Phase alterations of spin echoes by motion along magnetic field gradients

Using a Taylor series expansion of the phase shift of a moving isochromatic spin group in the presence of a magnetic field gradient, the refocusing effects of the Carr-Purcell-Meiboom-Gill pulse sequence on stationary nuclei and those with constant, rectilinear velocity are readily demonstrated. Continuing the analysis to higher orders of motion reveals that nuclei with a constant, rectilinear acceleration have a phase shift at the spin echoes which increases linearly with echo number. Constant, rectilinear jerk (the time rate of change of acceleration) leads to an increase in phase shift from echo to echo which is quadratic in nature with an overlying reduction of the odd-numbered echoes by a constant amount. Motion parameters may be measured by parameter identification techniques. These principles may be applied to phase-sensitive NMR imaging.