A new MRI formulation for flow and motion applications

Abstract

A rigorous reformulation of the magnetic resonance (MR) image formulation model (IFM) can use the integrally cumulative nature of MRI phase shifts for encoding and of time-of-flight travel corrections for magnitude. This approach characterizes each independent gradient element by its cumulant waveforms,K _N (t), instead of by particular time expansion in gradient moments. The lowest-order cumulant gradient that gives a simple monopolar waveform governs all resulting phase-encoding properties. Each gradient element specifically encodes one and only one motion-order variable. Phase sensitizations to “higher order” do not exist; they are mathematical psuedophasings. Magnetization isochromats may have arbitrarily complicated velocity history,V(t), appearing in both time-of-flight and motion phase-shift formulas. The subject's intravoxel motion subdistributions each automatically reference the correct mean time of encoding action and its encoding duration. This formulation yields very simple and generalizable IFM expressions for MRI acquired data, with no theoretical confusion regarding higher-order phase shifts and nonphased time-of-flight effects.