Introduction

Quantitative MRI offers diverse physical properties of tissue, reflecting the physiological information. Multi-contrast quantitative mapping can further provide comprehensive information, promising the clinical diagnosis and pathological research in neurosciences, such as Parkinson’s disease¹. However, the conventional quantitative MRI, such as ME-GRE and ME-SE², prolongs the acquisition time and may induce inter-scan misalignment between multiple scans. In this work, we proposed a new framework to simultaneously quantify T1, T2, T2* mapping and subvoxel QSM. An unsupervised reconstruction model based on implicit neural representation (INR)³ was proposed to reconstruct quantitative images.

Methods

Sequence and data acquisition:
The schematic diagram of the multi-contrast quantitative mapping sequence is shown in Fig. 1. The sequence is composed of T2-prep modules, IR modules, and ME-GRE readout. The IR module generates T1 weighting at each segment (TI) and the T2-prep module produces T2 weighting at each shot. The FLASH excitation is repeated throughout the shot followed by ME-GRE readout, generating T2* weighting. The high-dimensional k-space data is acquired following the Gaussian variable density sampling strategy along the ky and kz directions to enhance the spatial and temporal incoherence.

Image reconstruction:
Fig. 2 displays the framework of the proposed multi-contrast mapping reconstruction. Inspired by the previous work⁴, the underlying quantitative maps, along with coil sensitivity maps are simultaneously estimated. Specifically, the quantitative image is generated by querying 3D spatial coordinates on the parameterized encoding module and $$$MLP_{\theta_{m}}(x,y,z)$$$, where $$$\theta_{m}$$$ represents the parameters of MLP to be optimized. The voxel-wise signal is calculated using the generated quantitative maps following Equation (1):
$$S\left(A,T_{1},T_{2},T_{2}^{*},\varphi_{e},B\right)=A\frac{1-e^{-\frac{T_{R}}{T_{1}}}}{1-e^{-\frac{T_{R}}{T_{1}}}cos\alpha}\left\lbrack 1+\left({Be^{-\frac{\tau}{T_{2}}}-1}\right)\left({e^{-\frac{T_{R}}{T_{1}}}cos\alpha}\right)^{n}\right\rbrack sin\alpha\cdot e^{-\frac{T_{E}}{T_{2}^{*}}}e^{j\varphi_{e}}\tag{1}$$
where $$$A$$$ denotes the proton density, $$$\varphi_{e}$$$ represents the phase on echo $$$e$$$, $$$B$$$ represents the inversion efficiency of the IR module, $$$n$$$ denotes the index of the FLASH excitation, and $$$\tau$$$ denotes the duration of the T2-prep module. The estimated high-dimensional k-space signal from the $$$j$$$th coil, i.e., $$$\hat{d_{j}}$$$, is predicted through the physical forward model:
$$\hat{d_{j}}=\mathbf{M}\mathbf{F}\mathbf{C}_{j}\left(\theta_{c}\right)S\tag{2}$$
where $$$\mathbf{C}_{j}\left(\theta_{c}\right)$$$ is the $$$j$$$th estimated coil sensitivity map, $$$\mathbf{F}$$$ denotes the Fourier transform and $$$\mathbf{M}$$$ represents the sampling mask. Then the parameters in MLP and encoding module can be optimized following the formulated problem:
$${\underset{\theta_{m},\theta_{c}}{argmin}{\sum\limits_{j=1}^{c}\left\|{d_{j}- \mathbf{M}\mathbf{F}\mathbf{C}_{j}S\left({A,T_{1},T_{2},T_{2}^{*},\varphi_{e},B}\right)}\right\|_{1}}} + \lambda\mathcal{R}\left({T_{1},T_{2},T_{2}^{*}}\right)\tag{3}$$
where $$$d_{j}$$$ is the acquired k-space signal of the $$$j$$$th coil, $$$\mathcal{R}( \cdot )$$$ denotes the regularizer that imposes the sharing features between the reconstructed quantitative images and $$$\lambda$$$ is a tunable parameter. After estimating T1, T2, T2* and phase maps, we applied a standard QSM reconstruction pipeline^5-7 and utilized APART-QSM⁸ to reconstruct the subvoxel QSM.

Experiment:
The simulation was conducted with the parameters of FOV=224$$$\times$$$224$$$\times$$$64mm³, voxel size=2$$$\times$$$2$$$\times$$$4mm³, $$$T_{R}$$$=28ms, $$$\tau$$$=25,50,70,90ms, $$$T_{E}$$$=3.3,9.5,15.2,20.9ms, number of segments=56 and number of shots=16. The proposed method was compared with the low-rank tensor reconstruction method⁹. A standard ISMRM/NIST phantom¹⁰ was scanned for validation on a 3T uMR790 scanner with a 24-coil head array. The sequence parameters were: FOV=256$$$\times$$$256$$$\times$$$200mm³, voxel size=2$$$\times$$$2$$$\times$$$5mm³, $$$T_{R}$$$=30ms, $$$\tau$$$=0,30,60,90ms, $$$T_{E}$$$=5.2,10.9,16.6ms, number of segments=64 and scan time=5.3min. IR-SE, ME-SE and ME-GRE were used to respectively estimate T1, T2 and T2* maps as references. The in vivo experiment was performed on a healthy volunteer with the parameters of FOV=240$$$\times$$$240$$$\times$$$144mm³, voxel size=1$$$\times$$$1$$$\times$$$4mm³, $$$T_{R}$$$=20ms, $$$\tau$$$=25,50,70,90ms, $$$T_{E}$$$=3.9,9.6,15.3ms, number of segments=80 and scan time=5.8min. MTP, ME-SE and ME-GRE were used to estimate T1, T2, T2* maps and subvoxel QSM as references.

Results

Fig. 3 shows the proposed method exhibits higher quantitative accuracy in terms of NRMSE and error maps on T1 and phase (the first echo) maps compared with the low-rank tensor reconstruction method on the simulation. Fig. 4 compares the multi-contrast quantitative maps and references on the phantom. The linear regression between the reconstruction values and the reference values exhibits a good consistency with a high $$$R^2$$$ and slope approaching 1. Fig. 5 exhibits the multi-contrast quantitative maps and references on a healthy volunteer. Our results show good image quality and agree well with the references.

Discussion

The results demonstrate the superiority and fidelity of the proposed method, with reduced errors on the simulation and the consistency of quantitative maps on the phantom and in vivo results. This advantage comes from the fact that our method does not need to explicitly reconstruct the weighted images then subsequently fit the quantitative images, avoiding the accumulation of reconstruction errors. In addition, our proposed framework eliminates the need for navigator data to estimate the temporal subspace for the high-order tensor reconstruction^11,12, consequently reducing scan times.

Conclusion

In this study, we developed a new framework for multi-contrast quantitative mapping acquisition and reconstruction. Our method can provide whole-brain coverage with 1$$$\times$$$1$$$\times$$$4mm³ resolution within 5.8min and offer quantitative agreement with the reference scans.

Acknowledgements

No acknowledgement found.