Free-breathing, fat-corrected T1 mapping of the liver with stack-of-stars MRI, and joint estimation of T1, PDFF, R 2 * , and B 1 +

Abstract

Purpose: Quantitative T₁ mapping has the potential to replace biopsy for noninvasive diagnosis and quantitative staging of chronic liver disease. Conventional T₁ mapping methods are confounded by fat and $B_1^{+}$ inhomogeneities, resulting in unreliable T₁ estimations. Furthermore, these methods trade off spatial resolution and volumetric coverage for shorter acquisitions with only a few images obtained within a breath-hold. This work proposes a novel, volumetric (3D), free-breathing T₁ mapping method to account for multiple confounding factors in a single acquisition.

Theory and methods: Free-breathing, confounder-corrected T₁ mapping was achieved through the combination of non-Cartesian imaging, magnetization preparation, chemical shift encoding, and a variable flip angle acquisition. A subspace-constrained, locally low-rank image reconstruction algorithm was employed for image reconstruction. The accuracy of the proposed method was evaluated through numerical simulations and phantom experiments with a T₁/proton density fat fraction phantom at 3.0 T. Further, the feasibility of the proposed method was investigated through contrast-enhanced imaging in healthy volunteers, also at 3.0 T.

Results: The method showed excellent agreement with reference measurements in phantoms across a wide range of T₁ values (200 to 1000 ms, slope = 0.998 (95% confidence interval (CI) [0.963 to 1.035]), intercept = 27.1 ms (95% CI [0.4 54.6]), r² = 0.996), and a high level of repeatability. In vivo imaging studies demonstrated moderate agreement (slope = 1.099 (95% CI [1.067 to 1.132]), intercept = -96.3 ms (95% CI [-82.1 to -110.5]), r² = 0.981) compared to saturation recovery-based T₁ maps.

Conclusion: The proposed method produces whole-liver, confounder-corrected T₁ maps through simultaneous estimation of T₁, proton density fat fraction, and $B_1^{+}$ in a single, free-breathing acquisition and has excellent agreement with reference measurements in phantoms.

Keywords: T1 mapping; compressed‐sensing; free‐breathing imaging; inversion recovery; multi‐contrast; non‐Cartesian imaging.

Figure 1:

The proposed data acquisition strategy provides volumetric images with ${\mathrm{T}}_1$ and chemical shift contrast. ${\text{TI}}_{\text{eff}}$, $\text{TR}$, $\text{TE}$, and $\text{TD}$ stand for effective inversion, repetition, echo, and idle time. (A, B) Each IR-Block consists of an adiabatic inversion pulse, radial stacks of multi-echo ${\mathrm{k}}_{\mathrm{z}}$-readouts, and an idle period. The imaging flip angle (FA) changes throughout the ${\mathrm{T}}_1$ recovery to correct for ${\mathrm{T}}_1$ bias arising from ${\mathrm{B}}_1+$ inhomogeneity and inversion efficiency. (${\theta }_1$, ${\theta }_2$) and ($N_1$, $N_2$) represent the FA pair, and the number of RF pulses corresponding to each FA used in imaging experiments. $\text{TI}$ is the duration of the adiabatic inversion pulse. (C) ${\text{TI}}_{\text{eff}}$ is defined as the acquisition time of the center of the k-space for each radial stack. (D) The proposed image acquisition strategy delivers multi-contrast images acquired at different ${\text{TI}}_{\text{eff}}$ and $\text{TE}$ points. Note that, the longitudinal magnetization (${\mathrm{M}}_{\mathrm{z}}$) curves are representative of the ${\theta }_1>{\theta }_2$.

Figure 2:

The Bloch equation simulations indicated that clinically relevant ${\mathrm{T}}_1$ times could be accurately estimated with moderate flip angles and a subspace dimension of four. (A, B) Larger FAs (${\theta }_1>12°$) failed to produce accurate ${\mathrm{T}}_1$ estimations for ${\mathrm{T}}_1<300\text{ms}$, whereas longer ${\mathrm{T}}_1$ estimations (${\mathrm{T}}_1>1500\text{ms}$) were prone to low SNR performance in the absence of subspace constraints. To investigate the impact of flip angle and subspace constraints on clinically relevant ${\mathrm{T}}_1$ values, 900 and 300 ms were chosen to represent pre- and post-contrast (hepatobiliary phase) ${\mathrm{T}}_1$ of the liver. (C, E) Within the clinically relevant range of ${\mathrm{T}}_1$ values, a minimum of 4-5 subspace dimensions were required to produce accurate ${\mathrm{T}}_1$ estimations, depending on the choice of flip angle. (D, F) For ${\mathrm{T}}_1=300\text{ms}$, small FAs (${\theta }_1<4°$) were prone to low SNR performance. For ${\mathrm{T}}_1=900\text{ms}$, FAs between 8-12° produced more precise ${\mathrm{T}}_1$ estimations. Note that the flip angle axis only shows the first element of the flip angle pair, i.e., ${\theta }_1$. Note that “w/o” in (C, D, E, F) indicates the set of simulation results without subspace constraints. As a result of the simulation study, flip angle pair (${\theta }_1$, ${\theta }_2$) of (8°,4°) and subspace dimension of 4 were used in the acquisition and reconstruction of the data.

