Time-Resolved Contrast-Enhanced MR Angiography with Single-Echo Dixon Fat Suppression

Abstract

Purpose

Dixon-based fat suppression has recently gained interest for dynamic contrast-enhanced MRI, but multi-echo techniques require longer scan times and reduce temporal resolution compared to single-echo alternatives without fat suppression. The purpose of this work is to demonstrate accelerated single-echo Dixon imaging with high spatial and temporal resolution.

Theory and Methods

Real-valued water and fat images can be obtained from a single measurement if the shared initial phase and that due to ΔB₀ are assumed known a priori. An expression for simultaneous SENSE unfolding and fat-water separation is derived for the general undersampling case, and simplified under the special case of uniform Cartesian undersampling. In vivo experiments were performed in extremities and brain with SENSE acceleration factors of up to R=8.

Results

Single-echo Dixon reconstruction of highly-undersampled data was successfully demonstrated. Dynamic contrast-enhanced water and fat images provided high spatial and temporal resolution dynamic images with image update times shorter than previous single-echo Dixon work.

Conclusion

Time-resolved contrast-enhanced MRI with single-echo Dixon fat suppression shows high image quality, improved vessel delineation, and reduced sensitivity to motion when compared to time-subtraction methods.

Introduction

Contrast-enhanced MR angiography (CE-MRA) uses the differential T₁ values between gadolinium-based contrast-agent-enhanced blood and other tissues to emphasize the luminal blood signal. However, because the lipid (fat) signal is also high in the T₁-weighted spoiled gradient echo images used in CE-MRA, some form of background suppression is typically used (1). Complex-valued time subtraction, where a pre-contrast image is subtracted from each subsequent contrast-enhanced time frame, is often used for background suppression but suffers from $\sqrt{2}$ signal-to-noise ratio (SNR) reduction and motion-induced subtraction artifacts. Fat suppression with short-tau inversion recovery (STIR) (2) or spectrally selective RF pulses (3, 4) can selectively suppress lipid signal, but these methods also extend scan time or reduce temporal resolution for dynamic imaging and can be sensitive to main magnetic field inhomogeneity (ΔB₀).

Dixon imaging (5) for CE-MRA (6–14) has recently gained interest as it: (i) reduces and ideally eliminates the bright fat signal that can obscure vasculature, (ii) accounts for main magnetic field inhomogeneity, and offers (iii) better motion immunity (9) and (iv) in some cases improved SNR and contrast-to-noise ratio (CNR) (9, 12) when compared to subtraction-based background suppression. The last of these points, the improvement in SNR and CNR, was examined in detail with theoretical derivations and verified experimentally in phantom/in vivo studies in Ref. (12), while a noise analysis and NSA comparison to the source image was performed in Ref. (15). Dixon imaging reconstructs images containing only water and only fat by exploiting the differential accrual of phase due to the chemical shift of fat. However, because non-idealities such as ΔB₀ also manifest as the accrual of phase, it is critical that ΔB₀-induced “nuisance” phase (field map) be accurately estimated and robustly mitigated (16, 17). If these steps are not taken, Dixon imaging is subject to the following artifacts: (i) fat/water swaps, in which complete fat signal appears in a portion of the water image and vice versa, and (ii) signal leakage, in which a portion of the fat signal appears in the water image and vice versa.

Dixon CE-MRA is often performed using images acquired at two or more echo times – and indeed, time resolved studies of the vasculature have previously been performed using this technique (10, 14). However, dual-echo Dixon is known to have a number of limitations. First, these techniques can be limited by diminished temporal resolution from the need to acquire a second image at a different echo time (TE), either due to prolongation of the repetition time (TR) to accommodate multiple images in a single repetition, or due to acquisition of additional echoes in separate repetitions. Second, flow-induced misallocation artifacts have been observed due to the additional phase induced by the flow of blood (18–21). If, however, the system non-idealities are known a priori (e.g. from a dual-echo calibration scan) a single image is sufficient to reconstruct fat and water images and avoids the above limitations, provided an appropriate TE is used (12, 15). Therefore single-echo Dixon CE-MRA can avoid the limitations of dual-echo Dixon CE-MRA while providing some of the benefits. Compared to time-subtraction CE-MRA, the benefits come at the expense of reduced temporal resolution due to some restrictions on appropriate TE.

Despite the potential temporal resolution advantages over dual-echo Dixon for time-resolved dynamic imaging, single-echo Dixon work (15, 22–28) has mostly comprised of static imaging. In 2005, Yu et al. (15) showed that single-echo Dixon-based dynamic contrast-enhanced MRI (DCE-MRI) was feasible in the breast and abdomen, but temporal resolution was still 30 seconds or longer with relatively low 1D SENSE-acceleration factors of R=2. To our knowledge, high temporal resolution time-resolved single-echo Dixon CE-MRA has not yet been reported.

As alluded to above, Dixon imaging has been combined with parallel imaging (15, 29–32) and/or advanced reconstructions such as compressed sensing (33–36) for a variety of applications. Many of these works treat the parallel imaging reconstruction and the Dixon signal separation separately, first performing the parallel imaging reconstruction and then decomposing the fat and water signals. However, recent works (e.g. Refs. (33–36)) perform a joint estimation of the water and fat images that solves the parallel imaging and fat water decomposition within a single framework. This joint-estimation approach has not yet been applied to single-echo Dixon imaging despite the suitability of the problem, where coil sensitivities, initial phase, and field map are all assumed known from calibration scans.

