Shreya Ramachandran^{1} and Michael Lustig^{1}

^{1}Electrical Engineering and Computer Sciences, University of California, Berkeley, Berkeley, CA, United States

For fast T1-weighted imaging, zero echo time (ZTE) imaging provides rapid sampling of 3D k-space, but lacks T1 contrast due to its small flip angle excitation with short hard pulses. To efficiently increase T1 contrast, longer phase-modulated pulses can be used. However, longer pulses lead to larger dead-time gaps and pulse profile-weighted images. Here, we formulate an inverse problem to directly reconstruct profile-compensated images from multi-coil data without any intermediate step for dead-time infilling. We demonstrate that leveraging coil sensitivities and alternating phase-modulated excitations sufficiently condition the inverse problem, allowing for iterative reconstructions of T1-weighted acquisitions.

Previous approaches

We use quadratic phase-modulated (chirp) pulses, which are near-optimal for B1 power

We formulate the inverse problem as a least squares minimization with an L1-wavelet regularization term as follows: $${\min}_x ||Ax-y||_2^2 + \lambda||\psi x||_1$$ Here, $$$x$$$ is the 3D image, $$$A$$$ is our forward model, $$$y$$$ is the multi-coil k-space data with dead-time gap, $$$\lambda$$$ is the regularization weight, and $$$\psi$$$ is the wavelet transform operator. We model the data acquisition forward operator as: $$A=P\cdot Q\cdot F_\theta \cdot S$$ As shown in Figure 2, $$$S$$$ is the multiplication with coil sensitivities, $$$F_\theta$$$ is the 3D NUFFT onto full-diameter radial lines, $$$Q$$$ is the 1D convolution of each line with the pulse waveform (implemented via DFT), and $$$P$$$ is the re-sampling onto radial spokes with the dead-time gap.

Since the gradient direction is constant for each TR, the 3D profile-weighting varies only in one direction

We iteratively solve this optimization problem using the Primal-Dual Hybrid Gradient algorithm

We simulated multi-coil k-space data by running a 2D version of the forward model with realistic coil sensitivities. To avoid an “inverse crime”

We acquired phantom scans and a head scan of a healthy volunteer on a GE-3T MR750W (with $$$\pm$$$31.25kHz rBW, 2.4ms TR). We simulated alternated pulses by retrospectively interleaving odd/even TRs from two acquisitions with different excitations. This method eliminated possible steady-state disruptions from alternate pulses. We also discarded the first one or two samples along each acquired spoke due to significant ripple from the digital filter applied by the scanner receiver unit. Furthermore, we heuristically accounted for gradient delays by reconstructing on coordinates shifted by half-sample. Reconstructions were performed on a GeForceRTX GPU and took ~20min.

In Figure 4, we demonstrate how parallel imaging significantly improves conditioning by comparing to a coil-by-coil version of our inverse problem, as well as gridding with WASPI

In Figure 5, we use alternated chirps and our inverse problem to reconstruct in-vivo images with significant T1 contrast. These images do contain some low-frequency variations and blurring, which is likely due to some model violations such as inaccurate pulse profiles and scanner digital filter ripple.

[1] Madio, D P, and I J Lowe. “Ultra-fast imaging using low flip angles and FIDs.” Magnetic resonance in medicine vol. 34,4 (1995): 525-9. doi:10.1002/mrm.1910340407

[2] 2 Frahm J, Haase A, Matthaei D. Rapid NMR imaging of dynamic processes using the FLASH technique. Magn Reson Med 1986; 3: 321–327.

[3] Ljungberg, Emil et al. “Silent zero TE MR neuroimaging: Current state-of-the-art and future directions.” Progress in nuclear magnetic resonance spectroscopy vol. 123 (2021): 73-93. doi:10.1016/j.pnmrs.2021.03.002

[4] Schieban, Konrad et al. “ZTE imaging with enhanced flip angle using modulated excitation.” Magnetic resonance in medicine vol. 74,3 (2015): 684-93. doi:10.1002/mrm.25464

[5] Froidevaux R, Weiger M, Pruessmann KP. Algebraic reconstruction of missing data in zero echo time MRI with pulse profile encoding (PPE-ZTE). In: Proceedings of the 30th Annual Meeting of ISMRM, 2020.

[6] Weiger, Markus et al. “Exploring the bandwidth limits of ZTE imaging: Spatial response, out-of-band signals, and noise propagation.” Magnetic resonance in medicine vol. 74,5 (2015): 1236-47. doi:10.1002/mrm.25509

[7] Wu, Yaotang et al. “Water- and fat-suppressed proton projection MRI (WASPI) of rat femur bone.” Magnetic resonance in medicine vol. 57,3 (2007): 554-67. doi:10.1002/mrm.21174

[8] Grodzki, David M et al. “Ultrashort echo time imaging using pointwise encoding time reduction with radial acquisition (PETRA).” Magnetic resonance in medicine vol. 67,2 (2012): 510-518. doi:10.1002/mrm.23017

[9] Schulte, R F et al. “Design of broadband RF pulses with polynomial-phase response.” Journal of magnetic resonance (San Diego, Calif. : 1997) vol. 186,2 (2007): 167-75. doi:10.1016/j.jmr.2007.02.004

[10] Froidevaux R et al. Enabling long excitation pulses in algebraic ZTE imaging by dead-time reduction via dual acquisition with alternative RF modulations. In: Proceedings of the 27th Annual Meeting of ISMRM, 2018.

[11] Li, Cheng et al. “Correction of excitation profile in Zero Echo Time (ZTE) imaging using quadratic phase-modulated RF pulse excitation and iterative reconstruction.” IEEE transactions on medical imaging vol. 33,4 (2014): 961-9. doi:10.1109/TMI.2014.2300500

[12] Chambolle, A., & Pock, T. (2011). A first-order primal-dual algorithm for convex problems with applications to imaging. Journal of mathematical imaging and vision, 40(1), 120-145.

[13] Wirgin, Armand. (2004). The inverse Crime. Math Phys.

[14] Oberhammer T, Weiger M, Hennel F, Pruessmann KP. Prospects of parallel ZTE imaging. In: Proceedings of the 19th Annual Meeting of ISMRM, Montreal, Canada, 2011. p. 2890

DOI: https://doi.org/10.58530/2022/0245