Field Gradients – Uses in NMR

BCMB/CHEM 8190May 2, 2005

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).

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

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

1D 1H Water-Suppressed Spectrum Pf-Rubredoxin in 1H2O

ppm-2024681012

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

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

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

90x 180y

gz gzδ δ

Δ

•ln[S/S0] = -γ2g2Dδ2(Δ - δ/3)

Stejskal and Tanner Pulse Sequencefor Diffusion Measurement

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

"for their discoveries concerning magnetic resonance imaging"

Paul C. Lauterbur Sir Peter Mansfield

The Nobel Prize in Physiology or Medicine 2003

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

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

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

(MRSI)Magnetic Resonance

Spectroscopy Imaging

Prostate CancerB- Spectral GridC- MRSI Array

Swanson et al. Cancer

Investigation19, 510-523 (2001)