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T1 quantification in fast field-cycling MRI using model-based reconstruction
Oliver Maier1, Markus Bödenler1,2, Rudolf Stollberger1,3, Mary-Joan MacLeod4, Lionel M Broche5, and Hermann Scharfetter1
1Graz University of Technology, Graz, Austria, 2Institute of eHealth, University of Applied Sciences FH JOANNEUM, Graz, Austria, 3BioTechMed Graz, Graz, Austria, 4Acute Stroke Unit, Aberdeen Royal Infirmary, Aberdeen, United Kingdom, 5Aberdeen Biomedical Imaging Centre, Univeresity of Aberdeen, Aberdeen, United Kingdom

Synopsis

T1 maps from fast field-cycling (FFC) MRI can provide insights to structural information and dynamics of molecular system not accessible by traditional MRI. The low SNR associated with the lower field strength in FFC imaging (0.2 T - 50 µT) leads to long acquisition times, impairing its clinical applicability. Hence, we propose a model-based reconstruction strategy to reduce acquisition time and improve image quality of multi-field T1 maps. The method is compared to standard fitting on numerical phantoms and a in vivo stroke patient. Model-based reconstruction clearly outperformed standard fitting, reducing noise and revealing previously unseen details in low-field T1 maps.

Indroduction

Fast field-cycling (FFC) is a technique that consists in changing rapidly the main magnetic field of MRI systems1 and is mostly used to investigate the field dependent changes of longitudinal relaxation times ($$$T_1$$$), also referred to as $$$T_1$$$ Nuclear Magnetic Relaxation Dispersion (NMRD)3,4. NMRD profiles can provide insights to underlying structural information and dynamics of molecular systems but can not be accessed by traditional MRI systems5,6,7,8.Recently, a whole-body FFC system has been developed and approved for clinical studies, allowing multi-field $$$T_1$$$ mapping at any field from 50 μT to 0.2 T2. This opens new prospects for clinical research but in vivo applications are limited by low SNR inherent to the lower field strength, potentially combined with a small dispersion signal9, leading to a long scan time. To this end, we propose a model-based reconstruction approach to quantify $$$T_1$$$ from multi-field FFC data, which had been previously shown to provide high quality quantitative maps in high-field applications10,11,12. The proposed method is tested on simulated head phantoms and subsequently applied to in vivo FFC data of a patient suffering from a stroke. Fitted $$$T_1$$$ maps are compared to results from a Tikhonov regularized, non-linear least squares (NLLS) approach13,14, applied to the complex imagedata.

Theory

Quantifying $$$T_1$$$ with FFC methods can be achieved by means of an inversion recovery sequence, including field switching during the inversion time, called evolution time ($$$T_E$$$) in FFC imaging15 (see Figure 1). The signal intensity ($$$S_{B_0^E,t^E}$$$) for such a sequence is governed by
$$S_{B_0^E,t_E}(u:=(C,T_{1}^{E})) = C\,[-\alpha_{B_0^E} \,B_0^D\,e^{\frac{-t_E}{T_{1}^{E}}} + B_0^E\,(1-e^{\frac{-t_E}{T_{1}^E}})]$$
with $$$C$$$ being proportional to proton density. $$$T_1^E$$$ describe the field dependent relaxation. $$$\alpha_{B_0^E}$$$ accounts for imperfections of inversion pulse and field ramping. The signal equation is combined with the Fourier and sampling operator $$$\mathcal{F}$$$ to directly quantify $$$T_1$$$ from complex k-space data. Joint spatial TGV16,17 constraints are posed on the unknown quantitative maps, utilizing common information between the maps18,19. This leads to the following optimization problem

$$\underset{u,v}{\min}\quad \frac{1}{2}\sum_{i=1}^{N_E}\sum_{n=1}^{{N_t^{E_i}}}\|\mathcal{F}S_{B^{E_i}_0,t^{E_i}_n}(u)-d_{n,i}\|_2^2 + \gamma( \alpha_0\|\nabla u - v\|_{1,2,F} + \alpha_1\|\mathcal{E}v\|_{1,2,F})$$

with $$$N_E$$$, $$$N_t^{E_i}$$$ and $$$d_{n,i}$$$ standing for the number of magnetic field strengths probed, the number of inversion times for each field and the NMR signal data acquired, respectively. $$$\mathcal{E}$$$ approximates the 2nd-order derivative and auxiliary variable $$$v$$$ balances between 1st and 2nd derivative. This problem is solved using a recently proposed model-based reconstruction framework20.