The purpose of this work is to derive the maximum likelihood estimate of water and fat images to perform the SENSE unfolding and water-fat decomposition in a single step from undersampled single-echo Dixon data and demonstrate single-echo Dixon imaging with high spatial and temporal resolution through the use of 2D SENSE acceleration factors up to R=8. Preliminary versions of this work have previously been presented at the annual meetings of the Society for Magnetic Resonance Angiography (37) and the International Society for Magnetic Resonance in Medicine (38).

Theory

Here we derive an expression for the minimum least squares estimate of water and fat for arbitrary k-space sampling and then further derive a simplified expression for the special case of uniform k-space undersampling. The mathematical conventions used in this work are as follows. $\overline{(·)}$, (·)*, and (·)^T refer to the complex conjugate, the conjugate (Hermitian) transpose, and the non-conjugate transpose of a matrix, respectively. denotes the Kronecker product, and Re(·) denotes the real part of a vector or matrix. Additionally, the subscript “r” indicates a quantity measured at a spatial position associated with index r, vec([·]) vectorizes the quantity [·], and diag([·]) indicates that the vector quantity [·] has been placed along the diagonal of a (square) matrix (39).

Fundamental Image Domain Signal

The image-space signal component of the measurement produced by a spoiled gradient echo acquisition at echo time τ is described in Eq. 1, where w_r and f_r are water and fat signal magnitudes, respectively, ϕ_w,r and ϕ_f,r are the water and fat signal phases, respectively, and ϕ_r = γΔB_0,rτ is the phase accrual due to main magnetic field inhomogeneity ΔB_0,r. $\rho ={\sum }_{p=1}^P{\rho }_p{e}^{i2\pi \mathrm{\Delta }{f}_p\tau }$ is the phasor resulting from the chemical shift of fat with a P-peak spectral profile, where ρ_p and Δf_p are the amplitude weights and chemical shifts of the pth chemical species, respectively, and ${\sum }_{p=1}^P{\rho }_p=1$.

$$y_{\mathrm{r}}=({\mathrm{w}}_{\mathrm{r}}{e}^{i{\varphi }_{\mathrm{w},\mathrm{r}}}+{\mathrm{f}}_{\mathrm{r}}{e}^{i{\varphi }_{\mathrm{f},\mathrm{r}}}\rho )e^{i{\varphi }_{\mathrm{r}}}$$ [1]

The chemical shift-induced phasor ρ is assumed to be known from literature values or a prescan (30), leaving five remaining real-valued unknowns – namely, w_r and f_r, initial phases ϕ_w,r and ϕ_f,r, and the ΔB₀-induced phase ϕ_r. The measurement of this data with a single radio-frequency (RF) coil would include additive zero-mean Gaussian noise. To solve for these five unknowns in a maximum likelihood framework, complex measurements from at least three different echo times, τ, are required (40–42).

By constraining the initial immediate-post-excitation phase of the water and fat signals to be equal (ϕ_w,r = ϕ_f,r = ϕ_0,r) the number of unknowns is reduced to four, necessitating only two complex measurements (i.e. images at two different echo times) (43, 44). The resultant signal component is shown in Eq. 2 where ϕ_0,r has replaced ϕ_w,r and ϕ_f,r.

$$y_{\mathrm{r}}=({\mathrm{w}}_{\mathrm{r}}+{\mathrm{f}}_{\mathrm{r}}\rho )e^{i({\varphi }_{\mathrm{r}}+{\varphi }_{0,\mathrm{r}})}$$ [2]

Further, if ΔB_0,r and ϕ_0,r are known or can be accurately estimated (from a dual-echo calibration scan, for example), only two real-valued unknowns remain, and w_r and f_r can be reconstructed from a single complex measurement (a single complex image at TE = τ).

Combined SENSE and Dixon Reconstruction

The k-space measurement g_k,c from coil c at k-space position k is shown in Eq. [3], where y_r is the signal component at each image-space position, the exponential is the Fourier harmonic modulation, s_r,c is the complex RF coil sensitivity of coil c, and n_r,c is zero-mean, proper complex Gaussian noise. The sum is over the entire volume of interest.

$$g_{\mathrm{k},\mathrm{c}}=\sum _{\mathrm{r}\in \text{VOI}}{y}_{\mathrm{r}}{s}_{\mathrm{r},\mathrm{c}}{e}^{-2\pi i{\overrightarrow{k}}_{\mathrm{k}}·{\overrightarrow{r}}_{\mathrm{r}}}+n_{\mathrm{r},\mathrm{c}}$$ [3]

The ensemble of all k-space measurements for a single coil may be expressed (as shown in Appendix A) as

$$g_{\mathrm{c}}={\mathit{\text{US}}}_{\mathrm{c}}\mathit{\text{BC }}\left[\begin{array}{c}\hfill w\hfill \\ \hfill f\hfill \end{array}\right]+n_{\mathrm{c}}={\mathit{\text{US}}}_{\mathrm{c}}\mathit{\text{BC}}x+n_{\mathrm{c}}$$ [4]

where g_c is the vector of all k-space measurements from a single coil, x contains the stacked vectorized water and fat images, C provides the phase induced by chemical shift, B contains the phase induced by ϕ and ϕ₀, S_c = diag([s_c,1 ⋯ s_c,N]^T) is a diagonal matrix containing the RF coil sensitivities for all N points for coil c, and U applies an undersampled Fourier transform using the presumed k-space sampling pattern that results in κ k-space points.

