Bas

ic B

iom

olec

ular

Tra

inin

g C

ours

e

Exp

erim

enta

l Bio

mol

ecul

ar N

MR

Tra

inin

g C

ours

e

Day

1

S

pect

rom

eter

Bas

ics:

mag

net,

prob

e, c

onfig

urat

ion,

tuni

ng, l

ocki

ng, s

him

min

g,

gr

adie

nt s

him

min

g.

Day

1,2

1D s

pect

ra: d

eter

min

ing

H2O

line

shap

e, c

alib

ratin

g 1 H

pul

se w

idth

s, a

cqui

ring

H2O

pre

satu

ratio

n sp

ectra

.

W

ater

sup

pres

sion

: cal

ibra

ting

wat

er fl

ip b

ack

puls

es, a

cqui

ring

flipb

ack-

wat

erga

te

1D s

pect

ra.

Day

2,3

Hom

onuc

lear

2D

: Flip

back

, wat

erga

ted

NO

ES

Y sp

ectra

.

Het

eron

ucle

ar 2

D: W

ater

gate

d an

d S

ensi

tivity

-Enh

ance

d H

-N H

SQ

C.

Con

stan

t-Tim

e, H

-C H

SQ

C.

Day

4

Het

eron

ucle

ar 3

D: N

OE

SY-

HS

QC

, HN

CA

B 0

xy

z

n↑n↓ ν 0 =

γ B 0

2 π

xy

z

xy

z

⇒

n↓n↑

≡

ν 0

Meq

A su

perc

ondu

ctin

g so

leno

idis

use

d to

gen

erat

e a

hom

ogen

eous

mag

netic

fie

ld B

0 al

ong

the

vert

ical

(z

) axi

s. A

sam

ple

cont

aini

ngN

MR

activ

e nu

clei

(e.g

. 1H

,13

C) i

s pla

ced

in th

e ce

nter

of th

e fie

ld.

The

nucl

ear s

pins

in

tera

ct w

ith B

0 an

d,

base

d on

thei

r spi

n st

ates

,di

stri

bute

d in

to

ener

gy le

vels

whi

ch a

rese

para

ted

by th

e La

rmor

fr

eque

ncy

ν 0, p

ropo

rtio

nal

to B

0 an

d nu

clea

r gy

rom

agne

tic ra

tio (γ

) (fo

r 1H

, B0

= 1

1.7

T ⇒

ν0

= 5

00 M

Hz)

. For

+ve

γ, t

he lo

wer

ene

rgy

"up"

spin

s are

in sl

ight

ex

cess

ove

r "do

wn"

spin

s, at

equ

ilibr

ium

.

Equi

vale

ntly

, the

spin

sm

ay b

e re

gard

ed a

spr

eces

sing

aro

und

B 0w

ith a

freq

uenc

y ν 0

, with

the

n↑ a

nd n

↓ sp

ins

poin

ting

in o

ppos

itedi

rect

ions

alo

ng th

e z a

xis,

and

the

xy

com

pone

nts d

istr

ibut

edra

ndom

ly.

At e

quili

briu

m, t

his

resu

lts in

the

deve

lopm

ent o

f a b

ulk

nucl

ear m

agne

tizat

ion

(Meq

) alo

ng th

e z a

xis (

para

llel t

o B 0

), pr

opor

tiona

l to

the

exce

ss o

f low

er e

nerg

ysp

ins. M

eq ∝

(n↑

− n↓

)

Bas

ic N

MR

Spe

ctro

scop

y: th

e M

agne

t

xy

zB 0

B 1 c

os (2

πν0t

)

n↑n↓

xy

zM

eq

B 1

B 1

M0

xy

z

Mt

≡

A tr

ansm

itter

gen

erat

esa

radi

o fre

quen

cy (r

f) fie

ld o

scill

atin

g at

the

Larm

or ("

reso

nanc

e")

frequ

ency

in rf

coi

ls

surr

ound

ing

the

sam

ple

in th

e pr

obe.

The

dire

ctio

n of

the

asso

ciat

ed o

scill

atin

g m

agne

tic fi

eld

B 1 is

pe

rpen

dicu

lar t

o B 0

.

The

rf fi

eld

indu

ces

tran

sitio

ns b

etw

een

the

nucl

ear s

pin

ener

gy le

vels

.

This

is e

quiv

alen

t to

aro

tatio

n of

the

bulk

nuc

lear

m

agne

tizat

ion

Meq

from

the

z axi

s tow

ard

the

xy p

lane

.C

ompl

ete

satu

ratio

n of

spin

pop

ulat

ions

cor

resp

onds

to a

900

rota

tion.

The

tran

smitt

er is

turn

ed o

ff,an

d th

e m

agne

tizat

ion

vect

orpr

eces

ses f

reel

y in

the

xypl

ane

at a

n an

gula

r fre

quen

cyv 0

. A B

1 fie

ld w

hich

indu

ces

a 90

0 ro

tatio

n is

cal

led

a 90

0

puls

e.

