Yavuz Muslu^{1,2}, Steven Kecskemeti^{2,3}, Diego Hernando^{1,2,4}, and Scott B. Reeder^{1,2,4,5,6}

^{1}Department of Biomedical Engineering, University of Wisconsin-Madison, Madison, WI, United States, ^{2}Department of Radiology, University of Wisconsin-Madison, Madison, WI, United States, ^{3}Waisman Center, University of Wisconsin-Madison, Madison, WI, United States, ^{4}Department of Medical Physics, University of Wisconsin-Madison, Madison, WI, United States, ^{5}Department of Medicine, University of Wisconsin-Madison, Madison, WI, United States, ^{6}Department of Emergency Medicine, University of Wisconsin-Madison, Madison, WI, United States

Quantitative T_{1} mapping in the liver is an emerging biomarker of hepatic fibrosis and characterization of liver function. Existing T_{1} mapping methods in abdomen are generally sensitive to tissue fat and B1 inhomogeneities , both of which confound estimates of T_{1}. Further, Cartesian methods may suffer from motion related ghosting artifacts. In this work, we propose to combine 3D-radial inversion recovery with chemical shift encoded imaging to jointly estimate T_{1} of water, T_{1} of fat, proton density fat fraction (PDFF), and B_{0} and B_{1} inhomogeneities. The feasibility and performance of the proposed method are evaluated with simulations, and phantom experiments.

$$S_{w,MPnRAGE}(TI,TR,TD,\alpha;T_{1,w},\kappa_1,\kappa_{2,w})=((1-E_{R,w})\cdot~\frac{1-a_w^n}{1-a_w}+((1-E_{I,w})+M_{SS,w}(E_{D,w})\cdot~cos(\kappa_{2,w}\cdot~180)\cdot~E_{I,w})\cdot~a_w^n)\cdot~sin(\kappa_1\cdot~\alpha)$$

$$S_{f,MPnRAGE}(TI,TR,TD,\alpha;T_{1,f},\kappa_1,\kappa_{2,f})=((1-E_{R,f})\cdot~\frac{1-a_f^n}{1-a_f}+((1-E_{I,f})+M_{SS,f}(E_{D,w})\cdot~cos(\kappa_{2,f}\cdot~180)\cdot~E_{I,f})\cdot~a_f^n)\cdot~sin(\kappa_1\cdot~\alpha)$$

$$S_{w,SGRE}(TE;\theta_w,\Delta B_0,T_2^*,\rho_w)=\rho_w\cdot~e^{-TE/T_2^*}\cdot~e^{i(\theta_w+2\pi~f_0TE)}$$

$$S_{f,SGRE}(TE;\theta_f,\Delta B_0,T_2^*,\rho_f)=\rho_f\cdot~e^{-TE/T_2^*}\cdot~e^{i(\theta_f+2\pi~f_0TE)}\cdot~\sum_{p=1}^P m_p\cdot~e^{i2\pi f_pTE}$$

$$E_{R(w,f)}=e^{-TR/T_{1(w,f)}},E_{I(w,f)}=e^{-TI/T_{1(w,f)}},E_{D(w,f)}=e^{-TD/T_{1(w,f)}},a_{(w,f)}=cos(\kappa_1\cdot \alpha)\cdot E_{R(w,f)}$$

$$S_{combined}=S_{w,MPnRAGE}\cdot~S_{w,SGRE}+S_{f,MPnRAGE}\cdot~S_{f,SGRE}$$

Where, subscripts 'w' and 'f' denote signal parameters for water and fat signals, 'n' denotes the index of the excitation pulse in the inversion recovery sequence, $$$M_{SS,(w,f)}$$$ denotes the longitudinal magnetization at the end of one inversion recovery cycle, $$$\rho_{w,f}$$$ denotes signal amplitudes, $$$\theta_{w,f}$$$ denotes initial phase, $$$\kappa_1$$$ and $$$\kappa_{2(w,f)}$$$ denote efficiencies of excitation and inversion RF pulses (note for adiabatic pulses, due to duration of the pulse efficiency may differ between fat and water), $$$f_0$$$ denotes the frequency shift due to B

A diagram of the proposed pulse sequence is given in Figure 1, where $$$\beta$$$ denotes the inversion and $$$\alpha$$$ denotes the excitation pulses. TE

The proposed acquisition and 2-compartment joint fitting method were tested using simulation data over a wide range of physiologically relevant liver T

Two sets of phantoms experiments are presented to demonstrate validation of the T

For the validation study, a single compartment phantom, consisting of 5 doped water vials with varying T

For the feasibility study, a phantom consisting of varying fat fractions (5-60%) and 2 different T

Monte-Carlo simulations demonstrated the proposed strategy converges to unbiased estimators for all parameters of interest. Figure 2 shows the median and standard deviations of estimated T

Validation of the proposed method is shown in Figure 3, where, estimated T

Feasibility for fat-correction of the proposed method is demonstrated by joint estimation of PDFF and T

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Figure 1. The proposed acquisition strategy combines inversion recovery and SGRE acquisitions to create modulations in T_{1} weighting by acquiring images at varying inversion times (TI+(n-1)*TR), and in T_{2}* and spin phase by acquiring images at different echo times (TE_{i}). Combined with the proposed 2-compartment signal equation, proposed method can correct for multiple confounding factors by jointly fitting B_{0}, B_{1}, T_{1f}, PDFF, and inversion efficiency.

Figure 2: Proposed acquisition strategy and fitting problem can estimate T_{1w} and PDFF with less than 2% bias, as predicted by simulations. At low PDFF values, T_{1f} estimation has higher bias at (maximum at 7%) due to low SNR of fat signal. For the rest of the confounding factors, T_{2}* bias remained under 20%, $$$\kappa_1$$$ bias remained under 3%, $$$\kappa_2$$$ bias remained under 1%, ∆B_{0} bias remained under 3% (results not shown due to space limitations).

Figure 3: Validation of the proposed method is demonstrated on a single compartment phantom consisting of 5 doped-water and 1 oil vials. An IR-SE method combined with magnitude fitting is selected as the reference due to the single compartment nature of the phantom. One ROI was drawn in each vial and mean of each ROI were compared with the reference acquisition. Estimated T_{1} values showed linear agreement with reference measurements from IR-SE, with a good noise performance.

Figure 4: Feasibility of the proposed method is demonstrated on phantom with varying T_{1} and PDFF values. T_{1w} values showed good agreement with the relaxivity and concentration of CuSO_{4}. T_{1f} values were not affected by the salt concentrations. Estimated PDFF values showed linear agreement with construction of phantom with reduced accuracy at high PDFF values.