Ultrafast 3D Bloch–Siegert B+1‐mapping using variational modeling

Purpose: Highly accelerated B ₁ ⁺-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 ₁ ⁺ 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 ₁ ⁺ -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 ₁ ⁺ -field. The method is evaluated on 3D in vivo data with retro- and prospective subsampling. The reconstructed B ₁ ⁺ -maps are compared to a zero-padded low resolution reconstruction and a fully sampled reference. Results: The reconstructed B ₁ ⁺ -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.