  Purpose: Asymmetric gradient waveforms are attractive for diffusion encoding
due to their superior efficiency, however, the asymmetry may cause a residual
gradient moment at the end of the encoding. Depending on the experiment setup,
this residual moment may cause significant signal bias and image artifacts. The
purpose of this study was to develop an asymmetric gradient waveform design for
tensor-valued diffusion encoding that is not affected by concomitant gradient.
Methods: The Maxwell index was proposed as a scalar invariant that captures the
effect of concomitant gradients and was constrained in the numerical
optimization to 100 (mT/m)$^2$ms to yield Maxwell-compensated waveforms. The
efficacy of this design was tested in an oil phantom, and in a healthy human
brain. For reference, waveforms from literature were included in the analysis.
Simulations were performed to investigate if the design was valid for a wide
range of experiments and if it could predict the signal bias. Results:
Maxwell-compensated waveforms showed no signal bias in oil or in the brain. By
contrast, several waveforms from literature showed gross signal bias. In the
brain, the bias was large enough to markedly affect both signal and parameter
maps, and the bias could be accurately predicted by theory. Conclusion:
Constraining the Maxwell index in the optimization of asymmetric gradient
waveforms yields efficient tensor-valued encoding with concomitant gradients
that have a negligible effect on the signal. This waveform design is especially
relevant in combination with strong gradients, long encoding times, thick
slices, simultaneous multi-slice acquisition and large/oblique FOVs.