B 0

Bas

ic N

MR

Spe

ctro

scop

y: th

e Tr

ansm

itter

x

y

x

y

z

The

freel

y pr

eces

sing

mag

netiz

atio

n ve

ctor

M0

trac

es a

spir

al tr

ajec

tory

as i

t exp

erie

nces

"fr

ictio

n"

in th

e fo

rm o

f rel

axat

ion

proc

esse

s (T 1

,T2)

whi

ch

retu

rn it

to e

quili

briu

m (M

xy d

ecay

s to

zero

, M

z gro

ws t

o M

eq ).

In

the

xy p

lane

, the

foot

prin

t of t

he p

rece

ssin

gm

agne

tizat

ion

indu

ces e

xpon

entia

lly d

ecay

ing

sinu

soid

al v

olta

ges i

n th

e rf

coi

l, al

ong

the

x an

d y

axes

: Fre

e In

duct

ion

Dec

ay (F

ID)

M0Mt

Mz(

∞) =

Meq

Mxy

(∞) =

0si

n (2

πν0t

) e− t

/T2

cos (2πν0t) e−t/T2

Bas

ic N

MR

Spe

ctro

scop

y: th

e R

ecei

ver

My(

t) =

A c

os (2

πν0t

) e− t

/T2

Mx(

t) =

A si

n (2

πν0t

) e−t

/T2

AD

C1

AD

C2

Com

pute

r

Rea

l

Imag

inar

y

The

NM

R si

gnal

com

pris

ing

of tw

o FI

Ds r

epre

sent

ing

x an

d y

com

pone

nts o

f the

pre

cess

ing

mag

netiz

atio

nis

fed

into

two

Anal

og to

Dig

ital C

onve

rter

s (AD

Cs)

, whe

re th

ey a

re sa

mpl

ed a

t equ

al ti

me

inte

rval

s.

The

digi

tized

dat

a is

tran

sfer

red

to a

com

pute

r and

stor

ed a

s the

"re

al"

and

"im

agin

ary"

com

pone

nts o

f a

com

plex

tim

e do

mai

n si

gnal

.

The

com

bine

d da

ta is

subj

ecte

d to

a c

ompl

ex F

ouri

er T

rans

form

(FT)

to y

ield

a fr

eque

ncy

dom

ain

spec

trum

.

FT

Mxy

(t) =

My(

t) +

i Mx(

t) =

A e

−i( 2

πν0t

) e−t

/T2

Re

ImR

e (A

bsor

ptiv

e)Im

(Dis

pers

ive)

ν 0

ν 0

Bas

ic N

MR

Spe

ctro

scop

y: th

e D

igiti

zer &

Com

pute

r

B 0

xy

z

RF

Tran

smitt

er+

Puls

e Pr

ogra

mm

er

Rec

eive

r+

Dig

itize

r

Com

pute

r

Mag

net

Prob

e +

Sam

ple

Bas

ic E

lem

ents

of a

n N

MR

Spe

ctro

met

er

Prea

mpl

ifier

Set

the

tem

pera

ture

Tune

the

prob

e

Lock

the

field

Shi

m -

man

ual +

gra

dien

t

Ana

lyze

H2O

or H

DO

line

shap

e

Det

erm

ine

1 H 9

00 p

ulse

wid

th

Det

erm

ine

H2O

/HD

O fr

eque

ncy

Acq

uire

a 1

H 1

D s

pect

rum

inte

rcha

ngea

ble

repe

at u

ntil

lines

hape

's

OK

Bas

ic S

tartu

p Pr

otoc

ol

ensu

res

rf p

ulse

sar

e op

tim

ally

abs

orbe

dby

the

sam

ple

corr

ects

for

mag

neti

cfi

eld

drif

t ov

er t

ime

ensu

res

unif

orm

m

agne

tic

fiel

d ov

ersa

mpl

e vo

lum

e

Fiel

d-Fr

eque

ncy

Lock

ing

The

spec

trom

eter

mon

itors

the

2 H si

gnal

from

the

deut

erat

ed so

lven

t to

(a).

Ach

ieve

spat

ial

hom

ogen

eity

of t

he B

0 fie

ld o

ver t

he sa

mpl

e vo

lum

e (s

him

min

g).

(b).

Smoo

then

out

tim

e-va

ryin

g flu

ctua

tions

in th

e B

0 fie

ld (l

ocki

ng).

x

yM

0

M0

sin

(2πν

0t) e

−t/T

2

M0 cos (2πν0t) e−t/T2

Mt

Re

(Abs

orpt

ive)

Im (D

ispe

rsiv

e)

ν 0

ν 0

mon

itore

d fo

r shi

mm

ing

mon

itore

d fo

r loc

king

A d

edic

ated

par

t of t

he sp

ectro

met

er c

ontin

uous

lym

onito

rs th

e a

bsor

ptiv

e an

d di

sper

sive

line

shap

esof

the

2 H si

gnal

.

