pulse techniques. off-resonance effects initial magnetization along z x-pulse ( = 0) on-resonance:...

Pulse Techniques

Off-Resonance Effects

Initial magnetization along z x-pulse ( = 0) On-resonance:

Mz -> -My

Off-resonance: phase

sin

cos)cos1(tan

sintan

)sincos(cos

sinsin

cossin)cos1(

01

220

0

0

y

x

z

y

x

M

M

MM

MM

MM

x

y

Mxy

z

y

x

B1

Br

Bo

Off-Resonance Effects – 90º Pulse

90º hard pulse works well for < 1

Phase shift is approximately linear

Effective flip angle increases 0 1 3 4

-0.5

0.5

1.0

/1

-1.0

Mxy

0 1 3 40

50

100

150

200

250

300

350

/1


Assume: Close to resonance 90º pulse (=/2) First-order

approximation Phase angle is

proportional to offset First-order phase

correction

90

901

90

1

12

1

1

2

2

1

2

2

2

1

2

1

00

1

2)arctan(cos

)/(1

)/(cos

cos)cos1(

cossin

cos

sintan

cossin

cos)cos1(tan

sin21


Initial magnetization state is irrelevant

Result: z-x-z

)()()(

)()()2/()(

)()()()2/(

)()()()2/(

)()()2/()(

)()2/()()2/()2/()(

),(

1sin

1

2,

2sin

2/

,2

)()()(),(

1

zxz

zxxz

zxyx

yxzx

yxxy

yyzzyy

x

yzyx

z

y

x

B1

Br

Bo

Off-Resonance Effects - Compensation

Not constant-time Subtract 290/ for each

90º pulse, or Add a short echo

Constant-time No compensation

needed if 90º pulses are identical

Shaped 90º pulses?

t1 - 4/

T - T +

t1 +

t12

t12

Pulse calibration – 180º or 360º?

180º pulse: Poor off-resonance

performance Mxy ~

Linear phase twist Saturation in repeated

experiments 360º pulse

Better off-resonance performance < 0.1 1

Uniform phase Minimal saturation

0.0 0.1 0.2 0.3 0.4 0.50.0

0.2

0.6

0.8180o

360o

/1

Mxy

0.0 0.1 0.2 0.3 0.4 0.50

5

15

20 180o

360o

/1


Inversion: Poor off-resonance

performance Refocusing:

Orthogonal better than parallel

Phase twist is the same Both work only for

< 0.2 1

0.0 0.2 0.6 0.8

0.2

0.4

0.6

0.8

1.0

0.0

-Mz (inv.)

Mxy (x/x)

Mxy (y/x)

/1

0.0 0.2 0.6 0.80

5

10

15

25

30

35

/1

Composite Pulses

Trains of rectangular pulses instead of a single pulse Off-resonance performance Tolerance to B1 inhomogeneity

90º – historic 180º inversion – most common

90x-180y-90x Composite Pulse

90x-180y-90x replaces 180x

for inversion The middle 180º

compensates for off-resonance behavior of the outer 90º pulses

x-2y-x Composite Pulse

90x-180y-90x has better broadband inversion performance < 1

90x-225y-90x has smoother, but narrower profile < 0.7 1

x-2y-x composite pulse is less sensitive to mis-calibration of 90º pulse

Cannot be used for refocusing 80 85 95 100

-0.998

-0.996

-0.994

-0.992

-0.990

-1.000

Mz

2x

x2.5yxx2yx

0.0 0.5 1.5 2.0-1.0

-0.5

0.5

1.0

Mz

/1

180x

90x1

80y9

0x

90x2

25y9

0x

Selective Pulses

Requirements: Uniform excitation (inversion) profile Minimal perturbation outside the target

frequency range Uniform resulting phase (for excitation) Short pulse length Low peak power Easy to implement shape

Soft Rectangular Pulses

Find 1, which produces a null in the excitation (inversion) profile at a certain offset off-resonance

33

1tan

2

3cos

2

1sin

1515

1tan

4

15cos

4

1sin

2

2sin2

sin

...,2...,,4,2,01cos

1sincoscos

)sincos(cos

)180(1

1

0

)90(1

1

0

00

22

022

0

n

MMM z

0 1 2 3 4 5

-0.75

-0.50

-0.25

0.25

0.50

0.75

1.00

-1.00

180

90

Mz

/1

Shaped Pulses

Approximated by a series of short rectangular pulses

Every point i: Amplitude i

Phase i

SEDUCE-1

Points

0 10 20 30 40 50 60 70 80 90 100A

plit

ud

e [

%]

