Interpretation of flow encoding and quantification in MRI: Time domain versus frequency domain

The traditional approach to flow effects in MRI is based on the gradient moment expansion, Recently, we have presented an alternative description by using linear response theory: the distortions of the velocity waveform induced by the gradient waveforms were analyzed in the frequency domain on the basis of the transfer function. In the present paper, we perform an analysis of flow encoding and quantification in the time domain, on the basis of the impulse response, The analysis shows that flow encoding should be interpreted as a weighted averaging process, Instantaneous flow encoding is determined by the centroid of the impulse response, but care should be taken regarding the physical meaning of the instant of encoding. The relationship of this approach to the frequency domain and gradient moment expansion approaches is clarified, By way of example, some interesting applications are investigated: asymmetrical phase encoding gradients to minimize misregistration and oscillating read-out gradients for flow quantification. A variety of new applications are expected to derive from the combination of both the time and frequency domains.