Correcting image distortions from a nonlinear B 1 + $$ {\boldsymbol{B}}_{\mathbf{1}}^{+} $$ -gradient field in frequency-modulated Rabi-encoded echoes

Abstract

Purpose: To correct image distortions that result from nonlinear spatial variation in the transmit RF field amplitude ( $B_1^{+}$ ) when performing spatial encoding with the method called frequency-modulated Rabi encoded echoes (FREE).

Theory and methods: An algorithm developed to correct image distortion resulting from the use of nonlinear static field (B₀ ) gradients in standard MRI is adapted herein to correct image distortion arising from a nonlinear $B_1^{+}$ -gradient field in FREE. From a $B_1^{+}$ -map, the algorithm performs linear interpolation and intensity scaling to correct the image. The quality of the distortion correction is evaluated in 1.5T images of a grid phantom and human occipital lobe.

Results: An expanded theoretical description of FREE revealed the symmetry between this $B_1^{+}$ -gradient field spatial-encoding and standard B₀ -gradient field spatial-encoding. The adapted distortion-correction algorithm substantially reduced image distortions arising in the spatial dimension that was encoded by the nonlinear $B_1^{+}$ gradient of a circular surface coil.

Conclusion: Image processing based on straightforward linear interpolation and intensity scaling, as previously applied in conventional MRI, can effectively reduce distortions in FREE images acquired with nonlinear $B_1^{+}$ -gradient fields.

Keywords: B1-gradient encoding; B1-nonlinearity correction; distortion correction; low-cost MRI; radiofrequency imaging; surface coil.