Limits to flow detection in phase contrast MRI

Abstract

Velocity detection with single pulsed gradient spin echo (PGSE) NMR is known to be limited by diffusion smearing the phase coherence and obscuring dispersive attenuation. We present an equation for the lowest detectable velocity with phase contrast velocimetry which incorporates the signal-to-noise ratio. We show how to best sample q-space when approaching this limit. We confirm that the apparent diffusion/dispersion coefficient can be used to infer fluid velocity for Péclet number Pé > 1. When measuring flow in biological systems we determined that with realistic experimental protocols the limits are roughly 1 µm/s for velocimetry and 300 µm/s for diffusometry.There is a strong interest to measure slow flows in vivo, e.g., measuring microcirculation of blood in capillary networks [6] and advective transport in the glymphatic system [7,8]. Knowledge of the lower limit of velocity resolution, as well as how to best measure slow velocities with PGSE MRI may open the door for these and other new applications. General TheoryOne beautiful aspect of magnetic resonance is the multitude of information which can be encoded into its complex signal. Pulsed gradient spin echo (PGSE) NMR exemplifies this in the solution to the Bloch-Torrey equations for the normalized complex signal E(q) arising from a fluid undergoing self-diffusion and coherent flow [9, 10, 11, 1],in which q sensitizes the signal to displacement during an observation time ∆. With rectangular gradient pulse shapes of amplitude g and duration δ, in the case that δ << ∆, q = γgδ where γ is the gyromagnetic ratio of the nuclei. Equation (1) shows that the phase shift between the real and imaginary channels and the attenuation of the signal intensity provide the ability to measure both mean coherent velocity, v, and random diffusion,

Low b‐value diffusion tensor imaging for measuring pseudorandom flow of cerebrospinal fluid

“…Thus, analysis combining these techniques is expected to provide further insight into CSF physiology. An example of the combination of the phase‐contrast and the diffusion techniques has been proposed to accurately measure slow velocities targeting glymphatic transport 32 . Although the target physiology and the range of velocities are different, a proposed mathematical framework dealing with these two techniques will be helpful in developing combined analysis techniques for investigating the CSF physiology.…”