10: mr spectroscopy

Fund BioImag 201310-1

10: MR spectroscopy

1. How can the Bloch equations be used to describe the effect of T1 on the magnetization ?

2. How can sensitivity be optimized ?

3. What nuclear property allows to distinguish the signal from different molecules ?

4. What is MR spectroscopy ?

After this week you1. can calculate the effect of multiple RF pulses on longitudinal magnetization 2. know the definition of Ernst angle3. Understand the two basic mechanisms by which electrons influence the

precession frequency of nuclear magnetization4. Know the definition of chemical shift 5. Know how and under what molecular conditions NMR spectroscopy can

provide non-invasive biochemical information


Fat and water in MRI: Examples

Retrobulbar fat

Fat suppressed breast MRI (cancer does not contain fat)

Fatty liver


Why is NMR spectroscopy important for (bio)chemists ?

Routine tool– Non-destructive analysis of samples

» Wine in bottles» Synthesis outcome control

Other applications– Structure determination in solution– Molecule dynamics– Chemical reactions in situ

Kurt Wüthrich

Biophysicist, 2002

Insert sample

Analyze

data

Determine structure


10-1. What is the effect of relaxation on M(t) ?

Bloch equations revisited

flip angle a = gB1t:

The effect of T1 and T2 on the signal :

cos)()( tMtM zz sin)()0( tMM zxy

1

0

T

)()( MtM

dt

tdM zz

11 //0 )0()1()( Tt

zTt

z eMeMtM cos)0( 0MM z

)cos11()( 1/0

Ttz eMtM

Effect of T2

Effect of T1

Mz(0)

TR, TIa

2)0()( T

t

xyxy eMtM

T1 T2

Mxy(0)

Longitudinal coherence:

Effect of T1 on signal depends on prior RF manipulations

Longitudinal coherence:

Effect of T1 on signal depends on prior RF manipulations

Longitudinal coherence


What are the optimal conditions to measure T1 ?Inversion recovery

Measured signal

TI

11 //0 )0()1()( TTI

zTTI

z eMeMTIM

cos)0( 0MM z

)cos11()( 1/0

TTIz eMTIM

Optimal choice of a for measuring T1 ?

Use noise error propagation calculation (Lesson 1)

FeT

t

T

tM Ttz

1/2

11

cos1)(

1/2

1

sin0 TteT

t

d

dF

sina=0 a=pConverts Mz to Mxy (signal)

)21()( 1/0

TTIz eMTIM

11 /3

1

/2

1

cos1cos11

0 TtTt eT

te

Tdt

dF

TI = T1TI = T1

1

/2

1

1cos11

0 1

T

te

TTt

Optimal t=TI to detect changes in T1 ?

Inversion-Recovery

Multipulse experiment with two RF pulsesUsual experiment to measure T1 (a=p)

a p/2


10-2. When is SNR (sensitivity) optimal ?

Situation: RF pulses aapplied every TR seconds n timesQuestion: M xy (=signal) maximal ?

Calculate the optimum flip angle a=f(TR)

)(nMM zz Immediately after nth TR

cos)()0( nMM zz After RF Flip a

1/00 cos)()1( TTR

zz enMMMnM After T1 recovery

Assume Mxy=M~0 after TR seconds

In equilibrium (steady-state condition):Mz(n+1)=Mz(n)=Mz

11 /0

/ 1cos1 TTRTTRz eMeM

Equilibrium transverse Magnetization: Mxy(0)=Mzsina

1

1

/

/0

cos1

sin1TTR

TTR

xy e

eMM

TRa

Mxy(0)

a

Mz(0)

Mz(n)

11 //0 )0()1()( Tt

zTt

z eMeMtM

Mz(n+1)

1

1

/

/0

cos1

1TTR

TTR

z e

eMM

11 //0 cos)(1 TTR

zTTR enMeM


How does the signal depend on TR, T1 and flip angle ?

Ernst Angle aE

0 45 90 135 1800

0.2

0.4

0.6

0.8

1

1.2

Signal vs. Flip Angle a

TR/T1=0.01

TR/T1=0.05

TR/T1=0.1

TR/T1=0.5

TR/T1=1

TR/T1=5

TR/T1=10

( )a degrees

Mxy

/M0

1

1

/

/0

cos1

sin1TTR

TTR

xy e

eMM

Mxy (signal) → maximum at aE

1/cos TTRE e

Where aE = Ernst Angle

Richard ErnstPhysical Chemist

1991

dMxy/da=0:

0.01 0.1 1 100

10

20

30

40

50

60

70

80

90

TR/T1

Ern

st a

ng

le a

E

Ernst Angle vs TR/T1

aE


10-3. What role does the chemical environment play?

Chemical shift: Effect of B0 on e-cloud

HProton: nucleus of 1H

H

Proton + e cloud: 1H atom

H

Reorientation of e cloud in magnetic field:e produce a small magnetic field DB at the proton:

B0

Resonance frequency

of the pure proton:

wL=gB0

w=wL(1+d)

(Larmor frequency)

Chemical shift d

HO

Hydrogen e-

H

Little shielding

H OH CH

HC

More shielding

Nearby electronegative atoms (e.g. O, Cl):

attract electrons

→ lower electron density

→ deshielding of nearby H

→ Resonance frequency is higher in OH than CH

0)1( BMMdt

d

DB=dB0


How is chemical shift d linked to electronegativity ?Example: Protons

Compound, CH3X CH3

F CH3O

H CH3Cl

CH3

Br CH3I CH4

(CH3)4

Si

X F O Cl Br I H Si

Electronegativity of X 4.0 3.5 3.1 2.8 2.5 2.1 1.8

Chemical shift, δ / ppm 4.26 3.4 3.05 2.68 2.16 0.23 0

1 1.5 2 2.5 3 3.5 4 4.50

1

2

3

4

5

elecronegativity

ch

em

ica

l sh

ift

d=(w-wLref)106/wL

ref d=(w-wLref)106/wL

ref

0 ppm is defined by resonance frequency of reference compound w Lref

(e.g. tetramethylsilane (TMS) for 1 H)


10-4. How can we measure chemical shift ?

