Shouchang Guo^{1}, Douglas C. Noll^{2}, and Jeffrey A. Fessler^{1}

^{1}Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI, United States, ^{2}Biomedical Engineering, University of Michigan, Ann Arbor, MI, United States

Oscillating Steady-State Imaging (OSSI) is a new fMRI acquisition method that can provide high SNR signals, but does so at the expense of imaging time. We previously used a physics-based regularizer for high-quality, undersampled reconstruction by modeling the oscillating signal with physics parameters. However, the reconstructions were not quantitative, as the key parameter $$$T_2'$$$ for BOLD effects was not studied. In this work, to quantify MRI parameters of physiological importance, we jointly reconstruct the images and the parameters. The proposed manifold model reconstructs high-resolution images from 12-fold undersampled data, while also providing quantitative $$$T_2'$$$ estimates for fMRI.

We simplify the manifold further because $$$T_1$$$ has primarily a scaling effect that we absorb into $$$m_0$$$, $$$t \approx$$$ TE for the short TR of OSSI, and we set $$$T_2$$$ to a textbook value. Therefore, our proposed approach for joint reconstruction and quantification using a manifold model regularizer becomes

$$\hat{\mathbf{X}},\hat{m_0},\hat{T_2'},\hat{f_0} =\underset{\mathbf{X},m_0,T_2',f_0}{\text{arg min}}\frac{1}{2}\lVert\mathcal{A}(\mathbf{X})-\mathbf{y} \rVert_2^2+ \beta \sum_{i,j} \lVert\mathbf{X}[i,j,:]-m_0 \mathbf{\Phi} (T_2',f_0)\rVert_2^2, \quad$$

where $$$\mathbf{X} \in \mathbb{C}^{N_x \times N_y \times n_c}$$$ denotes $$$n_c$$$ OSSI images to be reconstructed, $$$\mathbf{y}$$$ represents sparsely sampled k-space data, and $$$\mathcal{A}(\mathbf{\cdot})$$$ is a linear operator consisting of coil sensitivities, NUFFT, and an undersampling function. For each voxel $$$\mathbf{X}[i,j,:] \in \mathbb{C}^{n_c}$$$ is a vector of fast-time signal values, and $$$m_0 \mathbf{\Phi}(T_2',f_0) \in \mathbb{C}^{n_c}$$$ is the simplified manifold model. $$$\beta$$$ is the regularization parameter.

We solve the parameter estimation problem with VARPRO

All the data were acquired on a 3T GE MR750 scanner with a 32-channel Nova Medical head coil. OSSI TR = 15 ms, $$$n_c$$$ = 10 TRs per signal oscillation, spiral-out TE = 2.7 ms, and flip angle = 10$$$^\circ$$$. The spatial resolution = 1.3$$$\times$$$1.3$$$\times$$$2.5 mm$$$^3$$$ for a 220 mm FOV, and the temporal resolution = 150 ms (after 2-norm combination of every $$$n_c$$$ OSSI images). We collected resolution phantom data with GRE imaging at varying TEs and estimated corresponding MRI parameters to validate the potential of using OSSI sequence and the proposed $$$T_2’$$$ manifold for quantification. For human data, the acceleration factor = 12 for both retrospective and prospective undersampling, and the sampling trajectory was a single-shot variable-density spiral with randomized rotations between frames. The functional task was a left/right reversing-checkerboard visual stimulus for 200 s (20 s L/20 s R $$$\times$$$ 5 cycles).

1. Shouchang Guo and Douglas C. Noll, ''High SNR Functional MRI Using Oscillating Steady State Imaging". Joint Annual Meeting ISMRM-ESMRMB, Paris 2018, In Proc. Intl. Soc. Mag. Reson. Med.

2. Olafsson, Valur T., Douglas C. Noll, and Jeffrey A. Fessler. "Fast Joint Reconstruction of Dynamic $$$ R_2^* $$$ and Field Maps in Functional MRI." IEEE transactions on medical imaging 27.9 (2008): 1177-1188.

3. Golub, Gene, and Victor Pereyra. "Separable nonlinear least squares: the variable projection method and its applications." Inverse problems 19.2 (2003): R1.

Figure 1. Estimated signal and parameters (blue curves) in comparison to ground-truth signal and physics parameters (overlaid red curves) demonstrating the importance of the proposed $$$T_2’$$$ manifold over a $$$T_2$$$ manifold for quantifying fMRI parameters. The functional signal of one voxel is simulated with $$$T_2’$$$ induced signal changes, respiration, field drifts, and Gaussian random noise.

Figure 2. Parameter maps reconstructed using OSSI sequence and the proposed $$$T_2’$$$ manifold in comparison to estimations from gradient-echo imaging with multiple TEs. The $$$\hat{m_0}$$$ estimates are on arbitrary scales. The resolution phantom has a uniform $$$R_2 \approx$$$ 10 Hz, and OSSI $$$\hat{R_2’}$$$ and GRE $$$\hat{R_2^*}$$$ demonstrates similar contrasts with an offset. We map the field map estimates to [-33.3, 33.3] Hz range as OSSI frequency responses are periodic with 1/TR = 66.7 Hz. Parameter estimations at regions with little or no signal are masked out.

Figure 3. OSSI images and parameter maps reconstructed from a factor of 12 retrospectively undersampled data (Proposed) are comparable to estimations from data that are nearly fully sampled (Mostly Sampled). The near-manifold regularization effectively recovers the high-resolution structures and quantitative properties of the data.

Figure 4. Functional activations and quantitative estimations from prospectively undersampled data using the $$$T_2’$$$ manifold. The activation threshold = 0.4. Compared to conjugate-gradient SENSE with an edge-preserving regularizer, the proposed reconstruction provides high SNR time courses and enables quantification of physiological parameters for every fMRI time point.