Possible Systematic Errors in Single-Shot Measurements of the Trace of the Diffusion Tensor

There have been recent proposals of diffusion-weighting pulse sequences that purport to measure the trace of the diffusion tensor, or to weight an image by that rotationally invariant quantity. Here the effect of a time-dependent diffusion tensor on such sequences is investigated theoretically. It is found that the time dependence of the diffusion tensor both breaks the rotational invariance of the pulse sequence and affects the overall magnitude of the diffusion weighting. These deviations are calculated for two pulse sequences, with parameters relevant to experiments on brain tissue. The departure from rotational invariance is found to be surprisingly small: <1%, for reasonable parameters and approximately5% for the most extreme choice of parameters. The overall magnitude of the diffusion weighting, however, may be significantly altered; 10% is estimated for reasonable parameters. It is proposed that this effect should prove a sensitive probe of time dependence in the diffusion tensor.