MR spectroscopy

Free induction decay (FID) signal:

distinguish resonance frequency

→ Fourier transformation (real part only):

Area of resonance M(0) number of nuclei concentration (if relaxation can be neglected)

2/)0()( Ttti eeMtS

)1(

1)0()(

2xMG

00 )()()0( MdGdeGS tti

2πTδ)(ωx

w=dIntegral (area) Ratio: 1:2:3(relative number of spins in molecule)

12

3

Example: Ethanol

1/pT2


Ex. illustration of chemical proximity (triplet & quartet)

Hyperfine splitting

nucleus tiny magnetic field linked to its dipole:

changes polarity if spin is “up” or “down”

affects the e cloud in the molecule→ alters the magnetic field at a nearby nucleus:

↑ H↓ HCH2 group → four combinations (with equal

probability): up-up, down-down, up-down, down-up

(The latter two produce the same magnetic field)→ methyl triplet (relative intensity ratio 1:2:1)

Nearby spin-1/2: 1H resonance will split into two of equal magnitude (doublet)

Example: Ethanol

11

2

B0

e- cloud nuclear spin-induced field

11

33


Ex. 31P NMR spectroscopyPhosphate metabolism is at the heart of cellular energetics

1: phosphocreatine (PCr)13: phospho-ethanolamine (PE)14: phosphocholine (PC)15: glycerophosphocholine (GPC)22: glycerophosphoethanolamie(GPE)23: ATP24: inorganic phosphate (Pi)25:dinucleotides (NAD(P)[H])

1

23

2413,1415,22

25

Also measured:Intracellular pHCreatine kinase activityATPase activity


What can MR spectroscopy measure ?

Concentration of biochemical compounds– signal is proportional to the number of spins present,

i.e. concentrationAfter FT, integrate (measure the area of the peak).

Rules for a compound to be detectable: 1. Concentration > 1mM 2. Water-soluble compounds (mobile)3. 1H is most sensitive nucleus (gyromagnetic ratio)

Concentration of biochemical compounds– signal is proportional to the number of spins present,

i.e. concentrationAfter FT, integrate (measure the area of the peak).

Rules for a compound to be detectable: 1. Concentration > 1mM 2. Water-soluble compounds (mobile)3. 1H is most sensitive nucleus (gyromagnetic ratio)

Spatial Resolution Voxel volume ~ 1/Signal

Water (80M 1H concentration)

~1mm (human)

~50µm (rodent)

Biochemical compounds (~mM concentration)

~ cm (human)

~ mm (rodent)

Why is spatial resolution better for rodent studies ?

Induced emf z depends on RF coil size (Lesson 9)


How can the huge water signal be suppressed in 1H NMR ?

NB. Resonance suppression:1. Minimize Mz : “selective” 900 pulse applied on-

resonance on the signal to be suppressed. 2. Selectivity achieved by using weak B1 (lecture

9), i.e. long RF pulse. 3. 900 (selective) followed by a0 for excitation and

detection [assume the suppressed signal is dephased (see Lecture 11)]

Full signal (no suppression)

Scaled signal (no suppression)

Scaled signal (with suppression)

Water + Phe suppression

fatwater

a900 Mz(water)=0


5 4 3 2 1 (ppm)

Ex. Proton spectroscopy of the brainBiochemical compounds detectable in vivo

1

9

8

5

4

3

12,13

1717

6,7,182

10

1,2

16

16

6

6,77

20

14,15

2111,20

19

Energy metabolism:1: phosphocreatine (PCr)2: creatine (Cr)3: glucose (Glc)4: lactate (Lac)5: alanine (Ala)

Neurotransmission:6: glutamate (Glu)7: glutamine (Gln)8: GABA9: N-acetyl-aspartyl-

glutamate (NAAG)10: aspartate (Asp)11: glycine (Gly)12: serine (Ser)

Membrane metabolism:13: phospho-ethanolamine (PE)14: phosphocholine (PC)15: glycerophosphocholine (GPC)16: N-acetyl-aspartate (NAA)

Antioxidants/osmolytes:17: glutathione (GSH)18: vitamin C (Asc)19: taurine (Tau)20: myo-inositol (Ins)21: scyllo-inositol (s-Ins)

Incompletely suppressed H 2O signal

14,1516

3

8


How can biochemical compounds be measured in vivo ?

Analysis of 1H NMR spectroscopy of the brain

in vivo

NAA

4.5 ppm4.0 3.5 3.0 2.5 2.0 1.5 1.0

fit

residual

Lac

Glu

Gln


Ex. Metabolic phenotyping of transgenic animals

R6/2 mouse (human Huntingtin gene knockin) at wk 8

0

2

4

6

8

10

12

14

16 A

la

Asp C

r

PCr

GAB

A

Glc

Gln

Glu

GSH In

s

Lac

NAA

NAA

G PE

Tau

conc

entra

tions

(µm

ol/g

)

Wild-type HD transgenic

Standard deviation

N=7


Brain tumor

1H 31P

Muscle

Example: Human brain and muscle


Ex. 1H NMR spectroscopy in vivoMouse brain

Mouse model of human glioma

Mouse model of stroke

10: mr spectroscopy

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