Ultrafast 3D Bloch–Siegert B‐mapping using variational modeling

Abstract

Purpose Highly accelerated B ‐mapping based on the Bloch–Siegert shift to allow 3D acquisitions even within a brief period of a single breath‐hold. Theory and Methods The B dependent Bloch–Siegert phase shift is measured within a highly subsampled 3D‐volume and reconstructed using a two‐step variational approach, exploiting the different spatial distribution of morphology and B ‐field. By appropriate variable substitution the basic non‐convex optimization problem is transformed in a sequential solution of two convex optimization problems with a total generalized variation (TGV) regularization for the morphology part and a smoothness constraint for the B ‐field. The method is evaluated on 3D in vivo data with retro‐ and prospective subsampling. The reconstructed B ‐maps are compared to a zero‐padded low resolution reconstruction and a fully sampled reference. Results The reconstructed B ‐field maps are in high accordance to the reference for all measurements with a mean error below 1% and a maximum of about 4% for acceleration factors up to 100. The minimal error for different sampling patterns was achieved by sampling a dense region in k ‐space center with acquisition times of around 10–12 s for 3D‐acquistions. Conclusions The proposed variational approach enables highly accelerated 3D acquisitions of Bloch–Siegert data and thus full liver coverage in a single breath hold.

Rapid T1 quantification from high resolution 3D data with model‐based reconstruction

“…Additionally, the numerical gradients were balanced after each GN‐step by calculating their ‐norm and applying a scaling to match each other in the forward and adjoint evaluation of the gradient. In a subsequent preprocessing step, coil sensitivities were estimated from parameter‐averaged data using the method of Uecker et al Deviations from the nominal flip angle were taken into account by performing mapping with a modified Bloch‐Siegert and DREAM method for VFA respectively IRLL data. The Bloch‐Siegert map was acquired on a Cartesian grid with half the resolution of the VFA data and a block undersampling pattern with size of 12 × 4 as described by Lesch et al, leading to an acquisition time of about 15s for the whole 3D volume.…”

“…In a subsequent preprocessing step, coil sensitivities were estimated from parameter‐averaged data using the method of Uecker et al Deviations from the nominal flip angle were taken into account by performing mapping with a modified Bloch‐Siegert and DREAM method for VFA respectively IRLL data. The Bloch‐Siegert map was acquired on a Cartesian grid with half the resolution of the VFA data and a block undersampling pattern with size of 12 × 4 as described by Lesch et al, leading to an acquisition time of about 15s for the whole 3D volume. The resulting map is normalized to the nominal flip angle of the Bloch‐Siegert encoding pulse, leading to a spatially dependent correction factor for α.…”

Robust 3D Bloch‐Siegert based mapping using multi‐echo general linear modeling

“…The greater robustness of the interleaved acquisition scheme has led to its adoption in more recent work using this technique. 11,26 In the interleaved case, however, our numerical simulations showed that the phase never reached steady-state but rather a pseudo-steady-state that alternated between two conditions depending on the frequency of the preceding offresonance BS pulse. As a result, the difference in phase between interleaves is not solely due to the BSS effect and, therefore, does not match the phase difference of the sequential ordering scheme (Figure 2).…”

“…The resulting maps had visible artefacts and large biases (see Figure , right column). The greater robustness of the interleaved acquisition scheme has led to its adoption in more recent work using this technique …”

“…The BSS technique is flexible and can be integrated into a multitude of pulse sequences, such as 2D 9 or 3D gradient echo (GRE), 8,10,11 interleaved echo planar imaging, spiral GRE, 12 and spin echo [13][14][15][16] acquisitions. The BSS technique, as typically implemented, requires two acquisitions with opposite off-resonance frequencies.…”