B =

B0

− ∆

B

ν 0

VV

+∆V

B =

B0

+ ∆

B

−∆V

ν 0

Posi

tive

err

or v

olta

ge +

∆V

at

lock

res

onan

cefr

eque

ncy:

neg

ativ

e fi

eld

drif

t: i

ncre

ase

curr

ent

to c

ompe

nsat

e B

by

+∆B

Neg

ativ

e er

ror

volt

age

−∆V

at

lock

res

onan

cefr

eque

ncy:

pos

itiv

e fi

eld

drif

t: d

ecre

ase

curr

ent

to c

ompe

nsat

e B

by

−∆B

Fiel

d D

rift C

orre

ctio

n by

Fee

dbac

k Lo

op

Lock

freq

uenc

yva

riatio

n

Fiel

d C

orre

ctio

n

B0(

t)

t

Tx

Rx

V

B0

∆B

The

err

or v

olta

ge i

s no

tco

mpu

ted

inst

anta

neou

sly,

but

afte

r in

tegr

atin

g th

e lo

ck s

igna

l ov

er a

per

iod

of t

ime

(> 1

s).

Prop

er lo

ckin

g (a

nd sh

imm

ing)

requ

ires t

he lo

ck p

hase

to b

e pr

oper

ly a

djus

ted

so th

at th

e re

sona

nce

freq

uenc

y of

the

disp

ersi

on m

ode

sign

al a

nd th

e pe

ak h

eigh

t of

the

abso

rptio

n m

ode

sign

al -

for s

him

min

g- a

re re

gist

ered

cor

rect

ly.

mis

adju

sted

lock

pha

se

The

Lock

ing

Proc

edur

e

lock

off

fiel

d no

t at

res

onan

ceos

cilla

tion

s re

duce

as

we a

ppro

ach

reso

nanc

e

adju

st z

0

lock

sig

nal l

evel

s ou

t at

res

onan

ce

turn

lock

on

NM

R P

robe

From

: Pro

tein

NM

R S

pect

rosc

opy,

P

rinci

ples

and

Pra

ctic

e,

J. C

avan

agh,

W.J.

Fai

rbro

ther

,

A.G

. Pal

mer

III,

N.J.

Ske

lton,

A

ssoc

iate

d Pr

ess,

San

Die

go, 1

996,

pag

e 98

.

Sche

mat

ic o

f an

NM

R P

robe

tuni

ng ro

dm

atch

ing

rod

Prob

e B

ase

coax

ially

m

ount

ed

obse

rve

coil

deco

uplin

gco

il

C

hara

cter

istic

s of a

n N

MR

pro

be (t

uned

LC

circ

uit)

:

freq

uenc

y

ω =

1/√

LC

L

= in

duct

ance

, qu

ality

fact

or Q

= ω

L/R

C =

cap

acita

nce,

im

peda

nce

Z =

R +

i[ ω

L −

1/(ω

C)]

R

= re

sist

ance

The

prob

e is

an

LC c

ircui

t whi

ch m

ust b

e tu

ned

to th

e re

sona

nce

freq

uenc

y of

the

nucl

eus b

eing

stud

ied

(impe

danc

e =

R w

hen

ω =

1/√

LC) a

nd,

The

impe

danc

e of

the

rf c

oil +

sam

ple

mus

t be

mat

ched

to th

at o

f the

sour

ce

(spe

ctro

met

er) e

lect

roni

cs.

Thes

e ar

e ad

just

ed u

sing

var

iabl

e ca

paci

tors

− tu

ning

and

mat

chin

g:

Coi

l Len

gth

rela

ted

to (

a). l

engt

h of

hom

ogen

eous

regi

on o

f B0.

(b)

. len

gth

of R

T sh

ims a

ctiv

e re

gion

. (

c). R

F ho

mog

enei

ty.

Coi

l Fill

ing

Fact

or η

(inc

reas

es w

ith η

).Pr

obe

Q (i

ncre

ases

with

Q).

Die

lect

ric c

onst

ant o

f sam

ple

(dec

reas

es w

ith

incr

easi

ng d

iele

ctric

- re

duce

s Q, t

unin

g/m

atch

ing

is d

iffic

ult).

Prob

e Se

nsiti

vity

V2 R

coil

(Rco

il +

Rso

urce

)2P c

oil =

Ctu

neCm

atch

L

Tuni

ng u

sing

a D

irect

iona

l Cou

pler Tr

ansm

itter

Ctu

neCm

atch

LD

.C.

Pow

er M

eter

Thes

e ad

just

men

ts a

re u

sual

ly in

depe

nden

t if y

ou a

re c

lose

to o

ptim

al tu

ning

/mat

chin

g. O

ther

wis

e,th

ey a

re li

kely

to in

tera

ct w

ith e

ach

othe

r.

or

exte

nt o

f mat

chin

g(m

axim

ize

dip)

ext

ent o

f tun

ing

(min

imiz

e se

para

tion)

tuni

ngfr

eque

ncy

Gra

phic

alD

ispl

ay

Adj

ust t

unin

g an

d m

atch

ing

capa

cito

rs

to m

inim

ize

refle

cted

pow

er in

the

pow

er m

eter

.

