Chapter 3
the diffusion time. Those spins that have diffused are not decoded to their original
phase and are no longer measured in the spin echo t12j. Hereby the amplitude of
spin-echoes in the presence of gradient pulses is smaller than that in the absence
Ofgradient pulses.
In the PGSE experiment, the amplitude ratio of spin-echoes in the presence
and absence of gradient pulses (g > O and g = O) R is measured.
D is the fluid diffusivity. R is the spin-echo attenuation ratio. For isotropic bulk
fluids in which molecules can diffuse freely (Fickian diffusion), the expression for
R is [12]:
‰=exp[-∕2g2Zλ52(Δ-<≡>∕3)]
[3.9]
The constant γ is the gyromagnetic ratio of the nuclei (y = 2.67 × 108
rad.T^1s^1 for 1H). This method can be used to measure self-diffusion coefficients.
In basic PGSE sequence, if T2 of water droplets is small (due to small drop
size or large surface relaxivity), spin echo amplitude becomes small because of
transverse relaxation, which will reduce SNR and measurement accuracy. Eq.
3.10 shows the spin-echo signal amplitude as the function of echo spacing [6].
Λ^(2r) = M0exp(--)
[3.10]
ɔ
44
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