We present a new imaging paradigm based on Rabi modulated continuous wave (CW) excitation. Recent work¹, inspired by quantum optics², has demonstrated that a spin system excited by a Rabi modulated CW excitation achieves a significant observable periodic magnetisation. The steady-state magnetisation can be fully described by harmonics of the excitation envelope modulation frequency³. Off-resonance effects influence the steady-state harmonics; we have previously shown that the encoded chemical shift information can be used to reconstruct a simple ethanol spectrum⁴. In this work, we encode frequency localisation in the steady-state Rabi harmonics and reconstruct radial projections of proton density, followed by filtered back projection (FBP) to complete the imaging paradigm. Rabi modulated CW imaging has the potential to image ultra-short T₂ tissues using prolonged steady-state trajectories rather than reliance on extremely short FIDs. Existing techniques such as UTE⁵, ZTE⁶ and SWIFT⁷ have shown that ultra-short T₂ imaging is clinically valuable in the diagnosis of muscular skeletal injury and disease.

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 (T₁=41ms, T₂=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 B₀ 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 protocol⁸ (Fig. 1), similar to that used in SWIFT⁷, 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.

The reference image (Fig. 3) depicts three test tubes aligned along the longitudinal axis. The reference sinogram (Fig. 4a) and FBP image (Fig. 4b) show an expected decrease in image quality due to a low number of projection angles. Two reconstruction cases are considered for the measurements taken under Rabi modulated CW excitation: the first assuming B₀ homogeneity and the second incorporating a measured voxel distribution in the forward model. The sinogram (Fig. 4c) and FBP image (Fig. 4d) assuming B₀ homogeneity show three clearly defined test tubes but have some error in shape and size, which can be attributed to low gradient strength. An improvement to the shape (Fig. 4f) was achieved when including knowledge of the voxel distribution in the forward model. Further improvements in experimental efficiency will enable 3D imaging, and the acquisition over a larger excitation parameter set using stronger gradients will lead to more accurate reconstruction. We have experimentally demonstrated an imaging paradigm using Rabi modulated CW excitation, in which gradient localisation information is encoded in the steady-state magnetisation and used to reconstruct a proton density image. Our current work is focusing on improving the accuracy of reconstruction, investigating image contrast, and evaluation of the method’s ability to image samples with ultra-short T₂.