Reflected Power

Freq

uenc

y

Hig

h Q

, Low

RLo

w Q

, Hig

h R

Q =

ωR

/∆ω

Inse

nsiti

ve to

cha

nges

in sa

mpl

e co

nditi

ons,

or c

hang

es in

cen

ter f

requ

ency

.Lo

w ω

, or l

ossy

sam

ples

: R =

hea

t, du

e to

high

salt/

cond

uctin

g co

nditi

ons

Hig

h se

nsiti

vity

aro

und

cent

er fr

eque

ncy

and

chan

ges i

n sa

mpl

e co

nditi

ons,

e.g.

diel

ectri

c co

nsta

nt. ω

R∆ωV

VR

∆ω =

wid

th c

orre

spon

ding

to

V=

VR

/√2

ωR

= re

sona

nce

freq

uenc

y

xmtr

prob

e

outp

ut tu

neou

tput

prob

e

From

Tx

(cha

n 1) To

Rx

To

Pro

be

1H/1

9Fpr

eam

p

B

Pro

beH

1

filte

ra b

A

C13 N15

From

Tx

(dec

2,

cha

n 3)

From

Tx

(dec

1,

cha

n 2)

15N filter

13C filter

xmtr

prob

e

outp

ut tu

neou

tput

prob

e

From

Tx

(cha

n 1)

To R

x

To

Pro

be

Pro

beH

1fil

ter

C13 N15

From

Tx

(dec

2,

cha

n 3)

From

Tx

(dec

1,

cha

n 2)

15N filter

1H filter

1/4

wav

ele

ngth

ca

ble

BB

pre

amp

Con

figur

atio

n fo

r 1H

Obs

erve

13C

,15N

(or X

) Dec

oupl

e

Con

figur

atio

n fo

r 13C

(or X

) Obs

erve

, 1H

Dec

oupl

e

xmtr

xmtr

outp

ut

prob

e

outp

utfilte

r

tune

outp

ut

prob

e

50

From

Tx

From

Tx

To R

xTo

Rx

1/4

wav

ele

ngth

cab

le

To

Pro

be

1H/1

9Fpr

eam

p40

-400

MH

zB

B p

ream

p

xmtr

xmtr

outp

ut

prob

e

outp

ut tu

neou

tput

prob

e

50

From

Tx

From

Tx

To R

xTo

Rx

1/4

wav

ele

ngth

cab

le

To

Pro

be

1H/1

9Fpr

eam

p40

-400

MH

zB

B p

ream

p

prob

epr

obe

atte

nch

anat

ten

chan

filte

r

Prea

mpl

ifier

Hou

sing

Con

figur

atio

n

H1

or F

19 O

bser

veX

Nuc

leus

Obs

erve

Dis

conn

ect c

able

from

A(f

ilter

) and

con

nect

it to

a

(por

t lab

eled

pro

be)

on th

e tu

ning

inte

rfac

e.

Pro

be

To

Pro

beH

1xm

tr

prob

e

outp

ut tu

neou

tput

prob

eFrom

Tx To

Rx

1H/1

9Fpr

eam

p

B

filte

ra b

Pro

be

Axm

tr

prob

e

outp

ut tu

neou

tput

prob

eFrom

Tx To

Rx

To

Pro

be

1H/1

9Fpr

eam

p

B

Pro

be

H1

filte

ra b

A

Cab

le c

onne

ctio

ns fo

rH

1 ob

serv

e op

erat

ions

To

Pro

beP

robe

H1

xmtr

prob

e

outp

ut tu

neou

tput

prob

eFrom

Tx To

Rx

1H/1

9Fpr

eam

p

B

filte

ra b

AD

isco

nnec

t cab

le fr

om B

on H

1 pr

eam

p (la

bele

d ou

tput

) an

d co

nnec

t it

to b

on

tuni

ng in

terf

ace

(labe

led

tune

out

put)

.

Tuni

ng C

onfig

urat

ion

for H

1

1

2

xmtr

prob

e

outp

ut tu

neou

tput

prob

eFrom

Tx

To R

x

1H/1

9Fpr

eam

p

B

a b

c h a n

a t t e n

- +0

- +9

prob

e To P

robe

a

LED

c h a n

a t t e n

- +0

- +9

prob

ea

LED

c h a n

a t t e n

- +1

- +9

prob

e To P

robe

a

LED

100

c h a n

a t t e n

- +1

- +9

prob

e To P

robe

a

LED

001

c h a n

a t t e n

- +0

- +9

prob

ea

LED

xmtr

prob

e

outp

ut tu

neou

tput

prob

eFrom

Tx To

RxTo

P

robe

1H/1

9Fpr

eam

p

B

filte

ra b

A

Ensu

re a

ttenu

atio

n is

8 o

r 9 a

ndch

anne

l sel

ectio

n is

0. T

he d

ispl

ay

is d

ark

and

LED

is fl

ashi

ng re

d.

Pres

s the

+ k

ey to

sele

ctch

anne

l 1. T

he d

ispl

ay tu

rns o

nan

d di

spla

ys re

flect

ed p

ower

(arb

itrar

y un

its).

Pres

s the

(−) k

ey to

sele

ctch

anne

l 0. T

he d

ispl

ay tu

rns o

ffbu

t LED

con

tinue

s to

blin

k.

Dis

conn

ect c

able

(LED

stop

sfla

shin

g) a

nd re

conn

ect t

ofil

ter.

Adj

ust m

atch

ing

and

tuni

ngca

paci

tors

to m

inim

ize

refle

cted

pow

er (<

10)

. DO

NO

T FO

RC

ET

UN

E/M

ATC

H R

OD

S IF

T

HE

Y A

RE

PE

GG

ED

OU

T !!

