Chapter3
1 T f)τ
Mxy(2τ^T) = -M^xp(--~-)
[3.11]
This procedure allows increasing the diffusion time while reducing the effect
of extended relaxation which will reduce the SNR. Eq. 3.8 can also be used to
calculated spin echo signal attenuation for stimulated spin-echo PGSE sequence.
3.3.2. Drop size determination from PGSE measurement
Eq. [3.9] is limited to bulk fluids. But in many cases, the fluids are confined in
small geometries such as pores or droplets and cannot diffuse freely, which is
referred as restricted diffusion. In these cases, Murday and Cotts [15] developed
the equation for the PGSE sequence. For restricted diffusion within a sphere of
radius a, the attenuation ratio Rsp is:
Rsb = exp<-2χ2g2∑ 7 7 7 ,
sp pl z s ^a2m(a2ma2-2)[a2mD
(⅛D)jj
[3.12]
Here Ψ = 2 + e~a2-D(&~S) - 2e~a^ - 2e~a-oδ
+ e-a^lD(Δ+δ)
[3.13]
am is the mth positive root of the equation:
ota ∙ Jr5z2(Qa)-Z372 (ota) = 0 [3.14]
Jk is the Bessel function of the first kind, order k.
If Δ » a2∕2D, Δ » δ, Eq. [3.8] can be simplified as1:
Rsp = exp(-y2g2δ2a2 /5)
[3.15]
Figure 3.4 shows the predicted attenuation of emulsified water droplets with
different drop diameters from 5 to 50 μm. Here the diffusion time Δ is 500 ms,
46
More intriguing information
1. Global Excess Liquidity and House Prices - A VAR Analysis for OECD Countries2. The name is absent
3. Ahorro y crecimiento: alguna evidencia para la economía argentina, 1970-2004
4. Meat Slaughter and Processing Plants’ Traceability Levels Evidence From Iowa
5. The name is absent
6. Effort and Performance in Public-Policy Contests
7. An Empirical Analysis of the Curvature Factor of the Term Structure of Interest Rates
8. DEMAND FOR MEAT AND FISH PRODUCTS IN KOREA
9. Picture recognition in animals and humans
10. The Effects of Attendance on Academic Performance: Panel Data Evidence for Introductory Microeconomics