in Fig. 5c was smoothed by 3 × 3 filter to reduce the effect of local CSF signals (see Fig. S13 for original high resolution B₁ map). The RF field map extracted with the phase-based approach shows a distribution similar to the separately acquired vendor map with, however, noticeable deviations in the ventricles, as well as in some of the CSF region. The ratio of the T₂ values and the relative deviation error between the phase-based method and SE–SE is shown in Fig. 6, for the different volunteers. Over all volunteers the T₂ ratio (T_{2 phase-based-method}/T_{2 SE–SE}) and relative deviation error are 0.80 and 15.45% for WM, and 0.85 and 19.76% for GM (detailed description is in Supplementary Information S4).

Figure 5

Human imaging—T₂ from the phase-based method or SE–SE, and α from the phase-based method or the vendor’s scan. (a) SE–SE Sagittal magnitude image at TE = 30 ms and the estimated T₂ maps in three main cross-sections. (b) An α map using the vendor’s pulse sequence. (c) Sagittal magnitude image with φ_inc = 3 and α = 15°, as well as the estimated T₂ and α maps in three main cross-sections. α map shown here was smoothed by a 3 × 3 filter to reduce the effect of local CSF signal. Orange arrows point to the cerebellum and brainstem regions suffering from low flip angles due to B₁ inhomogeneity; their inner structure is much more pronounced—and clearly visible—in the phase-based T₂ images. Purple arrows point to a region in the CSF that resulted in a low magnitude signal.

Figure 6

Comparison of T₂ estimation between the phase-based method and SE–SE. The plot shows the ratio T_{2 phase-based-method}/T_{2 SE–SE} per volunteer, both for WM and for GM. The error bars depict the relative deviation error [see Eq. (1)].

Finally, high-resolution whole-brain T₂ mapping was performed with the phase-based method, with 1 mm and 0.85 mm isotropic voxels. To acquire whole-brain high-resolution images, × 5.11 acceleration was used—combining elliptic sampling and × 2 acceleration in both phase encoding directions. Each of the four scans with 1 mm resolution was 1:13 min giving a total scan time of 4:52 min. For 0.85 mm each scan was 1:42 min long and the total scan time was 6:48 min. Figure 7 shows the estimated T₂ maps for the 0.85 mm scan (Fig. S12 shows the 1 mm resolution images). To provide even higher robustness following the reduced SNR of the high-resolution datasets, we also incorporated denoising based on a DnCNN deep-learning network³³ (provided in MATLAB, The Mathworks, Natick MA, for Gaussian noise removal). This entailed denoising of θ₁ and θ₂ before the estimation of T₂. The denoising greatly improved the observed details of the cerebellum structure, a region with especially low flip angles (Fig. 7b).

Figure 7

Human whole-brain T₂ maps with a 0.85 mm isotropic voxel. (a) without denoising, (b) with denoising, based on DnCNN model for Gaussian noise removal. Arrows point to the cerebellum region, which especially benefits from denoising. Top row, Sagittal and Coronal planes. Bottom two rows, six slices of the Axial plane, at 10 mm intervals.

Discussion

The expected rewards of pushing the limits and moving to 7 T MRI are increased spatial resolution and shorter scan durations. Both these features are essential for clinical and research imaging, all the more so for quantitative methods. However, scanning at 7 T also poses new challenges, including high power deposition and severe RF field inhomogeneity. The extended phase-based method shown here delivers high-resolution brain T₂ imaging while overcoming the above challenges. This is achieved by relying on a modified 3D SGRE sequence, using the phase of the signal to encode the T₂ dependence. The 3D SGRE images are also highly robust to B₀ inhomogeneity. This can be seen in the magnitude images of both the phantom example (Fig. 3a) and the human images (Fig. 5). The SE–SE is more distorted both at the edges of the agar tubes and near the nasal areas in the human images. The B₀-dependent phase is reliably canceled out by the two scans with opposite phase increments (φ_inc) of the RF pulse train. However, shifts in the global phase between scans may occur, which will require corrections. Similarly, the scans may be sensitive to movements, which will affect the phase. Incorporating a second echo acquisition could be used to correct for both the phase shifts and motion³⁴. Aiming to shorten the total scan duration, one can also consider estimation of the global phase from a single pair, thus reducing the number of scans to three. However, in this case careful analysis and phase unwrapping will be required in the third, non-paired, scan. In this case, phase unwrapping can be especially challenging in regions with short T₂^*, where B₀ changes rapidly, resulting in high local changes in the background phase. Very short T₂^* may also affect T₂ estimation due to limited SNR in such regions.