0

20

40

60

80

100

Examples - Gaussian Pulse

Truncated at 1% of max amplitude

Excitation profile - gaussian

Examples - Sinc Pulse

One-lobe of the sinc function

Needs less power for the same length

Similar excitation profile

Examples - SEDUCE-1

Essentially a gaussian, smoothed at both ends

Used mostly for decoupling

Examples - Q5 Gaussian Cascade

~300 s pulse used as 90º 13C excitation pulse in Bruker pulse sequences

Better than a soft rectangular 90º pulse

For Iy -> Iz application needs to be time-reversed

Q5 Gaussian Cascade – Excitation Profile

Examples - Q3 Gaussian Cascade

~200 s pulse used as 180º 13C refocusing pulse in Bruker pulse sequences

Q3 Gaussian Cascade – Refocusing Profile

Q3 Gaussian Cascade – Inversion Profile

It also provides good inversion

Examples - E-BURP2

Used in L-optimized experiments

E-BURP2 – Excitation Profile

Phase-Modulated Pulses – Frequency shifting

Linear phase ramp 0 controls the phase of the

resulting pulse: 90º (Iz -> Iy): N = 0

90º (Iy -> Iz): 0 = 0

180º (Iy -> -Iy): N/2 = 0

180º (Iz -> -Iz): arbitrary

Nii

f

i ,...1),(

2

21

0

Phase-Modulated Pulses – Resolution Issues

Time resolution More points = better shape approximation Minimal pulse delay

Phase resolution More points = smaller phase steps Minimal phase step

Phase-Modulated Pulses – Multi-band excitation

Cosine modulation 10 kHz

Needs 2x more power

Adiabatic Pulses

“Conventional” pulses: Stationary Beff

orientation Magnitude may be

variable Precession around Beff

Adiabatic pulses: Non-stationary Beff

orientation Magnetization follows

Beff, while precessing around it

z

y

xB1

Beff

Bo

xr

yr

zr

1

ddt

Adiabatic Pulses –Performance Conditions

Beff magnitude should be changed gradually

dt

BdMBBM

dt

BdMB

dt

Md

dt

Md

BMdt

Md

effeffeff

effeff

eff

2

2

2

2

2

2

,

effeff

effeffeffeff

effeffeff

effeff

effeffeff

dt

d

BBdt

Bd

BMBBM

dt

BdM

dt

BdM

BBMdt

BdM


A second rotating frame {xr, yr, zr} within the first rotating frame

Beff magnitude should be tilted slowly

rreff

reff j

dt

diBB

1

z

y

xB1

Beff

Bo

xr

yr

zr

1

ddt


Adiabatic condition

Adiabaticity factor

00 /

/

1

dtdQ

dtdQ

dt

d

Bdt

d

eff

eff

eff

eff

Adiabatic Pulses - Chirp

180 13C inversion on Bruker 60 kHz sweep 500 us 20% smoothing

Chirp – Inversion Profile

Very broad inversion profile Low peak power

~50% of high power

Adiabatic Pulses – Tolerance B1 Inhomogeneity

Power 3 dB higher than calibrated

Power 3 dB lower than calibrated

Adiabatic Pulses - Wurst

Smoothed ramp-up and ramp-down

Adiabatic Pulses - sech

Pseudo Bloch-Siegert Shifts

Assume: x-pulse ( = 0) Very far off-resonance Magnetization along y Third order

approximation

z

y

x

B1

Br

Bo


The result is a z-rotation by an angle

In the absence of 1 the rotation = p – the chemical shift evolution!

Pulse phase and initial magnetization phase are irrelevant

2

12

11

11

10

0

0

0

0

0

0

2

1

2

11

1

2

11

21

1sin

sin

cos

sin

)(

sinsin

cos

cossin

)(

0

0

)0(

2

11cos

2

11sin

01

ppp

p

p

M

M

M

M

M

M

M

MMM


An off-resonance pulse incurs a phase shift PBS

It is proportional to time-averaged square of 1

Also valid for shaped pulses

Continuous application of 1 leads to a frequency shift PBS

SEDUCE decoupling during chemical shift evolution

2

)(

2

)(

2

1

21

21

21

t

t

PBS

p

PBS

PBSppp

PBS Phase Shifts - Compensation

Small-phase adjustment of a 90º pulse or phase correction in the frequency domain Depends on whether

there is chemical shift evolution

Works only for a narrow range of resonances far off-resonance

Partial compensation Used in BioPack

t12

t12


Using a second identical pulse and an echo Perfect compensation

over a broad spectral range

Limited by the broadband performance of refocusing 180º pulse

Default for Bruker sequences

T - Tt12

t12


A second pulse with opposite offset Must be far off-

resonance Imperfect

compensation – first-order phase correction required

Not widely used Cosine modulation

Requires twice the power

t12

t12

2mod

21 )(t

PBS

PBS Frequency Shifts – SEDUCE decoupling

Train of cosine modulated SEDUCE-1 shaped pulses Modulation frequency

mod

Signals of interest are near the carrier

Decoupling is very far off resonance

The result is a scaling of the spectrum by a factor Compression around

the center2mod

21

2mod

21

2mod

21

2mod

22

1

mod

21

mod

21

mod

)(1

)(1

)()(

)(2

)(

)(2

)(

t

t

tt

tt

PBSobs

PBS

rf

rf rfmodrf mod

PBS Frequency Shifts – SEDUCE decoupling

600 MHz example 15 s hard 13C pulse 252 s SEDUCE-1 1

max = 2.1 kHz Scaling factor = 0.36

For squared shapes, relative to a rectangle of the same amplitude

mod = 17.7 kHz For 80 ppm spectral width

0.2 ppm shift at edges Unsuitable for 15N-, 13Cali-,

13Caro-NOESY

995.07.17

1.236.01

1)(

1

)()(

2

2

mod

max1

2mod

21

2max1

21

t

t

pulse techniques. off-resonance effects initial magnetization along z x-pulse ( = 0) on-resonance:...

Documents