Analysis of spin-echo rephasing with pulsatile flow in 2D FT magnetic resonance imaging

The effects of pulsatile flow on spin phases in spin-echo magnetic resonance imaging are considered. General expressions for the spin phases of the first four echoes are derived in terms of the Fourier coefficients of flow. These expressions are valid for any time-dependent acceleration and, hence, are not restricted to constant acceleration. The derived expressions are then theoretically evaluated for aortic flow and examined at different points in the cardiac cycle. Our results show that rephasing may occur at certain points in the cardiac cycle for either even or odd echoes depending upon the particular Fourier coefficients of the velocity function and the spin-echo delay time. However, even-echo rephasing is not always necessarily valid. Furthermore, the possibility of determining the flow velocities in the body with an appropriate series of imaging studies is also discussed.