Synopsis

Quantitative first-pass myocardial perfusion imaging is a potentially powerful tool for diagnosing coronary artery disease. However, quantification is complicated by ECG misfires and the nonlinear response of signal intensity to contrast agent concentration. Here we propose a method overcoming the curse of dimensionality to simultaneously image cardiac motion, contrast dynamics, and T1 relaxation in 2D and 3D, using a low-rank tensor imaging framework for cardiovascular MR multitasking. This non-ECG, first-pass myocardial perfusion T1 mapping method accounts for the signal intensity nonlinearity, allowing direct quantification of contrast agent concentration at any cardiac phase in any cardiac cycle.

Purpose

Methods

For ECG-free, time-resolved T1 mapping, the desired multidimensional image $I(\mathbf{x},c,\tau,t)$ is a function of spatial location $\mathbf{x}$, cardiac phase $c$, saturation recovery (SR) time $\tau$, and heartbeat index $t$. Representing this image as a 4-way tensor $\mathcal{A}$ with elements $A_{ijk\ell}=I(\mathbf{x}_i,c_j,\tau_k,t_\ell)$, signal correlation can be exploited by modeling $\mathcal{A}$ as low-rank^4,5, i.e., as the outer product of a core tensor $\mathcal{C}$ and basis matrices⁶: $$\mathcal{A}=\mathcal{C}\times_1\mathbf{U_x}\times_2\mathbf{U}_\mathrm{c}\times_3\mathbf{U}_τ\times_4\mathbf{U}_\mathrm{t},\qquad(1)$$ or in collapsed form, $$\mathbf{A}_{(1)}=\mathbf{U_xC}_{(1)}(\mathbf{U}_\mathrm{t}\otimes\mathbf{U}_τ\otimes\mathbf{U}_\mathrm{c})^T,\qquad(2)$$ where each $\mathbf{U}$ contains a limited number of basis functions for the corresponding dimension. $\mathcal{A}$ can then be reconstructed by estimating $\mathbf{\Phi}=\mathbf{C}_{(1)}(\mathbf{U}_\mathrm{t}\otimes\mathbf{U}_τ\otimes\mathbf{U}_\mathrm{c})^T$ from subspace training data^4,5 and then fitting $\mathbf{\Phi}$ to the remainder of the sparsely sampled data to recover $\mathbf{U_x}$: $$\hat{\mathbf{U}}_\mathbf{x}=\arg\min_\mathbf{U_x}\|\mathbf{d}-E(\mathbf{U_x\Phi})\|_2^2+R(\mathbf{U_x}),\qquad(3)$$ where $\mathbf{d}$ is the measured data, $E(\cdot)$ describes multichannel MRI encoding and sampling, and $R(\cdot)$ is a regularization functional.

The proposed method employed an ECG-free continuous-acquisition SR-FLASH prototype pulse sequence with readouts collected throughout the entire SR period. For 2D, radial acquisition was performed using a golden-angle ordering scheme, interleaved with 0° radial spoke acquisition every other readout as subspace training data. For 3D, stack-of-stars acquisition was performed with golden-angle ordering for the polar coordinates and variable-density Gaussian random sampling for $k_z$, interleaved with 0° spoke acquisition at $k_z=0$ every other readout.

Explicit-subspace low-rank matrix imaging⁷ was first used to obtain an image $I(\mathbf{x},t')$ with a single “real-time” dimension $t'$. $I(\mathbf{x},t')$ depicts the overlapping effects of cardiac motion, T1 recovery, and contrast agent dynamics, allowing image-based cardiac phase identification. The matrix $\mathbf{\Phi}$ was estimated after LRT completion of the subspace training data⁴. $\hat{\mathbf{U}}_\mathbf{x}$ was reconstructed according to Eq. 3, using spatial total variation as the regularization functional $R(\cdot)$.

To assess repeatability of resting myocardial blood flow (MBF) measurements, n=8 healthy volunteers were imaged on a 3 T Siemens Verio. Pulse sequence parameters were FA=10°, TR/TE=3.6/1.6 ms, FOV=270$\times$270 mm², matrix size=160$\times$160, spatial resolution=1.7$\times$1.7 mm², and slice thickness=8 mm. Image reconstruction was performed for 15 cardiac bins and 42 saturation times. Two 0.1 mmol/kg doses of Gadovist were administered 20 to 30 minutes apart. Subjects were instructed to hold their breath for as much of the 45 s scan duration as possible, followed by shallow breathing. To demonstrate the feasibility of 3D imaging, the same process was performed for a healthy volunteer using FA=10°, TR/TE=5.9/2.7 ms, FOV=256$\times$256$\times$96 mm³, matrix size=128$\times$128$\times$12, spatial resolution=2.0$\times$2.0$\times$8.0 mm³.

For quantification, $T_1(t)$ was calculated for the left ventricular (LV) blood pool and six myocardial segments in the 2D images at end-diastole. Contrast agent concentration was calculated as $$Gd(t)={\Delta}R_1(t)/\gamma=\left(\tfrac{1}{T_1(t)}-\tfrac{1}{T_1(0)}\right)/\gamma,\qquad(4)$$ where $\gamma$ is the T1 relaxivity of the contrast agent. Fermi deconvolution⁸ of each myocardial $Gd(t)$ by the LV $Gd(t)$ yielded MBF for each myocardial segment.

Results

Conclusions

Acknowledgements

References

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