Stacking the k-space measurements for each coil in a multi-coil acquisition results in

$$\underset{[\mathrm{C}\kappa \times 1]}{g}=(\underset{[\mathrm{C}\kappa \times \text{CN}]}{\underset{[\mathrm{C}\times \mathrm{C}]}{{\mathrm{I}}_{\mathrm{C}}}\otimes \underset{[\kappa \times \mathrm{N}]}{U}})\underset{[\text{CN}\times \mathrm{N}]}{S}\underset{[\mathrm{N}\times \mathrm{N}]}{B}\underset{[\mathrm{N}\times 2\mathrm{N}]}{C}\underset{[2\mathrm{N}\times 1]}{x}+\underset{[\mathrm{C}\kappa \times 1]}{n}$$ [5]

where g is the vector of all k-space measurements from all coils, and the block-diagonal matrix S = [S₁ ⋯ S_c]^T contains the RF coil sensitivities.

The maximum-likelihood (ML) estimate of the water and fat images, x̂, may be found via least-squares minimization of Eq. [5]:

$$\hat{x}=\text{arg }\underset{x\in ℝ}{\text{min}}{\Vert \mathit{\text{USBCx}}-g\Vert }_{{\stackrel{\sim }{\mathrm{\Psi }}}^{-1}}^2$$ [6]

where Ψ̃ = Ψ ⊗ I_κ is the ensemble noise correlation matrix (45). Due to the large matrix sizes and non-separability of this problem in the general case (e.g. non-uniform Cartesian, or non-Cartesian sampling), iterative methods such as the linear conjugate-gradient method (46) are typically used to find a solution.

Special Case: Uniform Undersampling

If the sampling within U is uniform along the cardinal dimensions, the effect after inverse Fourier transformation of g (Eq. [5]) is a set of aliased coil images which expressed in stacked fashion are:

$$h=({\mathrm{I}}_{\mathrm{C}}\otimes F_{\kappa }^{-1})g=({\mathrm{I}}_{\mathrm{C}}\otimes F_{\kappa }^{-1}U)\mathit{\text{SBCx}}+n.$$ [7]

In this special case, only a small subset of the aliased voxels interact with each other, and reconstruction may be performed individually with each subset (45). The matrix signal equation for the qth group of an M-fold accelerated, single-echo acquisition with C coils is

$$\underset{[\mathrm{C}\times 1]}{h_{\mathrm{q}}}=\underset{[\mathrm{C}\times \mathrm{M}]}{S_{\mathrm{q}}}\underset{[\mathrm{M}\times \mathrm{M}]}{B_{\mathrm{q}}}\underset{[\mathrm{M}\times 2\mathrm{M}]}{C_{\mathrm{M}}}\underset{[2\mathrm{M}\times 1]}{x_{\mathrm{q}}}+\underset{[\mathrm{C}\times 1]}{n_{\mathrm{q}}}$$ [8]

where the subset “q” indicates the vectors or matrices which contain the terms relevant to the qth group of M interacting aliased voxels. C_M = [I_M ρI_M], x_q = [w₁ ⋯ w_M f₁ ⋯ f_M]^T, and n_q contains zero-mean Gaussian noise with noise covariance Ψ.

The least-squares solution for x_q can be found by minimizing the cost function

$${\hat{x}}_{\mathrm{q}}=\left[\begin{array}{c}\hfill {\hat{w}}_{\mathrm{q}}\hfill \\ \hfill {\hat{f}}_{\mathrm{q}}\hfill \end{array}\right]=\text{arg }\underset{x_{\mathrm{q}}\in ℝ}{\text{min}}{\Vert S_{\mathrm{q}}{B}_{\mathrm{q}}{C}_{\mathrm{M}}{x}_{\mathrm{q}}-h_{\mathrm{q}}\Vert }_{{\mathrm{\Psi }}^{-1}}^2$$ [9]

$$=\text{Re }{\{C_{\mathrm{M}}^{\ast }{B}_{\mathrm{q}}^{\ast }{S}_{\mathrm{q}}^{\ast }{\mathrm{\Psi }}^{-1}{S}_{\mathrm{q}}{B}_{\mathrm{q}}{C}_{\mathrm{M}}\}}^{-1}\text{ Re }\{C_{\mathrm{M}}^{\ast }{B}_{\mathrm{q}}^{\ast }{S}_{\mathrm{q}}^{\ast }{\mathrm{\Psi }}^{-1}{h}_{\mathrm{q}}\}.$$ [10]

where Eq. [10] follows from Eq. [9] using analysis similar to the unaccelerated single coil derivation in the appendix of Ref. (43) and the unaccelerated multi-coil derivation in Appendix C of Ref. (12). As shown in Appendix B, the chemical shift components can be separated from the encoding components giving