The current implementation used a non-selective hard pulse for the 3D acquisition. Although this works well for whole brain acquisition as in this study, in other cases it can be a limitation. For faster acquisition and to limit potential aliasing, the use of slab-selective pulses is beneficial. Figure S9 shows that as long as the slab is thick enough, compared to the slice thickness, the estimated T₂ is correctly estimated. However, for a single slice-selective acquisition, the simulation by which the T₂ and RF field maps are estimated must also account for the slice profile. This was already demonstrated in other T₂ mapping methods such as balanced SSFP¹⁹.

Another sensitivity of the method that requires discussion is the sensitivity to movement and potential inaccuracy in the RF pulse phase. Although we did not observe noticeable movement in our human scanning, a simulation to examine these vulnerabilities was performed (see Supplementary Information, Section S5). The movement was simulated assuming a constant velocity during the scan, which will result in an additional parabolic phase term accumulated during the scan. Examining the error due to potential head movement of 1–2 voxels during the scan, it resulted in a small error, less than 1% for a movement of up to 5 mm/min. However, for large movement within a voxel, such as due to flow, the error of the estimated T₂ can be significant; reaching 20%, for a velocity of 0.5 mm/s.

Two simulations were also performed to analyze possible hardware inaccuracies: (i) a constant error in the actual RF-phase increment, (ii) a randomly distributed error in the actual phase of the RF pulse. In the first case, a constant error of 0.1° resulted in < 4% error, In the second, a randomly distributed error with σ = 0.2° resulted in a negligible error with standard deviation of 0.07 ms in the estimated T₂. It is also important to note that the estimation of the T₂ in the CSF and other tissues with high T₂ values (> 0.5 s) is challenging with this method, since the signal’s phase curve slowly converges for T₂ > 100 ms (see Fig. 2a) and so the T₂ contours in the (θ₁,θ₂) space grow denser with T₂ (see Fig. 2b). In addition, local intensity drops in CSF voxels, resulting in low SNR voxels, can occur due to fluid movement (purple arrows in Fig. 5 point to such area), thus further limiting T₂ estimation of CSF.

The important advantage of the phase-based approach for T₂ mapping is its whole-brain coverage ability. The method shows robust results in the brainstem region and even in parts of the spinal cord (see Fig. 5). These results are achieved without the need for additional hardware to reduce the RF field inhomogeneity, such as dielectric pads or multi-channel transmit coil. Naturally, the method can also benefit from a dielectric pad or multi-channel transmit coils to improve the SNR, especially in regions with low flip angles. The current configuration (φ_inc1, φ_inc2, α_scan1, R_FA, and TR) was designed for the RF field distribution in the brain, and was shown to robustly extract the RF field distribution in the 3D head-shaped phantom (which has a slightly larger RF field inhomogeneity than in vivo). If another region will be of interest, the configuration—the RF pulse phase increments and the scan flip angles—can be adapted accordingly.

It is worth noting that θ₁ on its own, calculated from the first pair of scans (with φ_inc1 = ± 3°), achieves a “T₂ weighted” image (see Fig. S10 for the 0.85 mm case), unlike the magnitude of these scans. θ₁, however, suffers from pronounced RF field inhomogeneity, which is removed by using two sets of scans (giving θ₁ and θ₂), as was implemented here, allowing the generation of T₂ maps.

