Time Resolved Flow Quantification with MRI Using Phase Methods: A Linear Systems Approach

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Abstract
Phase‐related unsteady (pulsatile) flow effects in MRI have been studied by means of linear response theory. These flow effects can be described in the frequency domain: the influence of the gradients on the phase shift is described by a transfer function, the spectrum of the gradient being the determining factor. An analysis of this transfer function is shown to provide information about the process of flow encoding: instant of encoding, induced distortions and how they are related to the gradient waveform. The connection with the traditional description in terms of the gradient moment expansion has also been investigated and clarified. This approach was applied to study the response of two time‐resolved flow quantification techniques (Fourier flow method and phase mapping) by analyzing their amplitude and phase transfer functions. By simulation it is shown that a better interpretation of the measured velocity waveform is obtained and that Fourier analysis in combination with a correction by the inverse transfer function results in an accurate reconstruction of the velocity waveform studied.