$${\hat{x}}_{\mathrm{q}}=\left[\begin{array}{c}\hfill {\hat{w}}_{\mathrm{q}}\hfill \\ \hfill {\hat{f}}_{\mathrm{q}}\hfill \end{array}\right]=\text{Re }{\left\{\right[\begin{array}{cc}\hfill 1\hfill & \hfill \rho \hfill \\ \hfill \overline{\rho }\hfill & \hfill {|\rho |}^2\hfill \end{array}]\otimes B_{\mathrm{q}}^{\ast }{S}_{\mathrm{q}}^{\ast }{\mathrm{\Psi }}^{-1}{S}_{\mathrm{q}}{B}_{\mathrm{q}}\}}^{-1}\text{ Re }\left\{\right[\begin{array}{c}\hfill 1\hfill \\ \hfill \overline{\rho }\hfill \end{array}]\otimes B_{\mathrm{q}}^{\ast }{S}_{\mathrm{q}}^{\ast }{\mathrm{\Psi }}^{-1}{h}_{\mathrm{q}}\}.$$ [11]

The entire uniformly-undersampled water and fat images can be unfolded and algebraically separated by performing this reconstruction for all small aliasing groups.

Methods

Imaging experiments were performed for a number of different vascular territories in healthy volunteers and patients to evaluate the feasibility of highly-accelerated time-resolved single-echo Dixon CE-MRA. All studies were approved by our institutional review board (IRB) and informed consent was obtained from all subjects.

Schematics showing the acquisition and reconstruction processes are shown in Figure 1. Acquisition was performed with a variant of the CAPR method (47, 48) in which the high-pass region consists of pseudo-random sets of points (8, 49) rather than the distinct “vanes” used previously (50, 51). An example of the pseudo-random sets is shown in Fig. 1a, which shows how these sets are view shared to create uniform coverage (with corner cutting) in uniformly (SENSE) undersampled k-space. All studies were performed at 3T (Signa HDx v16.0; GE Healthcare, Waukesha, WI). Imaging parameters for the time-resolved single-echo Dixon CE-MRA exams are shown in Table 1. Echo times for the single-echo exams were chosen to provide near optimal SNR (defined here as >85% optimal SNR) in the single-echo Dixon water images (12). Optimal SNR is obtained when the fat has dephased to an odd multiple of π/2 – at 3.0T, this corresponds to TE≈0.6, 1.7, 2.8, … ms, as shown in Figure 2. In dynamic contrast-enhanced imaging, a short TE is desired to allow for short TR and image update times. For a given field of view, the minimum achievable TE is mainly affected by the number of readout samples, the readout bandwidth, and gradient capability. For all territories TE=2.8 ms was possible. In the brain exams, the number of readout samples was small enough to also allow imaging at TE=1.7 ms with the same protocol.

Figure 1.

(a) An N3 pCAPR acquisition and view-sharing scheme as used in this work. Schematics of the acquisition and reconstruction for time-resolved contrast-enhanced imaging with single-echo Dixon and time-subtraction are shown in (b) and (c), respectively. In this work, the same data from the contrast-enhanced acquisition was used for both the single-echo Dixon and time-subtraction reconstructions.

Table 1.

Imaging and reconstruction parameters used in this work. Field of view, sampling matrix, and resolution are reported as S/I×L/R×A/P.

	Calve Fig. 3	Hands Fig. 4	Brain 1 Figs. 5, 6	Brain 2 Fig. 6
Single-Echo Dixon:
Field of View (cm3)	34.0×34.0×16.0	30.0×30.0×7.2	22.0×16.8×22.0	22.0×16.8×22.0
Sampling Matrix	240×240×100	304×304×72	160×120×160	160×120×160
Resolution (mm3)	1.42×1.42×1.60	0.99×0.99×1.00	1.38×1.40×1.38	1.38×1.40×1.38
TR / TE (ms)	4.9 / 2.8	5.4 / 2.8	3.5 / 1.7	4.6 / 2.8
FA / BW (kHz)	18°/ ± 62.5	30°/ ± 62.5	25°/ ± 62.5	25°/ ± 62.5
Number and Arrangement of Receive Coil Elements	8 circumferential	8 circumferential	8 circumferential	8 circumferential
SENSE R (=RY × RZ)	4 × 2	4 × 2	2 × 2	2 × 2
Image Update Time (s)	11.1	5.2	4.5	6.0
Temporal Footprint (s)	11.1	13.2	13.2	17.3
Dual-Echo Calibration:
TR / TE1 / TE2 (ms)	5.6 / 2.3 / 3.5	6.1 / 2.3 / 3.5	5.4 / 2.3 / 3.5	5.4 / 2.3 / 3.5
SENSE R (=RY × RZ)	1	1	1	1
Regularization Parameter	6e14	1e12	3e12	1e13
Refinement Reduction	$\sqrt{10}$	$\sqrt{10}$	$\sqrt{10}$	$\sqrt{10}$
Reconstruction Time (h:mm)	2:04	0:38	0:11	0:15
Hypothetical Time-Subtraction:
Min Achievable TR / TE (ms)	4.1 / 1.9	4.8 / 2.1	3.2 / 1.4	3.2 / 1.4
Min Achievable	9.4	4.6	4.1	4.1
Image Update Time (s)
Min Achievable	9.4	11.8	12.0	12.0
Temporal Footprint (s)
Theoretical SNR Analysis:
Theoretical SNR of acquired SE $\text{Dixon }/\text{ SNR Efficiency }(=\frac{\text{SNR}}{\sqrt{\text{TR}}})$	0.25 / 3.56	0.35 / 4.72	0.34 / 5.67	0.30 / 4.49
Theoretical SNR of subtraction with min TE / SNR Efficiency	0.13 / 2.08	0.18 / 2.62	0.17 / 2.96	0.17 / 2.96
Theoretical SNR ratio $(\frac{{\text{SNR}}_{\text{Dixon}}}{{\text{SNR}}_{\text{subtraction}}})$	1.87	1.91	2.00	1.82
Theoretical SNR efficiency ratio $(\frac{{\text{SNReff}}_{\text{Dixon}}}{{\text{SNReff}}_{\text{subtraction}}})$	1.72	1.80	1.92	1.52