In our study, the estimation algorithm is based on an interpolation procedure, where the simulated data serves as the ground-truth. This method is similar to the dictionary-based approach in MRF, but is based on two measurement points (θ₁, θ₂) that allow us to represent the parameters of interest, T₂ and α, in the (θ₁, θ₂) 2D space. This offers the advantage of mapping the T₂ of interest by a simple linear interpolation. An improvement in the estimation algorithm was implemented in the low flip angles’ range, which extended the viable flip angles (Figs. S5 and S8). In this study, we demonstrated the low variability and small bias of the estimations in both simulations and phantom experiments. In the phantom experiment with agar tubes, the method provides T₂ estimation with low variability—a × 3.2 (1.4 × 2.3) lower variability-to-scan-time factor than that of SE–SE. The T₂ values were estimated by the phase-based method with a small bias (a_slope = 1.01 and relative deviation error of 0.5% compared to SE–SE).

However, the in-vivo T₂ ratio of the phase-based method to SE–SE was 0.79 ± 0.16 for WM and 0.86 ± 0.19 for GM. Similarly, there is a ratio of × 0.82 and × 0.88 between the reported values with 4-scans in Table 1 to the values in Ref.¹⁸. This result is also similar to the results in Ref.^22,34. Possible reasons for the different ratios found for WM and GM are a partial volume of GM and CSF as well as deviations due to T₁. Although T₁ has a small impact on the phase of the signal and its effect was reduced in our implementation. The ~ 0.8 ratio between the T₂ estimated by the phase-based approach and by SE–SE could arise for several reasons, among which are a contribution due to exchange and magnetization transfer³⁵, diffusion³⁶, and different contributions of the fast and slow T₂ components to the two methods^37,38. For the magnetization transfer no discrepancy was observed between the estimated T₂ values in the agarose tubes, although exchange mechanisms are known to be at work in agarose and therefore produce magnetization transfer effects. However, different effects of exchange in the living tissue can still be a factor contributing to the acquired complex signal of the steady state acquisition. We also examined potential diffusion contributions to the estimated T₂ by scanning a sample of smoked fish (which had and ADC of ~ 0.6 × 10⁻³ mm²/s, similar to white matter) and did not observe a significant effect (not shown). One of the potential factors is the larger contribution of the fast-relaxing species compared to SE–SE, primarily due to much shorter echo times, which was also observed in several previous studies³⁸. Thus, although the estimated T₂ was robustly repeated in the volunteers’ data, the resulting ratio between the phase-based method and SE–SE in-vivo still requires further analysis.

The fast high-resolution T₂ maps of the whole brain that were acquired—1 mm isotropic in 4:52 min and 0.85 mm isotropic in 6:49 min—offer a significant clinical gain. Further acceleration of the method should be possible. One option is to reduce the TR, however, this will require switching the SAR monitoring to the less restrictive “First” level. For this, the effect of the TR on the variability of the estimation was examined (see Fig. S4) and showed that shorter TR result in similar estimation variability. In addition, acceleration methods, tuned to the 3D SGRE acquisition and employing the Compressed Sensing technique, can achieve even higher acceleration factors. We also demonstrated the option of employing denoising based on deep-learning techniques that is trained to remove Gaussian noise. This further improves the quality of the images and can be used to further accelerate the scan.

Overall, the extension of the phase-based steady-state method to estimate both T₂ and RF field map, demonstrated in this work, provides a fast and high-resolution acquisition method for quantitative T₂ mapping of the whole brain at 7 T acquired with a single-channel transmit coil. Standardized high-resolution methods are imperative for 7 T MRI to advance multi-site studies and promote personalized medicine.

Materials and methods

Bloch simulations

1D single voxel simulations based on the Bloch equations were performed with a custom MATLAB (The Mathworks, Natick MA) code³⁹ to examine the signal in steady state. The simulations included an excitation pulse, an acquisition and a net total spoiler (including the area of the acquisition) of 3/Δx (Δx the 1D voxel size). The number of initial repetitions to reach steady-state (“dummy scans”) was set to 500, which was verified to provide reliable steady states. Following the dummy scans, a single acquisition was simulated. The simulation was repeated over a grid of flip angles and T₂ values, for different values of T₁, φ_inc, and TR. The grid covered T₂ from 0 to 200 ms with a resolution of 4 ms, and flip angles from 0° to 70° with a resolution of 1°. The resulting θ(T₂, α) map was interpolated prior to its use in the estimation algorithm with 1 ms in T₂ and 0.1° in alpha, generating θ₁(T₂, α) and θ₂(T₂, α) for relevant φ_inc and R_FA factors.