Figure 3:

The proposed ${\mathrm{T}}_1$ mapping method can correct for multiple confounding factors in a single acquisition, showing excellent agreement with the ground truth IR-FSE ${\mathrm{T}}_1$ measurements. (A) Reference ${\mathrm{T}}_1$, PDFF, ${\mathrm{R}}_2^{\ast }$, and ${\mathrm{B}}_1+$ maps. (B) Confounder corrected water-specific ${\mathrm{T}}_1$ (${\mathrm{T}}_{1,\mathrm{W}}$), PDFF, ${\mathrm{R}}_2^{\ast }$, and ${\mathrm{B}}_1+$ maps reconstructed with the proposed method. (C-D) The ${\mathrm{T}}_1$ map generated with the IR-FSE is confounded by the presence of fat, resulting in shorter apparent ${\mathrm{T}}_1$ in vials with 10 and 20% PDFF. (E-F) ROI measurements taken from vials with 0% PDFF in IR-FSE ${\mathrm{T}}_1$ maps reflect the true ${\mathrm{T}}_{1,\mathrm{W}}$ for a given NiCl₂ concentration, which shows excellent linear agreement and a small bias of 25.8±19.6 ms with the proposed method.

Figure 4:

The single- and multi-shot imaging protocols, acquired in different days, produced highly repeatable results that agree with the ground truth IR-FSE measurements. (A) Both imaging protocols acquired on different days produced similar ${\mathrm{T}}_{1,\mathrm{W}}$ maps. (B-C) Bland-Altman analysis against ground truth ${\mathrm{T}}_1$ measurements did not reveal significant bias for ${\mathrm{T}}_1$ estimations with the proposed method. (D-E) ${\mathrm{T}}_{1,\mathrm{W}}$ maps reconstructed with the proposed method on different days showed excellent agreement and negligible bias. (F-G) ${\mathrm{T}}_{1,\mathrm{W}}$ maps reconstructed with the single- and multi-shot protocols were highly correlated and did not show significant bias. A minor underestimation of longer ${\mathrm{T}}_{1,\mathrm{W}}$ (>1000 ms) was observed in the multi-shot protocol.

Figure 5:

Confounder corrected ${\mathrm{T}}_{1,\mathrm{W}}$ maps from a healthy volunteer, acquired with two sets of imaging parameters are generally in agreement with the reference SMART₁Map measurements. Confounder (PDFF and ${\mathrm{B}}_1+$) maps are also shown. ${\mathrm{B}}_1+$ inhomogeneity and inversion efficiency maps are smoothed in a multi-pass parameter estimation algorithm (see Sec. 2.3) to improve the noise performance of the final ${\mathrm{T}}_{1,\mathrm{W}}$ maps.

Figure 6:

Both reference SMART₁Map and the proposed ${\mathrm{T}}_{1,\mathrm{W}}$ maps were acquired pre- and post-contrast (5, 10, 15, and 20 min) injection to track ${\mathrm{T}}_{1,\mathrm{W}}$ shortening. While SMART₁Map is capable of acquiring a single slice in a breath-hold, the proposed method can provide whole liver coverage in a free-breathing acquisition. Reference ${\mathrm{T}}_1$ and multiple slices from the proposed ${\mathrm{T}}_{1,\mathrm{W}}$ maps are displayed at different stages of the contrast-enhanced study.

Figure 7:

The proposed method shows moderate agreement with the reference in vivo ${\mathrm{T}}_1$ measurements. (A) Regression analysis conducted on ROI measurements taken from pre- (blue) and post-contrast (red) ${\mathrm{T}}_1$ maps across all human subjects indicate a moderate agreement between the proposed method and the SMART₁Map. (B) Bland-Altman analysis reveals an average difference of −6.1±57.9 and −68.1±28.4 ms between the proposed method and the SMART₁Map for pre- and post-contrast measurements, respectively. Note that, blue and red dashed lines represent the 95% confidence intervals for pre- and post-contrast measurements, respectively.

Figure 8:

${\mathrm{T}}_{1,\mathrm{W}}$ times experienced statistically significant shortening following the administration of the contrast agent. (A) Data points show the average of a single ROI drawn in the proposed ${\mathrm{T}}_{1,\mathrm{W}}$ maps, and corresponding reference SMART₁Maps, avoiding major veins. An additional SMART₁Map is acquired following the acquisition of post-HBP ${\mathrm{T}}_{1,\mathrm{W}}$ map (~26 min) to ensure GA concentration remained approximately constant during the final 6-minute acquisition of the high-resolution ${\mathrm{T}}_{1,\mathrm{W}}$ map. (B) ROI measurements from SMART₁Map and the proposed method averaged across volunteers, plotted against time after contrast injection, highlight that SMART₁Map consistently estimates longer post-contrast ${\mathrm{T}}_1$ than the proposed method. Note that, due to longer imaging times, the mid-time point of the acquisition is reported as the effective measurement time for the proposed method.