Abstract
Pulsed gradient spin echo (PGSE) complex signal behavior becomes dominated by attenuation rather than oscillation when displacements due to flow are similar or less than diffusive displacements. In this "slow-flow" regime, the optimal displacement encoding parameter q for phase contrast velocimetry depends on the diffusive length scale qslow=1/lD=1/√2DΔqslow=1/lD=1/2DΔ<math> <mrow><msub><mi>q</mi> <mrow><mi>s</mi> <mi>l</mi> <mi>o</mi> <mi>w</mi></mrow> </msub> <mo>=</mo> <mn>1</mn> <mo>/</mo> <msub><mi>l</mi> <mi>D</mi></msub> <mo>=</mo> <mn>1</mn> <mo>/</mo> <msqrt><mrow><mn>2</mn> <mi>D</mi> <mi>Δ</mi></mrow> </msqrt> </mrow> </math> rather than the velocity encoding parameter v enc = π/(qΔ). The minimum detectable mean velocity using the difference between the phase at +q slow and -q slow is ⟨vmin⟩=1/SNR√D/Δ〈vmin〉=1/SNRD/Δ<math> <mrow><mrow><mo>〈</mo> <mrow><msub><mi>v</mi> <mrow><mi>m</mi> <mi>i</mi> <mi>n</mi></mrow> </msub> </mrow> <mo>〉</mo></mrow> <mo>=</mo> <mn>1</mn> <mo>/</mo> <mi>SNR</mi> <msqrt><mrow><mi>D</mi> <mo>/</mo> <mi>Δ</mi></mrow> </msqrt> </mrow> </math> . These theories are then validated and applied to MRI by performing PGSE echo planar imaging experiments on water flowing through a column with a bulk region and a beadpack region at controlled flow rates. Velocities as slow as 6 μm/s are detected with velocimetry. Theories, MRI experimental protocols, and validation on a controlled phantom help to bridge the gap between porous media NMR and pre-clinical phase contrast and diffusion MRI.