Ultrafast 3D Bloch-Siegert B <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mrow/> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo></mml:msubsup> </mml:math> -mapping using variational modeling.
PURPOSE
Highly accelerated B <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mrow/> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo></mml:msubsup> </mml:math> -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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mrow/> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo></mml:msubsup> </mml:math> 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mrow/> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo></mml:msubsup> </mml:math> -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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mrow/> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo></mml:msubsup> </mml:math> -field. The method is evaluated on 3D in vivo data with retro- and prospective subsampling. The reconstructed B <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mrow/> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo></mml:msubsup> </mml:math> -maps are compared to a zero-padded low resolution reconstruction and a fully sampled reference.


RESULTS
The reconstructed B <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mrow/> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo></mml:msubsup> </mml:math> -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.
['Lesch|Andreas|A|', 'Schlöegl|Matthias|M|', 'Holler|Martin|M|', 'Bredies|Kristian|K|', 'Stollberger|Rudolf|R|']
D000328:Adult D000465:Algorithms D062485:Breath Holding D064368:Healthy Volunteers D006801:Humans D007091:Image Processing, Computer-Assisted D021621:Imaging, Three-Dimensional D016014:Linear Models D008099:Liver D008297:Male D009068:Movement D011446:Prospective Studies D015203:Reproducibility of Results D012189:Retrospective Studies
total generalized variation B<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                        <mml:msubsup xmlns:mml="http://www.w3.org/1998/Math/MathML">
                            <mml:mrow xmlns:mml="http://www.w3.org/1998/Math/MathML"/>
                            <mml:mn xmlns:mml="http://www.w3.org/1998/Math/MathML">1</mml:mn>
                            <mml:mo xmlns:mml="http://www.w3.org/1998/Math/MathML">+</mml:mo>
                        </mml:msubsup>
                    </mml:math>
-Bloch-Siegert shift B<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
                        <mml:msubsup xmlns:mml="http://www.w3.org/1998/Math/MathML">
                            <mml:mrow xmlns:mml="http://www.w3.org/1998/Math/MathML"/>
                            <mml:mn xmlns:mml="http://www.w3.org/1998/Math/MathML">1</mml:mn>
                            <mml:mo xmlns:mml="http://www.w3.org/1998/Math/MathML">+</mml:mo>
                        </mml:msubsup>
                    </mml:math>
-mapping fast imaging single breath hold acquisition