Dis

conn

ect t

une

out c

able

from

b a

nd re

conn

ect t

o H

1 pr

eam

p ou

tput

(B).

Proc

edur

e fo

r Tun

ing

H1/

F19

Spat

ial

Mag

neti

c Fi

eld

Inho

mog

enei

ty

B(z) B0

ν 0 z

B(z) B0

ν 0 z

ν(z)

= γ

B(z

)/(2

π)

Inho

mog

enei

ty o

f th

e st

atic

fiel

d al

ong

the

z axi

s, B

(z).

Diff

eren

t par

ts o

f the

sam

ple

reso

nate

ove

ra

rang

e of

freq

uenc

ies

(∆ν)

due

to th

e fie

ld

inho

mog

enei

ty:

The

spec

trum

co

nsis

ts o

f con

tribu

tions

from

eac

h of

thes

esp

in is

ochr

omat

s

The

reso

nanc

e is

bro

ader

th

an th

e in

trins

ic li

ne-w

idth

line

λ, a

nd th

e lin

e-sh

ape

refle

cts t

he fi

eld

inho

mog

enei

ty p

rofil

e

Shim

min

g

Idea

lized

, per

fect

lyho

mog

eneo

us st

atic

fiel

d pr

ofile

alo

ng th

e z

axis

:

B(z

) = B

0

Ever

y pa

rt of

the

sam

ple

reso

nate

s at t

he sa

me

freq

uenc

y:

ν(z)

= γ

B0/

(2π)

The

linew

idth

(λ) o

f eac

h re

sona

nce

is d

icta

ted

sole

ly b

y ph

ysic

o-ch

emic

al p

rope

rties

of t

he m

olec

ule

(rel

axat

ion,

exc

hang

e, e

tc)

The

sign

al h

eigh

t is t

hesu

m o

f all

thes

e co

ntrib

utio

ns.

If λ

is sm

all,

the

peak

is in

tens

ean

d na

rrow

.

∆v

λ

shor

t,bro

ad, d

isto

rted

inte

nse,

narr

ow, s

ymm

etric

B(z

) = B

0 +

b 1 z

+ b

2 z2

+ b

3 z3

+ …

B'(z

) = −

b1

z −

b 2 z

2 −

b 3 z

3 −

…

B(z

) − B

'(z) =

B0

The

field

inho

mog

enei

ty is

exp

ress

edas

a p

olyn

omia

l in

z (ac

tual

ly

sphe

rica

l har

mon

ics,

or a

ngul

arpa

rts o

f ato

mic

orb

itals

).

The

user

(or s

oftw

are)

man

ipul

ates

curr

ent i

n sh

im c

oils

surr

ound

ing

the

sam

ple

to g

ener

ate

a co

unte

ract

ing

mag

netic

fiel

d B

'(z).

Adj

ustin

g a

shim

z2, f

or e

xam

ple,

mod

ulat

es th

e b 2

z2 te

rm.

Idea

lly, a

per

fect

B'(z

) fie

ld w

ill c

ompl

etel

yca

ncel

the

field

inho

mog

enei

ty a

nd

yiel

d a

perf

ectly

hom

ogen

eous

fiel

d, B

0.

z2 z4 z6

z z3 z5

Impr

ovem

ent i

n fie

ld h

omog

enei

ty is

ass

esse

d by

obs

ervi

ng

an in

crea

se in

the

heig

ht o

f the

abs

orpt

ion

mod

e di

spla

y lo

ck si

gnal

(loc

k le

vel)

duri

ng th

e sh

imm

ing

proc

edur

e

Shim

min

g

Fiel

d in

hom

ogen

eitie

s alo

ng x

and

y d

irect

ions

als

o ne

edto

be

shim

med

out

. Ind

ivid

ual s

him

s are

not

inde

pend

ent

and

inte

ract

with

one

ano

ther

. Hig

her o

rder

z sh

ims a

re

"con

tam

inat

ed"

by lo

wer

ord

er sh

ims.

B(x

,y,z)

= B

(z) +

c1

x +

c 2 y

+ c

3 xz

+ c

4 yz

+ c

5 xy

+ …

Th

ere

are

28 sh

ims o

n ou

r 500

MH

z sp

ectro

met

er

(type

dgs

in v

nmr)

.

Shim

min

g is

a c

ompl

ex a

nd o

ften

tedi

ous p

roce

ss, b

ut is

key

to o

btai

ning

goo

d sp

ectr

a.

Shim

min

g

lock level

z2 z4z z3

Low

er o

rder

z sh

ims (

z, z2

) affe

ct th

e ce

ntra

l par

t of t

he sa

mpl

e; h

ighe

r ord

er sh

ims (

z3−z

6 ) a

ffect

the

edge

s of t

he sa

mpl

e.

