Mapping of turbulent intensity by magnetic resonance imaging

The signal produced by turbulent flow in NMR pulse sequences has been analyzed by considering the effects of variations in fluid velocity on the net signal phase variance. It is shown that in a bipolar field gradient, the signal is dependent on the gradient amplitude and the precise time dependence of the velocity fluctuations. This dependence is described using an autocorrelation function, whose characteristic width is the correlation time. When the correlation time is short, the signal from fluid elements decreases as though they are diffusing in a random walk, whereas when the time is long, the signal falls more rapidly with an increase in the duration of the gradient waveform. However, many situations fall into an intermediate regime. A general expression appropriate for all correlation times has been derived and used to characterize the turbulent flow distal to a stenosis in a tube. By use of multiple images of the spatial distribution of NMR signal obtained with differing readout gradients and analyzed by application of the general expression for signal loss, the spatial variations in the correlation time and turbulent intensity have been obtained. The measured variations correlate well with computer calculations obtained by numerical simulation of the flow. This method permits turbulent and complex flows to be characterized without disturbing the flow and may have general applications.