Figure 2.

Relative SNR vs. TE for single-echo Dixon imaging at 3T assuming a 440 Hz chemical shift for fat excluding any effects of ${\mathrm{T}}_2^{\ast }$ decay. The maximum SNR corresponds to echo times that allow fat to dephase to odd multiples of π/2 (e.g. π/2, 3π/2, …). At 3.0T, a window of about ±0.2 ms around each optimal TE provides >85% of the max SNR.

Noting that the TE and TR for optimal single-echo Dixon acquisition are typically longer than the minimum achievable TE and corresponding TR used for time-subtraction acquisition, these scanner-dependent minimum achievable times have been included in Table 1. Additionally, the theoretical SNR and SNR efficiency (defined as $\text{SNR}/\sqrt{\text{TR}}$) for single-echo Dixon and subtraction were determined as a metric of performance. SNR was computed using Eqs. (16a) and (21a) from Ref. (12). The signal component was computed using the steady state signal equation for spoiled gradient echo (52), with T₁ and ${\mathrm{T}}_2^{\ast }$ relaxation times of blood and CE-blood as reported in Ref. (53) assuming 16 mM of gadobenate dimeglumine. It was also assumed that (SΨ⁻¹S*)⁻¹=1. To show the relative improvement of single-echo Dixon vs. time-subtraction in terms of SNR and SNR efficiency, ratios of theoretical SNR and SNR efficiency were also computed.

For the contrast-enhanced scans, gadolinium-based contrast agent was injected after one full k-space dataset (all shared views) had been acquired (“inject” arrow, Fig. 1b–c). All studies used gadobenate dimeglumine (MultiHance; Bracco Diagnostics, Princeton, New Jersey).

Single-echo images were reconstructed for each time frame using the formulation in Eq. 11 for these uniformly-undersampled (after viewsharing) Cartesian data sets (Fig. 1b). S, ϕ(τ), and ϕ₀ were estimated from a fully-sampled dual-echo dataset acquired before contrast injection using a constrained-phase signal model with graph-cuts optimization scheme (44). In short, water, fat, ΔB₀ and ϕ₀ maps are estimated in a maximum-likelihood framework through the use of variable projection (54) to reduce the dimensionality of the data fidelity cost, and a global cost function that is regularized to promote smoothness in ΔB₀. Both the dual-echo calibration scan and the single-echo time-resolved scan used the multi-peak fat spectrum from Ref. (55). Imaging and reconstruction parameters for the dual-echo calibration acquisition are shown in Table 1. All reconstructions were performed offline on a system with 64GB of RAM and two E5-2670 v2 Xeon CPUs for a total of 20 2.5GHz cores and 40 threads. The bulk of the computation occurs in the estimation of ΔB₀ and ϕ₀, with reconstruction times reported in Table 1. Reconstruction of the time-series of single-echo Dixon volumes was performed in under 5 seconds.

For comparison, time-subtraction images were generated by matched-subtraction (56) of the views acquired before contrast injection from all subsequent contrast-enhanced frames (Fig. 1c). Both reconstruction techniques used the same raw data.

Results

Image results from a calf exam are shown in Figure 3. Rows (a) and (c) depict the coronal maximum intensity projections (MIPs) and a single coronal slice through the single-echo Dixon water images of the time series, respectively, and rows (b) and (d) depict the same for the time-subtracted images. Both reconstruction techniques produced diagnostic quality images. A motion-induced artifact can be seen in the late enhancement images of the time-subtraction images (red arrowheads) but is avoided with the single-echo Dixon technique. Additionally, the small superficial subcutaneous veins are better visualized in the coronal slices of the single-echo Dixon water image vs. the time-subtraction images (yellow arrows).

Figure 3.

MIPs (a, b) and individual coronal partitions (c, d) from the single-echo Dixon (a, c) and time-subtraction (b, d) CE-MRA reconstructions. Red arrowheads show a motion-induced subtraction artifact in the partitioned images in (d), which manifests as shading in (b). The Dixon partitions and MIPs (a, c) are unaffected. Yellow arrows show that small superficial subcutaneous veins are well seen in the Dixon CE-MRA images (d). Enlargements of portions of the images (dashed and dotted boxes) are shown in (e)–(h).

Figure 4 shows images from a time-resolved hand study reconstructed with single-echo Dixon (a) and time-subtraction (b). Both time series depict the contrast dynamics well. Some increased background signal is observed in the index finger and thumb of the left hand in the Dixon images, but does not affect the diagnostic quality of these images.