Odd

ord

er sh

ims d

isto

rt th

e lin

esha

pe sy

mm

etri

cally

; Eve

n or

der s

him

s dis

tort

the

lines

hape

asy

mm

etri

cally

B0

+b z3

−b z3

ν 0 =

γB

0ν +

= γb

z3ν −

= −γ

b z3

B0

+b z4

ν 0 =

γB

0ν +

= γb

z4ν +

= γb

z4

z3z4

ν −ν 0

ν +ν 0

ν +

b <

0b

> 0

b >

0, b

< 0

Shim

min

g

Man

ual S

him

min

g adju

st s

him

s to

m

axim

ize

lock

leve

l

Puls

ed F

ield

Gra

dien

ts

B0

G z

−G z

ν(0

) = γ

B0

ν(+z

)= γ

G z

ν(−z

) = −

γ G

z

z

ν(−z

)ν(

0)ν(

+z)

A g

radi

ent i

s a li

near

var

iatio

n of

the

stat

ic fi

eld

impo

sed

on th

e sa

mpl

e, th

roug

h gr

adie

nt c

oils

in th

e pr

obe,

an

d st

rictly

und

er u

ser c

ontro

l, as

opp

osed

to v

aria

tions

in B

0 fie

ld d

ue to

fiel

d in

hom

ogen

eity

.

A fi

eld

grad

ient

is d

efin

ed th

roug

h it'

s slo

pe a

s a fu

nctio

n of

dis

tanc

e. A

z-gr

adie

nt (G

z) is

def

ined

as:

B

(z) =

Gz z

As

a re

sult,

eac

h pa

rt of

the

sam

ple

tube

reso

nate

s at a

diff

eren

t fre

quen

cy d

epen

ding

upo

n it'

s pos

ition

alo

ng

the

z axi

s (le

ngth

of t

he tu

be):

B(z

)

ν(z)

= γ

G z

A sp

ectru

m m

easu

red

in th

e pr

esen

ce o

f a fi

eld

grad

ient

est

ablis

hes a

cor

rela

tion

betw

een

freq

uenc

y an

d po

sitio

n

∆ν ∝

L (l

engt

h of

sam

ple)

A g

radi

ent i

n B

o in

the

Z di

rect

ion

is a

chie

ved

with

an

antih

elm

holtz

type

of c

oil.

Cur

rent

in th

e tw

o co

ils fl

ow in

op

posi

te d

irect

ions

cre

atin

g a

mag

netic

fiel

d gr

adie

nt

betw

een

the

two

coils

. The

B fi

eld

at th

e ce

nter

of o

ne c

oil a

dds t

o th

e B

o fie

ld, w

hile

the

B fi

eld

at th

e ce

nter

of t

he o

ther

coi

l sub

tract

s fro

m th

e B

o fie

ld.

From

: The

Bas

ics o

f NM

R, J

. Hor

nak

http

://w

ww

.cis

.rit.e

du/h

tboo

ks/n

mr/

Puls

ed F

ield

Gra

dien

t (PF

G):

A li

near

gra

dien

t G a

pplie

d fo

r a b

rief p

erio

d of

tim

e (τ

)

B 0G

zB 0

Gz

B 0G

zB 0

B 0

Gz

τ

The

max

imum

gra

dien

t stre

ngth

s are

~ G

= 6

0−70

Gau

ss/c

m. M

ost g

radi

ent p

robe

s are

z-ax

is o

nly.

The

rapi

d tu

rnin

g on

and

off

of th

e gr

adie

nts l

ead

to e

ddy

curr

ents

in th

e pr

obe

and

mag

net

bor

e tu

be. T

hese

dis

turb

ance

s tak

e se

vera

l mill

isec

onds

to su

bsid

e, d

urin

g w

hich

obs

erva

tion

of sp

ectra

is im

poss

ible

. G

radi

ent p

robe

s con

tain

act

ivel

y sh

ield

ed g

radi

ent c

oils

whi

ch d

o no

t pro

duce

sign

ifica

nt e

ddy

curr

ent o

utsi

de th

e sa

mpl

e vo

lum

e, a

nd th

e gr

adie

nt st

abili

zatio

n tim

e is

typi

cally

50−

250

µs.

Usi

ng sp

ecia

l pul

se se

quen

ces,

PFG

s can

be

used

to m

ap th

e m

agne

tic fi

eld

inho

mog

enei

ty a

long

the

z axi

s i.e

., de

term

ine

the

coef

ficie

nts b

n in

B(z

) = B

0 +

b 1 z

+ b 2

z2 +

b3

z3 +

… in

a sh

ort p

erio

d of

tim

e (f

ew m

inut

es).

The

inho

mog

enei

ty c

an th

en b

e re

mov

ed b

y su

btra

ctin

g a

coun

tera

ctin

g fie

ld B

'(z) =

B0

− b 1

z −

b 2 z2

− b

3 z3

+ …

A st

rong

sign

al (u

sual

ly so

lven

t) is

requ

ired

for g

rad

shim

min

g: 1 H

for H

2O so

lven

t, 2 H

for D

2O so

lven

t.

This

form

s the

bas

is fo

r Gra

dien

t Shi

mm

ing.

