4673
Simultaneous B1- and Fat-Corrected T1 Mapping Using Chemical-Shift Encoded MRI1Radiology, University of Wisconsin - Madison, Madison, WI, United States, 2Electrical and Computer Engineering, University of Wisconsin - Madison, Madison, WI, United States, 3Medical Physics, University of Wisconsin - Madison, Madison, WI, United States, 4Biomedical Engineering, University of Wisconsin - Madison, Madison, WI, United States, 5Medicine, University of Wisconsin - Madison, Madison, WI, United States, 6Emergency Medicine, University of Wisconsin - Madison, Madison, WI, United States
Synopsis
Spatially varying B1 inhomogeneities and tissue fat are known to be confounders of quantitative T1 mapping methods that use multiple flip-angle techniques. Separately acquired B1 calibration maps can be used to correct flip angle errors caused by B1 inhomogeneities, but this requires an additional acquisition. In this work we propose a comprehensive approach that combines concepts from actual flip-angle imaging with variable flip-angle imaging to simultaneously estimate B1 inhomogeneity, T1, proton density fat-fraction and R2*. The feasibility and noise performance of this joint acquisition and fitting approach are evaluated using Cramer-Rao Lower Bound analysis, simulations, phantom experiments, and preliminary in vivo examples.
Introduction
T1 mapping using the variable flip angle (VFA) method has multiple applications, particularly when imaging speed and motion robustness are important (1,2). However, VFA is confounded by the presence of tissue fat (due to its short T1) and B1 inhomogeneities (which cause spatially varying flip angle errors) (3,4).
The presence of fat can be addressed through fat-water separated chemical shift encoded MRI (CSE-MRI) techniques (5,6); however, standard B1-corrected VFA methods require a separate calibration acquisition (4,7).
Therefore, the purpose of this work is to present a novel B1- and fat-corrected CSE-MRI T1 mapping method. Our approach combines an alternating TR SGRE “actual flip angle” (AFI) acquisition strategy (7) with a traditional VFA strategy (2) to jointly estimate B1- and fat-corrected T1, as well as provide proton density fat fraction (PDFF) and R2* maps without an additional calibration scan.
Theory
AFI allows fast and accurate 3D B1 measurements through repeated SGRE excitations with identical flip angles and alternating TRs (7). Similar to work done by Hurley et al (8), we propose a joint estimation, including a term for B1 inhomogeneity ($$$\beta$$$), from one AFI dataset and one VFA SGRE dataset; however, distinct from this previous work, we utilize a multi-echo, fat/water separated approach (9-11). Given complete spoiling of transverse magnetization after each TR, the respective steady-state signals are as follows:
$$S_{1}(TR_{1},TR_{2},\alpha_{1},\alpha_{2},TE;\theta)=(\rho_{W}\cdot{K(TR_{1},TR_{2},\alpha_{1},\alpha_{2},T1_{W})}+\rho_{F}\cdot{K(TR_{1},TR_{2},\alpha_{1},\alpha_{2},T1_{F})}\cdot{C_{n}})\cdot{e^{-R2^{*}\cdot{TE}}}\cdot{e^{i(2\pi\psi\cdot{TE}+\phi)}}\\\\S_{2}(TR_{1},TR_{2},\alpha_{1},\alpha_{2},TE;\theta)=(\rho_{W}\cdot{K(TR_{2},TR_{1},\alpha_{2},\alpha_{1},T1_{W})}+\rho_{F}\cdot{K(TR_{2},TR_{1},\alpha_{2},\alpha_{1},T1_{F})}\cdot{C_{n}})\cdot{e^{-R2^{*}\cdot{TE}}}\cdot{e^{i(2\pi\psi\cdot{TE}+\phi)}}\\\\S_{3}(TR_{3},\alpha_{3},TE;\theta,\beta)=(\rho_{W}\frac{sin(\beta\cdot{\alpha_{3}})\cdot{(1-e^{-\frac{TR_{3}}{T1_{W}}}})}{1-e^{-\frac{TR_{3}}{T1_{W}}}\cdot{cos(\beta\cdot{\alpha_{3}})}}+\rho_{F}\frac{sin(\beta\cdot{\alpha_{3}})\cdot{(1-e^{-\frac{TR_{3}}{T1_{F}}}})}{1-e^{-\frac{TR_{3}}{T1_{F}}}\cdot{cos(\beta\cdot{\alpha_{3}})}}\cdot{C_{n}})\cdot{e^{-R2^{*}\cdot{TE}}}\cdot{e^{i(2\pi\psi\cdot{TE}+\phi)}}$$
Where:
$$$K(TR_{A},TR_{B},\alpha_{A},\alpha_{B},T1)=\frac{sin(\beta\cdot{\alpha_{A}})(1-e^{-\frac{TR_{B}}{T1}}+(1-e^{-\frac{TR_{A}}{T1}})\cdot{e^{-\frac{TR_{B}}{T1}}cos(\beta\cdot{\alpha_{B}})})}{1-e^{-\frac{TR_{A}}{T1}}e^{-\frac{TR_{B}}{T1}}cos(\beta\cdot{\alpha_{A}})cos(\beta\cdot{\alpha_{B}})}\\\theta=(\beta,~T1_{W},~T1_{F},~\rho_{W},~\rho_{F},~R2*,~\phi,~\psi)$$$
$$$\rho_{W}~\text{and}~\rho_{F}~=~\text{real-valued}~\text{signals}~\text{from}~\text{water}~\text{and}~\text{fat}$$$
$$$T1_{W}~\text{and}~T1_{F}~\text{=}~\text{T1}~\text{of}~\text{water}~\text{and}~\text{fat}$$$
$$$\phi~=~\text{initial}~\text{phase}~\text{(11)}$$$
$$$\psi~=~\text{fieldmap}$$$
$$$\theta$$$ is the set of unknown parameters; β relates the transmitted flip angle (αT) to prescribed flip angle (αP) by the equation αT=βαP; Fat is corrected by the inclusion of a 6-peak spectral model, denoted $$$C_{n}$$$(9,12).