Figure 4.

MIPs of a hand study reconstructed with single-echo Dixon (water images, a) and time subtraction (b). Enlargements of the portion of the images within the dashed box are shown in (c). Note the excellent depiction of the vasculature in both time series.

Time-resolved contrast-enhanced images of the brain with an image update time of 4.5 s are shown in Figure 5. Again, both reconstruction techniques provide diagnostic images, but the images reconstructed with single-echo Dixon appear to have higher SNR and can better depict the smaller vessels. Additionally, structures such as the brain, cerebrospinal fluid, and skull are depicted as benign background signal in the single-echo Dixon images and provide contextual anatomy.

Figure 5.

Brain images reconstructed with a single-echo Dixon reconstruction (a) and time subtraction (b). Note the high SNR of the single-echo Dixon images compared to the subtraction images, and good depiction of the cerebral vasculature. Enlargements of the portion within the dashed box from each of the enhanced time frames are shown in (c) and (d).

The result of reducing the TE from 2.8 ms to 1.7 ms in a brain exam is shown in Figure 6. Both echo times provide near optimal SNR for single-echo Dixon imaging (12), but the use of the shorter TE allows for a reduction in image update time/temporal footprint from 6.0/17.3 s to 4.5/13.2 s. The advantage of the improved temporal resolution is apparent when observing the contrast dynamics. In the images acquired with the shorter TE (a) a clear arterial phase is depicted, while the images acquired with the longer TE (b) show either partial arterial enhancement or venous contamination.

Figure 6.

Brain MIPs reconstructed from data acquired with an echo time of TE=1.7ms (a) and TE=2.8ms (b). Both echo times provide near optimal SNR for single-echo Dixon, but the shorter echo time allows for a shorter TR and thus a shorter image update time (4.5 vs. 6 seconds) and more images acquired within the same window of time.

Theoretical SNR and SNR efficiency are reported in Table 1 for the acquired single-echo Dixon parameters and the minimum achievable TE and TR that would be used for time-subtraction acquisition. Despite the lengthening of TE (and in turn TR) in the single-echo Dixon acquisition, the SNR and SNR efficiency ratios (Dixon:subtraction) remain greater than 1, indicating an improvement when using single-echo Dixon. Note that the SNR efficiency advantage of single-echo Dixon compared to subtraction is reduced from the SNR advantage due to the TR lengthening as a result of TE restrictions in single-echo Dixon.

Discussion

In this work we have demonstrated 2D accelerated time-resolved single-echo Dixon 3D contrast-enhanced MRI for multiple anatomic regions. Compared to other single-echo Dixon techniques (15, 22–28), the image update time and temporal footprint have been reduced by factors of 3 to 7 times. This work also included the derivation of the maximum-likelihood solution to the problem of joint SENSE unfolding and single-echo fat-water decomposition, and this was the basis of the reconstruction used in this work.

While previous single-echo Dixon work showed compatibility with SENSE accelerations of R=2 (15), this work has shown that SENSE acceleration factors as high as R=8 are also compatible with the single-echo Dixon background suppression technique. This is comparable to previous work in time-subtraction CE-MRA that demonstrated SENSE acceleration factors of R=8 and greater (57, 58). The image quality of the single-echo Dixon images reconstructed from highly-undersampled data remained high despite the possibility of additional undersampling artifacts. That is, time subtraction reconstruction avoids spurious signal as the (static) artifacts are subtracted along with the other static signal. Single-echo Dixon imaging, however, doesn't employ a subtraction, so can be susceptible to increased artifacts from undersampling. In practice, object masking eliminates the background signal, but can shift artifacts from the background into the unmasked (object) regions. Nonetheless, at the relatively high acceleration factors used in this work, these artifacts did not degrade image quality. Even higher acceleration factors may be possible though the use of CAIPIRINHA-type (59) sampling (as in Ref. (10)) and acceleration apportionment which has successfully improved temporal resolution and image quality in time-subtraction CE-MRA (58, 60). Additional performance gains may be achieved in the future by extending this framework and utilizing advanced reconstruction techniques such as non-linear regularization as in Refs. (33–36).

Single-echo Dixon CE-MRA techniques can provide higher temporal resolution compared to dual-echo Dixon techniques. In this work, image update times as short as 4.5 s were attained in the brain with SENSE undersampling factors of R=4 and a relatively low readout bandwidth of BW=±62.5 kHz at 3.0T. Direct comparison to dual-echo studies in the literature is difficult due to differences in protocol choices and hardware capabilities; however, in general higher readout bandwidths are used in dual-echo studies to keep TE and TR values short (9, 10, 14, 21). This strategy can keep image update times short but at the cost of SNR. Dual-echo Dixon imaging with biploar readout has also been shown to be susceptible to flow-induced artifacts that mimic thrombus (19, 21) due to the mismatched gradient moments at the center of each readout. This problem is unique to multi-echo Dixon imaging with a bipolar readout, and is not an issue in imaging with a flyback gradient, or a multi-TR interleaved TE technique as used in the calibration scan in this work. Single-echo Dixon is also immune to these artifacts as long as the dual-echo calibration scan avoids use of bipolar gradients. Changes in flow between the calibration scan and the time-resolved series may lead to artifacts similar to those seen in Refs. (19, 21). However, the inherent velocity encoding that results from a bi-polar dual-echo readout gradient is prone to produce artifacts when flow is along the readout direction, while the proposed technique would only produce artifacts in the less-likely event of large changes in flow between the calibration and the time-resolved series.