Bas

ic P

rinci

ples

of G

radi

ent S

him

min

g

B 0

Gz

z

B(z)

B 0

Gz

z

B(z)

Rec

ord

spec

tra in

pre

senc

e of

stro

ng, u

ser c

ontro

lled

grad

ient

Gz,

to a

mpl

ify e

ffect

s of

rel

ativ

ely

wea

k st

atic

fiel

d in

hom

ogen

eity

B(z

).

wea

k

stro

ng

B 0

Gz

z

B(z)

B 0

Gz =

0

z

B(z)

= 0

B 0

Gz

z

B(z)

B 0

Gz =

0

z

B(z)

perfe

ctly

hom

ogen

eous

line

wid

th, i

n ab

senc

e of

any

field

gra

dien

tsbr

oade

ned

line,

in p

rese

nce

of s

tatic

fiel

d ho

mog

enei

ty, l

inew

idth

is te

ns o

f Hz.

B 0

Gz

z

B(z)

B 0

Gz

z

stro

ng

broa

dene

d lin

e, in

pre

senc

e of

a s

trong

z-g

radi

ent a

ndno

sta

tic fi

eld

hom

ogen

eity

, lin

ewid

th is

sev

eral

kH

z.in

pre

senc

e of

a s

trong

z-g

radi

ent a

nd s

tatic

fiel

d ho

mog

enei

ty,

effe

ct o

f B0

inho

mog

enei

ty is

am

plifi

ed.

10-5

0 H

z

~ 10

kH

z

B 0

Gz

z

B(z)

B 0

Gz

z

B(z)

wea

k

stro

ng

Step

1G

radi

ent S

him

min

g B

asic

s

Step

1: o

btai

n a

grad

ient

pro

file

poin

ts t

o re

mem

ber

grad

ient

s no

t on

(pfg

on='

nnn'

)

tpwr

too

hig

hpw

too

long

gain

too

hig

h

tpwr

too

low

pw t

oo s

hort

gain

too

low

The

effe

ct o

f var

ying

diff

eren

t shi

ms

(z1,

z2,

etc

) on

thes

e gr

adie

nt p

rofil

es g

ener

ate

info

rmat

ion

rega

rdin

g th

eco

ntrib

utio

n of

diff

eren

t shi

ms

to B

(z).

This

is c

alle

d a

shim

map

:

This

shi

m m

ap s

how

s th

at th

ere

is a

larg

e z2

, z4

and

z5 c

ontri

butio

n to

B(z

) and

rela

tivel

y m

inor

z1,

z3

and

z6 c

ontri

butio

ns

Bas

ed o

n th

ese

shim

map

s, th

e gr

adie

nt s

him

min

g pr

ogra

m c

an c

alcu

late

how

muc

h to

alte

r diff

eren

t shi

ms

in o

rder

tore

mov

e th

eir c

ontri

butio

ns fr

om B

(z).

This

is u

sual

ly a

qui

ck, i

tera

tive

proc

edur

e.

z1

sam

ple

leng

th

fieldz2

z6z5

z4

z3

Step

2: o

btai

n a

shim

map

ω(z

) ∝ z

φ(z)/τ ∝ Β(z)

Firs

t It

erat

ion

Fin

al I

tera

tion

whit

e: f

ield

pro

file

ove

r sa

mpl

e le

ngth

red:

bes

t fi

t

mag

neti

c fi

eld

shou

ld b

e as

"fla

t" o

ver

the

sam

ple

leng

th

as p

ossi

ble

Step

3: c

arry

out

iter

ativ

e gr

adie

nt s

him

min

g

Acq

uiri

ng S

pect

ra

Set

the

tem

pera

ture

Tune

the

prob

e

Lock

the

field

Shi

m -

man

ual +

gra

dien

t

Ana

lyze

H2O

or H

DO

line

shap

e

Det

erm

ine

1 H 9

00 p

ulse

wid

th

Det

erm

ine

H2O

/HD

O fr

eque

ncy

Acq

uire

a 1

H 1

D s

pect

rum

inte

rcha

ngea

ble

repe

at u

ntil

lines

hape

's

OK

Bas

ic S

tartu

p Pr

otoc

ol

ensu

res

rf p

ulse

sar

e op

tim

ally

abs

orbe

dby

the

sam

ple

corr

ects

for

mag

neti

cfi

eld

drif

t ov

er t

ime

ensu

res

unif

orm

m

agne

tic

fiel

d ov

ersa

mpl

e vo

lum

e

A ra

dio

freq

uenc

y pu

lse

at a

tran

smitt

er fr

eque

ncy

ν T a

nd a

mpl

itude

(rf f

ield

stre

ngth

) B1

may

be

repr

esen

ted

as a

vec

tor o

f le

ngth

B1

in a

refe

renc

e fr

ame

rota

ting

at ν

T.

The

phas

e of

the

B 1 fi

eld

coin

cide

s with

the

x ax

is o

f the

rota

ting

fram

e.

The

B 1 fi

eld

act

s on

the

mag

netiz

atio

n ve

ctor

(M0)

of n

ucle

ar sp

ins w

ith re

sona

nce

freq

uenc

y ν 0

.

