B0 concomitant field compensation for MRI systems employing asymmetric transverse gradient coils

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MRI ideally utilizes linearly varying magnetic fields to encode position over the imaging field of view (FOV). This linear assumption violates a principle of the magnetic field described by Maxwell's equations, namely that its divergence is zero, or JOURNAL/mrim/04.02/01445475-201803000-00032/math_32MM1/v/2018-01-24T161827Z/r/image-png . This deviation from the linear assumption, known analytically and well described for variety of situations, is commonly termed the Maxwell field or concomitant field1. Note that concomitant fields are created simultaneously with the spatial encoding gradient fields, which differs from eddy currents generated in response to such fields and have associated delay time constants 2. The presence of the concomitant fields causes undesired phase to accumulate within the measured k‐space data. If not properly accounted for during image reconstruction or pulse sequence design, this results in image blurring and spatial shifts in a variety of applications, including but not limited to phase‐contrast 1, spiral 4, fast spin‐echo 5, and echo‐planar imaging (EPI) 6.
For standard, whole‐body MR systems, all three cylindrical gradient coils are typically symmetric, that is, the gradient isocenter coincides with the geometrical center of the gradient coil. Due to this symmetry, the leading terms of the concomitant field have second‐order spatial dependence. These terms add significant phase contributions to the measured data 1; compensation for these effects has been well studied and typically already has been implemented with software modifications on the MR scanners 1. For phase‐contrast and EPI applications, a joint pulse sequence and reconstruction correction based on tracking the applied gradient waveform and applying exactly the inverse concomitant fields phase term to the image resulted in almost complete elimination of this artifact 7. For spiral imaging, a similar technique, which compensates for the known frequency shift associated with gradient activities during the reconstruction, usually is performed 4.
Previously, head‐only or compact gradient systems with asymmetry in the transverse (i.e., physical x and y) gradient axes have been described 10. With these gradient coils, the gradient isocenter is shifted along the longitudinal axis toward the patient‐entry side of the magnet bore, typically by approximately 10 cm. The reduced size of these gradient coils enables greatly reduced peripheral nerve stimulation compared to whole‐body coils 15 and lower self‐inductance 16. These in turn permit increased slew rate capability 17, lending themselves to pulse sequences with high‐performance gradient requirements such as EPI. Asymmetric gradient coils, however, produce additional concomitant fields with zeroth and first‐order spatial dependence, which require additional compensation 18.
The first‐order concomitant gradient terms result in blurring in spiral, shifting that depends on z‐axis slice location in axial EPI, and spatially dependent phase accumulation in a phase‐contrast type sequence. A partial correction was proposed in 18 for several imaging sequences. Later, a preemphasis method 20 fully compensated for the linear concomitant field without the need for any pulse sequence modification.
The zeroth‐order terms manifest as global phase offsets in phase‐contrast type imaging, shifts along the phase‐encoding direction in axial EPI acquisition, and again as blurring similar to off‐resonance in spiral imaging. Previous work 18 suggested protocol changes and gradient lobe reordering to mitigate the concomitant field‐induced artifacts and demonstrated the effectiveness of B0 concomitant field correction with one example; however, it did not describe the specific implementation. The work described in this paper exploits the real‐time hardware frequency shift capability for B0 eddy current correction 2 to fully compensate for the global off‐resonance without any pulse sequence or protocol modification. The proposed method is experimentally demonstrated in phantom and volunteer datasets with Cartesian and non‐Cartesian acquisitions, including phase‐contrast, fast spin echo (FSE), spiral, and EPI.

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