Estimation algorithm

The estimation algorithm included the following steps:

Preparatory step #0.1: global phase removal

In practice, the phase ($\angle S$) of the signal S at a voxel is comprised of the steady-state phase θ(α, T₂, T₁) plus a global phase θ₀. The global phase θ₀ arises from several factors, with a dominant contribution from B_0. It can be eliminated by repeating the scan twice, once with + φ_inc and once with -φ_inc, and setting θ(α,T₂,T₁)=$\angle \left({S}_{{+\varphi }_{inc}}\cdot conj\left({S}_{{-\varphi }_{inc}}\right)\right)/2$ (as was shown in Ref.²⁷). The implemented acquisition thus includes four scans: the two scans (φ_inc1, α_scan1) and (φ_inc2, α_scan2), and their repetition with a negative phase increment to remove θ₀.

Preparatory step #0.2 (optional): denoising

For high-resolution human imaging, a denoising procedure based on a DnCNN deep-learning network³³ (provided in MATLAB 2021a, for Gaussian noise removal) was incorporated. The denoising procedure was implemented on the measured θ1, θ2 with the command denoised_θ1 = denoiseImage(θ1, net), where the net was set by the command net = denoisingNetwork('dncnn').

Estimation step #1: T₂ and α estimation by interpolation

First, using Matlab’s scatteredInterpolant(), we generated two interpolants, T₂(θ₁, θ₂) and α(θ₁, θ₂), which map (θ₁, θ₂) to the desired quantities T₂ and α. These interpolants were then used to estimate T₂ and α from any (θ₁, θ₂) pair, at each voxel.

As mentioned, phase dependence on T₁ is small, but it can account for ~ 15% of the final T₂ estimation. Thus, in human imaging, to reduce the error due to T₁, voxels were classified as either “high” or “low” T₁ by empirically thresholding $\left|{S}_{{\alpha }_{\text{scan2}}}\right|/\left|{S}_{{\alpha }_{\text{scan1}}}\right|$. Separate maps—T₂(θ₁, θ₂) and α(θ₁, θ₂)—were used for each classification, based on T₁ = 1 s (representing white matter—WM) and T₁ = 2 s (the rest). With this correction, the error was further reduced (see simulation results in Fig. S6).

Estimation step #2: T₂ estimation update for low flip angles

First, the flip angles α found in the previous step were smoothed, generating α_smoothed. For low flip angle voxels with α_smoothed < 4.5°, the flip angles were temporarily set to α_temp = 4.5°, and the matching temporary T₂ quantities, T_2-temp, were found by interpolation—using α_temp and θ₂ (the phase from the scan using the higher flip angle, αscan₂ = RFA∙αscan₁). The final T₂ was found through the linear connection T₂ = (α_temp/α_smoothed)∙T_2-temp.

Estimation step #3: handling of negative θ₁ or θ₂

For θ₁ < 0 (and θ₂ > 0), the θ₂ from step #1 together with α_smoothed from step #2 were used to estimate T₂; using the above simulated θ₂(T₂,α) for the known α. Similarly, for θ₂ < 0 (and θ₁ > 0), θ₁ and α_smoothed were used to estimate T₂.

Validation of the estimation algorithm was performed by generating N = 100 noisy repetitions of each point in the simulated datasets of θ₁(T₂,α) and θ₂(T₂,α). This was done using a fixed noise which resulted in the SNR varying with T₂ and α, depending on the intensity at each point. The noise was fixed to produce an SNR of 180 for the simulated data at T₂ = 38 ms and α = 13°; resembling the SNR in the human images acquired with 1.5 mm resolution. The SNR was set as an average SNR over the two signals |S₁| and |S₂|. To validate the simulations, the standard deviation of T₂ was compared to a measured one in an agar-tubes experiment, both with the same SNR. For this validation two agar-tubes were used—with T₂ values of T₂ = 34 ms and T₂ = 38 ms, representing WM and GM at 7 T. The flip angle distribution in this experiment was uniform (α = 13°). The measured and simulated SNR was 298, resulting in a T₂ standard deviation of 0.36 ms in the measurement and 0.32 ms in the simulation, providing comparable results. The variability and bias of the method, under the simulated noise, were examined as a function of T₂, α, φ_inc, TR and R_FA.