If th

e tra

nsm

itter

freq

uenc

y is

on

reso

nanc

e, i.

e. ν

T =

ν 0, M

0 "s

ees"

B1

as t

he o

nly

effe

ctiv

e m

agne

tic fi

eld

for

the

dura

tion

of th

e pu

lse

(τP)

(M0 d

oes n

ot h

ave

to b

e al

igne

d al

ong

the

z axi

s).ν T

= tr

ansm

itter

freq

uenc

y (e

.g. s

frq,

dfr

q)

=

freq

uenc

y of

rota

ting

fram

e

B 1 =

am

plitu

de o

f rf p

ulse

(rf p

ower

∝ B

12 )

x ≡

phas

e of

rf p

ulse

(axi

s of a

lignm

ent o

f B1

v

ecto

r in

rota

ting

fram

e)

M0

= m

agne

tizat

ion

vect

or fo

r a p

eak

o

n re

sona

nce

(ν0

= ν T

)

τ P =

dur

atio

n of

the

rf p

ulse

(pul

se−w

idth

)

x

y

z

B 1

ν 0 =

νT

M0

B 1

ν T

M0

The

RF

Puls

e B 1 (p

w)

(sfr

q)

(tpw

r)

τ P

x

y

z

B 1

M0

θ

τ P =

τ90

θ=π/2

x

y

z

B 1

M0

x

y

z

B 1

M0

θτ P

pw90

ω1=γB1

θ=ω1τP

The

RF

puls

e ro

tate

s th

e nu

clea

r mag

netiz

atio

n fr

om th

e z a

xis

tow

ards

the

xy p

lane

A 9

00 p

ulse

(pw

90) r

otat

es M

0 int

o th

e xy

pla

ne, g

ivin

g ris

e to

max

imum

sign

al.

A 3

600 p

ulse

(pw

360)

rota

tes

M0 b

ack

to th

e z a

xis,

yie

ldin

g m

inim

um si

gnal

.

H2O

Lin

esha

pe, 1

H 9

00 P

ulse

-Wid

th, H

2O F

requ

ency

ar

e de

term

ined

usi

ng v

aria

tions

of t

he s

ame

puls

e se

quen

ce(t2

pul o

n Va

rian,

zg

on B

ruke

r)

pw

acqu

isiti

on ti

me

recy

cle

dela

y (d

1)

H2O

Lin

esha

pe

1 H 9

00 P

ulse

-Wid

th

H2O

Fre

quen

cy

1 H c

arrie

r aw

ay fr

om H

2O.

shor

t pw

(1-2

µs)

, low

pow

er.

long

acq

uisi

tion

time

(1-2

s).

no w

indo

w fu

nctio

ns b

efor

e FT

.

shor

t rec

ycle

del

ay (d

1) 1

-2 s

.

low

rece

iver

gai

n in

H2O

.

1 H c

arrie

r on

H2O

.

vary

(arr

ay) p

w.

shor

t acq

uisi

tion

time

(0.2

5-0.

5 s)

.

win

dow

func

tion

befo

re F

T.

long

d1

for D

2O s

ampl

es (5

s).

low

rece

iver

gai

n in

H2O

.

vary

H2O

pre

satu

ratio

n fre

quen

cy.

pw c

lose

to p

w90

.

shor

t acq

uisi

tion

time

(0.2

5-0.

5 s)

.

win

dow

func

tion

befo

re F

T. sh

ort r

ecyc

le d

elay

(d1)

1-2

s.

high

rece

iver

gai

n.

1 H P

ulse

Wid

th D

eter

min

atio

n

Load

par

amet

ers

Set

1H

car

rier t

o H

2O fr

eque

ncy

Set

pow

er le

vel

Arr

ay th

e pu

lsew

idth

(pw

) to

dete

rmin

e a

null

(zer

o si

gnal

)

Bes

t: de

term

ine

a 36

00 p

ulse

: no

radi

atio

n da

mpi

ng, s

hort

recy

cle

dela

ys. H

owev

er, i

s af

fect

ed b

y rf

inho

mog

enei

ty.

- nu

lls a

re e

asie

r to

det

ect

than

max

ima.

A 1

800

pw is

the

fir

st n

ull b

ut r

esul

ts in

sig

nal d

isto

rtio

n a

nd A

DC

over

flow

bec

ause

of

radi

atio

n da

mpi

ng in

H2O

sam

ples

.

- A

180

0 pu

lse

requ

ires

long

rec

ycle

(d1)

del

ays

betw

een

puls

ewid

ths.

signal intensity

puls

e-w

idth

9018

0

270

360

10

radi

atio

n da

mpi

ng, s

igna

l dis

tort

ion,

long

d1

mea

sure

men

t wi

ndow

1st n

ull

2nd

nullpw

atd1

360

null

Det

erm

inin

g th

e H

2O F

requ

ency

In H

2O s

ampl

es, t

he H

2O li

ne is

too

broa

d (>

30

Hz)

to a

llow

pro

per p

eak

iden

tific

atio

n us

ing

the

curs

or

A be

tter w

ay is

to p

resa

tura

te th

e H

2O s

igna

l prio

r to

dete

ctio

n an

d ar

ray

the

satu

ratio

n fre

quen

cy.

The

H2O

freq

uenc

y co

rres

pond

s to

a m

inim

um in

the

H2O

sig

nal i

nten

sity

(max

imum

sat

urat

ion)

.

pres

at fr

eque

ncy

intensity

choo

se t

his

one

pres

at

pw90

at

1−1.

5 s

End