Rabi Modulated Continuous Wave Imaging

James C Korte^{1}, Bahman Tahayori^{1}, Peter M Farrell^{1}, Stephen M Moore^{2,3}, and Leigh A Johnston^{1}

Experiments were conducted on a 4.7T Bruker Biospec scanner with an AVANCE III console. An imaging phantom of three test tubes of Gadolinium doped water (T_{1}=41ms, T_{2}=33ms) was aligned in the longitudinal axis.

FLASH Image: A reference image was acquired as the average of 10 axial slices using FLASH (FOV=60mm, Matrix=128x128, Slice Thickness=2mm). A Radon transform of the reference image was used to generate projections along the set of projection angles, $$$\theta$$$, used in the Rabi CW experiment. A reduced projection reference image was formed using a standard FBP algorithm.

Field Map: The distribution of off-resonances was measured using the field-mapping sequence, MAPSHIM (Bruker Biospin). A B_{0} voxel distribution, $$$\rho\left(\delta_{B_0}\right)$$$, was extracted via a histogram of non-background voxels.

Rabi CW Image:

A Rabi modulated excitation envelope $$\gamma B_\textrm{1}^\textrm{e}\left(t\right)= \omega_\textrm{1}\left(1+\alpha \cos{\omega_\textrm{1}t}\right)$$ was used, where $$$\alpha$$$ is the modulation depth and $$$\omega_\textrm{1}$$$ is the average excitation strength and the envelope modulation frequency.

*Acquisition:* A gapped excitation measurement protocol^{8} (Fig. 1), similar to that used in SWIFT^{7}, was used to achieve near-simultaneous transmit and receive with a 90% duty cycle. The phantom was excited by a set of $$$N$$$=4030 Rabi modulated CW excitations $$$\left\{\left(\alpha^{\left(1\right)},\,\omega_\textrm{1}^{\left(1\right)},\,\delta_\textrm{rf}^{\left(1\right)}\right),\,\left(\alpha^{\left(2\right)},\,\omega_\textrm{1}^{\left(2\right)},\,\delta_\textrm{rf}^{\left(2\right)}\right),\,\cdots,\,\left(\alpha^{\left(\textrm{N}\right)},\,\omega_\textrm{1}^{\left(\textrm{N}\right)},\,\delta_\textrm{rf}^{\left(\textrm{N}\right)}\right)\right\}$$$ where $$$\delta_\textrm{rf}$$$ is an offset to the RF carrier frequency. The modulation depth, $$$\alpha$$$, ranged from 0.5 to 5.0, the modulation frequency, $$$\omega_\textrm{1}$$$, ranged from 30 Hz to 90 Hz and the offset to RF carrier, $$$\delta_\textrm{rf}$$$, ranged from -4.5 kHz to 4.5 kHz. For each CW excitation the phantom was measured over 18 projections angles, $$$\theta$$$, as shown in the sequence diagram (Fig. 2). A low gradient strength of 102.1 Hz/mm was used to reduce experimental time, and is 0.5% of the maximum available.

*Reconstruction:* The DC component and first five harmonics of the envelope modulation frequency, $$$\omega_\textrm{1}$$$, were extracted from the measured steady-state magnetisation, $$$\boldsymbol{M}_\textrm{xy}$$$, and used to construct a measurement vector,$$$\boldsymbol{z}_\theta$$$, for each projection. The linear forward model matrix, $$$\boldsymbol{H}$$$, was constructed from a Fourier series approximation of the Bloch equation, numerically integrated over a voxel distribution, $$$\rho\left(\delta_{B_0}\right)$$$. Each proton density projection, $$$\boldsymbol{x}_\theta$$$, was solved by least squares optimisation with a nonnegative and smoothness constraint. $$\underset{\boldsymbol{x}_\theta\in[0,\infty)}{\operatorname{minimise}}\,\left(1-g\right)\parallel\boldsymbol{H}\boldsymbol{x}_\theta-\boldsymbol{z}_\theta\,\parallel_2+\,g\parallel\Delta\,\boldsymbol{x}_\theta\,\parallel_2$$ where $$$g$$$ is a smoothing factor and $$$\Delta$$$ is a finite difference matrix. A 2D proton density image was formed from the radial projections using a standard FBP algorithm.

1. Layton KJ, Tahayori B, Mareels IM, Farrell PM, Johnston LA. Rabi resonance in spin systems: Theory and experiment. Journal of Magnetic Resonance. 2014; 242:136-142.

2. Cappeller U, Müller H. Phase modulated excitation of an optically pumped spin system. Annals of Physics. 1985; 497(3):250-264.

3. Tahayori B, Johnston L, Layton K, Farrell P, Mareels I. Solving the Bloch equation with periodic excitation using harmonic balancing: Application to Rabi modulated excitation. IEEE Transactions on Medical Imaging. 2015; 34(10):2118-2130

4. Korte JC, Layton KJ, Tahayori B, Farrell PM, Moore SM, Johnston LA. Encoding chemical shift with Rabi modulated continuous wave excitation. ISMRM, Milan, Italy. 2014.

5. Bergin CJ, Pauly JM, Macovski A. Lung parenchyma: projection reconstruction MR imaging. Radiology. 1991; 179(3):777-781.

6. Weiger M, Pruessmann KP, Hennel F. MRI with zero echo time: hard versus sweep pulse excitation. Magnetic Resonance in Medicine. 2011; 66(2):379-389.

7. Idiyatullin D, Corum C, Park JY, Garwood M. Fast and quiet MRI using a swept radiofrequency. Journal of Magnetic Resonance. 2006; 181(2):342-349.

8. Korte JC, Tahayori B, Farrell PM, Moore SM, Johnston LA. Gapped measurement of spin system response to periodic continuous wave excitation. ANZMAG, Bay of Islands, New Zealand. 2015.

Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)

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