field gradients – uses in nmrtesla.ccrc.uga.edu/courses/bionmr2005/lectures/may2.pdf · 2018. 7....
TRANSCRIPT
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Field Gradients – Uses in NMR
BCMB/CHEM 8190May 2, 2005
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Pulsed Field Gradients – NMR Applications
• Coherence selection using pulsed field gradients. J. R. Tolman & J. H. Prestegard, Concepts in Magnetic Resonance, 7, 247-262 (1995).
• Water suppression (WATERGATE), M. Piotto, V. Saudek & V. Sklenar, J. Biomol. NMR, 2, 661-665 (1992).
• Diffusion measurements. Altieri, Hinton & Byrd, J. Am. Chem. Soc., 117, 7566-7567 (1995).
• NMR Imaging, Levitt, “Spin Dynamics”, pp 325-335 (2002).
• Echo Planar Spectroscopic Imaging, Concepts in Magnetic Resonance, 13, 213-237 (2001).
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Pulsed Field Gradients – How they Work
i
iB0(z)
B’
z
B0
time
G(z)
Magnetization vectors precess at different rates depending on G(z) and γ for each volume element. They dephase - net Mx, My = 0
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Effects of Gradients can be RefocussedApplication: Water Suppression
90x 90-y 180y 90-y
x y
z
ωa ωbx y
ωaωb
zG1 G1
Resonance notaffected by 90refocuses
x y
z
ωb
ωa
x yωb
ωa
zResonance affected by 90dephases (H2O)
x yωa
ωb
z
x y
z
ωa
ωb
x y
z
ωb
ωa
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1D 1H Water-Suppressed Spectrum Pf-Rubredoxin in 1H2O
ppm-2024681012
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Coherence Selection Using Pulse Field Gradients
• H(r) = -Σkγk [B0 + Bz(r)]Ikz(in radians s-1 and neglecting chemical shifts)
• Effects on product operators for a z gradient:
• Ikz -γk Bz(z) Ikz τ Ikz
• Ik+ -γk Bz(z) Ikz τ exp[i γk Bz(z) τ ] Ik+
• Ik- -γk Bz(z) Ikz τ exp[-i γk Bz(z) τ ] Ik-
• For linear gradients Bz(z) = Gz z• Observables are integrals over z – zero for Ik+ , Ik-
B’
z
B0
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1H(I)
15N(S)90-x 180y 90y
90y
τ τ
t1/2 t1/2 ττ decouple180x 90-x 180x
180y 90-x 180x
t2
GG1
-G1G2
Gradient Selected HSQC
σmn(t2) = Integralz {σmn(t1) exp[iγN2G1z] exp[-iγHG2z]}
= Integralz {σmn(t1) exp[i(γN2G1z- γHG2z)]}
σmn(t2) finite only if γN2G1 = γHG2All 1Q proton transverse magnetization eliminated
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Translational Diffusion Constants for Macromolecules
• Determine aggregate size• Determine protein-protein interactions• Screen for bound ligands
• = nDt where D = kT/(6πηr)• Key: if molecule moves, field is different,
magnetization doesn’t refocus
r
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90x 180y
gz gzδ δ
Δ
•ln[S/S0] = -γ2g2Dδ2(Δ - δ/3)
Stejskal and Tanner Pulse Sequencefor Diffusion Measurement
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Diffusion Measurement Continued
• Measurements are limited by natural T2• Improved sequence uses z storage
(Altieri, Hinton and Byrd, 1995)
ln(S/S0)
g2
Large molecule
Small molecule
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"for their discoveries concerning magnetic resonance imaging"
Paul C. Lauterbur Sir Peter Mansfield
The Nobel Prize in Physiology or Medicine 2003
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Simple Imaging Strategy
• During gradient spins in each volume element have their own precession frequency
• Can get a 1D image of sample – used in gradient shimming
High positive frequency
Zero frequency
High negative frequency
Zν
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Simple 2D Image• For 2D imaging use gradients in different directions (x, z)
in different evolution periods (t1, t2)
90x
Gz
Gx
t1 t2
z
x
ν1
ν2
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Echo Planar Imaging – Speeding up Acquisitions
90x
Gz t2 t2 t2 t2 t2
t1
dw-1 dw-2 dw-3 dw-4 dw-5
• t2 will have spatial image (needs to be reversed in even dw)• t1 can sample a number of different properties • t1 could have a gradient in another dimension – 2D map• t1 could sample chemical shift dispersion - MRSI
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(MRSI)Magnetic Resonance
Spectroscopy Imaging
Prostate CancerB- Spectral GridC- MRSI Array
Swanson et al. Cancer
Investigation19, 510-523 (2001)