The SNR of the water image in single-echo Dixon is related to the phase offset between water and fat at the image echo time as shown in previous works (12, 15). In practice, echo times within ±0.2 ms of these optima provide >85% of the optimal SNR (Figure 2) at 3T. Factors including gradient performance, readout bandwidth, and number of readout points can push the minimum achievable echo time outside this range of acceptable SNR. When this happens, one option is to acquire images within the next shortest optimal echo time range, and extend TR and image update time accordingly. Alternatively, the readout bandwidth or number of readout points can be changed to retain the shorter echo time (and the shorter image update time) (61). At lower field strengths, the optimal TEs will have wider separation than at the 3T field used in this work and provide less flexibility. For example, at 1.5T the echo times for optimal SNR would be TE≈1.1, 3.4, 5.6, … ms. The restriction on TE is a disadvantage of single-echo Dixon compared to time-subtraction which has more flexibility.

Compared to subtraction imaging, there is also some additional exam time associated with single-echo Dixon imaging for acquisition of the dual-echo calibration scan for ΔB₀ and ϕ₀ estimation. While SENSE-accelerated time-subtraction imaging acquires a fully-sampled single-echo image from which coil sensitivities are estimated, this single-echo Dixon implementation requires a dual-echo image from which the additional “nuisance” phases are estimated. Any technique that uses information from another time will be susceptible to artifacts due to data mismatch. In time-subtraction, the misregistration between the pre-contrast image and the post-contrast images can cause an incomplete subtraction of the background tissue, or even artifactual elimination of the contrast-enhanced blood signal. Single-echo Dixon uses a pre-contrast estimate of the “nuisance” phase parameters, and is also susceptible to changes between the dual-echo calibration and the time-resolved series that can result in the following artifacts. First, any movement between these datasets can cause artifactual signal leakage. However, because the ΔB₀-induced and initial phases are smooth, more motion is tolerated than in time-subtraction imaging (as shown by the red arrow-heads in Fig. 3). Time-subtraction uses a pre-contrast image as prior information and the spatial frequency content is high – equal to that of the time-resolved images. Single-echo Dixon imaging uses ΔB₀ and ϕ₀ maps as prior information, and due to the smoothness in these maps the spatial frequency content is lower and more tolerant of motion. Second, the inflow of gadolinium-based contrast agent can result in susceptibility-induced phase changes between the calibration and time-resolved datasets, resulting in fat/water signal leakage. This can be mitigated by performing the dual-echo calibration after the time-resolved scan, while contrast is still on board, or by performing a hybrid reconstruction with virtual shimming (62).

This work does have limitations. First, in the estimation of the sensitivity profiles from the dual-echo calibration data S was estimated from the image at TE=2.3 ms, where water and fat are assumed to be in phase. However, due to the differential phase dispersion between the multiple fat peaks, water and fat are not truly in phase at any TE after excitation in a spoiled gradient echo sequence. Second, there is no comparison to existing methods (15, 22–28) of single-echo Dixon reconstruction included in this work. Such a comparison is outside the scope of this work, but may be valuable to study in the future. Third, the comparison between time-resolved single-echo Dixon and time-subtraction CE-MRA was done using the same dynamic raw data reconstructed with each of the two methods. In practice, however, a single-echo Dixon CE-MRA acquisition in general will have poorer temporal resolution than an acquisition tailored to time-subtraction imaging due to the TE restrictions (c.f. Fig. 2). To try to quantify this, the minimum achievable TE and corresponding reduced TR, image update time, and temporal footprint have been included in Table 1. Note that the reduction in temporal resolution is provided at the benefit of an improvement in SNR, and these factors can be traded off – e.g. better temporal resolution could be prioritized by reducing the TE to a less optimal point, with the potential of maintaining some (reduced) SNR advantage.

In conclusion, the maximum-likelihood estimator for combined single-echo Dixon and 2D SENSE unfolding has been derived and demonstrated with acceleration factors up to R=8 for time-resolved subtractionless CE-MRA. The single-echo Dixon technique benefits from higher temporal resolution than multi-echo Dixon techniques, and is shown to be less susceptible to motion-induced artifacts than time-subtraction.

Appendices

Appendix A Matrix Construction Details

Equation [3] can be expressed using matrix notation as

$$g_{\mathrm{k},\mathrm{c}}={\delta }_{\mathrm{k}}^T{\mathit{\text{US}}}_{\mathrm{c}}\mathit{\text{BC }}\left[\begin{array}{c}\hfill w\hfill \\ \hfill f\hfill \end{array}\right]+n_{\mathrm{c}}={\delta }_{\mathrm{k}}^T{\mathit{\text{US}}}_{\mathrm{c}}\mathit{\text{BCx}}+n_{\mathrm{c}}$$ [A.1]

where ${\delta }_{\mathrm{k}}^{T}U$ is a single row of the Fourier encoding matrix U and encodes a single k-space point over all image-space positions, S_c = diag([s_c,1 ⋯ s_c,N]^T) is a diagonal matrix containing the RF coil sensitivities at each of the N image-space positions, B = diag ([e^{i(ϕ₁+ϕ_0,1)} ⋯ e^{i(ϕ_N+ϕ_0,N)}]^T) is a diagonal matrix containing the “nuisance” phase due to ΔB₀ inhomogeneities and initial phase ϕ₀ at each image-space position, and C = [I_N ρI_N] is the appropriately sized chemical shift matrix. $x=\left[\begin{array}{c}\hfill w\hfill \\ \hfill f\hfill \end{array}\right]$ contains the stacked, vectorized water and fat images.