A diagram and description of the proposed pulse sequence are shown in Figure 1.
Methods
Optimization of Acquisition Parameters
A Cramer-Rao Lower Bound (CRLB) (13) was calculated for the acquisition strategy described above (ETL1=6, ETL2=1, ETL3=2) and used to determine the set of SNR-optimal acquisition parameters (SNR defined as: average |Sn|/σ, where σ=standard deviation of the noise). Optimization was constrained to realizable TRs, TEs, and flip angles.
Numerical Simulations
The proposed acquisition and a nonlinear least squares joint reconstruction strategy was tested in simulated data using common 1.5T liver tissue parameters, i.e. β=0.95,T1W=576ms,T1F=288ms,PDFF=20%,R2*=30 (14,15) and acquisition parameters determined by the CRLB and scan time constraints (α1=60o/α2=60o/α3=3o, TR1=29.4ms/TR2=4.9ms/TR3=6.8ms, TE1=1.3ms,ΔTE=2ms, ETL1=6,ETL2=1,ETL3=2). For each SNR value (ranging 5-50), 10000 realizations of CSE-MRI were simulated with added zero-mean complex Gaussian noise. For each realization, a joint nonlinear least squares fitting algorithm was used to estimate the set of unknown parameters.
Phantom Acquisitions
The proposed acquisition and reconstruction strategy was tested in a multi-vial agar gel phantom including varying T1W and PDFF values. Imaging was performed with a 32-channel body coil on a 1.5T system (GE Healthcare Optima MR450W, Waukesha, WI) with acquisition parameters identical to the numerical simulation. Multi-TE multi-TR spectroscopy (STEAM) (16) was acquired once in each vial to provide reference T1 and PDFF measurements. Parameters were estimated using nonlinear least squares and a region of interest (ROI) analysis compared our proposed method to STEAM-based measurements in each vial.
In Vivo Acquisition
The proposed acquisition and reconstruction strategy was tested with a 16-channel Flex coil on a 1.5T system (GE Healthcare Optima MR450W, Waukesha, WI) in the knee of a healthy volunteer. The following acquisition parameters were used: α1=60o/α2=60o/α3=3o, TR1=80ms/TR2=5.5ms/TR3=10ms, TE1=1.4ms,ΔTE=2.2ms, ETL1=6,ETL2=1,ETL3=2.
Results
Optimization of Acquisition Parameters
CRLB analysis showed T1W estimation to be largely orthogonal to PDFF and R2* estimation which dictated optimal echo time choices. Plots showing the CRLB optimization are shown in Figure 2.
Numerical Simulations
Monte-Carlo simulations demonstrated the proposed strategy converges to unbiased estimators for all parameters of interest. Figure 3 shows mean and standard deviations of estimated β, T1W, R2*, and PDFF.
Phantom Acquisitions
Phantom experiment results showed linear agreement with STEAM, with variability of estimated T1 increasing with T1. Results are plotted in Figure 4.
In Vivo Acquisition
Reconstructed images are shown in Figure 5.
Discussion
In this work we have successfully presented a novel B1- and fat-corrected CSE-MRI T1 mapping method. This strategy combines alternating TR SGRE acquisitions with traditional VFA strategies to estimate B1- and fat-corrected T1. Theoretical analysis determined optimal acquisition parameters and performance was confirmed in Monte-Carlo simulations and phantom experiments.
Continued development will focus on improving estimation performance over a wider range of T1 values to address the variability of T1 estimates in the phantom experiments. Additionally, the STEAM MRS pulse sequence used to make reference measurements in the phantom experiments is susceptible to B1 inhomogeneities. Future work will validate performance of the proposed strategy against flip-angle corrected T1 mapping.
Overall, the proposed strategy demonstrates initial feasibility for a B1- and fat-corrected T1-mapping technique without needing a separate B1 calibration scan.
Acknowledgements
The authors wish to acknowledge support from the NIH (grants R01 DK088925 and K24 DK102595). The authors also acknowledge GE Healthcare who provides research support to the University of Wisconsin-Madison.References
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