Pulse sequence considerations

The sequence is based on a Siemens 3D GRE sequence that was modified to enable control over both the φ_inc and the gradient spoiler moment. The RF pulse we used was a hard pulse.

An important aspect to consider is the gradient spoiler moment intensity and its effect on the T₂ estimation, as well as on image artifacts (in the form of residual signals from spurious echoes). A set of scans was performed to examine the spoiler effect. The gradient spoiler moment needs to provide complete dephasing inside a voxel, which defines a preferable gradient moment size to be $\succsim$ 1/Δr (Δr = √(Δx² + Δy² + Δz²)). We found it useful to add a parameter to the pulse sequence that directly controls the net gradient spoiler moment (after all previous gradients had been rephased). The net spoiler was set to be equally distributed in all three directions, which was found useful in reducing artifacts. However, our experiments also showed that the gradient moment affected the measured phase, and thus the estimated T₂. Figure S7a shows this dependence. Phantom experiments were used to calibrate the gradient spoiler moment to provide the T₂ estimate closest to that from SE–SE. Accordingly, the gradient moment was set in all experiments to 0.015 [mT/m∙sec] in each direction. This moment is expected to provide dephasing for Δr $\succsim$ 0.9 mm. As shown in Fig. S7b, under this moment, the estimated T₂ did not change for the voxel sizes tested.

MRI scanning

All scans in this study were performed on a 7 T MRI system (MAGNETOM Terra, Siemens Healthcare, Erlangen) using a commercial 1Tx/32Rx head coil (Nova Medical, Wilmington, MA).

When comparing the results of the phase-based method to SE–SE, inside a region, the relative deviation error from the fit was calculated as

$$\text{rel. dev. err}=100\cdot \frac{\sum_{i=1}^{N}\left|\left({T}_{2}^{\text{(phase-based-method)}}-{a}_{slope}{T}_{2}^{\text{(SE-SE)}}\right)\right|}{N}/{\text{ave}}\left({a}_{slope}{T}_{2}^{\text{(SE-SE)}}\right)$$

(1)

where a_slope is the slope found for each fit, and N is the number of voxels in the comparison.

Phantom imaging

Five tubes with agar concentrations of 1.5, 2, 2.5, 3 and 3.5% were used to compare the phase-based T₂ estimation to the gold standard SE–SE, using three TE values (10, 30 and 50 ms). A 3D head-shaped phantom that was designed to model the RF field distribution in the brain was used to examine the T₂ and RF field estimation. This phantom was originally designed to include three sub-compartments³⁰, suitable for mimicking brain, muscle and lipid tissues. However, the version used in this study was filled with two “tissue” types: the inner compartment mimicked the “brain” and the outer one, “muscle” (the planned lipid layer was also filled with “muscle”). Both compartments contained 0.1 mM gadopentetate dimeglumine (GdDTPA), for a T₁ close to that of human white matter, and consisted of an agarose suspension of 2.5% and 3% for the “brain” and “muscle” compartments, respectively. NaCl (5.5 gr/L) was used to achieve an in-vivo-like RF field distribution. For details, see Ref.³⁰.

α maps from the phase-based method were compared to the equivalent α maps generated by the vendor. As the RF field maps provided by the vendor are scaled to 90°, they were rescaled to the α_scan of the phase-based method, before comparison. The average deviation between the α maps by the phase-based method and by the vendor were calculated in two main planes (Sagittal and Axial).