The signal model for a single point in k-space can be expanded to the ensemble of points by summing over all k:

$$g_{\mathrm{c}}=\sum _{\mathrm{k}}{\delta }_{\mathrm{k}}{g}_{\mathrm{k},\mathrm{c}}={\mathit{\text{US}}}_{\mathrm{c}}\mathit{\text{BCx}}+n_{\mathrm{c}}$$ [A.2]

and a C-coil acquisition can be expressed by summing Eq. [A.2] over all coils. The result is

$$g=\sum _{\mathrm{c}}{\delta }_{\mathrm{c}}\otimes g_{\mathrm{c}}=({\mathrm{I}}_{\mathrm{C}}\otimes U)\mathit{\text{SBCx}}+n$$ [A.3]

where S = [S₁ ⋯ S_c]^T contains the stacked coil sensitivity matrices.

Appendix B Separation of Chemical Shift and Encoding Matrices

Starting with Eqn. [10], The quantity in the left-side term, $C_{\mathrm{M}}^{\ast }{B}_{\mathrm{q}}^{\ast }{S}_{\mathrm{q}}^{\ast }{\mathrm{\Psi }}^{-1}{S}_{\mathrm{q}}{B}_{\mathrm{q}}{C}_{\mathrm{M}}$, can be expanded and expressed with Kronecker’s product as follows.

$$C_{\mathrm{M}}^{\ast }{B}_{\mathrm{q}}^{\ast }{S}_{\mathrm{q}}^{\ast }{\mathrm{\Psi }}^{-1}{S}_{\mathrm{q}}{B}_{\mathrm{q}}{C}_{\mathrm{M}}=\left[\begin{array}{c}\hfill {\mathrm{I}}_{\mathrm{M}}\hfill \\ \hfill \overline{\rho }{\mathrm{I}}_{\mathrm{M}}\hfill \end{array}\right]B_{\mathrm{q}}^{\ast }{S}_{\mathrm{q}}^{\ast }{\mathrm{\Psi }}^{-1}{S}_{\mathrm{q}}{B}_{\mathrm{q}}\left[\begin{array}{cc}\hfill {\mathrm{I}}_{\mathrm{M}}\hfill & \hfill \rho {\mathrm{I}}_{\mathrm{M}}\hfill \end{array}\right]$$ [B.1]

$$=\left[\begin{array}{cc}\hfill B_{\mathrm{q}}^{\ast }{S}_{\mathrm{q}}^{\ast }{\mathrm{\Psi }}^{-1}{S}_{\mathrm{q}}{B}_{\mathrm{q}}\hfill & \hfill \rho B_{\mathrm{q}}^{\ast }{S}_{\mathrm{q}}^{\ast }{\mathrm{\Psi }}^{-1}{S}_{\mathrm{q}}{B}_{\mathrm{q}}\hfill \\ \hfill \overline{\rho }{B}_{\mathrm{q}}^{\ast }{S}_{\mathrm{q}}^{\ast }{\mathrm{\Psi }}^{-1}\mathit{\text{ SB}}\hfill & \hfill {|\rho |}^2{B}_{\mathrm{q}}^{\ast }{S}_{\mathrm{q}}^{\ast }{\mathrm{\Psi }}^{-1}{S}_{\mathrm{q}}{B}_{\mathrm{q}}\hfill \end{array}\right]$$ [B.2]

$$=\left[\begin{array}{cc}\hfill 1\hfill & \hfill \rho \hfill \\ \hfill \overline{\rho }\hfill & \hfill {|\rho |}^2\hfill \end{array}\right]\otimes B_{\mathrm{q}}^{\ast }{S}_{\mathrm{q}}^{\ast }{\mathrm{\Psi }}^{-1}{S}_{\mathrm{q}}{B}_{\mathrm{q}}$$ [B.3]

Likewise, the quantity in the right-side term, $C_{\mathrm{M}}^{\ast }{B}_{\mathrm{q}}^{\ast }{S}_{\mathrm{q}}^{\ast }{\mathrm{\Psi }}^{-1}{h}_{\mathrm{q}}$, can be expanded and expressed in a similar way.

$$C_{\mathrm{M}}^{\ast }{B}_{\mathrm{q}}^{\ast }{S}_{\mathrm{q}}^{\ast }{\mathrm{\Psi }}^{-1}{h}_{\mathrm{q}}=\left[\begin{array}{c}\hfill 1\hfill \\ \hfill \overline{\rho }\hfill \end{array}\right]\otimes B_{\mathrm{q}}^{\ast }{S}_{\mathrm{q}}^{\ast }{\mathrm{\Psi }}^{-1}{h}_{\mathrm{q}}$$ [B.4]

Substituting [B.3] and [B.4] into Eq. [10], results in Eq. [11].