In this paper, we show that in cases where the diffusion sequences that purport to measure the trace of the diffusion tensor, coefficient has some time dependence, due to the presence or to weight an image by that rotationally invariant quantity. Here of restrictions to motion, such single-shot measurements fail the effect of a time-dependent diffusion tensor on such sequences to produce the desired trace. The deviations are twofold: (i) is investigated theoretically. It is found that the time dependence the putative trace differs from the true trace of the effective of the diffusion tensor both breaks the rotational invariance of the diffusion tensor, and (ii) the quantity measured is not compulse sequence and affects the overall magnitude of the diffusion pletely rotationally invariant. The second effect is somewhat weighting. These deviations are calculated for two pulse sequences, subtle, and we estimate that the quantitative deviations from with parameters relevant to experiments on brain tissue. The derotational invariance may range from being negligible to parture from rotational invariance is found to be surprisingly several percent. The first effect, however, is quite large, small: รต1%, for reasonable parameters and ร5% for the most extreme choice of parameters. The overall magnitude of the diffu-given appropriate parameters.
sion weighting, however, may be significantly altered; 10% is esti-Some related underlying phenomena have been described mated for reasonable parameters. It is proposed that this effect in the past in an earlier paper (8). The interest of the present should prove a sensitive probe of time dependence in the diffusion calculation lies not only in the fact that small systematic tensor.