The common scan parameters for the phase-based method and SE–SE used in the agar-tube experiments in Fig. 3a) were: FOV 200 × 200 × 104 mm³, resolution 1.1 × 1.1 × 2 mm³, acquired matrix size 176 × 176 × 52. The phase-based method specific parameters were (φ_inc1 = 3°, α₁ = 15°) and (φ_inc2 = 1.5°, α₂ = 30°), TR/TE 10/2.2 ms, using 4 scans with a total scan duration of 6:06 min. The specific scan parameters for SE–SE were: TR—6500 ms, 3 scans with TE = 10,30,50 ms, × 3 in-plane acceleration, with a total scan duration of 19:04 min. The T₂ and α maps were estimated based on Bloch simulation with T₁ = 2 s.

The common scan parameters for the phase-based method and SE–SE that were used for the 3D head-shaped phantom in Fig. 3b): FOV 220 × 220 × 144 mm³, isotropic resolution of 1.5 mm, bandwidth per pixel 400 Hz. The phase-based method specific parameters were acquired matrix size 150 × 148 × 96, (φ_inc = 3, α = 15°) and (φ_inc = 1.5, α = 30°), TR/TE 10/2.1 ms, using 4 scans with a total scan duration of 9:28 min. The specific scan parameters for SE–SE (Fig. 3c) were: acquired matrix size 144 × 144 × 96, TR—6500 ms, 3 scans with TE = 10, 30, 50 ms, × 3 acceleration, with a total scan duration of 21:12 min. The vendor RF field map scan parameters (Fig. 3d): FOV 220 × 220 × 144 mm³, resolution 2.3 × 2.3 × 4 mm. The T₂ and α maps were estimated based on Bloch simulation with T₁ = 1.5 s (based on estimated T₁ of the “brain” tissue).

Human imaging

All methods were carried out in accordance with the Weizmann Institute of Science guidelines and regulations. This study was approved by the Internal Review Board of the Wolfson Medical Center (Holon, Israel) and all scans were performed after obtaining informed suitable written consents. Human scanning of six volunteers with isotropic 1.5 mm resolution was acquired for the comparison with SE–SE. The comparison was performed after the SE–SE and the phase-based method images were realigned using SPM12 (https://www.fil.ion.ucl.ac.uk/spm/) to ensure there was no movement between the scans.

An additional volunteer was scanned with the phase-based method with 1 mm and 0.85 mm resolution. These scans were acquired with an acceleration of × 5.11—using elliptical sampling and × 2 acceleration in both phase encoding directions. The BART⁴⁰ software was used to reconstruct this dataset.

Scan parameters for the phase-based method and SE–SE comparison with isotropic 1.5 mm voxel

Phase-based method: FOV 220 × 220 × 144 mm³, acquired matrix size 150 × 148 × 96, bandwidth per pixel 400 Hz, TR/TE 10/2.1 ms, (φ_inc1 = 3°,α_scan1 = 15°), (φ_inc1 = 1.5°, α_scan2 = 24–26°) (the α_scan2 varied from 24° to 26° according to the specific volunteer’s 100% “Normal” SAR level), with duration of 4 scans—9:28 min. SE–SE: FOV 220 × 220 × 132 mm³, acquired matrix size 144 × 144 × 88, bandwidth per pixel 400 Hz, TR- 6500 ms, TE = 10, 30, 50 ms, using 3 scans with a total scan duration of 21:12 min. Vendor RF field map scan parameters: FOV 220 × 220 × 192 mm³, resolution 3 × 3 × 4 mm.

Phase-based method 1 mm resolution parameters

FOV 220 × 220 × 160 mm³, bandwidth per pixel 400 Hz, TR/TE 10/2.7 ms, (φ_inc1 = 3°,α_scan1 = 15°), (φ_inc1 = 1.5°, α_scan2 = 25°), duration of 4 scans—4:52 min.

Phase-based method 0.85 mm resolution parameters

FOV 220 × 220 × 163 mm³, bandwidth per pixel 400 Hz, TR/TE 10/2.7 ms, (φ_inc1 = 3°,α_scan1 = 15°), (φ_inc1 = 1.5°, α_scan2 = 25°), duration of 4 scans—6:49 min.