Methods

The simulated phantom consisted of five regions mimicking the dispersive characteristics of an axial head scan: subcutaneous fat (ROI-1), tissue surrounding the brain (ROI-2), the brain (ROI-3), and a stroke-like lesion (ROI-4). The image resolution was chosen as 90x90 voxels; simulated evolution times and fields are given in Table 1. To simulate noise, complex-valued Gaussian noise with a standard deviation of four percent of the highest signal as added to the images. The in vivo brain data was selected from the PUFFINS study (Potential Use of Fast Field-cycling IN Stroke), a pilot study for the imaging of acute brain stroke by FFC imaging currently taking place at the University of Aberdeen and approved by the local Ethics Committee (NoSREC reference 16/NS/0136/AM01). Informed consent was given by all participants. The acquisition was performed on a patient with right occipital infarct (previously validated by CT scan) using a whole-body FFC scanner with an adapted inversion-recovery spin echo sequence. The image size was 128x128 with 10 mm slice thickness, 62.5% partial Fourier, 29 kHz bandwidth, 290mm FOV and pre-polarisation at 200 mT for 300ms. Total acquisition time was 40 minutes. Evolution times were the same as in the numerical simulation.

Results

Applying the proposed method on the simulated data gave cleaner $$$T_1$$$ maps compared to standard fitting (NLLS, see Figure 1). Quantitative values for ROIs 1-4 are given in Table 2, showing a decrease in standard deviation for the proposed method. The in vivo results are given in Figure 2: again, the proposed method reduced the noise in the image compared with standard voxel-wise fitting, even showing some structural details of the brain in the 21.1 mT images. The stroke can be clearly delineated in the smaller fields. The algorithm ran an NVIDIA Geforce GTX 1080 TI and fitting took ~3 minutes for the shown $$$T_1$$$ maps.

Discussion

The model-based reconstruction approach proposed, combined with the joint spatial TGV regularization, clearly outperforms the current standard of voxel-wise $$$T_1$$$ fitting dispersion maps of FFC data. Due to the redundant information present in the FFC imaging technique, a joint regularization approach fully utilizes the available information in the data. This reveals previously unseen structures, hidden in noise, in high as well as low field $$$T_1$$$ maps (Figure 3). Poor SNR can lead to a bias in both methods but the proposed method stays generally closer to the true values and offers a huge decrease in standard deviation. Selecting smaller regularization weights lead to smaller bias at the expense of increased noise in the reconstructed images. The framework used here can be readily extended to a multi-coil setting or to non-Cartesian sampling strategies to speed up the acquisition of FFC imaging in the future. This shows exciting potential for the exploration of low magnetic fields and $$$T_1$$$ dispersion effects as illustrated here on a stroke patient.

Acknowledgements

Oliver Maier acknowledges grant support from the Austrian Academy of Sciences under award DOC-Fellowship 24966.

The authors would like to acknowledge the NVIDIA Corporation Hardware grant support.

References

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Figures

Figure 1: Schematic pulse sequence employed for the inversion recovery FFC sequence. After the magnetization is inverted (middle), the main field is switched to a pre-defined value (top). Prior to detection (bottom) this switch is reversed15.

Table 1: List of evolution fields and times for the simulated phantom and the in vivo measurement.

Table 2: Results of a ROI based evaluation compared to the ground truth values. Values are given as mean with standard deviation in brackets.

Figure 2: Reference T1 maps (top) and reconstruction results for simple non-linear least squares fitting (standard, bottom left) compared with the proposed model-based reconstruction and fitting algorithm (bottom right).

Figure 3: Comparison of T1 maps obtained with standard fitting (top) and the proposed method (bottom) for all three evolution fields. One can clearly see the lesion in the low field T1 maps. The proposed method is able to reduce noise in all T1 maps and enables a clear distinction of the lesion.

Proc. Intl. Soc. Mag. Reson. Med. 29 (2021)
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